 
### UNIFIED AND PURE FIELD THEORY

### The Mystery of the Fundamental Principle of the Universe

### Jack Gerber

### UNIFIED AND PURE FIELD THEORY

### The Mystery of Fundamental Principle of the Universe

Copyright 2008 Jack Gerber

Smashwords Edition

Jack Gerber

60 Watson Avenue 1H

Elizabeth, New Jersey 07202

TABLE OF CONTENTS

Chapter PREFACE

Chapter 1. UNIFIED FIELD THEORY (THE PRIMARY PRINCIPLE)

Chapter 2. PURE FIELD THEORY

Chapter 2.1 Model 1

Chapter 2.2 Model 2

Chapter 2.2.1 Quantum Mechanics

Chapter 2.2.2 Wave Mechanics

Chapter 2.3 Plato

Chapter 2.4 Aristotle

Chapter 2.5 Giordano Bruno and the Infinite

Chapter 2.6 Galileo

Chapter 2.7 Newton

Chapter 2.8 Faraday: Gravity, Magnetism, and the Field

Chapter 2.9 Maxwell: Molecular Vortices and Gravity

Chapter 2.10 Einstein

Chapter 2.11 Model 3

Chapter 3. TOPICAL DISCUSSION

Chapter 3.1 Redshift

Chapter 3.2 The Direction of Time

Chapter 3.4 The Spark: The Primary Singularity

Chapter 3.6 The Non-Euclidean Universe

Chapter 3.8 The Primary Equation
Chapter 4. SPECULATIVE HYPOTHESES

Chapter 4.1 DNA

Chapter 4.2 Reversal of the Earth's Magnetic Field (Direction of Polarity)

Chapter 5. AFTERWORD

Chapter 6. SELECTED BIBLIOGRAPHY

APPENDIX

U.S. Patent, "Apparatus and Method for Processing Material in a Magnetic Vortex"

Permission granted, copyright indeterminable, or use per 17 _U.S.C_. § 107 as to the following:

Aristotle _, The Complete Works of ——_ , ed. Jonathan Barnes, Princeton: Princeton University Press, 1985.

Giordano Bruno, _His Life and Thought with Annotated Translation of His Work "On the Infinite Universe and Worlds_ ," trans. Dorthea Waley Singer, New York: Henry Schuman, 1950.

——— _The Infinite in Giordano Bruno with a Translation of His Dialogue "Concerning the Cause, Principle, and One_ ," trans. Sidney Greenberg, Ph.D. dissertation, [Columbia University] Kings Crown Press, 1950.

Albert Einstein, _Essays in Physics_ , New York: Philosophical Library, 1950.

———et al., _The Principle of Relativity_ , New York: Dover Publications, 1952.

——— _Sidelights on Relativity,_ New York: Dover Publications, 1983.

Michael Faraday, _Diary_ , London: George Bell and Sons, 1932-36.

Galileo Galilei, _Dialogues Concerning Two New Sciences_ , New York: Dover Publications, 1954.

William Gilbert, _On the Loadstone and Magnetic Bodies_ , New York: Dover Publications, 1993.

Edwin Hubble, _The Realm of the Nebulæ_ , New Haven: Yale University Press, 1936.

James Clerk Maxwell, _Matter and Motion_ , New York: Dover Publications, 1991.

——— _Scientific Papers_ , New York: Dover Publications, 1965.

——— _Treatise on Electricity and Magnetism_ , New York: Dover Publications, 1954.

Charles Misner and John Wheeler, "Classical Physics as Geometry: Gravitation, Electromagnetism, Unquantized Charge, and Mass as Properties of Curved Empty Space," _Annals of Physics_ , 2:525 (1957).

Isaac Newton, _Mathematical Principles of Natural Philosophy and His System of the World_ [ _Principia_ ], Berkeley: University of California Press, 1962.

——— _Opticks_ , New York: Dover Publications, 1979.

Henri Poincaire, _Science and Hypothesis_ , New York: Dover Publications,1952.

Plato, _The Collected Dialogues_ , ed. Edith Hamilton and Huntington Cairns, Princeton: Princeton University Press, 1987.

Jagjit Singh, _Great Ideas and Theories of Modern Cosmology_ , New York: Dover Publications, 1959.

Eugene Smith, _A Source Book in Mathematics_ , New York: Dover Publications, 1959.

Oswald Veblen and John Wesley Young, _Projective Geometry_ , Boston: Ginn and Company, 1916.

DEDICATION

To my nephew

RICHARD HOWARD LUTERMAN

Who presented me with the problem

and to

KAI JOHN BAUMANN, Ph.D.

Who wished me luck in pursuing it

To understand the unified and pure field theories you must be able to think like Aristotle but you must not think like Aristotle.

1. When the objects of an inquiry, in any department, have principles, causes, or elements, it is through acquaintance with these that knowledge and understanding is attained. For we do not think that we know a thing until we are acquainted with its primary causes or first principles, and have carried our analysis as far as its elements. Plainly, therefore, in the science of nature too our first task will be to try to determine what relates to its principles.

Aristotle, "Physics," _The Complete Works_ , Book I, Section 1, p. 315.

* * * Whereas the main Business of natural Philosophy is to argue from Phaenomena without feigning Hypotheses, and to deduce Cause from Effects, till we come to the very first Cause, which is not mechanical; and not only to unfold the Mechanism of the World, but chiefly to resolve these and such like Questions. What is there in places almost empty of Matter, and when is it that the Sun and Planets gravitate towards each another, without dense Matter between them? When is it that Nature doth nothing in vain; and whence arises all that Order and Beauty which we see in the World?

Isaac Newton. _Opticks_ , Book Three, Part 1, p. 369.

LIST OF ILLUSTRATIONS

Figure 1 Response to my nephew that initiated the project.

Figure 2 Full Moon aligned directly over center of Routes 1/9/439 looking east at Bayway

Circle.

Figure 3 Full Moon at Routes 1/9/439 looking east at Bayway Circle.

Figure 4 National State Bank, Bayway Office, Elizabeth, New Jersey.

Figure 5 National State Bank, Roselle Park Office, Roselle Park, New Jersey.

Figure 6 Demonstration of unidirectional time.

Figure 7 The primary principle.

Figure 8 Generation of "the field" (opolarity).

Figure 9 Unidirectional waveforms converging at a point locus to generate a singularity.

Figure 10 Sketch of Model 1 as originally envisioned (January 28, 1988).

Figure 11 Model 1.

Figure 12 Close-up of Model 1 showing compaction and suspension of mass by converging

magnetic field (opolarity).

Figure 13 Lines of force projected from magnet on the crank handle.

Figure 14 Lines of force focused to a locus of convergence.

Figure 15 Generation of a stellar precursor (proto-singularity).

Figure 16 Illustration associated with entry 13242.

Figure 17 Illustration associated with entry 13245.

Figure 18 Illustration associated with entry 13358.

Figure 19 Illustration associated with entry 13555.

Figure 20 Illustration associated with entry 13556.

Figure 21 Illustration associated with entry 13557.

Figure 22 Illustration associated with entry 13558.

Figure 23 Illustration associated with entry 13583

Figure 24 Illustration associated with entry 13591.

Figure 25 Iron filings sprinkled on platform around wooden dowel.

Figure 26 Model 2A-magnet lowered onto dowel showing initial disturbance of iron filings.

Figure 27 Iron filings realigned after lightly tapping platform.

Figure 28 Iron filings "pirouetting" in concentric orbital shells.

Figure 29 Model 2B-magnets in opolarity with iron filings "pirouetting" in concentric orbits on

the platform and filings extended into space in Maxwellian spires on surface of plastic

bottle.

Figure 30 Model 2C-magnets in compressed configuration with freshly sprinkled iron filings on

platform.

Figure 31 Model 2C-magnets in compressed interlineations and iron filings in concentric orbits

on platform..

Figure 32 Quantum mechanical model of photoelectric effect.

Figure 33 Model of wave mechanics.

Figure 34 Galileo's illustration of the force of gravity.

Figure 35 Illustration associated with entry 10086.

Figure 36 Illustration associated with entry 10087.

Figure 37 Illustration associated with entry 10104.

Figure 38 Illustration associated with entry 403.

Figure 39 Convergence of "right-hand rule" waveforms at locus.

Figure 40 Maxwell's "Fig. 25" illustrating three right-hand waveforms on the respective x, y,

and z axes intersecting at the origin.

Figure 41 Maxwell's "Fig. 2" illustrating "molecular vortices."

Figure 42 Magnetic lines of force of four magnets configured to

generate a field in opolarity focused to a locus of convergence.

Figure 43 Demonstration of direct effect of "invisible" magnetic lines of force on "light."

Figure 44 Sketch for "redshift" experiment.

Figure 45 Model with opposing electromagnets.

Figure 46 Model attempting to detect shift in interference patterns.

Figure 47 Model attempting to detect shift in spectrum.

Figure 48 Model attempting to detect shift in angle of polarization.

Figure 49 Model with beam splitter attempting to detect shift by comparison of superimposed

interference patterns.

Figure 50 Model attempting to compare spectra.

Figure 51 Model with magnets in opolarity around incandescent bulb.

Figure 52 Model with permanent horseshoe magnets in opolarity attempting to detect shift in

interference patterns.

Figure 53 Model with spectroscope, electromagnets, and fluorescent bulb opolarity, and

fluorescent bulb.

Figure 55 Model with spectroscope, coil for electromagnet, and fluorescent bulb outside coil.

Figure 56 Model with bulb inside coil.

Figure 57 Lines of force projected from face of 1-ton electromagnet.

Figure 58 Lines of force projected from coil of electromagnet.

Figure 59 Reinterpretation of Hubble's graph for redshift as result of interstellar space as a field

of uniform pressurized radiation (opolarity) and suggested simplified experimental

schemes.

Figure 60 Metrification of the perceptible universe.

Figure 61 Compressibility.

Figure 62 Close-up of Model 1 generating double helix (DNA).

Figure 63 Reconsideration of mechanism of formation of symmetrical sections of reversed

polarity along mid-ocean ridges.

**Chapter** **PREFACE**

This work began with a question put to me in a telephone call from my nephew sometime in the Fall (October?) of 1983 of a question put to him and his fellow classmates by their high school science teacher of whether "Energy Can Be Recycled?" For the greater part of the 1970's I had been a technical writer at the Westinghouse Research Laboratories in Pittsburgh (the research laboratories has been dismantled as has the Westinghouse Electric Corporation itself circa 2004) that was deeply involved in all areas of scientific and technical research associated with all forms of electric power generation so that essentially I had a ready-made answer waiting for the question. Having first resolved the ethical question of whether he was allowed to get outside help, "Yes," I thought a moment and began to dictate the answer "off the top of my head" and then suggested that it might be better if I were to write the answer out and then dictate it to him over the telephone into a portable tape recorder that I had given to his mother (my older sister) several years earlier. I told him to get the tape recorder, check to see that it worked and call me back, and if it worked, I would then call him back in about 20 minutes or so after I had written out a more precisely articulated answer and I would then dictate the answer over the telephone into the tape recorder. He would then transcribe the answer and call me back so that I could confirm the transcription. We proceeded in that manner and over the passage of years by chance he happened to have saved the originally submitted and graded paper and sent it to me for inclusion herein. Accordingly it is Figure 1. The issue left outstanding in that answer was "What happens to all of the radiation that is generated in all mass-energy conversion processes?" After dictating the answer I had no particular further interest in the subject as by then I had left Westinghouse and Pittsburgh and began my career as an attorney practicing in New Jersey.

Following the mid-east oil crisis of the 1970's, there was a renewed interest in unified and pure field theory1 as a potential key to new sources of energy, an interest that had waned after Einstein's death in 1955 and his lack of success on a project to which he had devoted the last some thirty years of his life. The 1980's, however, saw an expanded interest in theoretical and experimental physics at the subatomic and cosmic levels—quasars, black holes, quarks, supernova remnants, gravitational waves, and so forth. Theoretical and experimental physics became topics covered by general publications and commercial TV as they continued to do to the end of the second millennium and even more so to the present. Although my work at Westinghouse and later as a patent attorney put me in daily contact with virtually all of the scientific and technical disciplines, industrial research and patent applications are rarely if ever concerned with the esoterics of cosmology, that in conjunction with the fact that my technical background is in chemistry, meant that I only became aware of "unified field theory" and subsequently "pure field theory" in the late 1980's that, because of their relationship to the outstanding issue in my answer to my nephew, renewed my interest in the initiating question.

Two separate and seemingly unrelated events occurred in late 1987 and early 1988 that converted my passive spectator interest into a dedicated autodidactic program to solve the problem of unified and pure field theory. The first event occurred, to the best of my recollection, in late Spring or early Summer of 1987 while I was driving east about one-half of a block from the intersection of Routes 439 and 1/9 nearing the "Bayway Circle" in Elizabeth, New Jersey and looked up and saw the Moon on the eastern horizon in a field of faint blue.2 It was an exceedingly powerful impression suspended there in space. IT WAS NOT JUST THE MOON, somehow it became an inexplicable emotional experience that raised the Moon to a very personal empathetic connection with the Platonic Ideal of a celestial body. (Figures 2 and 3) At that same intersection was a branch of the National State Bank that did not have a clock (Figure 4) but that had essentially the same architecture as another branch of the same bank at the corner of Westfield Avenue and Chestnut Street in nearby Roselle Park, New Jersey that did have a clock.3 (Figure 5) When I saw the Moon, the word that immediately came to mind was "round," every celestial body is "round!" and directly associated with "round" was the clock at Roselle Park that the hands of all clocks "go 'round'." These otherwise unrelated thoughts immediately fused into "round," immediately followed by the fact that time itself was a function of a celestial body (Earth) that "goes [a]round" its axis and that therefore "time" itself was "round." In fact, everything in the Universe was "round" or goes "around," from subatomic particles to all celestial bodies, and omnidirectional round was spherical, a round object [like the marker on the sign at the Bayway Circle] if rotated on an axis was spherical.

Therefore,

**TIME IS SPHERICAL**.

All of this occurred while I was still moving in traffic toward the circle and that took no longer than the time that it took to drive from the middle of the block into the traffic going "'round" the circle—perhaps ten to fifteen seconds. By the time that I got to the light at the intersection the concept of "spherical time" had solidified in my mind. I made the circle and to the best of my recollection these many years later drove to Newark (?). I could not get the thought out of my mind.

The second event occurred sometime between 8 and 10:00 a.m. on January 10, 1988 and arose out of watching a machinist drilling holes in a steel plate. As the drill bored through the plate, metal spirals came out. Although I had seen this operation countless times before, at that particular moment it had an extraordinary impact on me. First, there was the relativistic effect that if the plate were held in place and the drill turned or vice versa, the result would be the same, i.e., as with a piece turning on a lathe where the cutting tool is held fixed. Secondly, as the spirals came out of the plate they equaled the mass that was "excavated" from the hole so that if the process could be reversed the spirals could be "screwed" back into the hole to reconstitute the plate. I went over to a waste bin and took out a spiral and studied the tool marks that were left that clearly showed that the tip of the drill works its way through the metal at a slower angular velocity than the outer circumference of the drill, i.e., just as skaters at the center of a rotating line turn slower than those at the end of the line, but they all go "'round" the same 360° in the same time . . . just as the center of the second hand on a clock sweeps out the same minute as the tip. But even more so, there was a coexistent relationship between "incorporeal" time and geometry associated with increases in radius of a "corporeal" object. Time and geometry were somehow joined such that there was a 'corporeal' quality to time that was tied up in geometry. Simultaneously with the thought [or the intuition of it], I took one of the spirals and broke it in half, turned one half 180° and "screwed" it into the other half, and it immediately became apparent that identical converging waveforms [within seconds of picking up the first spiral my mind had already transformed the spirals into generic waveforms] will "screw" into each other to form a spherical mass at the locus of convergence that has a density equal to that of both waveforms that together constitute a "singularity."4 In other words, I could reconstitute the "sphere" of steel out of which all of the spirals had been generated. I could reconverge the waveforms into a singularity. The question was "could I also put electromagnetic radiation (waveforms) back together again?" And here I was some five years or so later reconsidering the outstanding issue of "Whether energy was recyclable." I was addressing the problem of "the singularity" that was "a" or " **the** " problem that everyone involved in field theory seemed concerned with, could not resolve, and could not get rid of. If the waveform were a generic frequency, and that generic frequency were time, then we had time that was not only round, but we had time that was "additive." It could be "combined." We could add frequencies/ waveforms back into mass—into singularities! But wasn't that exactly what Newton had done with his prisms in recombining the spectrum back into a pencil of white light! Something was going on here of monumental proportions that needed looking into!

All of this reasoning took perhaps about 1½ hours to work out, including the time to find a variety of spirals that could be broken into pieces, inverted, and screwed back into each other to generalize the process so that I could visualize the mechanics of converging waveforms and its implications for electromagnetic waves. The question of "round," the question of spirals converging, the question of spheres . . . there was something going on here that had to do with time . . . with Nature!

If time seemed so pervasive and its presence so intuitively and empirically evident, instead of time being just a passive concept, what if I were to consider time itself as an active force of Nature. Rather, what if I were to consider time as a force that had an incorporeal quality in the same way that an interest in property had an incorporeal existence coextensive with the corporeal entity to which it is attached. If I took that perspective, perhaps instead of Nature becoming more complex, I could make it more simple. If the solution to the unified and pure field theories were going to satisfy the criteria of a great theory—that it be simple, elegant, universal, and obvious [once recognized], for example Newton's F = ma or Einstein's E = mc2 — then if I measured every idea against the "rule of simplicity" until I had resolved even the most seemingly unsolvable disparity, then perhaps I might solve the problem.

The solution, if it existed, certainly must pervade all of existence, and the failure to find it I reasoned was not due to a shortcoming in knowledge, for if the half-life of cesium were known to 10-23 and Avogadro's number to 1026 then one more decimal place was hardly going to make a difference in solving the problem and the failure to do so was therefore not due to a lack of knowledge but rather due to a misperception or misconception of the evidence, the problem itself, physics as a whole, or some combination of any or all of these. Simply put, it was not a problem of the lack of intellect. It was a problem of the lack of insight. If the theory were there, it was there in a glass of water. I could make time and mass concurrent in the same geometry. Since all mass seemed to be spherical, and time itself was derived from the periodicity of a sphere, if I nominalized all mass to a sphere, time would be but a gradation of radius r. The problem was, "What is time?" in the "objective" sense. With that, I began to study "time" as if it were an academic discipline and gradually expanded my investigation until I determined that no one had any "substantive" empirical understanding of "time" at all. "Time" was as much an enigma today as it was in Aristotle's time. As my work progressed, the resolution and implications of spherical time ultimately became the key that unlocked the door to unified and pure field theory. The search ultimately led to the resolution of the issue of "What happens to the radiation that is emitted in all mass-energy conversion processes" and ultimately to the answer of 'Whether energy is recyclable?"

In the final analysis, there is nothing new in the present theory except that time has been given a geometrical configuration concurrent with the mass to which it is attendant. Accordingly, what is new is the way in which phenomena5 are perceived. "Time" becomes

THE FORCE

of the Universe, of Nature. With the exception of "pure spacetime," the actual dimensions of spherical mass, its radius r, "relative spacetime," what is generally called "space," "opolarity," the condition that exists when magnetic poles of the same polarity oppose (face) each other, and "hemilarity," one-half of a "singularity," no new terms are introduced or needed to discuss either the unified or pure field theories. All other terms have been in existence since classical antiquity.

Some prefatory remarks, however, are appropriate. If you are a layperson not familiar with physics or philosophy all of this may sound like a "jumble of gobbledygook" [from time to time "Aristotlespeak" [you will understand that when you read Aristotle] akin to Orwell's _1984_ "Newspeak"] that results from an initial disruption to your learned perceptions of the physical world and the association of philosophical considerations. Things that have traditionally been treated separately—time, space, energy, mass—notwithstanding Einstein's addition of "spacetime" to the vernacular, are here interchanged so that spacetime has a corporeal existence. The jumble is a result of breaking down your learned perceptions of existence and replacing those perceptions with ones that are more fundamental, fluid, and closer to physical reality. Instead of perceiving yourself as "apart" from Nature, you will hopefully perceive yourself as "a part' of Nature. You will become physics. Your external intuition about space and time will be replaced with an "internal intuition" about space and time until you yourself become spacetime. The ultimate emotional experience will be to look up at the Moon suspended in the sky and be able to feel, understand, and empathize with it as you recognize your own unity with the Universe . . . you will "understand" the Moon (and the cover to the book as well) and I will have succeeded in my task of trying to explain it to you. When that moment comes, something has changed in the Universe . . . you!

It is impossible for me to tell you what type of preparation you will need to read this work. It is above all a work about **THE** fundamental principle of the Universe, about existence itself. There are virtually no citations to other sources in the text itself, although there is an extensive bibliography at the end. First, I am addressing material that has been in the intellectual community for several thousand years (Euclid, Archimedes, Plato, Aristotle), nearly half of a millennium (Copernicus, Kepler, Bruno, Galileo), several hundred years (Newton), over a hundred (Faraday, Maxwell, Hertz), and nearly a hundred (Einstein).

Secondly, all of the primary source material about which the unified and pure field theories are concerned is conveniently found in any college physics textbook and is implied in every physical discipline.

Thirdly, three types of readers are anticipated: academically trained scientists and engineers who are thoroughly familiar with the literature so that citations are superfluous; laypersons who cannot reasonably be expected to go beyond this work in any event; and a few others who will independently pursue their reading and who will benefit from the bibliography, at least in part. As to the present material, you will not find it anywhere, and although others have addressed parts of it, their perspective is wholly different than mine. To track down each point would be both cumbersome and unfruitful. For example, to discuss just the "spark" you would have to locate its first scientific appearance in classical antiquity and then follow that with a lugubrious listing of references as it again appears in the seven volumes of Faraday's _Diary_ , his _Experimental Researches in_ _Chemistry and Physics_ , and the two volumes of his _Experimental Researches_ _in Electricity_ just to see how it is associated with electricity and other phenomena. As to the _Diary_ , you will have to get a copy—seven thick volumes that have been out of print for at least fifty years and than presumably dedicate a substantial period of your time to reading them [and then some if you are as slow a reader as I am] and have to earn a living doing something else in the meantime. From a general knowledge of physics you would know that a "spark" is a photon although no one has ever expressly said that, that directly implicates Newton's _Opticks_ that implicates quantum mechanics that leads to plasma physics and ultimately to cosmology. The task can be done, but it is like plowing through a field of bubblegum and it would be helpful only to those who have access to the sources and the time and training to read them just to end up with the conclusion that a "spark is light," an obvious fact that no one has ever expressly stated either and no one has ever fully understood, hardly worth several months or years of effort when I have already done that for you. The argument simply comes down to "a spark is a spark." To the uninitiated, that statement is rather simplistic and certainly does not require the training of a "rocket scientist" to understand. On the other hand, to an electrician, explosives expert, forest ranger, or fireman, people who are experts in **sparks** , they will tell you, "Yes, that's true, but there are sparks" and there are

SPARKS!

Furthermore, you do not have to have a laboratory to understand or undertake anything herein . . . Galileo did his work with a simple ball, incline, and candelabra; Newton with pendulum, prism, stars and planets; Kepler and Einstein with only pencil and paper. I used simple magnets, ball bearings, iron filings, wood, and metal rods . . . all except for the magnets, scrap that was lying around a machine shop in dumpsters and cans of scrap metal. Of course there is no charge for looking at the Universe itself or of being a part of it.

Finally, this is not a mathematical work; it is empirical, although there is a world of mathematics to describe it. On the other hand, you should understand that we are dealing with the physical Universe so that you should have some understanding, appreciation, and acceptance of physical reality and at least some understanding of solid geometry, at least through the standard American high school course, to recognize that a sphere is round, has a surface area described by 4/3πr2and a volume of 4/3πr3, and that the only difference between spheres is the length of their radius r.

As to the style of the work itself, as it turns out, it is a collection of many styles, sometimes vaguely historical, sometimes analytical, sometimes merely explicative.6 This is neither a textbook nor a novel. It is an attempt to explain a seamless web as I tried to unravel it. Accordingly, it became apparent that the only way to begin was to plunge right in—

We begin with the proposition that

**TIME IS SPHERICAL**.

There is just no other way "'round" it. As to the point of view, from  
time to time I talk in the first person when the text seems to be appropriately personal, from time to time in the "modest we" when I consider that you and I are going through this together, from time to time "you" because quite clearly I consider this to be a "one-sided dialogue" the same as if _you_ and _I_ were in a quiet room inside a large library so that we could go through this step-by-step, you could go off and read Aristotle for a couple of weeks after which we would come back and move ahead a little more, and so on to the end. As to the courage that it will take to go through this work, quite frankly, I anticipate the material is going to be very, very, very shocking to you, and I fully expect that it is not going to "sink in" at one sitting or one reading after which you will walk outside, look up at the Moon and say "Got It!" It would be nice, but not reasonable. And, of course, many of you are not going to accept it at all.

I leave it at that.

Jack Gerber

Elizabeth, New Jersey

April 2010

NOTES

1 From time to time I refer to both theories in the singular when I view them as a single integrated theory and at times in the plural when I view them as distinct, but related, theories.

2 My initial impression was that I saw the Moon sometime around May 1987 going to the Essex County Court House in Newark that suggests that I may have seen it earlier in the day and at a slightly higher and less advanced position. However, the sense of seeing it lined up with Route 439 still retains its power and therefore favors the later impression, while on the other hand the Moon nonetheless lines up with Route 439 in daylight at different times of the day throughout the latter part of Spring. After consistently watching the Moon one, two, and three days at 90+% full luminosity prior to each full Moon from 1992 to 1994, apparently I saw it at or around the mid-summer full Moon nearest the summer solstice around June 22 when the Moon is still in full daylight and when it precisely lines up with the centerline on Route 439 (Elmora Avenue) directly across the middle of the Bayway Circle intersection in the early evening. (Figure 2) On the other hand, I have no recollection why I was going in that direction at that time of night as certainly the Court had already closed by 4:00 p.m.! In any event, an equally powerful and moving impression occurred during the lunar eclipse of December 3, 1993 at about 1:00 a.m. (0100 hrs) when only the hazy silhouette of the Moon is visible with the stars clearly visible in the background, and essentially every full Moon thereafter. But of course those are not the ones that got the project started. Additionally, the naked eye does not see the Moon as photographed in either Figures 2 or 3, i.e., as a solid yellow-white disk, but rather as the pale white disk with the characteristic shadows of the craters that constitute the distinct face of the "Man in the Moon."

3 The building at Bayway Circle still exists but the branch has been closed and the clock at the Roselle Park location still exists but the site has been occupied by a succession of branches of other banks.

4 For a full discussion of the geometry of converging waveforms and fields that will be essential to our discussion you should read thoroughly Veblen and Young's _Projective Geometry_ , especially the various theorems and discussions involving conjugate imaginaries and " _I_ " (√-1) as pregnant with all of the important considerations here. The text and the statements in the exercises should in their own way be taken as equivalent, and in some sense superior, to that of Riemann's "Hypothesis" for it is not just a geometry on a different premise, it is geometry from a different perspective, one that has until now neither been fully explored and in some aspects has never even been broached. It remains a singularly important "event" in our discussion. Its implications herein are so far reaching and important as to not warrant particular citation; it is taken as a primary work such as those of Galileo, Newton, Faraday, Maxwell, and Einstein with which you should be or become intimately familiar. You will also note that the concept of "locus" is not new to the present discussion.

Projective geometry is exceedingly more important for the physics of unified and pure field theory than is classical Cartesian geometry that starts with the construction of a coordinate system whereas projective geometry is a system that is itself capable of generating a coordinate system, i.e., a singularity. You may also see in projective geometry the inference for making the sphere the logarithmic base for geometry and therefore of all mass.

110. The principle of transference. We have seen how the geometry of the inversion group in the plane, arising initially as an extension of the Euclidean group, is equivalent to the projective geometry of the complex line and also to that of the real quadric which may be specialized as a sphere. We have also seen the equivalence of the projective groups of all one-dimensional forms in any properly projective space. Since the regulus is a one-dimensional form, this gave a hold on the group of the general quadric. The latter group in a complex space has been seen to be isomorphic with the complex inversion group and also with the fundamental group of the function plane.

Veblen and Young, 2 _Projective Geometry_ 284.

You should also see the drawing of Figure 82 at 416 not as a projective coordinate system but as the "right-hand rule" of electricity. The geometry of converging fields has been thoroughly broached, although not expressly recognized in a multitude of drawings in standard textbooks on elementary and advanced differential equations per se as well as within field theory and the general corpus of physics as a whole. See for example, Boyce and DePrima, _Elementary Differential Equations_ , Figure 7.6 at 360, Figure 7.8 at 370, Figure 7.12 at 376, and elsewhere; Thorne, "Gravitational Radiation," in Hawking, _300 Years of Gravitation_. Figure 9.1 at 341. You will recognize in the literature the consistent absence in any discussions of the basic principles of Veblen and Young, which if they were added as conjugate inverses in the form of an omnidirectional field converging about a point locus, would be able to generate the "singularity," i.e., Model 1 below. The insights of projective geometry, if they were added to quantum mechanics and especially wave mechanics, would be especially revealing, in fact explicitly descriptive of the phenomena itself. You may now hopefully recognize that to encumber the present work with a plethora of citations that merely evidence a longstanding concern about an issue belabors our task. Rather, I believe that a judicious listing of source material in the bibliography may equally accomplish the task for those with a penchant for perseverance. Having set out the theory, you will have an adequate basis for reviewing the literature from the perspective of the unified and pure field theories and of making the necessary transformations that will bring the work of previous investigators into harmony with the theory as well as possibly harmony amongst the various respective divergent views. However, I have indulged a comment here and there as I believe it may be helpful and hopefully poignant in directing you over a particular point or to attach the argument to extant material to which you can refer to align or extend the perspective. All of us, of course, are plowing the same field.

In general, however, you should be looking for phenomena that involve spheres, _i_ , conjugates, pressure and especially radiation pressure, and most of all, "sparks," for it is the spark. i.e., the common spark, that resolves the problem of the singularity.

5 For simplicity, throughout this work I have elected to use the one form for the singular, the collective plural, and the plural, or as Bruno would say, the one, the many, and the all.

6 One small note, however, is required. The appearance of a set of parentheses, ( ), inside the text of a quotation indicates that the text inside the parentheses and the parentheses themselves are in the text itself whereas any of my emendations are marked by brackets and my initials, i.e., [ . . . JG]. The use of parenthesis and brackets outside direct quotations are in conformance with the stylistic use of the _Government Printing Office_ _Style Manual_.

Figure 1 Response to my nephew that initiated the project (page 1).

Page 2

Rich Luterman per 5,6

Is Energy Recycled or Not?

The first law of thermodynamics states that energy is neither gained nor lost in a chemical reaction or physical system but only transferred from one object or form to another in accordance to the law of conservation of energy. However, the law of conservation of mass and energy is true only in the theoretical sense of the totality of energy and mass on the universal scale. In truth, in every chemical reaction heat is either produced, that is exothermic reactions, or absorbed, endothermic reactions. In any movement of physical bodies, such as rolling, pushing, or lifting, heat is expended by the mover in producing usable work energy, friction may occur causing energy to be lost as heat, or energy can be stored, as in a strained or lifted object, as kinetic energy. Upon the completion of the chemical reaction or physical movement the heat energy is dissipated into the environment, generally at so low a caloric value that it has no useful work content. Much research has been expended to harness this low energy content, such as waves as tidal falls of the ocean, solar energy, all with little success. Windmills and solar panels have been marginally successful, however, operation is tied to unpredictable and uncontrollable (sic) natural events.

In terms of energy recycling then, in a real world applicable system energy is generally lost and nonrecapturable for purposeful controlled work. The exhaust fumes and low energy water vapor from automobiles is a supreme example of non-recyclable (sic) energy, only a fraction of the burning of hydrocarbons in gasoline is being used to drive the piston, the rest remains as lost heat. In fact, studies have been done on the savings in energy by not having vehicles with water-pumps, fans, air-conditioning systems, and the amounts of energy needed to manufacture the components themselves. On the grand scale, work energy is lost to the atmosphere and to the space surrounding the earth and then dissipated into deeper space with no feasible means of recapturing and recycling.

Define energy—the capacity to do work; the property of a system which diminishes when the system does work on any other system by an amount equal to the work done.

Figure 2 Full Moon aligned directly over center of Routes 1/9/439looking east at Bayway Circle, Elizabeth, New Jersey on July 1, 1993 at 7:50 p.m. Contrast of the Moon slightly computer enhanced to more closely approximate sighting with naked eye. Enlarged from Polaroid SX-70 film.

Figure 3 Full Moon at Routes 1/9/439 looking east at Bayway Circle, June 22, 1994 about 8:15 p.m. Enlarged from 35 mm.

Figure 4 National State Bank, Bayway Office, Elizabeth, New Jersey (faces Routes 1/9/439). [Office has since closed, 2004].

Figure 5 National State Bank, Roselle Park Office, Roselle Park, New Jersey. [Office has since closed, 2004].

**Chapter** **1. UNIFIED FIELD THEORY**

(THE PRIMARY PRINCIPLE)

OVERVIEW

The object of the unified field theory is to unify into one consistent theory the four major forces believed to exist in Nature, namely, gravity, electromagnetism, and the "strong" and "weak' forces believed to exist at the subatomic level. Gravity, of course, was the work of Newton, electromagnetism the work of Faraday, and the "strong" and "weak" forces the work of Steven Weinberg, Abdus Salaam, and Norman Glashow. The concept of unification was itself the brainchild of Einstein who devoted essentially the last thirty years of his life to its solution and left it unfinished at his death in 1955. It is generally considered to involve a "primary principle" that has some mechanical or quantum mechanical quality. The object of the pure field theory is to go beyond the unified field theory to account for all of the other outstanding issues that would remain in physics, most particularly the mechanism by which matter itself comes into existence—the singularity—and the nature and origin of the "dark matter" believed to exist in the Universe. There are various other names in current use for pure field theory, for example, Grand Unified Theory (GUT'S) and the "Theory of Everything" (TOE) but for historical reasons I have stayed with "pure field theory." In practical terms, the unified field theory is a stepping-stone to pure field theory that is also the way that it evolved for me.

Thus arises the problem to discover the simplest matter of fact from which the measure-relations of space may be determined; a problem which from the nature of the case is not completely determinate, since there may be several systems of matters of fact which suffice to determine the measure-relations of space—the most important system for our present purpose being that which Euclid has laid down as a foundation. These matters of fact are—like all matters of fact—not necessary, but only of empirical certainty; they are hypotheses. We may therefore investigate their probability, which within the limits of observation is of course very great, and inquire about the justice of their extension beyond the limits of observation, on the side both of the infinitely great and of the infinitely small.

Bernhard Riemann, "On the Hypotheses Which Lie at the Bases of Geometry," _Nature_ , 8:15 (May 1, 1873); see also Smith, _A Source Book in Mathematics_ at 412.

The question of the validity of the hypotheses of geometry in the infinitely small is bound up with the question of the ground of the metric relations of space. In this last question which we may still regard as belonging to the doctrine of space, is found the application of the remark made above; that in a discrete manifoldness, the ground of its metric relations is given in the notion of it, while in a continuous manifoldness, this ground must come from outside. Either therefore the reality which underlies space must form a discrete manifoldness, or we must seek the ground of its metric relations outside it, in the binding forces which act upon it.

The answer to these questions can only be got by starting from the conception of phenomena that has hitherto been justified by experience, and which Newton assumes as a foundation, and by making in this conception the successive changes required by facts which it cannot explain. Researches starting from general notion, like the investigation we have just made, can only be useful in preventing this work from being hampered by too narrow views, and progress in knowledge of the interdependence of things from being checked by traditional prejudices.

This leads us into the domain of another science, of physic, into which the object of this work does not allow us to go today.

Bernhard Riemann, _Nature_ , 8:37 (May 8, 1873); See also Smith. _A Source Book in Mathematics_ at 424-425.

13942. Time in relation to magnetic force.

13943. If the necessity of time could be experimentally proved for the propagation of magnetic force. It would prove physical lines of force and the probable existence of a medium—on the other hand. If there be a medium, and if physical lines of magnetic force exist, time is almost certainly concerned.

13944. But the time (if concerned) will most probably be exceedingly short, like that of its relation to light, and so perhaps forever remain insensible to us. Still, there is the case of time in the transmission of nervous energy and that is comparatively slow—and there is the fact that when soft iron is magnetized by an electric current, it takes time to rise to a maximum; and here the forces themselves are magnetic.

13945. There are two or three great difficulties in the way of comparing the times of the propagation of magnetic force over different distances. First the quickness of the action.

13946. Second—the great distance required therefore to make the propagation such as to require sensible time—and with that great distance the rapid diminution of the magnetic action that is to be made sensible.

13947. Third—the want of instantaneous indicators of magnetic action, such slow things as ordinary galvanometers being utterly unfit for the purpose because of the great time they require to start their needles and give them a sensible motion.

+13948. Fourth—the want of a sudden source of magnetic power, for the bringing of a magnet into position either from a distance or by inversion, or the making of an electromagnet, both require too much time to allow the small differences I want being rendered sensible to them.

[13949 is omitted in the MS.]

13950. But in respect of these points, consider whether experiments on the following principles may be at all likely to be useful. If, considering the reasons before given (13944), there be the least hopes of finding the time, these hopes ought to be verified or exhausted. Can that be done thus?

Michael Faraday, 6 _Diary_ 434, entries for August 15, 1855. In addition to other entries throughout the _Diary_ in particular Volume 7, January 19, 1856 et seq., "Time—in Electrodynamic or Magnetic Induction"; March 30, 1857, 15404, "Time in Magnetism"; September 26, 1857, 15685, "Time"; October 6, 1857, 15711 et seq.; April 5, 1858, 15740; and various places throughout the _Experimental Researches in Electricity_.

Accordingly, we begin with the proposition that

TIME IS SPHERICAL

and through that geometry is both finite and infinite, unidirectional, omnidirectional, progressive, simultaneous, relative, absolute, and constant. Time is prospective only. It is **NOT** reversible. Events do not repeat themselves although fundamental processes do. Time is a constitutional organic element of the Universe and therefore of existence itself. It is the "engine" of existence—the primary force that binds the Universe together, the essence of gravity, magnetism, electricity, electromagnetism, and radiation. When spherical time is severed it becomes "linear," hemispheric time.

SPHERICAL TIME IS GRAVITY

HEMISPHERIC—SEVERED SPHERICAL TIME—

IS

STATIC ELECTRICITY AND MAGNETISM

Spherical and linear time exist simultaneously just as a ball spins on its own axis as it rolls across the surface of the floor or gets thrown through space. Time makes objects "round" and makes the world go "'round" as well. A point on a surface of a rotating sphere does not itself rotate on the surface. It is "unified" and "at rest" with the sphere. The circumference of a circle on a sphere depends on its location on the sphere and the radius r of the sphere. This circumference constitutes "pure" time, i.e., one rotation around the sphere. The distance is independent of any external context. "Relative" time considers the rotational periodicity of that sphere relative to external objects. A sphere in motion has both pure time and relative time. The present theory takes as a given that all mass is spherical, that pure time is identical with the sphere to which it is attendant, and that all spheres and all mass are identical to each other except as to gradations of r and therefore can be nominalized to r.

Accordingly, the "4/3π" in the formula of a sphere is merely a "quantitative descriptive modifying coefficient" and as no calculations are made in the present work since all spheres are the same it is dropped from our discussion. Reference is simply to "r." The unification of time with geometry results in the fusion of time and space into a "spacetime" that pervades the Universe and therefore existence itself. There is no space without time nor time without space, notwithstanding that there are local gradations in the density of spacetime. Accordingly, there is no such thing as a "vacuum" as that implies the nonexistence of spacetime and therefore the nonexistence of existence. The unified and pure field theories postulate that existence is undivided, pervasive, continuous, and infinite, that Nature defines all existence, and existence has always existed and will always continue to exist. Spacetime that has been condensed to a defined geometry constitutes "corporeality," 'mass." All mass is equivalent except for gradations of r. That does not mean that the Universe or existence itself has a defined geometry, shape, or "r," it only means that mass does; nor does it mean that all of the Universe or existence consists of mass, only that part of existence that has been condensed constitutes "mass." The rest of the Universe is "incorporeal" and exists concurrently and contemporaneously with corporeal existence. The incorporeal Universe does not have a defined geometry and is homogeneous and uniform. It is what is generally called "space." The totality of the Universe constitutes

**THE** **FIELD**

in which all of existence is to be found. Since the continuity of existence is pervasive, the field constitutes that continuum, and since there is no lower or upper limit to the metrification of existence, there is also no lower or upper limit to the metrification of the field.

The severance of spherical time and the relationship between gravity and magnetism begins with a pair of horseshoe magnets, chosen because that configuration most closely resembles a circle and therefore most easily propagates a sphere when rotated about an axis. Take two horseshoe magnets and place their faces next to each other so that they attract each other to constitute a continuous circuit. Draw a series of arrows all in the same direction around the three outer respective surfaces without regard to which way the arrows point just so they all point in the same direction relative to each other to indicate a unified directionality. Proceed now with the following demonstration to derive the concept of "spherical" time and "hemispheric" "severed" spherical time that is the

PRIMARY PRINCIPLE

of the Universe. In "circular" form the magnets constitute an undivided, continuous circular circuit in which all parts are equal. I submit that whatever property "magnetism" is, in this configuration it has no beginning and no end and if propagated about an axis it would constitutes a sphere. Now take one of the horseshoe magnets and mentally sever it along a line that is perpendicular to the faces so that there are two horseshoe magnets each the half-width of the original. As a practical matter do not even try to physically sever the magnet as you will be able to achieve (essentially) the same result if you take the other magnet and place it alongside of the first so that the arrows of both point the same way, i.e., they have the same poles adjacent but not oppositely facing each other. In this configuration, turn them so that the adjacent faces now "face" each other and you will immediately recognize that what a moment ago was a contiguous unidirectional circuit held together by an attractive force is now a repulsive force. (Figure 6) Now take these symmetrical halves and axially rotate one 180° so that the opposing ends again face each other to restore the attractive force. (Figure 7) The condition in which the poles of the same polarity face (oppose) each other so that they repel each other I call "opolarity." I submit that this demonstrates that magnetism embodies an incorporeal force that is unidirectional, irrepressible, irreversible, persistent, replicable, and universal. This, of course, is not new, except for the name "opolarity."

Yet the loadstone and all magnetic bodies—not only the stone but also magnetic, homogeneous matter seem to contain within themselves the potency of the earth's core and of its inmost viscera, and to have and comprise whatever in the earth's substance is privy and inward: the loadstone possesses the actions peculiar to the globe, of attraction, polarity, revolution, of taking position in the universe according to the law of the whole; it contains the supreme excellencies of the globe and orders them: all this is token and proof of a certain eminent combination and of a most accordant nature. For, if among bodies one sees aught that moves and breathes and has senses and is governed and impelled by reason, will he not, knowing and seeing this, say that here is a man or something more like a man than a stone or a stalk? The loadstone far surpasses all other bodies around us in the virtues and properties that pertain to the common mother of all; but those properties have been very little understood and noted by philosophers. Toward it, as we see in the case of the earth, magnetic bodies tend from all sides, and adhere to it; it has poles—not mathematical points, but natural points of force that through the cooperation of all its parts excel in prime efficiency; such poles exist also in the same way in the globe, and our forefathers always sought them in the heavens. Like the earth, it has an equator, a natural line of demarkation between the two poles; for of all the lines drawn by mathematicians on the terrestrial globe, the equator (as later will appear) is a natural boundary, and not merely a mathematical circle.

William Gilbert, _On the Loadstone and Magnetic Bodies_ at 24.

The question for us is whether there is any body that drives another away to a distance without material impetus, as the loadstone attracts. Now a loadstone does repel another loadstone; for the pole of one repelled by the pole of another that does not agree naturally with it; driving it, it makes it turn round so that they may come together perfectly according to nature. But if a weak loadstone floating freely in water cannot, on account of obstacles, readily turn about, then it is repelled and driven farther away to the other.

_On the Loadstone and Magnetic Bodies_ at 59.

But the question arises, why does iron touched with loadstone take a direction of movement toward the earth's opposite pole and not toward that pole of earth toward which looked the pole of the loadstone with which it was magnetized? Iron and loadstone, we have said, are the same primary nature; iron when joined to the loadstone becomes as it were one body with it, not only is one extremity of the iron altered, but the rest of its parts are affected.

_On the Loadstone and Magnetic Bodies_ at 65.

But if the loadstone be in any way divided either of the parallels or on the meridians so that in consequence of the change of its shape either the poles or the equator migrate to other seats, then if the part that has been cut off be but set in its natural position and conjoined to the rest, though they be not cemented or otherwise fastened together, the terminal points go back again to the former places as though no part of the body had been cut away. When the body is whole the form remains whole; but when the mass of the body is reduced a new whole results, and a new wholeness necessarily arises in each minutest place of loadstone, even in magnetic gravel and fine sand.

_On the Loadstone and Magnetic Bodies_ at 74.

I submit that this force is what we call " **time**."

Oersted established that a direct electric current propagated a magnetic field such that electricity, if it were not equivalent to magnetism, at least had some property that was capable of generating it. Correlatively, Faraday established that magnetism could generate an electric current that raised the inference that electricity if it were not equivalent to magnetism, had at least some undisclosed common origin with it. Since magnetism can generate electricity and electricity can generate magnetism, I submit that

THE "RIGHT-HAND RULE" IS UNIDIRECTIONAL TIME

" **TIME" IS THE FUNDAMENTAL FORCE OF THE UNIVERSE**

DIRECT CURRENT IS SPHERICAL TIME

and

ALTERNATING CURRENT IS HEMISPHERIC/

SEVERED SPHERICAL TIME

With this in mind, and with the fusion of time and space into "spacetime," I submit that the

THE PRIMARY PRINCIPLE OF THE UNIVERSE

is

THE SEVERANCE OF SPHERICAL TIME

The "primary principle" results in the axial rotation of unidirectional time under the conditions of opolarity so that attraction becomes repulsion and conversely repulsion becomes attraction. Since polarity is a constitutional element of the primary principle, polarity is a constitutional element of existence itself. Accordingly, I submit that

POLARITY IS TENSE

POLARITY IS THE OUTWARD MANIFESTATION OF

UNIDIRECTIONAL TIME

By this I mean that "polarity," i.e., "north' is to "south," as "+" is to "-," as the "past" is to the "present," and the "present" is to the "future," so that one irrevocably and irreversibly follows the other. That is, "polarity" is the outward manifestation of "time" that always moves into the future. Therefore, there is no such thing as time "reversal' nor has there ever been a beginning of time.

THE PRIMARY PRINCIPLE IS PERPETUALLY REPETITIOUS

Unidirectional time—polarity—is the animus of existence, the consequence of which means that all mass rotates with a unidirectional rotation. It does not mean that all of existence rotates uniformly or in the same relative direction, nor that all mass rotates the same, nor that all of existence rotates with the same apparent velocity. Implied in unidirectional time and unidirectional rotation is perspective and opposition.

JUXTAPOSED UNIDIRECTIONAL SPACETIMES OPPOSE EACH OTHER UNIDIRECTIONALLY

Namely, if we take two contiguous masses rotating unidirectionally their periods of rotation oppose each other. Contiguous masses do not rotate in the same direction, only alternate masses rotate in the same direction, although each may rotate synchronously with each other, hence the need for idler wheels in the mechanical arts. The severance of spherical time results in hemilarities that are juxtaposed in opolarity with each other such that they repel each other and propagate an intermediary interstitial relative spacetime, a "field" in which there is no defined polarity and that pushes the masses apart. This intermediating field is what we commonly call (unoccupied) "space.' (Figure 8)

OPOLARITY GENERATES RELATIVE SPACETIME

We may now postulate that polarity itself is the indicia of the existence of an "entity."

AN ENTITY IS UNIFIED SPACETIME

" **MASS" IS AN ENTITY**

" **MASS" IS THE CONVERGENCE OF THE FIELD AT A LOCUS**

INTO A DEFINED GEOMETRY

Just as a magnet may be continuously divided without destruction of polarity in each division, so an entity may itself consist of a multitude of subentities, each having a defined geometry separated by an interstitial field in opolarity. Having separated an entity from others, each entity becomes a distinct inertial system that may itself have a multitude of inertial subsystems. An entity is therefore at rest with itself and in motion as to all other entities. Under the primary principle the laws of conservation of energy and momentum result in a dynamic adiabatic Universe. The integration of all of these principles can easily be seen in the clock. The clock demonstrates the interchangeability of linear time and spherical time, the mass-energy conversion process of special relativity and electrodynamics and the emission of linear electromagnetic radiation. The hand of a clock is a radius that sweeps out equal areas in equal times by gradations of r and the angular velocity with which any point on the hand travels is a function of its distance from the center. Since all points on the radius make the sweep in the same unit of time, each point is governed by the same rules of proportion and conservation of angular velocity. The face of the clock displays the nominalization of pure spacetime as gradations of r without violation to unidirectional time. The rotation of the hand around the face is the outward manifestation of the expenditure of energy inherent in the mechanism itself, which energy drives the hand through "space" in 'unidirectional time."

When all of this is taken into consideration, it simply means that the primary principle underlying hemispheric/severed unidirectional time becomes the ponderamotive force of alternating current that results from the continuous uninterrupted cycling of the north and south poles of the magnet into fields of opolarity that are induced into and through conducting wires or even through "space" itself either generally or focused as by Hertz or Marconi and all of their progeny.

Figure 6 Demonstration of unidirectional time (original drawings).

Figure 7 The primary principle (original drawings).

Figure 8 Generation of "the field" in opolarity (original drawings).

**Chapter** **2. PURE FIELD THEORY**

2.1 MODEL 1

Pure field theory is embodied in "Model 1."1 The concept of Model 1 arose out of an exceedingly intense heightened state of anxiety derived from the self-posed question of "Whether the force necessary to push two permanent horseshoe magnets together when the poles of the same polarity face each other (subsequently "opolarity") could push [compress] mass together if it were actually interposed between the faces of the two magnets?" The anxiety was further heightened by an intense apprehension and immediate full recognition that if the force could compact mass then I would have unlocked the door to step through the threshold of the nature of existence and the Universe itself to confront head on the whole panoply of theophilosophical issues that are implicated therein, and that having stepped through that threshold, I could not turn back. This

EXCEEDINGLY INTENSE

anxiety lasted for upwards of certainly at least two, three, four, or perhaps even five or six months, to the best of my recollection the latter part of a winter and better part of a spring, until I had mustered enough courage and determination to want to know and to then go out and buy at least one pair of magnets to find out. I bought the first pair of magnets [about $35.00 **each** for which I had no other current or anticipated use] on June 1, 1988 according to one receipt that I have managed to save. In short, to get to the point where I was irrevocably committed to resolve the issue, that I knew exactly where it led, and that I was prepared to be a "fool who rushed in where angels feared to tread." In my favor, however, was the fact that buying a few pairs of magnets would not be the most foolish thing that I had ever done or probably would ever do in my life and since I do not believe in angels I had nothing to fear.

The plot thickens however. If two magnets could compress mass, could a series of magnets focused to a point compress mass to a point, and if so, could a series of magnets rotated about the point generate a vortex in the field so that the mass would be compacted into a sphere within the vortex. (Figures 9, 10)

Although the unified field theory is primarily directed toward the unification of gravity, magnetism, electromagnetism, and inferentially electricity, it does not per se involve compressive forces of opolarity and the compaction of mass and the generation of a sphere, although it does involve spherical time. The unified field theory is essentially concerned with the geometry of time, the primary principle, and not particularly with celestial mechanics, singularities, and pure field theory. However, because it is concerned with roundness, and the initiating inquiry was the roundness of celestial bodies, cosmic implications are clearly present. Thus the unified field theory—opolarity and the concept of force that results from opolarity—has within it a potential means by which "roundness" may be generated. The issue is could it actually generate "round." Thus, although magnets are used in the demonstration of the two theories, the unified field theory and Model 1 are derived from two wholly different perspectives and traced to wholly different "anxieties," although both embody the same deeper underlying theory. On the other hand, one must accept as a given that the unconscious is itself a unified whole in which such compartmentalized distinctions do not exist and where the cross-pollination of free uncensored associations are the seeds from which such flowers are germinated.

The theoretical premise underlying Model 1 begins with the proposition that every stellar object is a mass-energy conversion system that generates electromagnetic radiation, that radiation is linear, and therefore is propagated perpendicularly from the surface of the generating body. If radiation is linear, then any two spherical celestial bodies that generate radiation are joined by an axis that defines the propagation of radiation toward each other perpendicular to their respective surfaces that at some point must come into opposition and therefore "opolarity." If we accept the proposition that the horseshoe magnet embodies the essence of all bodies capable of generating an electromagnetic field, then opposing horseshoe magnets embody all of the essential mechanics of the Universe and therefore all stellar bodies. Since one of the characteristics of electromagnetic radiation is that it has a frequency, inferentially it must have a spirality, and therefore a horseshoe magnet that can be rotated on an axis would replicate the spirality of "frequency." If we accept the proposition that all radiation rotates in the same direction (the right-hand rule), then the direction of all radiation in all frequencies from all bodies are identical subject to a translation of 180° from those bodies that are at the respective opposite ends of the converging axis, which in three-dimensional space applies to all sets of generating bodies. Accordingly, every celestial body not only generates radiation but is also subject to the radiation generated by all other celestial bodies so that they all are subjected to omnidirectional equipotential lines of force in essential equipoise identical to that generated by opposing magnets. Therefore a pair of rotating magnets would generate a pair of opposing frequencies that would generate a magnetic vortex about a focal point. If the opposing frequencies were omnidirectional and equipotential they would constitute a spherical vortex that would compact mass into a sphere. Accordingly, it was not only necessary to demonstrate that opposing magnetic fields could compact mass, it was also necessary to demonstrate that they could generate a spherical vortex. Therefore a handle or crank was necessary to rotate at least one magnet that was focused to a point. It was not necessary to rotate more than one magnet since all of the others were under the pressure of opolarity and would be driven by the rotated magnet in a constant state of opolarity as the respective poles came into sequential rotation and opposition. Thus by arranging at least four magnets in crossed position a converging field could be generated at a locus essentially duplicating an omnidirectional field.

With that in mind, Model 1 began with the two small horseshoe magnets that I bought in 1988 for the work on the primary principle, one of which is shown opposite to the magnet that is affixed to the handle. (Figure 11) By putting some iron filings into a small glass jar and placing the two small magnets on opposite sides of the jar, I tried to generate some kind of motive force into the filings but was only able to move them vertically and horizontally around the inside of the jar and only "twist" them somewhat across the space by rotating the magnets in opposite directions—actually by rotating just one of the magnets while holding the other in a fixed position. I could not, however, compact the filings toward the center. First, it became obvious that I would need somewhat larger magnets to generate a stronger field across the space of several inches of even a relatively small jar. Secondly, the experiment, although apparently viable, was inartistic because the iron filings became so entangled that they did not reveal the discreteness of the vortex mechanism and the fineness of observation that was masked by the tangle. I therefore took my little jar of filings to a local industrial supply house and with the courtesy of the counterperson tried the experiment with ever increasing larger magnets until I got up to magnets of about 3 lbs. force that induced at least a few filings to "twist" across the space of the jar. With that pair I went home and continued to attempt to generate a vortex with smaller and smaller jars until it became apparent that at least another pair of equally sized magnets were needed to focus the field to a point. In the meantime, sometime during this period, I was back in the same machine shop where I first obtained the metal "waveforms" and was walking by a 55-gallon drum of scrap metal when I saw a set of continuous feed ball bearings lying in the drum along with some lengths of ¼-inch diameter metal rods. The ball bearings were exactly what I needed to study the discrete mechanism of motion in the converging magnetic vortex that would not get entangled and that still could be manipulated with some degree of "fluidity" and the metal rods could be used to hold the opposing magnets in place and to make a crank that I could use to turn and generate a 'frequency" that would rotate the focused field into a compressive vortex.

The first task was to mount the magnets on some type of brackets so that they could be rotated perpendicular to each other and still retain opolarity and for that I used the metal spines from a loose-leaf binder that I no longer needed and had kept around my apartment for some future use. This was the use for which they had been kept. Because of the close proximity of the magnets to each other on the transverse axle, they had a proclivity to rotate into an alignment in which they attracted each other so that I had to fabricate a collar that would keep them in opolarity while at the same time close enough to each other to generate a densified field. To that end I took a piece of copper tubing and split open the ends and bent them into brackets that would prevent the magnets from repelling each other as they were forced into opolarity and that kept them in a fixed position while they were rotated around the axle. With this configuration I could rotate the crank that rotated the one magnet that was attached to the crank and thereby induce a frequency into the field that would be transferred perpendicularly to the two other transversely mounted magnets under the pressure of opolarity. I incidentally mounted one of the original little magnets on a bracket opposite to the magnet affixed to the crank handle just to see if the little magnet would turn on its own axis and on the first turn of the handle the little magnet

INSTANTLY

rotated concurrently with the magnets on the axle and at that moment I

INSTANTLY

recognized the mechanism that rotated Uranus, the only planet in the solar system whose magnetic poles are parallel to the ecliptic rather than essentially perpendicular to it. Therefore, a magnetic field unquestionably propagates unidirectional radiation that generates a ponderomotive force capable of rotating celestial bodies whose polar axes are either perpendicular or parallel to the equatorial plane of the field. The undeniable inference is that the field was omnidirectionally ponderomotive. At the same time, the larger magnets on the axle whirled away under the force of opolarity. Thus was conducted the _experimenta crucis_ for unified and pure field theory. The question now was whether the model could compact mass into a sphere. Although an elaborate scheme of axles with bevel gears that would translate the rotation around a central open space between the magnets had originally been contemplated, and in fact I had already purchased a pair of comparatively expensive plastic bevel gears to do just that, having already made a simple basic model that worked to this point, I merely put some of the ball bearings into a test tube and positioned the tube in the gap between the three large magnets and concentrated the field as much as possible by adjusting the nut on the threaded end of the crank (Figure 11), allowing just enough clearance for the rotation of the magnets. I was able to get the test tube within some approximation of a focal point so that within a few turns of the handle the ball bearings "took flight," compacted into a central mass, and began to swirl around in the tube exactly as I had envisioned. By turning the handle just so and stopping I could levitate the ball bearings motionless in the middle of the test tube . . . in space. (Figure 12) When I saw that I

INSTANTLY

recognized the mechanism by which celestial bodies were suspended in space. I understood the Moon! In other words, Model 1 embodies the essential mechanism of the Universe. From there, all other issues became understandable, articulable, and demonstrable.

The generation of the omnidirectional equipotential radiation pressure that constitutes "the field" of interstellar space and in which all celestial bodies are "suspended," i.e., levitated, may be seen by the progression of the magnetic lines of force visualized by iron filings sprinkled onto a clear plastic sheet over Model 1 and then lightly tapping the sheet so that the filings align themselves along the magnetic lines of force in the manner of Faraday. In Figure 13, the filings have been sprinkled and the plastic sheet tapped when the magnet affixed to the crank handle is in what may be conveniently called "position 1." In Figure 14, the crank handle has been rotated somewhat so that the magnetic lines of force begin to oppose the magnetic lines of force (opolarity) generated by the magnet on the crank handle and those affixed on the concentric tubular sleeve placed around an axle that supports the two magnets essentially perpendicular to the magnet affixed to the crank handle to generate an essentially circular configuration, "position 2," constituting the "locus of convergence" of 'the field" in an omnidirectional equipotential manner so as to levitate the ball bearings in "the field."

The configuration of the ball bearings shown in Figure 12 may be considered as a 'stellar precursor," (Figure 15) i.e., the convergence of "the field" as it begins to compress the mass toward the center. If one were to take a series of pictures as the magnets revolve, one would be able to see all of the various effects associated with "spiral galaxies" as the magnetic vortex works its action upon matter that comes within its effect. One must also accept, on the one hand, that at the nearly zero temperature of interstellar space that the angular velocity of converging waveforms and even of miniscule particles of dust has been slowed down so much that the conditions under which they would be compressed into larger aggregates is "astronomically" increased and enhanced. On the other, one must also accept that the "spark" evidences the convergence of waveforms even at terrestrial ambient and that all of the phenomena in the Universe and therefore all of existence is an outward manifestation of the primary principle.

The problem was, "Had this ever been done before?" Putting aside a multitude of experiments that had incorporated focused fields to achieve some particular effect, for example the Compton effect, Milliken's measurement of the mass of the electron, the exotic focusing of lasers in the Tokomak fusion project, all of which were not intended to study the force of the field as a theoretical entity per se, I knew to a reasonable degree of scientific certainty that this type of simple fundamental experiment could only have been done at the very earliest stages of electrical research, certainly only within the period of Ampere, Faraday, and Oersted, and absolutely not after Maxwell. Ultimately, my research led me to the beginning of the investigation of the magnetic field itself and finally to Faraday's laboratory notes that are preserved in his _Diary_. To my knowledge, Faraday is the only investigator who attempted to conduct detailed, fundamental investigations of the ponderomotive force upon mass suspended between converging fields.

13189. The polarity or the condition of bismuth when in the magnetic field: is it as I think or is it as Weber thinks? Will not the following considerations help to develop this matter?

13190. It is conceded that the magnetic power throws paramagnetics into a polar state, and I suppose Weber and others admit that it throws diamagnetics into their peculiar state of reverse polarity. Now admitting, as I am inclined to do, that the force does make all bodies submitted to it assume a new state for the time, then bismuth will have a state which it gains as it goes into the magnetic field and loosed as it comes out of it.

13191. In the case of iron, the acquirement of this state takes time—the Electro magnet takes considerable time to rise to its maximum, and it takes time to fall again. So if bismuth and phosphorous assume a new state, time will probably be concerned there also.

13192. If this state exists, it must be one favouring the transmission or conduction of the magnetic force. It is so in the case of iron, and it would seem unnatural that it should not be so in the case of bismuth.

13193. But if the supposed reverse polarity be occasioned by the magnetic force, it must be the same as the state set up; and it would be equivalent to setting up a resistance, not to the removal of one. Therefore the assumption of a reverse polarity, and the assumption of a state which tends to diminish the resistance to magnetic conduction, are in opposition to each other and both cannot be true.

13194. It seems possible to determine experimentally which of these is the truth of nature upon the following principles. Suppose a piece of iron between two magnetic poles: it becomes polar, i.e. acquires its state. Suppose it turned half way round; the state it retains will be adverse to the magnetic conduction, but then it will in time acquire the new polar or peculiar state which is favourable. If it be again turned half way round, and the same sequence of changes will occur. So that as the iron moves round, it will become less favourable to magnetic induction, and the lines of force across it from Pole to Pole of the magnets will open out and pass more through the surrounding air or other body occupying the magnetic field; and as it is resting and rising to its final state, it will conduct better and the lines of force will draw in and concentrate within it. This alternation of the lines of force which must accompany the change of magnetic conduction power are well fitted to prove experimentally the conditions of the body; if only currents which the changes are competent to produce can be gathered up by proper commutators and sent on to a galvanometer.

6 _Diary_ 288, entries for August 1, 1854.

13242. In reference to another point. A north pole of a magnet has lines of force issuing from it which are polar. If two north poles are opposed to each other, the lines of force have the form indicated. But suppose four N Poles–the lines (what few there might be) would proceed to the middle and then rise upwds. and downwards. But suppose further, six north poles inclosing a cubical space. What would be the condition of that space? What would a magnetic needle do in it? Probably nothing. What would a moving wire or evolving ring do in it? Would it have any state, as a state of tension; and as the magnets should receed from it or open out any way what would be its state and how would it come on? (Figure 16)2

13243. There can be no lines of force in the inclosed space. Can it have a state of tension distinct from the polar or current state, and is it that I tried to find by analogy with static electricity—a state of magnetic tension without polarity. Would it affect the Electro chemical state and so give voltaic terminations?

13244. The inside of a hole in the end of an iron ought to have a same state. Perhaps two holes at the ends of a core might serve as chambers for experiments.

13245. How would a piece of bismuth behave there? If N and S were two poles of magnets, a piece of iron allowed to move along the oblique line would go from a towds. the angle more strongly than one magnet away. Then a piece of bismuth ought to tend to go from the angle. If the two poles are both N or both S, the piece of iron should tend to go out, I think, and a piece of bismuth tend to go in; for the angle would partake of the character of the inclosed space before spoken of, i.e. the spot b would have weaker magnetic power than any where else. (Figure 17)

6 _Diary_ 299, entries for September 2, 1854.

13358. The inside of a steel chamber (13421) coincides with the chamber enclosed by six square like poles, Which must also be a place deprived of magnetism. There may be a tension in the latter (or there may not); there will not be in the former. Both are analogous to the state of the inside of a metal vessel charged with static electricity.

6 _Diary_ 316, entry for September 11, 1854. (Figure 18)

13395. The Ring magnet is a beautiful case of a magnet needing no surrounding medium. The reason why? The lines of magnetic force being closed curves are all complete within it.

13396. Yet they have some external force or some kind of external force; for when a double helix is round it, a current sent through one helix induces a current in the other, which is greatly increased by the soft iron acting as core.

13397. We live and experiment within a magnetic flood of force and subject to a mixed magnetic medium. We ought to live and experiment in a hard steel or an iron house. A good soft iron chamber will give a magnetic vacuum when it is wanted.

13400. Initial polarity. Perhaps accept that as polarity which belongs to an independent permanently excited body, as a steel magnet, a loadstone, a helix with its electric current. How is the polarity of the soft iron ring magnet related, and how are all these polarities related, to the ring of polarity round an electric current?

13401. Conduction polarity is variable for the same body because it depends, not on the body itself only, but upon the surrounding media. The initial polarity does not depend on the medium in the same manner, though it does in most cases, for its existence.

6 _Diary_ 323, entries for September 13, 1854.

13430. So the term polarity may apply for the time to both, but I think it must be ever dependent upon the direction of the lines of force in those bodies. It should not merely imply a concentration of the lines of force, as in a magnet or a conducting body, but also their direction. Else polarity might change whilst direction of the lines of force would remain the same, as weak sol. Sul. iron in stronger solution or in water.

6 _Diary_ 328, entry for September 15, 1854.

On or around December 14, 1854, Faraday began to construct an apparatus of four bar magnets whose north poles were joined to form a box constituting a converging field.

13555. I have four very hard bar magnets; each 6 inches long, 1 inch broad and nearly 0.4 of an inch thick. With these it was easy to build up chambers having the properties of those just described. They are arranged thus on a horizontal plane, having a piece of cardboard placed in the middle square space midway in the thickness of the magnets. Iron filings were then placed carefully on the cardboard or else put on it first, and then the magnets regularly approached. As they came up, the filings formed radii from the center of the cardboard to the edges against the magnets, and by careful tapping they ultimately arranged themselves as in the figure. The four S poles produced the same effect. (Figure 19)

13556. Here it is easy to see that the lines of force proceed from all sides inwards in this central plane, to turn up and then over and outwards above the plane, and in the reverse direction below it. The lines of force are stronger and more direct from the middle of the sides than at the angles—the cause of which is again easy to see, for at the angles there is distributing space back in the same plan[e] as well as above to a far larger extent than at the middles, and part of the northness gets disposed of there, through the corners of the magnets as it were. (Figure 20)

13557. When a little needle (13550) was applied to magnet chamber made up in the air and with the cardboard removed, it shewed beautifully the lines of force as radii to the very center in the medium plane; then there was a double axis, i.e. northness proceeded from a upwards and downwards, rapidly decreasing in force. But when the needle was raised above the medium plane, it was seen that the lines of force according to their places soon took a direction the reverse of the former proceeding back to the S poles—and all the lines of force from the outside angles c, c, c, c, were also in that direction, i.e. north outwards and toward the souths. When the axis of exit x x shall be stopped by two more poles, as in the case of the six magnets, making [ ], then these lines will disappear as nearly so from the cubical chamber formed. (Figure 21)

13558. I placed the poles together edgeways so as to make a narrower and deeper chamber, and then introduced the needle. The disposition of the power near and about the upper and lower aperture of the chambers was as before, but in the middle of the chamber there was scarcely a trace of power, though the needle was very sensitive. It is easy to see how this coincides on the one hand with the cavity in a pole ( ) and on the other with the chamber of six poles ( ). (Figure 22)

6 _Diary_ 350, entries for December 14, 1854.

He again took up the experiment on December 19.

13583. Have formed a magnetic chamber with Six like poles, thus. Six cores of soft iron, 3 inches long by 1 inch square, with rounded edges—each has had 128 inches in length of covered copper wire 0.05 of inch in diameter wound round it in 32 spirals or coils. These are fixed on a wooden frame so as to be held pretty firmly in their places, and then the wires soldered together in one continuous series, so that when the electric current of 10 pr. of Grove's battery was sent through them, all the inner poles were S poles, or else N poles. (Figure 23)

13584. By separating the poles a little, access could be had to the interior, and so the effects on this or that test observed; but the effect of such openings was always evident.

13585. A little magnet supported by a single cocoon thread was weighted by a little copper wire, without which it could hardly be kept from the iron at the edges of the entrance when the iron was in its unmagnetized state. The frame and magnets were tilted, so that it might hang in the middle of the chamber. When there, it was not affected when the magnets were excited; but if nearer to the apertures, then it shewed a little pointing action. But it was as nothing to the amount of force on the outside of the chamber, even when the needle was several inches away from the nearest part of the system.

13586. When the currents were taken from the electro magnets, they sank exceedingly well.

13587. A crystal of bismuth was suspended in the chamber; it gave no magnetic indication of any kind—neither old nor new.

13588. A little piece of iron hung at the end of a jointed piece of copper wire shewed no sensible traces of attraction within the chamber, except near the edge openings. At the inside it was powerfully held.

13589. Filings on a card were introduced, then the magnets made and unmade and the filings examd. Those in the middle part of the chamber were undisturbed though the card has been tapped—those near the edge apertures and also middle of the side were a little arranged.

13590. A small helix ring of several convolutions of wire was revolved in the chamber—and with it were connected at different times two commutators, changing at different periods. My Rhumkorf and my thick wire Galvanometer were both used (the latter is the best), but by no arrangement could any but very feeble results be obtained, due to the disturbance of power at the opening of introduction. When these helices were brought near one of the Six outside poles and revolved, than abundant currents of electricity were obtained.

13591. Bismuth and like magnet poles—a cube of bismuth suspended by a fine wire 13 feet long—N the cylinder electro-magnet; when excited it drove the bismuth 0 away; then another electro magnetic N brought up at the side caused the bismuth to approach again, but the suspension is not long enough and the effects are small—the torsion balance suspension is better. (Figure. 24)

6 _Diary_ 356-357, entries for December 19, 1854.

Having obtained a negative result, Faraday did not pursue the matter further. My research has not revealed any subsequent investigator who has reconsidered the experiments nor the theory upon which they were built. Recognizably, the first significant difference between Faraday's experiment and Model 1 is that Model 1 sustains the force of the field with permanent horseshoe magnets rather than with bar magnets and that the focal point continuously turns back upon itself as the N-N and S-S poles repeatedly face each other.3 Secondly, the introduction of frequency replicates the actual nature of radiation to generate a dynamic vortex that compacts the mass into a sphere whereas Faraday's modal is static. The condition that he considered to be a "vacuum" was in fact the essence of the force of the field itself. The other differences in structure are obvious. In any event, he was thinking rightly about all of the right things within the limits of his model.

NOTES

1 Model 1 is protected by U.S Patent 7,479,959 B2. See appendix below.

2 In the _Diary_ figures are not so designated or numbered consecutively but are variously placed in the margins directly adjacent to the entry or the text is otherwise marked and the figure is placed at the foot with the associated entry number, e.g., *[13555]. For simplicity of reproduction, all figures herein are aggregated at the end of the respective sections.

3 In addition to Faraday's use of his "great" horseshoe electromagnet, most notably in which he advanced the angle of polarization of light, he was also aware of the use of permanent horseshoe magnets in Ampere's 1820-1821 experiments to detect molecular currents and to which he referred in his own experiments using permanent horseshoe magnets described in his _Experimental Researches in Electricity_ , "On Some New Electromechanical Motions, and on the Theory of Magnetism," 2:127-147. See also below, Maxwell, "Molecular Vortices."

Figure 9 Original drawing of omnidirectional waveforms converging at a point locus to generate a singularity.(Say circa late 1987?)

Figure 10 Sketch of Model 1 as originally envisioned. (January 28, 1988)

Figure 11 Model 1 (March 31, 1989).

Figure 12 Close-up of Model 1 showing compaction and levitation of mass by magnetic field in opolarity converging at a point locus (omnidirectional equipotential field of electromagnetic radiation pressure).

Figure 13 Lines of force projected from the magnet on the crank handle toward magnets in opolarity on opposite sides of a mass containment vessel into which has been placed some steel ball bearings.

Figure 14 Lines of force focused to a locus of convergence by the magnet on the crank handle and magnets held in opolarity on a rotating axle thereby generating an essentially spherical shell-like space into which the ball bearings have been levitated by the equipotential omnidirectional field in opolarity (the æther field).

Figure 15 Generation of a stellar precursor (proto-singularity). Jagjit Singh, _Great Ideas and Theories of Modern Cosmology_ at 31.

Figure 16 Illustration associated with entry 13242.

Figure 17 Illustration associated with entry 13245.

Figure 18 Illustration associated with entry 13358.

Figure 19 Illustration associated with entry 13555.

Figure 20 Illustration associated with entry 13556.

Figure 21 Illustration associated with entry 13556.

Figure 22 Illustration associated with entry 13558.

Figure 23 Illustration associated with entry 13583.

Figure 24 Illustration associated with entry 13591.

**Chapter** **2.2 MODEL 2**

Model 1 demonstrates the primary principle of the unified field theory as the operating mechanism for generating a singularity, the cornerstone of pure field theory. The mechanism by which cosmic and microcosmic entities are allocated to specific orbits around a central body is demonstrated by Model 2, an issue, at least to my knowledge, that has never even been broached. The impetus for Model 2 lies in the proposition that if a horseshoe magnet were placed on a vertical axis and spun around, the lines of force projected from the respective polarized faces would generate a series of concentric lines of force separated from each other by interlineating lines of opolarity and that this could be demonstrated by iron filings just as the principle of Model 1 was demonstrated by ball bearings.

Accordingly, I constructed a small plywood platform through which I drilled a hole into which I inserted a short wooden dowel through which I drilled a hole along the lengthwise axis. I then cut the top from an clear plastic soft drink bottle and drilled a hole through the center of the base that aligns with the hole in the wooden dowel. The bottom of the bottle was set on the wooden dowel and by lightly tapping the dowel up or down in the platform the base of the bottle was positioned to clear the surface of the platform upon which iron filings were sprinkled to demonstrate the concentric orbits. I constructed an axle with a handle that went through the holes in the magnets to align with that in the bottom of the bottle and that in the dowel that then put the bottle and magnet in a vertical position perpendicular to the platform. A second dowel was fabricated to suspend the magnet above the convolutions of the bottle and brackets were made to hold the magnet to the axle as it rotated. The model was assembled and a piece of plain white paper was placed on the platform around the wooden dowel and filings were evenly sprinkled onto the surface with a small kitchen strainer. (Figure 25) The magnet, handle, and bottle were then aligned with the hole in the dowel and lowered to the platform at which time the iron filings instantly responded to the intervention of the magnetic without any rotation or movement. (Figure 26) The surface of the platform was then lightly tapped several times and the filings further aligned themselves to accentuate the lines of force. (Figure 27) The handle was then gently and slowly rotated clockwise (the direction is irrelevant) at which time the filings aggregated themselves into discrete entitles in concentric circles around the vertical axis, projected themselves vertically from the surface, and "pirouetted" around the surface like little spinning tops. (Figure 28) When the magnet was raised from the surface, the lines of force dissipated and the filings fell back to the paper. When the magnet was brought too close to the platform the filings "jumped" onto the bottle itself, which was why the bottle was used as an intermediary barrier since I learned early on in these experiments that getting filings from the face of a magnet is not only a tedious, frustrating experience but often painful when a filing got stuck in my finger. The plastic bottle makes it convenient to just push the filings down from the surface of the bottle, remove the magnet through the top to weaken the field, and the filings drop from the bottle of their own accord. Accordingly, Model 2A demonstrates the mechanism by which concentric orbits are generated.

Model 2B is a somewhat more elaborate version in which a second magnet is added and held in opolarity with the first. The bottom magnet was inverted to face upwards into the downward facing second magnet. The two magnets were held in opolarity by a piece of ⅛-inch thick clear plastic sheet that is held to the sides of the magnets by clear cellophane tape. Fresh filings were sprinkled onto the platform and the assembly was again lowered into the bottle and onto the dowel and the filings instantly responded to the field, the platform was again lightly tapped, and the filings aligned into their respective lines of force.

The handle was rotated slowly and the filings aggregated themselves and pirouetted around the axis in concentric orbits. Some of the filings, however, jumped to the bottle and migrated up the side to become spires that projected out into space perpendicular to the vertical surface of the bottle exactly as Maxwell described the lines of force projecting into space by opposing fields. When the magnet was moved within the bottle relative to the bottle itself, the spires turned over and over on themselves as the lines of force generated vortices of current around the outside of the bottle. (Figure 29) One may see here the probable mechanism for the position and rotation of the "rings" of Saturn, a problem to which Maxwell had also addressed his attention. See below.

In Model 2C, two horseshoe magnets are "compressed" by interposing themselves into the spaces between the two respective "prongs" of the horseshoe. Iron filings were freshly sprinkled onto the paper, the magnets were placed into the bottle and lowered onto the dowel and the magnets were then turned. (Figure 30) In this case, instead of the iron filings pirouetting around in orbits they "tumble" end over end in their respective concentric orbits and somewhat aggregate into larger clusters at various nodal points. (Figure 31)

I submit that Models 2A, 2B, and 2C demonstrate the mechanism by which planets and electrons become aligned in their respective orbits. As to the latter, the filings form aggregates of essentially the same size at approximately equal distances apart from each other in their respective orbits and the respective orbits are approximately equidistant from each other thereby making the number of "electrons" in the orbit essentially proportional to the circumference (radius) of the orbit itself. Unquestionably the respective lines of force have a rotatory quality that spins the "entities." If we extend these models to the Bohr model and Milliken's discovery of the uniformity of the mass of the electron and transform our magnet to a positively charged nucleus revolving in three dimensions, the concentric orbits become spherical shells of spinning electrons separated by fields in opolarity directly analogous to the layers of the common onion. Given the uniformity of the electron, its own inertial velocity, and therefore the propagation of its own field of opolarity, the number of electrons that can occupy a given spherical shell is directly proportional to the surface area of the shell that is directly related to the shell's distance from the nucleus, i.e., a gradation of r. Additionally, since the electrostatic forces that hold the electron to the nucleus are directly proportional to the distance of the orbit to the nucleus, Model 2C directly demonstrates the relationship between the "strong" and "weak" forces of quantum electrodynamics. Since juxtaposed electrons rotate unidirectionally to generate their own opolarity, Models 2A, 2B, and 2C demonstrate the mechanism underlying "spin" and the fine line structure of spectral lines designated by the spin indices of "+½" and "-½," and the mechanism underlying "strangeness" in small particle physics.

Thus if Model 1 is the _experimenta crucis_ for unified and pure field theory and the generation of the singularity then Model 2 is the companion _experimenta crucis_ that demonstrates the mechanism by which singularities move in space and come into relative position with each other.

**Chapter** **2.2.1 QUANTUM MECHANICS**

The principles set out above equally demonstrate quantum mechanics and the photoelectric effect. "Quantum mechanics" derives its name from Max Planck's discovery that radiation is emitted in pairs of "quanta" whose energy is a multiple of a baseline amount, designated Planck's constant "h." His experiments in "black body" radiation revealed that the intensity of radiation is always some multiple of the constant. When the radiation is directed to a plate an electric current is produced in the plate in increasing amounts that gave rise to the "photoelectric effect." The precise relationship between the amount of radiation and the amount of electric current, however, was not known. Einstein explained that the amount of energy produced is directly proportional to the intensity of the radiation times Planck's constant, E = hλ, where the Greek letter lambda λ is generally Anglicized to frequency f. In the primary principle, all mass-energy conversion processes are nominalized, that for our purposes here can be h, as a quantifier, and therefore Einstein's equation reduces simply to f, the intensity of the light striking a metal plate that converts the light to an electric current. Figure 32 illustrates the relationship between the frequency of waveforms and "quanta" (ball bearings). Going from top to bottom, the top is a single waveform that begins at the right. The next are increasingly larger ball bearings (quanta). The next are waveforms that "screw" into additional waveforms of greater frequency (density) as it approaches the diameter and density of the larger ball bearing (quanta). The last two are waveforms with essentially the same amplitudes but different frequencies. In quantum mechanical terms, the greater the intensity/frequency (density) of the waveform the greater the quanta and therefore the greater the current.

**Chapter** **2.2.2 WAVE MECHANICS**

Just as the early history of light had its proponents who advocated that light was corpuscular, so it had proponents who advanced that it was a wave, and so likewise just as quantum mechanics had proponents who advanced that radiation was a quantum phenomena, so there were those who advanced that radiation was a wave, hence wave mechanics. Wave mechanics is essentially the work of Louis deBroglie and Erwin Shrödinger. The phenomena is illustrated in Figure 33, in which the center is the nucleus surrounded by an aggregate of concentric waves generated by orbiting electrons again separated by interposed fields of opolarity. Because of the differences in the circumferences of the respective orbits that are directly related to their respective distances from the nucleus, the angular velocity of the electrons in their respective orbits is a direct measure of their energy that can be detected spectroscopically. Simply put, quantum mechanics and wave mechanics are merely different manifestations of a concurrent duality.

Additionally, taking the above discussion and Figures 28, 29, 30, 31, and 33 into conjunctive consideration, one may readily advance that Einstein's "gravitational waves" are none other than the continuous "undulation" of the magnetic lines of force that emanate from a mass undergoing the mass-energy conversion process under the imperative of "unidirectional time" (E = mc2) attendant on the compression of the æther field that continuously reduces the size of the mass itself. The outward manifestation of that process is readily made observable by the continuous volcanic eruptions and other like phenomena and the overwhelming geological record that the current size of the Earth is substantially smaller than when originally formed.

The present theory also rejects Einstein's concept of "the curvature of space" that is predicated on a wholly gravitational model as the present theory reconstructs the entire theoretical premises upon which Einstein based his model of the Universe. However, if "push came to shove" to somehow require that "curvature of space" must survive for reasons other than those advanced here, "curvature" simply reduces to a series of concentric "spherical orbits" (see for example Figures 10, 31, and 33) of alternating fields in opolarity analogous to the "interference patterns" in phenomena such as "Newton's rings" or one- or two-slit like-kind apparatuses with the dissipation of the energy in the "orbits" by the law of inverse squares. The energy of the orbits continues to lessen as the spherical geometry of the orbits approach a straight line as a limit to dissipate into the uniformity of the omnidirectional equipotential radiation pressure of the surrounding æther such that "curvature" no longer exits as a geometrical construct.

F   
igure 25 Iron filings sprinkled on platform around wooden dowel.

Figure 26 Model 2A—magnetic lowered onto dowel showing initial disturbance of iron filings.

Figure 27 Iron filings realigned after lightly tapping surface.

Figure 28 Iron filings "pirouetting" in concentric orbital shells.

Figure 29 Model 2B―magnets in opolarity with iron filings "pirouetting" in concentric orbits on the platform and filings extended into space in Maxwellian spires on the surface of the plastic bottle.

Figure 30 Model 2C―magnets in compressed configuration with freshly sprinkled iron filings on platform.

Figure 31 Model 2C―magnets in compressed interlineate configuration and iron filings in concentric orbits on platform.

Figure 32 Quantum mechanical model of photoelectric effect.

Figure 33 Model of wave mechanics.

**Chapter** **2.3 PLATO**

To advance the primary principle from the unified field theory to the pure field theory requires the consideration of subtle and profound philosophical issues that will ultimately affect our investigation of the empirical evidence and our conclusions about the nature of the Universe, and therefore the nature of existence itself. Operationally, the concept of a unified field theory begins with Faraday's conceptualization of "the field" itself and the exhaustive empirical study of its characteristics. To Einstein, however, belongs the honor of taking the first step toward its actual unification by equating mass with energy and the explicit pursuit of a unified and pure field theory. The concept of a unified Universe in which there is an underlying primary principle, however, begins in classical antiquity.

The Greek effort to unify the Universe in one grand theory supported by empirical evidence—notwithstanding that the view of the evidence may have been experimentally or empirically suspect, incorrect, or incomplete in many particulars—was not wholly theophilosophical or supernatural even though it may have included incorporeal elements that were purely the product of hypothecation. Even at that, it was a structured hypothecation that looked to empirical evidence to explain empirical events and it attempted to disinterestedly describe the external world as a physical entity. To the extent that human perception was involved, it attempted to analyze that perception as if it were external in much the same way that psychoanalysis attempts to examine internal psychological processes by articulating them externally and thereby making them available for further analysis. Finally, the investigation called itself science rather than mythology or theology and did so with a great deal of credibility.

The study begins with Plato as the first investigator who sought to integrate all of the phenomena of existence into one unified theory. Accordingly, to be able to articulate philosophical issues in our inquiry becomes as important as matters of technical physics, perhaps even more so, for the latter can be found in any textbook, whereas the former can only be found in the quiet amber lit recesses of the mind. As previously noted, the philosophical preconceptions that are made about the evidence inevitably become the prejudices of what becomes evidential. Thus, the capacity to contemplate and conceptualize the magnetic field as a real entity having form, substance, force, and corporeality is a philosophical imperative that requires one to be intellectually amenable to such arguments, open to evidence that supports those arguments, and courageous enough to commit one's intellectual and emotional resources to consider existence as structured on those terms. When we get done with Plato, hopefully you will appreciate how close Aristotle got by pure contemplation alone to the resolution of a pure field theory, and how far Plato took it away from that goal. What is most important to realize is that I am not the first person to consider the fundamental nature of existence as a physical entity or the subtle philosophical issues that occur along the way. The little, sometimes seemingly insignificant, individual differences that distinguish the present theory from those that have gone before, however, become in the aggregate substantively significant. For example, the use of horseshoe magnets fitted with a handle focused to an open space rather than rigid bar magnets focused essentially to the same space makes all the difference "in the world." The cumulative effect of those differences and the inferences to which they lead results in a restructuring and reconsideration of the principle arguments historically advanced. With all that said, however, I think that one is still forced to begin with Plato's discussion of time and space and the Universe as he presents it in the _Timaeus_ , and at the same time I wish that I did not have to begin there, for to me, Plato uses all of the right words and addresses all of the right issues, all wrongly. But I must also add, would that what I do here would equally be read three thousand years hence!

As much as I want to give Plato credit for broaching the first view of a unified and pure field theory, I cannot, for Plato is not an empiricist—although he _almost_ is, he is a mythotheologist who found the Universe and existence a place in which he could embed the phlogiston theory and a creationist mythology. Perhaps he came too early in history, too close to the Pythagoreans, the classical geometers, who, having discovered the golden proportion and the rules of triangles, converted everything to triangles. But what is more astounding is that Plato built a theory on a spherical Universe and "then dropped the ball." Having divined the harmony of the spheres, the elegance and simplicity of the circle, the repetitiveness without end of the circumference, he opted for the jagged cube and triangle as the more perfect forms. Having described that matter rolls off each other, perceived the cyclicity of the diurnal and yearly cycles, looked at the Moon and Earth, the concentric pheres and circles of the planets—of course his cosmology was wrong—but his geometry was absolutely right—he became captive to the institutionalized knowledge of his time. He recognized the issue of probabilities as an essential element of physics, looked it straight in the eye, understood it, said it, and misunderstood it at the same time. He was like a gambler at a convention of statisticians; they are all using the same words but they are not talking the same language.

If then, Socrates, amidst the many opinions about the gods and generation of the universe, we are not able to give notions which are altogether and in every respect exact and consistent with one another, do not be surprised. Enough if we adduce probabilities as likely as any others, for we must remember that I who am the speaker and you who are the judges are only mortal men, and we ought to accept the tale which is probable and inquire no further.

_Collected Dialogues_ at 1162.

Plato's concept of probabilities is the hypothecation "more likely than not" rather than the statistical probability of an event occurring. But even putting that aside, he "inquired no further" that separates him from the scientific tradition in which there is a search for underlying unrevealed processes. Thus what distinguishes Plato from Aristotle is Aristotle's search for objective truth by the process of an ordered system of logical reasoning. Although Newton also declined to pursue first causes that were not mechanical, he did pursue first causes that were mechanical, and therefore discoverable, or at least open to objective investigation.

Notwithstanding Plato's creationist view, he advances a spherical Universe predicated on circular movement that was derived from his concept of the ideal being.

Now to the animal which was to comprehend all animals, that figure would be suitable which comprehends within itself all other figures. Wherefore he made the world in the form of a globe, round as from a lathe, having its extremes in every direction equidistant from the center, the most perfect and most like itself of all figures, for he considered that the like is infinitely fairer than the unlike. * * * But the movement suited to his spherical form was assigned to him, being of all the seven that which is most appropriate to mind and intelligence, and he was made to move in the same manner and on the same spot, within his limits revolving in a circle. All the other six motions were taken away from him, and he was made not to partake of their deviations. And as this circular movement required no feet, the universe was created without legs and without feet.

Such was the whole plan of the eternal God about the god that was to be; he made it smooth and even, having a surface in every direction equidistant from the center, a body entire and perfect, and formed out of perfect bodies. And in the center he put the soul, which he diffused throughout the body, making it also to be the exterior environment of it, and he made the universe a circle moving in a circle, one and solitary, itself, and needing no other friendship or acquaintance.

_Collected Dialogues_ at 1164-1165.

Clearly, the Earth and the Universe are anthropomorphic analogies.

Plato's concept of "time" derives from "number" rather than periodicity. Time is derivative of eternity embodied in a "unity" that I take to mean an integrated whole rather than the number "1" or perhaps it is just the repetition of 1 upon itself. In either event, the sense of original periodicity does not suggest itself from the context. However, time does have a moving quality to it, and time is associated with tense.

Now the nature of the ideal being was everlasting, but to bestow this attribute in its fullness upon a creature was impossible. Wherefore he resolved to have a moving image of eternity, and when he set in order the heaven, he made this image eternal but moving according to number, while eternity itself rests in unity, and this image we call time. For there were no days and nights and months and years before the heaven was created, but when he constructed the heaven he created them also. They are all parts of time, and the past and future are created species of time, which we unconsciously but wrongly transfer to eternal being. For we say that it "was," or "is," or "will be," but the truth is that "is" alone is properly attributed to it, and that "was" and "will be' are only to be spoken of becoming in time, for they are motions, but that which is immoveable the same forever cannot become older or younger by time, nor can it be said that it came into being in the past, or has come into being now, or will come into being in the future, nor is it subject at all to any of those states which affect moving and sensible things and of which generation is the cause. These are the forms of time which imitates eternity and revolves according to the law of number. Moreover, when we say that what has become is become and what becomes is becoming, and that what will become is about to become and that the nonexistent is nonexistent—all these are inaccurate modes of expression. But perhaps this whole subject will be suitably discussed on some other occasion.

Time, then, and the heaven came into being at the same instant in order that, having been created together. If ever there was to be dissolution of them, they might be dissolved together. It was framed after the pattern of the eternal nature—that it might resemble this as far as possible, for the pattern exists from eternity, and the created heaven has been and is and will be in all time. The sun and moon and five other stars, which are called the planets, were created by him in order to distinguish and preserve the numbers of time, and when he made their several bodies, he placed them in the orbits in which the circle of the other was revolving—in seven orbits seven stars.

_Collected Dialogues_ at 1167.

Having now heavenly bodies, man can observe their orbits that embody numbers, and therefore,

But now the sight of day and night, and the months and the revolutions of the years having created number and have given us a conception of time, and the power of inquiring about the nature of the universe.

_Collected Dialogues_ at 1174.

As to space:

And there is a third nature, which is space and is eternal, and admits not of destruction and provides a home for all created things, and is apprehended, when all sense is absent, by the kind of spurious reason, and is hardly real—which we, beholding as in a dream, say of all existence that it must of necessity be in some place and occupy a space, but that what is neither in heaven nor in earth has to existence. Of these and other things of the same kind, relating to the true and waking reality of nature, we have only this dreamlike sense, and we are unable to cast off sleep and determine the truth about them. For an image, since the reality after which it is modeled does not belong to it, and it exists ever as the fleeting shadow of some other, must be inferred to be in another [that is, in space], grasping existence in some way or other, or it could not be at all. But true and exact reason, vindicating the nature of true being, maintains that while two things [that is, the image and space] are different they cannot exist one of them in the other and so one and also two at the same time.

_Collected Dialogues_ at 1178-1179.

Plato now enters a short discussion of volume;

And every sort of body possesses volume, and every volume must necessarily be bounded by surfaces, and every rectilinear surface is composed of triangles, all triangles are originally of two kinds,

_Collected Dialogues_ at 1180.

Having opted for a triangular model of existence we never hear anything more substantively about the spherical Universe, the circle of the orbits, and certainly no association between the endlessness inherent in circular geometry. Of the finite and the infinite, it is cryptic and uninformative.

Now he who, duly reflecting on all this, inquires whether the worlds are to be regarded as indefinite or definite in number will be of opinion that the notion of their indefiniteness is characteristic of a sadly indefinite and ignorant mind. He, however, who raises the question whether they are to be truly regarded as one or five, takes up a more reasonable position. Arguing from probabilities, I am of opinion that they are one; another, regarding the question from another point of view, will be of another mind. But leaving this inquiry, let us proceed to distribute the elementary forms, which have now been created in idea, among the four elements.

_Collected Dialogues_ at 1181.

At this point, Plato expounds on the phlogiston theory of fire, air, earth, and water and then as the elements of nature associated with geometric form. i.e., the earth is a cube, fire a triangle, and so forth. That every celestial body is spherical, that his own Universe was spherical, that his planets went in concentric circles, that

For as the universe is in the form of a sphere, all the extremities, being equidistance from the center, are equally extremities, and the center, which is equidistant from them. is equally to be regarded as the opposite of them all. Such being the nature of the world, when a person says that any of these points is above or below, may he not be justly charged with using an improper expression. For the center of the world cannot be rightly called either above or below, but is the center and nothing else, and the circumference is not the center, and has in no one part of itself a different relation to the center from what it has in any of the opposite parts. Indeed, when it is in every direction similar, how can one rightly give to it names which imply opposition. For if there were any solid body in equipoise at the center of the universe, there would be nothing to draw it to this extreme rather than to that, for they are all perfectly similar, and if a person were to go round the world in a circle, he would often, when standing at the antipodes of his former position, speak of the same point as above and below. For, as I was saying just now, to speak of the whole which is in the form of a globe as having one part above and another below is not like a sensible man.

_Collected Dialogues_ at 1187.

All of this is of no empirical value to Plato, for he is not deriving a theory of existence from the evidence, he is explaining the evidence from the perspective of his theory, which will shackle the investigation until Copernicus. We cannot say that Plato was oblivious to the obvious, he was not, he just did not give the obvious any credibility.

But he broaches the laws of inertia as well.

Unless a person comes to an understanding about the nature and conditions of rest and motion, he will meet with many difficulties in the discussion which follows. Something has been said of this matter already [discussion on time and orbits of planets JG], and something more remains to be said—which is that motion never exists in what is uniform. For to conceive that anything can be moved without a mover is hard or indeed impossible, and equally impossible to conceive that there can be a mover unless there is something which can be moved—motion cannot exist where either of these is wanting, and for these to be uniform is impossible; wherefore we must assign rest to uniformity and motion to the want of uniformity. Now inequality is the cause of the nature which is wanting in uniformity, and of this we have already described the origin.

_Collected Dialogues_ at 1183.

That, however, is all we learn about inertial systems as he goes on to a discussion of the four elements. That is the essence of Plato, and that is the subject matter with which all of physics is concerned: time, space, matter, existence, volume, energy, motion, the finite, and the infinite. He saw "bubbles" everywhere, except that they were round. He saw respiration like the rotation of the wheel of the wagon because breathing was repetitive, not because it had periodicity but "because there can be so such thing as a vacuum."

**Chapter** **2.4 ARISTOTLE**

The unified and pure field theory properly begins with Aristotle's four essays, _Physics_ , _On the Heavens_ , _On Generation and Corruption_ , and _Metaphysics_. Notwithstanding that many think that modern science has cast off the yoke of Aristotelian reasoning, Aristotle still controls modern physics to its very core. Certainly it would be a vary rare scientist who still believed in the phlogiston theory that fire, air, water, and earth are the primary elements of nature, but as we shall shortly see, Aristotle himself was not such a firm believer in that theory either. Our interest here is not so much in his substantive arguments, for a great many will not survive modern standards of relevance or of switching arguments or analogies in mid-stream from something empirical or quasi-empirical to something semantic. Rather we must keep in mind that Aristotle is reported to be the one who discovered that if A equals B, and B equals C, then A equals C. Unfortunately his own reasoning is not so clear-cut. Instead, our concern here is with those topics that are still relevant even when the arguments, authorities, and conclusions are often wrong for the wrong reasons, wrong for the right reasons, right for the wrong reasons, right for the right reasons, and sometimes simply just plain not half-bad for any number of other reasons. Above all we are dealing with a mind that is relentlessly pursuing the essence of a problem to the point where he can go no further. In fact, as it turns out, he gets so close to the solution of the unified and pure field theories and knows it so consummately that he has controlled the debate ever since.

Aristotle says a great deal about a great many things, but my concern here is rather with the core issues. Aristotle takes on the nature of existence and attempts to consolidate the core issues in each of the four essays, and in doing so, undoubtedly discovered that that could not be done without talking about what he had talked about elsewhere. Accordingly, I take as a given that you will thoroughly read the complete text and be aware that I have left out a great deal because it is anachronistic, because the reasoning will not withstand scrutiny, because it bespeaks of another age, because it is a review of what everyone else had to say about the topic, and because I have proffered a solution to the problem which cuts short a long discussion when we can get right to the chase. For example, I anticipate that no reader is still concerned about the various theories of whether the Earth is flat or round or the circumstantial evidence supporting the latter because of the variations in the constellations that can be seen either only in the respective northern or southern hemispheres or the shadow cast on the waxing or waning Moon. In plain language, we have already landed on the Moon and taken pictures of the Earth from afar; the Earth is round, we have moved on from there. On the other hand, as to many issues we have not taken even one tiny step for mankind since Aristotle first addressed the problem.

Accordingly we begin with the proposition that—

Again, how is one to know what all things are made of, and how is this to be made evident!

_Metaphysics_ at 1569.

We begin with the statement that obviously Aristotle did not solve the problem, yet by the sheer power of deductive reasoning he described the solution precisely in all of its essential particulars. In other words, he tells us exactly what the solution looks like but he cannot tell us what it is, and while on the one hand we may be prompted to say that it is because he did not have the fund of knowledge that would have filled in the gap, on the other, no one else has since gotten any closer, notwithstanding the rest of the knowledge! And this in itself speaks for the initiating proposition that the solution to the problem is not predicated on the fund of knowledge—although it certainly is important—it is not critical per se. Rather the solution does not so much depend upon what is known but rather what is known about what is known. It is a matter of perception, and it is from that perspective that I offer the following discussion. For purely mechanical reasons I have followed the order in which the essays appear in the Bollingen edition, often reserving for later a more full discussion of a particular subject, e.g., "infinity," that is so essential and esoteric that as much as possible the discussion should be done all at once in one place, and in this case because it involves the great work of Giordano Bruno _On the Infinite Universe_. From time to time, however, I have summarized a sentence or string of subjects that are irrelevant, superfluous, obviated, and meaningless within the context and scope of our discussion, for example, the "purpose of the Universe." Anyone who believes that the Universe and existence needs to justify itself should leave now and go do something else. This is not for you.

PHYSICS

That nature exists, it would be absurd to try to prove; for it is obvious that there are many things of this kind, and to prove what is obvious by what is not is the mark of a man who is unable to distinguish what is self-evident from what is not.

_Physics_ at 329.

The core issue of the _Physics_ is to determine the primary principle underlying the nature of existence. As advanced here, it is but one principle—primary—so that Aristotle's long discussion about the consensus of opinion and how many others there could be is meaningless, as is the semantic discussion of "one," "is," "past," "whole," and so forth. One must keep in mind that when Aristotle is unable to resolve a problem empirically he invariably tries to resolve it semantically. Therefore as he whittles down a physical problem to its essence, for the most part it becomes semantics, and there as we shall see, it will remain for several thousand years.

But it is in the _Physics_ that Aristotle controls the debate forever after, namely:

The most pertinent question with which to begin will be this: in what sense is it asserted that all things are one?

_Physics_ at 316.

As we shall see, for our purpose, the emphasis on "are" is meaningless, the hidden importance is in "all things," for we must recognize that from that moment till the present day, physics is dominated by, and only by "THINGS," i.e., the _perceptible_ Universe, **SUBSTANCE**! If it is not **SUBSTANCE** , it does not exist, and as we shall see later, therein lays the enigma to the solution. What Plato, Melissus, Parmenides, Anaxagoras, Democritus, Empedocles, Leucippus, and others said is of no concern to us anymore.

The problem deepens, however, with the proposition that the nature of existence is predicated on "contraries," rareification-condensation, hot-cold, and so forth; ultimately is there a substance that is not a substance? Of course if the Universe consists of contraries is it possible for the one to be many? We do not find that the contraries constitute the substance of anything, but as we have set forth above in the primary principle, the concept of contraries underlies the structure of existence itself notwithstanding the outward manifestation of the form.

The concept of "causes/causation," like that of purpose is not something with which the present theories are concerned for it necessarily implies the laws of probability that have no meaning in infinite unidirectional time as the laws of probability themselves stand on the primary principle. Since the primary principle is constitutional with the Universe, causation does not apply to it, nor does chance, spontaneity, accidental, ends, the good, and so forth, all of which are dialectic anthropomorphic concepts that are meaningless in the unified and pure field theories.

The concept of motion/mover/movant pervades the four essays and the best that Aristotle can do, and no one has since done better, is to resolve the problem by bifurcating the issue into the "potential" and the "actual" in which

It is the fulfillment of the potential when it is already fulfilled and operates not as itself but as the movable, that is motion.

_Physics_ at 343.

The immobility of motion is "rest." The solution of the difficulty is plain:

. . . motion is in the movable.

_Physics_ at 344.

The "infinite" we will take up later.

The concept of "time" is resolved dialectically into a continuous series of 'nows' eventually ending up as the sequence of numbers. i.e., repetitions around a circle, or as Hamilton approached it, graduating time along the algebraic line. Aristotle recognizes that time is infinite because as number it has no limit. As the measure of movement time is dialectically fused with space in which movement takes place.

What in the world, then, are we to suppose place to be? If it has the sort of nature described, it cannot be an element or composed of elements, whether these be corporeal or incorporeal; for while it has size, it has not body. But the elements of sensible bodies are bodies, while nothing that has size results from a combination of intelligible elements.

Also we may ask: of what in things is space the cause? None of the four modes of causation can be ascribed to it. It is neither cause in the sense of the matter of existents (for nothing is composed of it), nor as the form and definition of things, nor as end, nor does it move existents. Further, too, if it is itself an existent, it will be somewhere. Zeno's difficulty demands an explanation; for if everything that exists has a place, place too will have a place, and so on ad infinitum turn.

_Physics_ at 356.

In a substance based theory in which existence consists of the perceptible, no less than in present cosmology, place is everything, for it is the measure of the Universe. Notwithstanding that Aristotle and others have put great stock in the concept, in an infinite Universe as advanced here, place has no relevance whatsoever. On the other hand, place for Aristotle incorporates the "space" in which the substance is located and as a consequence requires another level of semantics to resolve the problem of the "void" and filling it up when the substance is moved; does the place move with it; what about the boundaries and surface of the substance that defines place?!

The void is thought to be a place with nothing in it.

_Physics_ at 363.

As we have demonstrated herein, the "void of space" is certainly not a "nothing," and as we shall subsequently see, it is what in fact Aristotle was "looking for," but since it is imperceptible he could not see it, and since it is not matter it does not exist—in his (or anyone else's) theory. It does in mine! And here we come down to our initial proposition that Aristotle has controlled the debate from its inception in that all of physics is a _substance/matter dominated discipline_ , so much so that even that which is not matter must now be considered dark matter that we cannot see!1 Even Einstein succumbed to that view even to the point of a confession mea culpa. That which is not a "thing,' a "body," does not exist, and we have decidedly proven otherwise herein. To no less an extent than Aristotle, modern physics attempts to solve an empirical problem by creating a semantic one. The problem of the void, since it is irrevocably intertwined with that of space and place, became irresolvable when matter/substance occupied a place—where did the void go? And how could matter move from one place to another if there were no intervening space through which matter could move? As the present theory is predicated on a continuum, all of these semantic problems are resolved empirically at both the cosmic and microcosmic levels. Additionally as "there is no ratio in which the void is exceeded by body," _Physics_ at 366, the attempt to determine the amount of "dark matter" in the Universe, as if it would somehow resolve the problem of gravitational collapse and the singularity, is in the first place meaningless since nothing finite can be known about the infinite other than the concept of the infinite, and secondly, the present theory rejects the "big bang' model and all of its theoretical progeny.

Although "force" is mentioned several times in the four essays, and continues to be a major topic to the present day, neither Aristotle nor anyone since has given it a structural basis in a constitutional, metaphysical sense. Certainly the effects of force are readily apparent to physicist and nonphysicist alike, but we are concerned with its roots as a fundamental principle of nature and that has been done in the present case with the reduction of force to the fundamental "contraries" of push-pull as the outward manifestation of unidirectional time (the right-hand rule) through polarity and opolarity. In other words, the present theory derives "force" from a constitutional element of the Universe itself. Since 'force" has now been made empirically ponderamotive in unidirectional time, the semantic amorphidity to describe time as the number of motion and motion being the actuality of the potential is cast aside in favor of something inherently and exclusively empirical. More precisely, the theory explains and demonstrates how all of these concepts can be made evident! Thus the layer upon layer of dialectics attempting to articulate "time" is replaced with something simple, physical, and so universally proved as to need no further discussion. In unidirectional time, everything is a "now." Of the "simultaneous" we will speak later.

Since time is the measure of motion it will be the

"measure of rest too."

_Physics_ at 375.

Although this statement is in part true, the concept of rest is tied up in "place" and "space," something that Aristotle appreciates in his attempt to unify time to rest to a body occupying the same place for successive "nows." He also appreciates the unification of two entities in contact with each other having a unified surface. Thus Aristotle poses the permutation of all bodies in motion, all bodies at rest, some in motion, and some at rest. However, in his continuous attempt to recognize the nonabsoluteness of any answer, and although he at times advances that a process is at work, it never seems to occur to him, or anyone else since, that the primary principle is a process rather than a sustance or substratum. As advanced above, rest is merely the limited case when one entity is unified with another in what Aristotle describes as a common shape or surface. As to everything else in the Universe, the entity is in motion. He gets it right dialectically and in part empirically but not conceptually in full measure. This I attribute to the limitations of the fund of knowledge upon which he had to draw, but the fact that he perceives something very fundamental that is tied to geometry is a testament to the power of his mind, particularly in view of the scope of the problem that he is trying to solve. On the other hand in attempting to resolve the process of change "there must be matter underlying all processes of becoming and changing." _Physics_ at 382.

The issue of bodies in motion and bodies at rest becomes fundamental to the laws of motion for Newton, but beyond that, the conceptual analysis has moved no further than that of Aristotle. The real issue is one of unification and separation that is buried in Aristotle's discussion of the continuous, contiguous, successive, part and whole, and so forth. Thus although Aristotle sees all of the elements, and sees them in a multiplicity of combinations, he does not see the process itself in its operative abstract form, which is the next higher and deeper level of generality. It is in that next higher generality that the answer to the underlying primary principle for which he searches lies.

In the primary principle we have advanced the cyclicity of time, a position advanced by Aristotle himself, although by a rather circuitous route of comparing the circle to a straight-line and then reversal to a starting point as the nature of contrary motion, whereas the circle enjoys a more respectable geometrical past. In the present theory these anomalies are resolved by recognizing that from a geometrical point of view, motion on a circle is both toward the very point from which the point in motion moves away such that motion on a circle combines both contraries in the same time, past, present, and future. The problem of tense, the "now" and so forth becomes empirical with the concept of polarity. Thus a body revolving about its own center constitutes a unified spacetime and is a body in motion as to the external context and a body at rest as to itself. It moves and yet moves not, something that is empirically true but semantically false. Something that Aristotle would not be able to resolve in a theory in which it is impossible for a thing to be and not to be at the same time! To resolve this semantic dilemma, Aristotle expands the dialectic to making rest the absence of change, "ceasing to be," and ultimately "rest is the privation of motion." As advanced here, the issue is simply one of geometry and perspective, something that in Aristotlespeak, he understood and understood not. Notwithstanding that we have solved the geometry of time, there is more to come.

The ultimate problem with motion, of course, is that

Everything that is in motion must be moved by something. For if it has not the source of its motion in itself, it is evident that it is moved by something other than itself, for there must be something else that moves it.

_Physics_ at 409.

Aristotle goes on to pulling, pushing, carrying, twisting, and locomotion. In a substance based theory, "action at a distance" has to wait until Cotes conceptualizes it in the Preface to the first edition of the _Principia_ 2 and the electricians of the late 16th Century and thereafter make much ado about it.

Now it is impossible to move anything either from oneself to something else or from something else to oneself without being in contact with it; it is evident, therefore, that in all locomotion there is nothing between moved and mover.

_Physics_ at 411.

Only matter can move matter. This of course poses problems of motion itself, as for example the arrow in the air no longer in contact with the archer. The issue, however, notwithstanding action at a distance, is that physics has not advanced any further, and even with "action at a distance," no current cosmological model suggests—much less advances—that a repulsive-propelling action at a distance is the cosmological mechanism. In fact Model 1 is the first evidence that opposing fields of the same polarity (opolarity) can do all the things that Model 1 can do. **A non-gravitational model is not only feasible but also decidedly demonstrable**.

Having gone through all of the above, notwithstanding the twists, turns, and permutations, an undaunted Aristotle whittles the problem down, at least within the limits of his time, to not the solution of the primary principle, but a description of what it is. Skipping over the reasoning that gets him there, we have;

Since there must be motion without intermission, there must necessarily be something eternal, whether one or many, that first imparts motion, and this first mover must be unmoved. Now the question whether each of the things that are unmoved but impart motion is eternal is irrelevant to our present argument: but the following considerations will make it clear that there must necessarily be some such thing, which, while it has the capacity of moving something else, is itself unmoved and exempt from all change, both unqualified and accidental.

* * * Motion, then, being eternal, the first mover, if there is but one, will be eternal also; if there are more than one, there will be a plurality of such eternal movers. We ought, however, to suppose that there is one rather than many, and a finite rather than an infinite number.

_Physics_ at 432.

He continues:

Let us proceed to maintain that it is possible that there should be an infinite motion that is single and continuous, and that this motion is rotatory motion.

_Physics_ at 437.

He then deduces that rotary circular motion can be eternal.

On the other hand in circular motion there are no such definite points; for why should any one point on the line be a limit rather than any other? Any one point as much as any other is alike beginning, middle, and end, so that they are both always and never at a beginning and at an end (so that a sphere is in a way both in motion and at rest; for it continues to occupy the same place).

_Physics_ at 443.

Since time is the enumeration of motion, and motion may be eternal on a circular route, time also may be eternal. The next point is to deduce that the primary mover must be incorporeal, i.e., without parts and magnitude, reaching the conclusion:

Now that these points are settled, it is clear that the first unmoved mover cannot have any magnitude. For if it has magnitude, this must be either a finite or an infinite magnitude. Now we have already proved in our course on Physics that there cannot be an infinite magnitude; and we have now proved that it is impossible for a finite magnitude to have an infinite force, and also that it is impossible for a thing to be moved by a finite magnitude during an infinite time. But the first mover causes a motion that is eternal and causes it during an infinite time. It is clear, therefore, that is indivisible and is without parts and without magnitude.

_Physics_ at 446.

The problem of the _Physics_ , therefore, is to find "something" that is infinite, incorporeal, unmoved, and whose force affects that which is finite, corporeal, variable, and by and through which it may be made evident. Model 1 and the other models presented herein satisfy those requirements. The only amendment necessary to bring the text into conformance with modern knowledge is to change "unmoved," "invariable,' and "continuous" to 'constant," i.e., c, and we have the substantive description—although not the solution—of the primary principle.

ON THE HEAVENS

_On the Heavens_ extends the concepts of the _Physics_ to cosmology. Again, this is a substance/matter/body/magnitude dominated theory, with the caveat that the search for the ultimate primary principle is outside these concepts. Thus, within the limits of the fund of knowledge upon which Aristotle had to draw and the vocabulary available to describe the phenomena, his reasoning and intuition pushes him elsewhere.

The science which has to do with nature clearly concerns itself for the most part with bodies and magnitudes and their properties and movements, but also with the principles of this sort of substance, as many as they may be. For of things constituted by nature some are bodies and magnitudes, some possess body and magnitude, and some are principles of things which possess these. Now a continuum is that which is divisible into parts always capable of subdivision, and a body is that which is every way divisible. A magnitude if divisible one way is a line, if two ways a surface, and if three a body.

_On the Heavens_ at 447.

He reaffirms his commitment to circular motion being the primary motion, yet advances that

On all these grounds, therefore, we may infer with confidence that there is something beyond the bodies, that are about us on this earth, different and separate from them; and that the superior glory of its nature is proportionate to its distance from this world of ours.

_On the Heavens_ at 449.

The problem is that it takes a body to move a body and that can only be done by contact between the two, and it is obvious that the Sun, Moon, Earth, and stars are in motion (the cosmological model does not change that, it only changes their respective orientations) and there is no perceptible contact between or amongst them. Accordingly, the mover must either be within the perceptible Universe or without it. Additionally, if it is imperceptible, it has no body and therefore no magnitude, and since time and space are not finite, the imperceptible body does not have the qualities or quantities of corporeality. Hence,

It is equally reasonable to assume that this body will be ungenerated and indestructible and exempt from increase and alteration, since everything that comes to be comes into being from a contrary and some substrate, and passes away likewise in a substrate by the action of a contrary into a contrary, as we explained in our opening discussions. Now the motions of contraries are contrary. If then this body can have no contrary, because there can be no contrary motion to the circular, nature seems justly to have exempted from contraries the body which was to be ungenerated and indestructible. For it is on contraries that generation and destruction depend. Again, that which is subject to increase increases upon contact with a kindred body, which is resolved into its matter. But there is nothing out of which this body can have been generated. And if it is exempt from increase and destruction the same reasoning leads us to suppose that it is also unalterable.

_On the Heavens_ at 450.

From this comes the "æther."

And so, implying that the primary body is something else beyond earth, fire, air, and water, they gave the highest place the name of æther, derived from the fact that it 'runs always' for an eternity of time.

_On the Heavens_ at 451.

Aristotle recognizes that the resolution to this problem implicates "the infinite" that we will defer to later.

That the shape of the heavens is a sphere or that all that is within the heavens is perceptible and therefore

First, however, we must explain what we mean by 'heaven' and in how many ways we use the words, in order to make clearer the object of our inquiry. In one sense, then, we call 'heaven' the substance of the extreme circumference of the whole, or that natural body whose place is at the extreme circumference. We recognize habitually a special right to the name 'heaven' in the extremity or upper region, which we take to be the seat of all that is divine. In another sense, we use this name for the body continuous with the extreme circumference, which contains the moon, the sun, and some of the stars; these we say are 'in the heaven'.

In yet another sense we give the name to all body included within the extreme circumference, since we habitually call the whole or totality 'the heaven'.

The word, then, is used in three senses. Now the whole included within the extreme circumference must be composed of all physical and sensible body, because there neither is, nor can come into being, any body outside the heaven. For if there is a natural body outside the extreme circumference it must be either a simple or a composite body, and its position must be either natural or unnatural. But it cannot be any of the simple bodies. For it has been shown that that which moves in a circle cannot change its place.

* * * For the world as a whole includes all its appropriate matter, which is, as we saw, natural perceptible body. * * * It is clear then that there is neither place, nor void, nor time, outside the heaven. Hence whatever is there, is of such a nature as not to occupy any place, nor does time age it; nor, is there any change in any of the things which lie beyond the outermost motion; they continue through their entire duration unalterable and unmodified, living the best and most self-sufficient.

_On the Heavens_ at 462-463.

The concept of a finite Universe is also of considerable importance to modern cosmology for on this point turns the problem of the singularity hypothecated on the "Hubble constant" whose interpretation leads to big bang theory and an expanding and contracting cyclic universe. Instead, Aristotle argues for a "steady state" model in which generation and destruction (the subject of _Generation and Corruption_ ) are unified in an underlying contrariety. The problem is resolved by an evolutionary continuous change in shape: a man begets a child, a child begets a man who in turn begets a child.

The solution then leads to the dialectic problem of

If there are things capable both of being and of not being, there must be some definite maximum time of their being and not being; a time, I mean, during which the thing can be and a time during which it can fail to be.

_On the Heavens_ at 466.

that then poses the incommensurability between something that has always existed and is imperishable and something that is perceptible, finite, and therefore destructible

It is therefore impossible that one and the same thing should be capable of always existing and of always not-existing. Thus it is impossible for a things always to exist and yet to be destructible.

_On the Heavens_ at 467.

Having reasoned through the labyrinth of the finite and infinite, destructible and indestructible, perishable and imperishable, Aristotle concludes

That the heaven as a whole neither came into being nor admits of destruction, as some assert, but is one and eternal, with no end or beginning of its total duration, containing and embracing in itself the infinity of time, we may convince ourselves not only by the arguments already set forth but also by a consideration of the views of those who differ from us in providing for its generation. If our view is a possible one, and the manner of generation which they assert is impossible, this fact will have great weight in convincing us of the immortality and eternity of the world. Hence it is well to persuade oneself of the truth of the ancient and truly traditional theories, that there is some immortal and divine thing which possesses movement, but movement such as has no limit and is rather itself the limit of all other movement. A limit is a thing which contains; and this motion, being perfect, contains those imperfect motions which have a limit and a cessation, having itself no beginning or end, but unceasing through the infinity of time, and of other movements, to some cause of their beginning, of other receiving the cessation.

_On the Heavens_ at 470.

Although he reasons that

The shape of the heaven is of necessity spherical; for that is the shape most appropriate to its substance and also by nature primary.

* * * * * * *

If then the complete is prior to the incomplete, it follows on this ground also that the circle is primary among figures. And the sphere holds the same position among solids. For it alone is embraced by a single surface, while rectilinear solids have several. The sphere is among solids what the circle is among plane figures.

_On the Heavens_ at 473.

all in accordance with modern observations of celestial bodies and the theories advanced here, although our theory deletes "of necessity" and our conclusion that celestial bodies are spherical is based on an entirely different evidential base. Of course Aristotle's concept of "heaven" does not apply herein.

But circular movement, having no beginning or limit or middle without qualification, has neither whence nor whither nor middle; for in time it is eternal, and in length it returns upon itself without a break.

_On the Heavens_ at 475.

With regard to the shape of each star, the most reasonable view is that they are spherical.

_On the Heavens_ at 480.

As to the Earth, its shape, location, and whether it is in motion or at rest, those issues have been fairly well resolved by now and need no further discussion. Equally, the concept of "element" has been revamped from the phlogiston 4 to over 100 in the periodic table premised on an entirely different scheme and structure.

But of the generation and destruction of the elements we are concerned for

Since they are generated, they must be generated either from something incorporeal or from a body, and if from a body, either from one or from something else. The theory which generates them from something incorporeal requires a separate void. For everything that comes to be comes to be in something, and that in which the generation takes place must either be incorporeal or possess body; and if it has body, there will be two bodies in the same place at the same time, viz. that which is coming to be and that which was previously there, while if it is incorporeal, there must be a separate void. But we have already shown that this is impossible. But, on the other hand, it is equally impossible that the elements should be generated from some kind of body. That would involve a body distinct from the elements and prior to them. But if this body possesses weight or lightness, it will be one of the elements; and if it has no tendency to movement, it will be an immovable or mathematical entity, and therefore not in a place at all. A place in which a thing is at rest is a place in which it might either by constraint, i.e., unnaturally, or in the absence of constraint, i.e., naturally. If, then, it is a place and somewhere, it will be one of the elements; and if it is not in place, nothing can come from it, since that which comes into being and that out of which it comes must needs be together. The elements therefore cannot be generated from something incorporeal nor from a body which is not an element, and the only remaining possibility is that they are generated from one another.

_On the Heavens_ at 499.

This poses the problem of the "void," that initiates the problem of the light and the heavy, the up and the down, a plenum, and ultimately a place for the void. The empirical gets tangled in the dialectic that is eventually resolved by the "force responsible for downward motion of the heavy body." The present theory reconstitutes "the void" as "the field" and demonstrates the dynamics of the field and how the imperceptible and infinite can be made empirically perceptible and finite.

ON GENERATION AND CORRUPTION

The third essay, _On Generation and Corruption_ , attempts to resolve "change," the mechanism by which substance comes-to-be (generation) and ceases-to-be (corruption). It is a search for a _single substance_ that underlies **all matter** **that is perceptible** , whereas that which is itself eternal and infinite cannot be material and finite, and therefore substance. Therefore we have the anomaly between that which is perceptibly material and finite and that which is imperceptible, incorporeal, and infinite. If all things are predicated on a theory of contraries, then that which is perceptible is that which is also imperceptible, and vice versa.

It follows, as an obvious corollary, that a single matter must always be assumed as underlying the contraries in any change—whether change of place, or growth and diminution, or alteration; further, that the being of this matter and the being of alteration must stand and fall together. For if the change is alteration, then the substratum is a single element; i.e. all things which admit of change into one another have a single matter. And, conversely, if the substratum is one, there is alteration.

_On Generation and Corruption_ at 513.

The starting point in dealing with these difficulties is this: Do things come-to-be and alter and grow, and undergo the contrary changes, because the primary things are indivisible magnitudes? Or is no magnitude indivisible?

_On Generation and Corruption_ at 515.

More simply, is existence new from old or merely change?

We must recognize that all of particle physics owes its origin to

For suppose that a body (i.e. a magnitude) is divisible through and through, and that this division is possible, involves a difficulty. What will there be in the body which escapes the division?

_On Generation and Corruption_ at 516.

But what Aristotle reasoned then did not exist, modern mathematical particle physicist reasons now does exist, namely if matter is infinitely divided down to a point

. . . it is in no way absurd that every perceptible body should be indivisible as well as divisible at any and every point. For the second predicate will attach to it potentially, but the first actually. On the other hand, it would seem to be impossible for a body to be potentially divisible at all points simultaneously. For if it were possible, then it might actually occur, with the result not that the body would simultaneously be actually both (indivisible and divided), but that it would be simultaneously divided at any and every point. Consequently, nothing will remain and the body will have passed away into what is incorporeal; and so it might come-to-be again out of points or absolutely out-of-nothing. And how is that possible?

But now it is obvious that a body is in fact divided into separable magnitudes which are smaller at each division—into magnitudes which fall apart from one another and are actually separated. Hence the process of dividing a body part by part is not a breaking up which could continue ad infinitum; nor can a body be simultaneously divided at every point (for that is not possible) but only up to a certain limit. The necessary consequence—especially if coming-to-be and passing-away are to take place by association and dissociation respectively—is that a body must contain atomic magnitudes which are invisible.

_On Generation and Corruption_ at 517.

The problem of the "singularity" is solved semantically by separating that which is 'potentially" from that which is "actually."

Our new question—to—viz. What is the cause of the unbroken continuity of coming-to-be?—is sufficiently perplexing, if in fact what passes-away vanishes into what is not and what is not is nothing (since what is not is neither a thing, nor possessed of a quality or quantity, nor in any place). If, then, some one of the things which are is constantly disappearing, why has not the universe been used up long ago and vanished away—assuming of course that the material of all the several comings-to-be was finite?

_On Generation and Corruption_ at 519.

The opinion, however, which most people are inclined to prefer, is that the distinction depends upon the difference between the perceptible and the imperceptible. Thus, when there is a change into perceptible material, people say there is coming-to-be; but when there is a change into invisible material, they call it passing-away.

_On Generation and Corruption_ at 520.

The cause of the continuous change is the "substratum."

We have explained why some things come-to-be without qualification, but not others—both in general, and also when the changing things are substances; and we have stated that the substratum is the material cause of the continuous occurrence of coming-to-be, because it is such as to change from contrary to contrary and because, in substances, the coming-to-be of one thing is always a passing-away of another, and the passing-away of one thing is always another's coming-to-be.

_On Generation and Corruption_ at 521.

Ultimately it still comes down to the perceptible and imperceptible.

Perhaps the solution is that their matter is in one sense the same, but in another sense different. For that which underlies them, whatever its nature may be is the same; but its being is not the same.

Since, then, we must distinguish the substratum, and the property whose nature it is to be predicated of the substratum; and since change of each of these occurs; there is alteration when the substratum is perceptible and persists, but changes in its properties, the properties in question being either contraries or intermediates.

_On Generation and Corruption_ at 522.

The resolution is semantic.

Our own doctrine is that although there is a matter of the perceptible bodies (a matter out of which the so-called elements come-to-be), it has no separate existence, but is always bound up with a contrarity.

_On Generation and Corruption_ at 539.

The anomaly is that although Aristotle seeks a solution that is not within the phlogiston theory, he does not abandon that theory. The problem therefore becomes entrenched in more semantics, eventually ending up in the geometry of the circle.

It is in circular movement, therefore, and in cyclical coming-to-be that the absolutely necessary is to be found. In other words, if the coming-to-be of any (sic) things is cyclical, it is necessary that each of them is coming-to-be and has come-to-be; and if it is necessary, their coming-to-be is cyclical.

_On Generation and Corruption_ at 554.

In modern lay terms, what goes around comes around.

METAPHYSICS

The _Metaphysics_ 3 is Aristotle's attempt to articulate the principles and causes of things that are, and as with the prior essays it is an exploration of substance and nonsubstance.

Evidently we have to acquire knowledge of the original causes (for we say we know each thing only when we think we recognize its first cause), and causes are spoken of in four senses. In one of these we mean the substance, i.e., the essence (for the 'why' is referred finally to the formula, and the ultimate 'why' is a cause and principle); in another the matter or substratum; in a third the source of the change, and in a fourth the cause opposed to this, that for the sake of which and the good (for this is the end of all generation and change).

_Metaphysics_ at 1555.

Underlying "things," as suggested previously is a "nothing" that

. . . is the cause of the change. And to seek this is to seek the second cause, as we should say,—that from which comes the beginning of movement.

_Metaphysics_ at 1556-1557.

The problem is how does one reason to such a cause within the limits of knowledge then available and the strictures of the classical analytical method. More simply, it is one thing to give something a name—substratum—and hypothecate its existence and another to demonstrate its existence empirically . . . to make it evident. Aristotle has already deduced that there must be an incorporeal content to existence but the theory comes to a stalemate when the substance upon which the entire structure is based is no longer perceptible and therefore ceases to exist. How does the corporeal come from the incorporeal, what are incorporeal "things," and if it is a "thing" does that imply substance? And if "substance" is that not corporeal and therefore the "thing" is disproved as being incorporeal? Substance in Aristotle is an elusive term caught somewhere between semantics and physics and this is as much a root of the problem that he is trying to solve as much as it is in the means of analysis with which he is trying to solve the problem. On the one hand, he is trying to work out the semantics of the term in the sense of a core idea, the heart of the matter, the substance of the argument, and on the other hand what do physicist/natural philosophers mean by "substance"—fire, earth, air, water. Thus in order to understand the latter he is resolute in trying to resolve the terms of the former. The result is that only when he gets away from either one of them is he able to make any progress at all.

Those, then, who say the universe is one and posit one kind of thing as matter, and as corporeal matter which has spatial magnitude, evidently go astray in many ways. For they posit the elements of bodies only, not of incorporeal things, though there are incorporeal things. And in trying to state the causes of generation and destruction, and in giving an account of the nature of all things, they do away with the cause of movement. Further, they err in not positing the substance, i.e., the essence, as the cause of anything, and besides this in lightly calling any of the simple bodies, except earth the first principle, without inquiring how they are produced out of one another,—I mean fire, water, earth, and air.

_Metaphysics_ at 1563.

Although from time to time he uses the term "entity" [and here I must accept that the translator has used an English term that is a faithful conceptual equivalent to the Greek] it does not rise to that abstract level to which I have given it where it becomes geometrically and physically evidential. In other words, it is a geometric term that has empirical significance—something whose "place," "space," and geometry can be defined, i.e., mass/matter, as well as the field itself that has now been proved to have all of the qualities of a corporeal "entity" notwithstanding its apparent "incorporeality." An entity is a noun—a person, place or "thing"—and as advanced herein, the field is certainly a thing whose existence may be physically demonstrated although it is not directly visually perceptible. It is more than just a Platonic ideal!

In general, though philosophy seeks the cause of perceptible things, we have given this up (for we say nothing of the cause from which change takes its start), but while we fancy we are stating the substance of perceptible things, we assert the existence of a second class of substance, while our account of the way in which they are substances of perceptible things is empty talk: for sharing, as we said before, means nothing.

_Metaphysics_ at 1568.

And we must inquire and discuss especially whether there is, besides the matter, any thing that is a cause in itself or not, and whether this can exist apart or not, and whether it is one or more in number. Once more, is there something apart from the concrete thing (by the concrete thing I mean the matter with something predicated of it), or is there nothing apart, or is there something in some cases though not in others, and what sort of cases are these?

_Metaphysics_ at 1573.

Further, does our investigation deal with substances alone or also with their attributes? I mean for instance, if the solid is a substance and so are lines and planes. Is it the business of the same science to know these and to know the attributes of each of these classes (the attributes which the mathematical sciences prove), or of a different science? If of the _same_ , the science of substance also must be a demonstrative science; but it is thought that there is _no_ demonstration of the essence of things. And if of _another_ , what will be the science that investigates the attributes of substance? This is a very difficult question.

_Metaphysics_ at 1575.

As with other considerations, infinity plays a part here as well and we reserve that to our separate discussion. The present work acknowledges on the one hand the difficulty of attempting to demonstrate the essence of things and on the other that the demonstration itself is quite simple. The present work advocates that there can be such a demonstrative science, i.e., a systematic method of analyzing data from which general principles and laws are derived that explain both similar and dissimilar facts within the data and by which those divergent facts and principles can be resolved and made evident.

Further, must we say that sensible substances alone exist, or that there are others besides these.

_Metaphysics_ at 1575-1576.

In reading Aristotle, one must distinguish between attempts to solve a physical problem semantically by constructing arguments that lead to what one believes the solution to be and actually solving a problem and then disclosing the reasoning by which the solution is discovered. Obviously the latter could not be achieved without a great deal of reasoning, but the former, no matter how great the reasoning, does not necessarily lead to the latter. The unified and pure field theory does not take the Aristotelian approach that the principle is separate from that which "is" but rather that the principle is incorporated in the nature of the thing per se. Thus the outstanding question in my response to my nephew—what happens to all of the radiation that is generated in the mass-energy conversion process—is the primary metaphysical question. Since the historical focus of the inquiry has always been to discover "things" and not "processes," the investigation has invariably become entangled in the dialectic and discontinuities between the finite and the infinite, being and not being, and so forth, whereas a process is oblivious to such things as it is inherently a continuum. Thus the very structure upon which the inquiry is based foreclosed from consideration other viable structures.

* * * But if there is nothing eternal, neither can there be a process of becoming to be; for that which comes to be, and that from which it comes to be, must be something, and the ultimate term in the series cannot have come to be, since the series has a limit and nothing can come to be out of that which is not.—Further, if generation and movement exist there must also be a limit; for no movement is infinite, but every movement has an end, and that which is incapable of completing its coming to be cannot be in a process of coming to be; and that which has completed its coming to be must be as soon as it has come to be.

_Metaphysics_ at 1578-1579.

The argument goes on and on to the perishable/nonperishable, being and unity, unity and substance, numbers, bodies, planes, all of which by the same reasoning reasons out "process."

For if substance, not having existed before, now exists, or having existed before, afterwards does not exist, this change is thought to be accompanied by a process of becoming or perishing; but points and lines and surfaces cannot be in a process of becoming nor of perishing, though they at one time exist and at another do not.

_Metaphysics_ at 1583.

The extent to which Aristotle and others are able to analyze a problem in all of its essential elements and to define and describe it with great precision while at the same time not perceiving the "essence" of the solution led me to coin the word "nonsight" as distinct from "insight," _Fermat's Proof_ _to His Last Theorem [A Restoration]_ , in which one may know all there is to know about a thing and yet not know its essence. At various times, Aristotle describes the primary principle and associates it with a process and then almost has the solution but for the fact of not going to the next higher level of abstraction—nonsight as distinct from insight. In the above, the problem is that the elements of geometry—points, planes—constitute forms, which in his elements of nature underlying the outward manifestation of philosophy are the substantive matter itself. The form defines the boundary of the object/entity/body. This prompts the inquiry whether forms have a separate existence apart from the body to which they are attendant. The defect in the theory lies in the proposition that the elements are also geometrical forms (triangles, squares, and so forth) and this preconception about the nature of substance irreversibly and irrevocably controls the argument thereafter and forever precludes it from an empirically based theory as advanced here. Hence one must be able to think like Aristotle but not think like Aristotle. Interestingly, the form that is of significance here, the sphere, is never perceived or understood for what it really is and the means by which it is "formed" notwithstanding that the essay _On Generation and_ _Corruption_ and all that is said about coming to be is spherically based. The fact that all celestial bodies seem to be invariably spherical [the "rings" of Saturn are planar "circles"] is a testament to the continuation of Aristotelian reasoning and that the sphere is still taught as the shape having the least surface area without one word ever having been said that it is the product of omnidirectional equipotential forces directed to a locus of convergence. Hellenic reasoning still dominates modern science! Accordingly, the power of Aristotle's reasoning often leads him to reach the right result for the right reason in a great many of the most important issues even within the limits of his physical and analytical state of knowledge as well as often to the right result for the wrong reason. The latter is often more destructive than no answer at all because of the power of the authority that goes with it. But one thing Aristotle is, he is virtually always on the right track after the right question, even if posed by himself to himself.

As with the previous essays, a great deal of the discussion is devoted to the determination of contraries into and from which unity must be derived all to lead down the same path that is constantly changing its name and ultimately ending in a blind alley. All of this leads to the conclusion that the first mover, whatever it is, is unmoved.

On the other hand, we yearn to know exactly what is substance and learn that it is what we thought it was, namely a whole bunch of semantic things that take us deeper into the dialectic and further away from the empirical. For example, the difficulty with the problem as stated:

We are seeking the principles and the causes of the things that are, and obviously of things qua being.

_Metaphysics_ at 1619.

is that a search for causes gets caught up in the semantics of "causes" that is laden with a whole range of concepts that take the search away from its objective—the primary principle. It also implies something separate from a principle that is of a higher generality than a cause.

It is obvious, therefore, from such a review of the sciences, that there is no demonstration of substance or of the essence, but some other way of revealing it.

_Metaphysics_ at 1619.

In the unified and pure field theory, matter, substance, and substratum are merely phase changes on the continuum of existence and therefore cut the semantic Gordian knot and the "'what' –knot" as well. Ultimately there must be some means by which the perceptible comes to be from the imperceptible and this is accomplished by recognizing that the imperceptible is the "potential" for that which is "actual," and thereby everything is resolved.

Clearly, then, if people proceed thus in their usual manner of definition and speech, they cannot explain and solve the difficulty. But if, as we say, one element is matter and another is form, and one is potentially and the other actually, the question will no longer be thought a difficulty.

_Metaphysics_ at 1650.

One of the many problems instigated by the dialectic dichotomy of a contradictory-based theory is the one from the many, the divisible and indivisible, finite and infinite, and whether two objects joined such that they have a common boundary are one or two entities, and if one, when they separate do they become one-half of the original or two separate entities. The unified and pure field theory makes this dialectic meaningless.

Having said all that, the search for the unified and pure field theory begins with Book XI of the _Metaphysics_. The anomaly is that Aristotle's reasoning leads to the existence of an incorporeal infinite force whereas his theory is predicated only on the substantive, material, corporeal, and perceptible. He precisely defines "the field" but his theory has no place for it. Until now no theory resolved the anomaly.

Further, must we suppose something apart from individual things, or is it these that the science we are seeking treats of? But these are infinite in number. But the things that are apart from the individuals are genera or species; and the science we now seek treats of neither of these. The reason why this is impossible has been stated. It is in general hard to say whether one must assume that there is a separable substance besides the sensible substances (i.e. the substances in this world), or that these are the real things and philosophy is concerned with them. For we seem to seek another kind of substance, and this is our problem, i.e. to see if there is something which can exist apart by itself and belongs to no sensible thing. Further, if there is another substance apart from sensible substances, which kinds of sensible substance must be supposed to have this corresponding to them? Why should one suppose men or horses to have it, and not the other animals or even all lifeless things? On the other hand to set up other and eternal substances equal in number to the sensible and perishable substances would seem to fall beyond the bounds of probability.—But if the principle we now seek is not separable from corporeal things, what has a better claim to the name than matter? This, however, does not exist in actuality, but exists in potency, and it would seem rather that the form or shape is a more important principle than this; but the form is perishable, so that there is no eternal substance at all which can exist apart and independent. But this is paradoxical; for such a principle and substance seems to exist and is sought by nearly all the best thinkers as something that exists; for how is there to be order unless there is something eternal and independent and permanent?

_Metaphysics_ at 1675.

As set out in the beginning premise, to understand the unified and pure field theory you must be able to think like Aristotle but you must not think like Aristotle. Obviously, by now you must recognize that means that you must turn a thought over and over in your mind from as many perspectives as you can possible think of while at the same time not be so structured or restricted in your thinking to commit yourself to a false premise or any other premise that precludes you from seeing the empirical truth. One need not prove the existence of the universal in order to build a theory to explain it. The theory of the Universe is already in the Universe; one needs only to accept _that_ as the primary proposition and devote the hard work to reveal it. While on the one hand no one said that it was going to be easy, on the other hand no one said that it was going to be impossible.

For example, Aristotle devotes a great deal of effort to articulating "the universal" whereas in the unified and pure field theory the universal is always incorporated in the particular and accordingly the particular always incorporates the universal. The present theory is predicated on the presumption that there is only one Universe of which everything is a part. The particular is that by which the universal is made evident!

Again, the attention to geometry, points, lines, planes, shapes, and most of all the sphere underlies all Greek philosophy, and that is fully embraced here. As it turns out, the form or shape is the solution to the problem but not for the reason advanced by Aristotle. And here we come to the unequivocal commitment to an empirical proof as against anything that even smacks of the semantic as the distinction between an approach that might lead to a solution and one that never could. One drop of semantics into the ocean of empiricism taints the problem forever. Had Aristotle fully understood how a sphere is formed and what it means to be a sphere and all of the reasonable inferences that could be drawn therefrom, the problem could have been solved 3000 years ago.

. . . but yet we say there is one and the same science of all these things—geometry.

_Metaphysics_ at 1677.

The distinction between the semantic and the empirical attack can be seen in

It is manifest, therefore, from these arguments that contradictory statements cannot be truly made about the same subject at one time, nor can contrary statements, because every contrariety depends on privation. This is evident if we reduce the formulae of contraries to their principle.

_Metaphysics_ at 1680.

that is a disputational proof. That does not mean, however, that contraries of the same or like things or kinds cannot exist simultaneously.

The origin of movement and its relationship to time we have discussed above. Change, of course, is what the primary principle is all about and is the surface effect of dynamic unidirectional time.

For everything that changes is something and is changed by something and into something. That by which it is changed is the primary mover; that which is changed, the matter; that into which it is changed, the form. The process, then, will go on to infinity.

_Metaphysics_ at 1690.

Aristotle had previously reasoned that there can be no beginning or end of time and therefore since time is the enumeration of movement there can be no beginning or end of movement. If that is the case,

But it is impossible that movement should either come into being or cease to be; fore it must always have existed. Nor can time come into being or cease to be; for there could not be a before and after if time did not exist.

Movement also is continuous, then, in the sense which time is; for time is either the same as movement or an attribute of movement. And there is no continuous movement except movement in place, and of this only that which is circular is continuous.

_Metaphysics_ at 1693.

But underlying movement must be force.

Now nothing is moved at random, but there must always be something present, e.g., as a matter of fact a thing moves in one way by nature, and in another by force or through the influence of thought or something else. Further, what sort of movement is primary? This makes a vast difference.

_Metaphysics_ at 1693.

This leads to

If, then, there is a constant cycle, something must always remain, acting in the same way. And if there is to be generation and destruction, there must be something else which is always acting in different ways.

There is, then, something which is always moved with unceasing motion, which is motion in a circle; and this is plain not in theory only but in fact. Therefore the first heavens must be eternal. There is therefore also something which moves them. And since that which is moved and moves is intermediate, there is a mover which moves without being moved, being eternal, substance, and actuality.

_Metaphysics_ at 1694.

If this is so, then it must logically follow that:

Therefore if the actuality of the heavens is primary motion, then in so far as they are in motion, in _this_ respect they are capable of being otherwise,—in place, even if not in substance. But since there is something which moves while itself unmoved, existing actually, this can in no way be otherwise than as it is. For motion in space is the first of the kinds of change, and motion in a circle the first kind of spatial motion; and this the first mover _produces_. The first mover, then, of necessity exists; and in so far as it is necessary, it is good, and in this sense a first principle.

_Metaphysics at_ 1694.

and that thus substance:

It is clear then from what has been said that there is a substance which is eternal and unmovable and separate from sensible things. It has been shown also that this substance cannot have any magnitude, but is without parts and indivisible. For it produces movement through infinite time, but nothing finite has infinite power. And, while every magnitude is either infinite or finite, it cannot, for the above reason, have finite magnitude, and it cannot have infinite magnitude because there is no infinite magnitude at all. But it is also clear that it is impassive and unalterable; for all the other changes are posterior to change of place. It is clear, then, why the first mover has these attributes.

_Metaphysics_ at 1695.

This leads to the conclusion:

The first principle or primary being is not movable either in itself or accidentally, but produces the primary eternal and single movement. And since that which is moved must be moved by something, and the first mover must be itself unmovable, and eternal movement must be produced by something eternal and a single movement by a single thing, and since we see that besides the simple spatial movement of the universe, which we say the first and unmoved substance produces, there are other spatial movements—those of the planets—which are eternal (for the body which moves in a circle is eternal and unresting; we have proved these points in the Physics), each of these movements also must be caused by a substance unmovable in itself and eternal.

_Metaphysics_ at 1696.

However, since all things are the result of contraries, the previous proposition raises fundamental questions about the primary principle as well as the mechanism that either generates or corrupts contraries.

But neither 'all things' nor 'out of contraries' is right; nor do they tell us how the things in which the contraries are present can be made out of the contraries; for contraries are not affected by one another. Now for us this difficulty is solved naturally by the fact that there is a third factor.

_Metaphysics_ at 1699.

And why some things are perishable and others imperishable, no one tells us, for they make all existing things out of the same principles. Further, why should there always be becoming, and what is the cause of becoming?—this no one tells us. . . . but what is primary has no contrary.

Again, if besides sensible things no others exist, there will be no first principle, no order, no becoming, no heavenly bodies, but each principle will have a principle before it, as in the accounts of the mythologist and all the natural philosophers.

_Metaphysics_ at 1700.

All of this leads to

Regarding this kind of substance, what we have said must be taken as sufficient. All philosophers make the first principles contrarities; as in natural things, so also in the case of unchangeable substances. But since there cannot be anything prior to the first principle of all things the principle cannot be the principle as being something else. To suggest this is like saying that the white is the first principle, not qua anything else but qua white, but yet that is a predicable of a subject, and is white as being something else; for then that subject will be prior. But all things are generated from contraries as belonging to an underlying subject; a subject, then, must be present in the case of contraries, if anywhere. All contraries, then, are always predicable of a subject, and none can exist apart. But appearances suggest that there is nothing contrary to substance, and argument confirms this. No contrary, then, is the first principle of all things in the full sense; the first principle is something different.

_Metaphysics_ at 1718.

The problem is that since the field is imperceptible and does not satisfy either the classical or modern sense of substance or matter it is categorically excluded from consideration as a candidate for the "something different" when in fact it is as different as any "thing" could possibly be. Underlying all of Aristotle and other unified and pure field theories is that the "something different" must still be within the recognized classes of "something same." Perceptible matter, if not white, must then be black. i.e., **dark matter**.

NOTES

1 The issue of **dark matter** is resolved herein by opolarity and the interstellar pressurized omnidirectional equipotential field that compacts mass at a locus.

2 Not in the Cajori translation cited here; attributed by Maxwell, see _Treatise on Electricity and Magnetism_ below.

3 Branch of philosophy that treats of first principles, including the science of being (ontology) and the origin and structure of the universe (cosmology). It is always ultimately connected with the theory of knowledge (epistemology). Philosophy, especially in its more abstruse branches.

**Chapter** **2.5 GIORDANO BRUNO: ON THE INFINITE**

Although the triumvirate of Copernicus, Kepler, and Galileo attacked the Ptolemaic system and therefore the Catholic Church's ability to maintain its stranglehold on cosmology on the local level, the theories of Giordano Bruno (1548-1600) attacked the structure, nature, and extent of existence itself and therefore inferentially posed the possibility of a cosmology that challenged in its ultimate conclusion the Aristotelian model underlying Catholicism itself even after it had adjusted to the Copernican-Keplerian model. Simply put, Bruno raised the possibility of something separate and apart from a _deified_ cosmos (Universe) that had the capacity to raise a reasonable doubt about the supremacy of a deity and therefore posed a challenge not to the _authority_ of the Church but to its efficacy. It was not a _quibble_ about "how much" it was a _postulation_ about 'whether." On the surface, a philosophical discussion about the infinite is not something that ordinary church-supporting people discuss during lunch break whereas _it is_ those very people who support institutionalized religion and therefore must be kept in check from such thoughts. Accordingly, debates about the extent of empirical existence a fortiori raises fundamental questions of exactly **where** does this deity exist if everything in the Universe has been otherwise accounted for and explained by an empirical theory. To put it bluntly, if everything in **Nature** has been physically accounted for, exactly where does the **super** natural fit in since we have now even accounted for "empty space." There is no "trap door" in the unified and pure field theories advanced here from which a _deus ex machina_ can make its appearance. Everything has been "locked up tight" with nowhere to go other than that which is, has been, and always will be here. Ultimately, the unified and pure field theory is a theory about the infinite and therefore we must address it.

There are three major approaches to infinity. The first advances a state of existence in which ends or beginnings are beyond metrification, where quantification is always _n_ \+ _p_ in which the investigator attempts to push _n_ to _p_ as the outer limit in the expectation that at _n_ \+ _p_ infinity will become finite and everything will thereby be resolved to everyone's satisfaction! This gives rise to the scientific inquiry predicated on the proposition that all may be made known by diligent inquiry, e.g., the solution lies at just one more decimal place. The second approach advances that infinity itself is beyond comprehension so that quantification is impossible. In this view, hypothecators of infinity advance that it is possible to describe and postulate the nature of the unknowable and incomprehensible were it knowable and comprehensible. These individuals seek first causes outside the empirical Universe, parallel with it, or separate and apart from it although somehow bound up in it as well. It is the basis for mythotheophilosophy. The third approach, that taken here, accepts infinity as inherent in the structure of the subject matter itself. For example, the dimensions of a circle or sphere may be fully quantified, but the beginning and end of a circle or sphere cannot be knowable so that the subject matter itself incorporates infinity constitutionally. Therefore, infinity itself is fully capable of quantitative and qualitative conceptualization and exists side by side with the finite without exacting or inducing any of the anomalies of the other two species of infinity. The search for infinity is an inquiry for structural principles that unify the apparent disparities of phenomena and that leads to a reconsideration of infinity not as a problem of knowledge but as a problem of perspective. That is, if you were to look at the sphere as the quintessence of infinity, you would discover a structure that has no beginning and no end, from which you could proceed in all directions unidirectionally both leaving and approaching the same point without end and yet with finite definition. In a theory predicated on sphericality, infinity takes on an operational aspect. When time itself is made spherical, the philosophical dimensions of an actual temporal infinity take on a physical geometrical reality. It undoes entropy as a thermodynamic imperative and contradicts the law against perpetual motion on the cosmic level.

The two works of Bruno with which we are concerned here are _Concerning the Cause, Principle, and One_ (shortened herein to _Concerning_ _the Cause_ ) and _On the Infinite Universe_ _and Worlds_ (shortened herein to _Infinite Universe_ ). As with Galileo, Bruno adopts the Socratic dialogue as a means to confront the orthodox view with those of his own, although the Catholic Church pierced the veil and applied the ultimate sanction for heresy, burning Bruno at the stake. We resurrect his views here.

_Concerning the Cause_ consists, as was often the case at the time, with a dedicatory "Introductory Epistle" in honor of the writer's patron, thereafter setting out a summary of the arguments. The first dialogue contains nothing of substantive interest here. Unlike Nicholas of Cusa's _Vision of God_ whose exploration of infinity is neither empirical nor insightful but merely an attempt to again prove the infinity and eternity of a Catholic divinity, Bruno advances a nontheocratic infinity that is cosmologically empirical—he attempts to describe the physical Universe, and therefore outside the infinity with which Cusa is concerned. Cusa's might be a theophilosophical infinity, if it exists at all, as separate and distinct, coexistent or parallel on some other level or on some other terms, but it is not in the physical world as Bruno advocates it.

Theo[philus]. I answer that when we call God first principle and first cause, we mean one and the same thing from divergent points of view; when we speak of principles and causes in nature, we speak of different things from different points of view. We call God first principle, inasmuch as all things are after him, according to a certain order of before and after, either according to their nature, or according to their duration, or according to their worthiness. We call God first cause inasmuch as all things are distinct from him as the effect from the efficient [cause], the thing produced from the producer. And these two points of view are different, because not everything which is prior and more worthy is the cause of that which is posterior and less worthy, and not everything that is cause is prior and more worthy than that which is caused, as is very clear to him who considered carefully.

_Dix[on]_. Then tell me, what difference is there between cause and principle in objects of nature?

_Theo_. Although at times one term is used in place of the other, nevertheless, properly speaking, not everything that is principle is a cause, because a point is the principle of a line, but it is not the cause of the line; the instant is the principle of activity, the "terminus a quo" is the principle of motion, the premises are the principle of the argument—but the former are not the cause of the latter. Therefore, principle is a more general term than cause.

_Dix_. Then, restricting these two terms to distinct and proper signification, in accordance with the custom of those who speak more correctly, I believe that you wish to say that the principle is that which intrinsically contributes to the constitution of things, and remains in the effect; as is said of matter and form which remain in their composite; or again, the elements of which the thing has been composed, and into which it is resolved (are principles). You call cause that which contributes to the production of things from without, and which has its being outside of the composition, as is the case with the efficient cause, and the end to which the thing produced is ordained.

_Theo._ Completely correct.

[Hereinafter the veil of the dramatis personæ is deleted. JG]

_Concerning the Cause_ at 110-111.

For Nicholas of Cusa the object was to show that the infinite and the first principles were manifestations of the Catholic god, whereas Bruno makes a distinction between the divine and the real. Accordingly, Bruno sets out to reason the characteristics of infinity from an empirical Universe not a philosophical or mythotheological one. However, one of the problems that Bruno consistently wrestles with is the distinction between a "principle" and a "cause." The difficulty in resolving the issue is that in a theory that continues to retain the existence of a mythotheological entity the argument must continue to account for that entity somehow or somewhere. Clearly Bruno neither abandons nor sets himself free from that dilemma and therefore he remains stuck in the quagmire of cause. However, if one were to accept the concept of an infinity in both space and time, having no limits and therefore no beginning nor end, "cause" removes itself from the argument. Accordingly, just as an internally consistent geometry can be built without the necessity of a theory of parallel lines, so Bruno could just as well have built a theory of principles without the necessity of causes. There is nothing inherent about a "principle" that requires a 'cause.' Consequently, he became ensnarled in a dialectic net of a "universal intellect' and 'world soul" that replicates the anthropomorphic paradigm of existence out of which he is, in essence, trying to extricate himself, all of which leads to an even more entangled bifurcation of his argument.

Accordingly, he is drawn into an analysis of the "three kinds of intelligences," implicating extrinsic and intrinsic efficient causes of all natural things, ultimately resulting in a purposeful directive that is

The aim and final cause that is pursued by the efficient cause is the perfection of the Universe that means that all the forms are actually existent in diverse parts of matter; the intellect takes such pleasure and delight in this end that it never tires of calling forth all sorts of forms from matter, as it appears that Empedocles would also wish it.

_Concerning the Cause_ at 114.

Having predicated a soul, hence an intellect embodied in form, the form becomes corporeal "in the matter of the Universe" and therefore animates all forms of natural objects. The rest of the argument is essentially phlogiston theory, the Aristotelian dialectic between matter and substance, potency and impotency. As with Aristotle, since Bruno does not know what the primary principle is [or at least can not hypothecate one] he cannot solve the problem empirically so that he attempts to solve it semantically. That, however, merely makes the problem more complex rather than more simple.

In the Fifth Dialogue, Bruno abandons the theophilosophical dialectic and engages in a didactic assertion of the characteristics of the infinite Universe and what are the logical inferences that would follow from such a condition. He sums up the case.

The Universe is, then, one, infinite, immobile. One, I say is the absolute possibility, one the act, one the form or soul, one the matter or body, one the thing, one the being, one the greatest and the best—which must not be capable of being comprehended and, therefore, is without end and without limit—and in so far infinite and indeterminate—and consequently immobile. This does not move itself locally, because it has nothing outside of itself to which to transport itself—since it is itself all. It does not generate itself because there is no other being which it might desire or expect—(it) being that which has all the being. It is incorruptible because there is no other thing into which it could change itself—(it) being that which is everything. It cannot diminish or grow—(it) being infinite, the infinite being that which has no proportional parts, being that to which nothing can be added, and being that from which nothing can be subtracted. It is not changeable into any other disposition because it has no external through which it is passive and through which it can be affected. Besides which, through comprehending in its being all contrariety in unity and fitness, and not having any inclination to other and new being, or yet to any other mode of being, it cannot be the subject of change according to some quality, nor can it have any contrary or different thing which could alter it because in it everything coincides. It is not matter because it is not configurated, nor figurable; it is not limited, nor limitable; it is not form because it does not in form or figure anything else, being that which is all, greatest, one universal. It is not measurable, nor does it measure. It does not include itself because it is not greater than itself; it is not included by itself because it is not less than itself. It is not equal to itself because it is not other and other, but one and the same. Being one and the same, it is not being and another being; and because it has not being and another being, it has not parts and again parts; and having no parts, it is not composed. It is a term in such a way that it is not a term; it is form in such a way that it is not form; it is matter in such a way that it is not matter; it is soul in such a way that it is not soul—because it is all indifferently and, in short, is one; the Universe is one.

_Concerning the Cause_ at 160.

These are the intangibles. He continues with quantification and metrification.

In it, most certainly, the height is not greater than the length and the depth; whence, through a certain similitude it is called, but is not, a sphere. In the sphere, the length, height, and depth are the same because they have the same end; but in the Universe, length, height, and depth, are the same thing because in the same manner they have no term and are infinite. If they have no halves, quadrants, and other types of measure, if there is no measure, there is no proportional part, nor is there absolutely any part that differs from the whole. Because if you wish to speak of parts of the infinite, it is necessary to call it infinite; if it is infinite, it coincides in one being with the whole; therefore, the Universe is one, infinite, and indivisible. And if the infinite does not find in itself difference, as part from whole, and other and other, the infinite certainly is one. Under the comprehension of the infinite there is no greater part and no lesser part because a greater part does not conform more to the proportion of the infinite than any other smaller parts; therefore, in its infinite duration, the hour does not differ from the day, the day from the year, the year from the century, the century from the moment, because the moment and the hours are not more than the centuries, and those have not less proportion than those to eternity. Similarly, in the immensity, the foot is not different from the furlong, the furlong from the mile, because the mile does not more conform to the proportion of immensity than does the foot, therefore, infinite hours are not more than infinite moments, or infinite feet than infinite miles. Thou canst not more nearly approach to a proportion, likeness, union, and identity with the infinite by being a man than by being an ant; not more nearly by being a star than by being a man; because you cannot more nearly approach that being by being sun, moon, than by being man, or an ant; for in the infinite these things are indifferent. And what I say of these, I mean to imply of all the other things of particular subsistence.

_Concerning the Cause_ at 160-161.

Although certainly Bruno had no knowledge of projective geometry, he certainly understands its essence and the implications it has for unified and pure field theory, i.e., a Universe that is its own entity.

Whence if all these particular things are not other and other in the infinite, are not different, are not species, they have, consequently, no number; therefore, the Universe is one immobile thing. This because it comprises all, and is not affected by one and another being, and does not bear with itself nor in itself any mutation, is, consequently, all that [it] can be; and in it, as I have said the other day, the act is not different from the potency [i.e., the potential. JG]. If the potency is not different from the act, it is necessary that in it the point, the line, the surfaces, and the body are not different; for then, the line is surface, as the line, in moving itself, can become surface; then, that surface is moved and becomes a body, since the surface can be moved, and with its movement can become a body. It is necessary, then, that in the infinite, the point does not differ from the body because the point, running away from being a point, becomes a line; running away from being a line, it becomes a surface; running away from being a surface, it becomes a body; the point then, since it is in potentiality a body, does not differ from being a body, where the potency and the act are one and the same thing.

Therefore, the indivisible is not different from the divisible, the simplest from the infinite, the center from the circumference. Because then the infinite is all that it can be; it is immobile; because in it everything is indifferent, is one; and because it has all the greatness and perfection that can be had altogether. It is the maximum and the greatest immensity. If the point does not differ from the body, the center from the circumference, the finite from the infinite, the maximum from the minimum, surely we can affirm that the Universe is all center, or that the center of the Universe is everywhere, and that the circumference is not in any part, although it is different from the center; or that the circumference is throughout all, but the center is not to be found inasmuch as it is different from that. Here, then, as it is not impossible but necessary that the best, the greatest, the incomprehensible, is all, is throughout all, is in all, because as simple and indivisible, it can be all, it can be throughout all, it can be in all. And so it has not been vainly said that Jove fills all things, inhabits all parts of the Universe, is in the center of all that has being—one in all, and through which one is all. Which, being all the things, and comprising in itself all being, brings it about that everything exists in everything.

_Concerning the Cause_ at 162-163

If the above principles apply, then metrification is meaningless because under the principle of nominalization everything is but the surface effect of everything else on the continuum of eternal transformation.

As a continuous entity consisting of all that which is within it although celestial bodies may move about in relationship to each other, the Universe itself moves not. Therefore the Universe, although its parts may be in motion, is itself immobile.

* * * Therefore, although a particular world moves itself toward and about the other, as the earth to and about the sun—in relation to the Universe—nothing is moved toward or about that, but in that.

* * * * * * *

You say that everything we see of difference in bodies. In relation to formations, complexions, figures, colors, and other properties or common qualities, is nothing else than a diversity of appearance of the same substance; a transitory, mobile, corruptible appearance of an immobile, stable and eternal thing; in which all forms, figures, and members are but indistinct and as conglomerated, . . . .

_Concerning the Cause_ at 164.

Under the circumstances, the most that Bruno can do—since there is nothing empirical about his theory—is to revert to the Aristotelian reasoning of a substance-based theory.

* * * and thus, arising from the lowest grade of nature to the highest level of that, from the physical Universe, known by philosophers, to height of the archetypal Universe, as believed by the theologicans—if you please; until you arrive at an original and universal substance of the whole, which is called being, the foundation of all diverse forms and species; . . . .

_Concerning the Cause_ at 165.

In an attempt to resolve the contrarieties of existence, Bruno resorts to the propagation of an infinitely larger circle whose curvature would approach a straight line as a limit. Unfortunately, of course, although all of this sounds very nice, Bruno has no clue or perhaps aptitude or predilection to push on to an empirical solution to the problem.

In _On the Infinite Universe and Worlds_ Bruno focuses his argument to the issue of infinity, what can be known about it and what are the reasonable inferences that can be drawn therefrom. The essay begins with:

ELP. How is it possible that the Universe can be infinite?

To which Philotheo (occasionally Theophilo) answers:

PHIL. How is it possible that the Universe can be finite?

_Infinite Universe_ at 50.

The first problem with the problem of infinity is an epistemological one, namely, how does a finite entity (you, me) perceive the infinite since all that we can perceive is the finite, and how can the infinite itself be conceived intellectually?

No corporeal sense can perceive the infinite. None of our senses could be expected to furnish this conclusion; for the infinite cannot be the object of sense-perception; therefore he who demandeth to obtain this knowledge through the senses is like unto one who would desire to see with his eyes both substance and essence. And he who would deny the existence of a thing merely because it cannot be apprehended by the senses, nor is visible, would presently be led to the denial of his own substance and being. Wherefore there must be some measure in the demand for evidence from our sense-perception, for this we can accept only in regard to sensible objects, and even there it is not above all suspicion unless it cometh before the court aided by good judgement. It is the part of the intellect to judge, yielding due weight to factors absent and separated by distance of time and by space intervals. And in this matter our sense-perception doth suffice us and doth yield us adequate testimony, since it is unable to gainsay us; moreover it advertiseth and confesseth his own feebleness and inadequacy by the impression it giveth us of a finite horizon, an impression moreover which is ever changing. Since then we have experience that sense-perception deceiveth us concerning the surface of this globe on which we live, much more should we hold suspect the impression it giveth us of a limit to the starry sphere.

_Infinite Universe_ at 251.

But an attempt to logically reason out infinity and then perhaps to push the argument on to an empirically based proof is a direct confrontation with the proponents of a dimension of existence that is neither contained nor contemplated to exist within the confines of empirical existence, namely those who have vested interests in mythotheophilosophy—institutionalized religion.

* * * it is I say impossible that I can with any true meaning assert that there existeth such a surface, boundary or limit, beyond which is neither body, nor empty space, even though God be there. For divinity hath not as aim to fill space, nor therefore doth it by any means appertain to the nature of divinity that it should be a boundary of a body. For aught which can be termed a limiting body must either be the exterior shape or else a containing body. And by no description of this quality canst thou render it compatible with the dignity of divine and universal nature.

_Infinite Universe_ at 252.

Bruno is fully aware of the internal problems in Aristotle's distinction between space and position and demonstrates the subtle analytical reasoning that could lay the foundation for the resolution of at least some of the apparent discontinuities that exist in the empirical Universe, for example, the relationship between the concave and the convex.

I would add that no mind can fail to perceive the contradiction implicit in this saying of the Paripatetic. Aristotle defined position occupied by a body not as the containing body itself, nor as a certain [part of] space, but as a surface of the containing body. Then he affirmeth that the prime, principle and greatest space is that to which such a definition least and by no means conformeth, namely, the convex surface of the first [outermost] heaven. This is the surface of a body of a particular sort, a body which containeth only, and is not contained. Now for the surface to be a position in space, it need not appertain to a contained body but it must appertain to a containing body. And if it be the surface of a containing body and yet be not joined to and continuous with the contained body, then it is a space without position, since the first [outermost] heaven cannot be a space except in virtue of the concave surface thereof, which is in contact with the convex surface of the next heaven. Thus we recognize that this definition is vain, confused and self-destructive, the confusion being caused by that incongruity which maintaineth that naught existeth beyond the firmament.

_Infinite Universe_ at 253.

Ultimately Bruno cannot endure the Aristotelian answers and confronts it head on.

Thus let this surface [the edge of space/position of the Universe. JG] be what it will, I must always put the question, what is beyond? If the reply is NOTHING, then I call that the VOID or emptiness. And such a Void or Emptiness hath no measure and no outer limit, though it hath an inner; and this is harder to imagine than is an infinite or immense Universe. For if we insist on a finite Universe, we cannot escape the void.

_Infinite Universe_ at 254.

Having pushed that hurdle aside rather than wasting energy in trying to jump over a phantom one, Bruno postulates whether the infinite space is amenable to the reception of matter.

As regards infinite space, we know for certain that this is apt for the reception of matter and we know naught else thereof; for me, however. it is enough that infinity is not repugnant to the reception of matter, if only because where there is naught, there at least is no outrage. It remaineth to see whether or not it is convenient that all space be filled? And here. if we consider no less what it may be than what it may do, we shall still find the Plenum not merely reasonable but inevitable. That this may be manifest I ask you whether it is well that this world exist.

_Infinite Universe_ at 255.

The issue presents itself, then, as to whether the world [the Earth and associated celestial bodies, our cosmology] is unique or merely a fair representative sample of that which occupies the space beyond our own perception and Bruno submits that there is every reason to believe that the space within our world is similar to the space beyond our perception and that in that space is to found worlds similar to our own.

Nevertheless it is well that there should be since there can be innumerable worlds similar to our own, even as our world hath achieved and doth achieve existence and it is well that it should exist.

_Infinite Universe_ at 258.

The problem in all of these propositions is simple.

This is indeed what I had to add; for, having pronounced that the Universe must itself be infinite because of the capacity and aptness of infinite space; on account also of the possibility and convenience of accepting the existence of innumerable worlds like to our own; it remaineth still to prove it.

_Infinite Universe_ at 260.

Having listened enough to Aristotelian arguments, Bruno cuts short the matter and gets the dialogue back on track.

For the solution that you seek you must realize FIRSTLY, that since the Universe is infinite and immobile, here is no need to seek the motive power thereof. SECONDLY, the worlds contained therein such as earths, fires and other species of body named stars are infinite in numbers, and all move by the internal principle which is their own soul, as we have shewn elsewhere; wherefore it is vain to persist in seeking an extrinsic cause of their motion. THIRDLY, these worlds move in the ethereal regions and are not fixed or nailed down on to any body, any more than is our earth, which is one of them. And we prove that this earth doth from innate animal instinct, circle her own centre in diverse fashion and around the sun. These matters having been thus declared, we are not, according to our principles, obliged to demonstrate either active or passive motion arising from infinite intensive force, for the moving body, as also the motor power is infinite; moving soul and moved body meet in a finite subject, that is, in each of the aforesaid stars which are worlds. So that the Prime Origin is not that which moveth; but itself still and immobile, it giveth the power to generate their own motion to an infinity of worlds, great and small animals placed in the vast space of the Universe, each with a pattern of mobility, of motion and of other accidents, conditioned by its own nature.

_Infinite Universe_ at 266-267.

Although technically wrong, Bruno, either on his own intuition or in response to the classical problem of the mover itself being moved, of the finite and infinite motion, advances that the finite object moves in time yet incorporates within itself the "soul" that moves instantaneously. Thus a body may be both at rest and in motion contemporaneously.

* * * The earth then hath two motions just as all bodies which move themselves have two principles of motion. Of these the principle is that which simultaneously moveth and hath moved, whereof according to that reasoning the mobile body is no less utterly stable than utterly mobile.

_Infinite Universe_ at 267-268.

In the Second Dialogue, Bruno begins with the problem of a primal cause that develops into a discussion of the relationship between the corporeal and the incorporeal, the finite and infinite, and that which occupies position and space (matter) and that which is left—the void.

* * * whence it would follow that the Prime Cause hath not a single simple active and absolute power, but hath one active power to which correspondeth infinite successive potentiality, and another to which correspondeth potentiality indistinguishable from action. I do not here emphasize that if we regard the world as bounded and since it is impossible to imagine a corporeal object whose circumference is bounded by an incorporeal object, this world would have the quality and power of self-destruction and self-annihilation; for, so far as we understand all bodies are dissoluble. I say that I will not remind you that no argument would then deny that the empty infinite (even though we cannot conceive it as endowed with active power) would on occasion absorb this world into non-existence. Nor will I point out that Position, Space and the Void, if not identical with matter, have a resemblance thereto, as it would seem is sometimes maintained perhaps not without reason, by Plato and by all those who define position as a certain space. Now if matter hath an appetite which should not exist in vain, since such appetite is according to nature and proceedeth from the order of primal nature. It followeth that Position, Space and the Void have also such an appetite. I leave aside the fact indicated above that none of those who aver that the world is bounded can, having affirmed the boundary thereof, invent any way how this may be; and at the same time some of them while denying in their propositions and in words the void and empty, nevertheless as they proceed and in fact come inevitably to posit them. If there is an emptiness and a void, then it certainly hath containing power, and this can in no way be denied; since the same argument as maintaineth it to be impossible that in the space wherein is our world there is also at the same time contained another world, this same argument must maintain that in the space beyond our world or in that Nullity (for so Aristotle nameth that which he doth not wish to call the Void) it is possible that such another world may be contained. The reason that he asserteth that two bodies cannot occupy the same space is the incompatibility of the dimensional volumes of the two bodies; it followeth then, in so far as this argument doth require, that where the dimensional volume of the one is not, there the dimensional volume of the other can be. If there existeth this possibility, then space is in a certain sense matter; if it is matter it hath quality, if it hath quality, by what argument can we deny it action?

_Infinite Universe_ at 271-272.

Having established that the Universe consists of both the world [all that which is filled and doth constitute a solid body] and the empty space beyond the world, the void itself must be characterized.

* * * We do not call aught Void as being mere nullity, but rather accept the view whereby that which is not corporeal nor doth offer sensible resistance is wont, if it hath dimension, to be named Void, since we do not usually understand as corporeal that which hath not the property of offering resistance; whence they say that just as that is not flesh which is not vulnerable, so that which doth not offer resistance is not corporeal. In the same way we name infinite that which is an immense ethereal region in which are innumerable and infinite [numbers of] bodies such as the earth, the moon, and the sun, and these are called by us worlds, composed of Plenum and of Void: for this spirit, this air, this ether not only surroundeth these bodies but also penetrateth within them and becometh inherent in everything. Furthermore we speak of the Void according to the view with which we replied to his enquiry, where is the infinite ether and its worlds? We replied. It is in an infinite space, a bosom in which the whole hath his being and is harmoniously conceived.

_Infinite Universe_ at 273.

The void therefore is occupied by the æther.

Bruno, consistent with the general propositions in _Concerning the Cause_ , reaffirms that the Universe itself does not move notwithstanding that that which is in it does, just as the road does not move although the car on it does and the earth upon which the road rests also moves. The road is one with the ground and so the Universe being one with itself does not itself move

. . . where is it to go?

I do not assert this of the Universe, to which by no reasoning should motion be attributed, for this is impossible; nor can, nor should motion appertain or be attributed to the infinite.

_Infinite Universe_ at 277.

Associated with this proposition is the diminution of an infinite body that raises the problem of infinite size, weight, and so forth. Throughout our discussion here, one must make the distinction between infinity as a characteristic or quality of the Universe and infinity in its quantitative sense as it applies to "mass" and to the field, i.e., space (the æther). This distinction is exceedingly important for it differentiates "substantive" infinity as advanced here from parochial, "procedural" infinity that applies to mathematics, physics, number theory, and so forth, that is concerned with the quantitative solution of particular problems that are inherently limited by the articulation of the problems themselves or the means by which the solutions are achieved, for example the various Zeno's paradoxes or the quadrature of the circle that involve transcendental numbers. Procedural infinity accepts as a given that the problem as stated is unsolvable and thereafter sets out a means to generate a solution that is acceptable "as if" the boundary between the finite and the infinite were lifted and one could drive through the"very just beyond it." It is a "for all practical purposes" solution.

It is only when we get to Heisenberg's uncertainty principle that procedural infinity is incorporated into practical physics as an underlying proposition and in which the incommensurability between the problem as posed and the problem as solved becomes evident. The uncertainty principle precisely marks the boundary between procedural infinity and substantive infinity where the "space' of "spacetime" and the 'time" of "spacetime" are sought to be studied separately only to discover that as one becomes more precise the other becomes reciprocally more imprecise suggesting that nothing exists outside the scope of time or space. Ultimately, substantive infinity implicates the microcosmic as well as the macrocosmic and therefore raises the inference of the existence of a continuum between the two.

The concept of infinity from the substantive point of view is the exclusive province of Bruno. What we do here is ground his philosophical postulates into the geometry of the Universe of which he certainly had an intuitive inkling and in many cases an articulated clarity, i.e., the relationship between the concave and the convex, celestial bodies in the æther and the æther itself, and the relativity of motion and the relationship between bodies in motion and bodies at rest that ultimately devolves to the unified geometry of an entity (a body having an undivided continuous surface) and two bodies separately situated. Bruno took these postulates and "ran out" the logical inferences that could be drawn from the observable Universe. Copernicus having dispelled that the Earth was the center of the Universe, Bruno advanced the infinity of the Universe and its homogeneity from which follows that there is no center for there is no periphery from which that center could be determined.

Thus the earth no more than any other world is at the centre; and no points constitute definite determined poles of space for our earth, just as she herself is not a definite and determined pole to any other point of the ether, or of the world space; and the same is true of all other bodies. From various points of view these may all be regarded either as centres, or as points on the circumference, as poles, or zeniths and so forth. Thus the earth is not in the centre of the Universe; it is central only to our own surrounding space.

_Infinite Universe_ at 280.

The inference is that there is no preferential direction in an infinite Universe so that it is only with respect to a particular celestial body that an object may be said to move upwards or downwards, or translated into Newtonian terms there is no preferential gravitational field in an infinite Universe.

* * * wherefore if we should wish to say that the migration of such things is upward or downward, it must be understood as applying only to a certain region from a certain viewpoint, so that if something receding from us proceedeth toward the moon, when we should say that it goeth upward, then the inhabitants of the moon, our own anticephali, would say that it is in descent. Motions then have no distinction of upward or downward, hither or thither in respect of the infinite Universe; but only in respect of finite worlds which are within that Universe, or according to the respective horizons of innumerable worlds, or to the number of innumerable stars. Hence it ensueth that the same thing, with the same motion, may be said to move upward and downward with respect to diverse bodies. Determinate bodies are therefore not endowed with infinite motion, but with motion finite and determined within their own limits. But the determined and infinite hath neither finite nor infinite motion, and knoweth no distinction of place or time.

_Infinite Universe_ at 280-281.

In an infinite Universe composed of finite entities, Bruno considers the transmutability of the substance of which corporeal entities are composed as substance that changes place and form.

Nevertheless, the Universe being infinite, and the bodies thereof transmutable, all are therefore constantly dispersed and constantly reassembled; they send forth their substance, and receive within themselves wandering substance. Nor doth it appear to me absurd or inconvenient, but on the contrary most fitting and natural that finite transmutations may occur to a subject; wherefore particles of [elemental] earth may wander through the ethereal region and may traverse vast space now to this body, now to that, just as we see the same particles change their position, their disposition and their form, even when they are yet close to us. Whence we deduce that if this earth be eternal. It is not so by virtue of the stability of any one part or individual, but through the vicissitudes of many parts, some being expelled therefrom, and their place taken by others.

_Infinite Universe_ at 285-285.

If then parts of the Universe are transposed to and transformed at other parts, the process constitutes a continuum of existence in which discrete entities are separated by the æther no less than the continuum of lesser entities such as atoms that are themselves separated by the all pervading æther.

And according to these reasonings the infinite Universe may be regarded as a single continuum in which discreteness is no more introduced by the interpolation of ether between the large celestial bodies than it can be within the mud by the interposition of air among the dry and the liquid particles, the difference being solely in the fineness and subtlety of the parts of the mud exceeding our sensible apprehension, as against the greatness, large size and sensible qualities of the parts of the Universe. And thus contrary and diverse mobile parts _converge_ to constitute a single continuous motionless body, wherein contraries _converge_ to the constitution of a single whole, and pertain to a single order and finally form a single whole.

[Emphasis added. JG]

_Infinite Universe_ at 287-288.

If in an infinite Universe in which existence constitutes a continuum, and Bruno rarely speaks in terms of "existence" although clearly that is what this is all about, then an infinity of time constitutes an eternity and therefore the demarcation of time analogous to those of space are also meaningless.

Expound then to me. What would you say are the parts that make up infinite duration. Parts of time duration which bear a ratio to the duration and to time, but not to infinite duration or infinite time. For in infinite duration, the maximum time, that is, the greatest proportional part of a duration, becomes equivalent to the minimum, since infinite centuries have no greater duration than infinite hours. I say, indeed, that in infinite duration, which is eternity, there are not more hours than centuries. So that everything which can be described as a part of the infinite is in virtue thereof itself infinite, both in duration and in size. From this teaching, you may judge how careful is Aristotle in his hypotheses when he imagineth finite parts of the infinite; and you may estimate the force of the arguments of certain theologians who consider that the eternity of time involveth the inconvenience of as many infinites, one greater than another, as there are species of numbers. By my teaching I say you may escape from innumerable pitfalls.

_Infinite Universe_ at 294.

Bruno makes clear that the Universe is an undivided continuum in which everything is "a part" and not "apart."

SECONDLY, Aristotle doeth not fortify his argument by demonstration. For since the Universe is infinite and since there are in it an infinity of parts (I do not say they are parts thereof, for it is different to speak of parts WITHIN and parts of the infinite); and since all these parts experience both action and passion, and in consequence can be transmuted one into another; therefore Aristotle would infer either that the infinite both experience action upon or passion from the finite, or that the infinite acteth upon the infinite and that this latter suffereth action and transformation from the former. We however maintain that this inference is not physically valid though logically it may be correct; since, however much, by competing with our intellect, we may discover infinite parts both active and passive; and these be regarded as contrary to those; yet, since the parts in nature are, as we see, not discrete or separate within distinct boundaries, they do not force or even incline us to say that the infinite is either agent or patient; but rather that within the infinite, innumerable finite parts exercise both action and passion. It may therefore be granted not that the infinite is mobile or alterable, but that there are therein innumerable mobile and alterable bodies; not that the finite sufficeth action from the infinite, nor the infinite from the finite, nor the infinite from the infinite, in the natural and physical sense of infinity; but that just as from a logical and rational aggregation, within the infinite all weights are as one weight, though all weights do not make up one weight; so the infinite whole, resting ever immobile, unalterable, incorruptible, within it there can be and are motions and alterations, innumerable and infinite, perfect and complete.

_Infinite Universe_ at 295.

Although Bruno does not profess to be a mathematical physicist, at the same time he is aware of the concept of force, certainly as much as was known in classical antiquity and his own time, and he is able to discern and articulate the false inferences that could be drawn from a false belief in an infinite body as distinct from a finite one and the incongruities that result.

* * * For if corporeal power were diffused throughout an infinite body, it would not thereby act on the finite body with infinite vigour and power, but it would be effective only with such force as it could diffuse from those finite parts within a certain limited distance; since it would be impossible that it should operate with the force of all the parts, but possible only with those nearest.

_Infinite Universe_ at 297.

He fully advances that just because that which is beyond the perceptible Universe is itself not perceptible does not mean that it does not exist, a fact that has been established time and again as man pushes the perceptible Universe out further and further with more powerful telescopes and more far reaching satellites.

I believe and understand that beyond this imagined edge of the heaven there is always a [further] ethereal region with worlds, stars, earths, suns, all perceptible one to another, that is each to those which are within or near; though owing to the extreme distance they are not perceptible to us. And in this manner, consider what foundation hath this man who maintaineth that because there are no bodies perceptible to us beyond our supposed circumference, therefore no such bodies exist.

_Infinite Universe_ at 298.

The Third Dialogue begins with:

[The whole Universe] then is one, the heaven, the immensity of embosoming space, the universal envelope, the ethereal region through which the whole hath course and motion. Innumerable celestial bodies, stars, globes, suns and earths may be sensibly perceived therein by us and an infinite number of them may be inferred by our own reason. The Universe immense and infinite, is the complex of this [vast] space and of all the bodies contained therein.

So that there are no spheres with concave and convex surfaces nor deferent orbs, but all is _one field_ , one universal envelope. That is so.

[Emphasis added. JG]

_Infinite Universe_ at 302.

Consistent with this, Bruno recognizes [or at least I submit that he did] that if one were to understand the principles of motion of our own Earth circling our own Sun then that understanding would apply equally to all other celestial bodies.

* * * But once the motion is understood of our own mundane star which is fixed to no orb, but impelled by her own intrinsic principle, soul and nature, taketh her course around the sun through the vastness of universal space, and spinneth around her own centre, then this opinion [Aristotle's cosmology. JG] will be dispelled. Then will be opened the gate of understanding of the true principles of nature, and we shall be enabled to advance with great strides along the path of truth which hath been hidden by the veil of sordid and bestial illusions and hath remained secret until to-day, through the injury of time and vicissitudes of things, ever since there succeeded to the daylight of the ancient sages the murky night of the foolhardy sophists.

_Infinite Universe_ at 302.

* * * Wherefore we may suppose that of the innumerable stars some are moons, some terrestrial globes, some worlds like our own, and around them our earth appeareth in their eyes to revolve just as they appear to us to revolve and to take their course around the earth. Why then should we affirm a difference between our own and those other heavenly bodies if we find every similarity between them [ _lit_. every convenience (in recognizing their similarity)]? And why should we deny that there is a similarity [ _lit_. this convenience] when neither reason nor sense-perception should lead us to doubt it?

_Infinite Universe_ at 313.

The Fourth Dialogue reaffirms the nonspeciality of the solar system or for that matter any part of the Universe. Although Bruno's translator at one point offers that Bruno considered the Universe as one infinite "sphere" (Footnote at 328) a fair reading of the text even as translated and the overall thrust of the work itself convinces me beyond a reasonable doubt that Bruno considered the Universe as an undivided integrated entity in which dimension is meaningless, although the limits of human perception may attribute dimensions to that which is perceived. What is most extraordinary for our purposes here, however, is the phrase "ethereal field."

The infinity of worlds is not then as the imagined complex of this earth surrounded by numerous spheres, some containing one star, some, innumerable stars. For space is such that innumerable stars can wander through it; moreover each one of these stars can be its own inner power and quality move toward communication with convenient things. Each is so large and comprehensive as to be worthy to be considered a world in itself; not one lacketh the efficient principle and power to preserve and maintain perpetual generation and life to innumerable and excellent individuals. As soon as we have recognized that the apparent world-motion is caused by the real diurnal motion of our earth (which happeneth similarly to other similar stars), no argument will constrain us to accept the vulgar opinion that the stars are equidistant from us, that they are as though nailed and fixed in an eighth sphere; and no persuasion will hinder us from knowing that the differences are innumerable in the distances from us of these innumerable stars. We shall understand that the orbs and spheres of the Universe are not disposed one beyond another, each smaller unit being contained within a greater—as, for example, the infoldings of an onion. But throughout the _ethereal field_ , heat and cold, diffused from the bodies wherein they predominate, gradually mingle and temper one another to varied degree, so as to become the proximate origin of the innumerable forms, and species of being.

[Emphasis added. JG]

_Infinite Universe_ at 328.1

* * * Moreover we have already on other occasions reflected that the Universe hath no edge, nor bound, but is immense and infinite.

_Infinite Universe_ at 338.

Although Bruno does not advance a universal substance/ substratum in the Aristotelian sense, he does advocate the existence of underlying "prime universal bodies from which the Universe was originally composed" and that these bodies are in a constant state of transformation within the multitude of solar systems that constitute the Universe and amongst the multitude of systems themselves. In the context of the entire theory I do not take it that the use of the word "originally" in anyway suggests a starting point of the existence of the Universe but rather refers to a base of substance from which any of the infinite celestial bodies was formed and at the depletion of which returns to the reservoir of substance out of which yet other celestial systems may be formed in the vast eternity that constitutes the Universe.

You understand that we speak of veritable parts; for concerning those prime indivisible bodies from which the whole Universe was originally composed, we must believe that they undergo certain vicissitudes through the immensity of space whereby they ebb and flow, now hither, now thither. And if by divine providence they do not form new bodies nor dissolve from the old, they are at least able to do so. For mundane bodies are in fact dissoluble, though through either intrinsic quality or external influence they may persist to eternity, suffering a certain influx and a similar and equal efflux of atoms; so they remain constant in number though their corporeal substance be, like ours, renewed from day to day, from hour to hour, from moment to moment, by the processes of attraction and digestion of all the parts of the body.

_Infinite Universe_ at 332.

A corollary to the concept of infinity and the immensity of the intermediary space is that no body moves toward another "spontaneously," i.e., both time and space are involved in all motion.

In the Fifth Dialogue Bruno presents a scholar, who from stating his own credentials is certainly much published and tenured, and who undoubtedly represents the institutionalized knowledge of "the establishment" and therefore Aristotelianism. The professor presents Aristotle's arguments point by point to which Philotheo responds in kind, reaffirming that in an infinite Universe one place is as much as another and that the common notion of perspective must give way to the reality of the inferences that follow from an infinite non-preferential Universe. The question as to what is beyond the perceptible Universe is answered by Philotheo:

Beyond the imagined convex circumference of the world is Time. For there is the measurement and true nature of motion, since similar moving bodies are there.

_Infinite Universe_ at 363.

Bruno advances as a fundamental proposition that the Universe consists of contraries, that which moves away from one place moves toward another, and so forth. Underlying this, therefore is a unifying contrary.

You see further that our philosophy is by no means opposed to reason. It reduceth everything to a single origin and relateth everything to a single end, and maketh contraries to coincide, so that there is one primal foundation both of origin and of end. From this coincidence of contraries we deduce that ultimately it is divinely right to say and to hold that contraries are within contraries, wherefore it is not difficult to compass the knowledge that each thing is within every other—which Aristotle and the other Sophists could not comprehend.

_Infinite Universe_ at 369.

Although Bruno does not abandon the phlogiston theory of the four elements—fire, earth, air, water—he advances that the æther constitutes a fifth element that accounts for the space between the various celestial systems.

* * * Besides the four elements that compose the heavenly bodies, there is as we have said a vast ethereal region in which they all move, live and grow, the ether which both envelopeth and penetrateth all things. In so far as it entereth into and formeth part of the mixture of the elements. It is commonly named air—the word applying to the vaporous layer around the waters and within the land, shut in among the highest mountains, capable of holding thick clouds and tempestuous winds from South and from North. In so far as it is pure and entereth not into composition, but formeth the site and the enveloping space through which the compound body moveth on its course, we name it properly ether, a name which means its course ( _corso_ ). This ether, though in substance identical with the air which is stirred within the viscera of the earth, is nevertheless differently named. Just as that which is around us is called air, yet when it is in some sort part of us or at least hath a part in our composition—as when it is found in our lungs, our arteries and other cavities and pores of our body—it is called spirit. The same, when around a cold body, becometh condensed into vapour, but around a hot star it is attenuated like flame, which is sensible only if joined to a denser body which becometh ignited by the intense heat thereof. Thus the ether is of his own nature without determined quality, but it receiveth all the qualities offered by neighbouring bodies, and carrieth them with his own motion to the furthest limits of the horizon wherein such active principles have efficacy.

_Infinite Universe_ at 372.

* * * But we postulate a single heaven in which the worlds have their own spaces, regions and convenient distances. It diffuseth throughout all, penetrateth all and it envelopeth, toucheth and is closely attached to all, leaving nowhere any vacant space; unless, indeed, like many others, thou [our professor] preferest to give the name of void to this which is the site and position of all motion, the space in which all have their course. Or thou mayest call it the primal subject denoted by that word space, so as to describe unto it no limited position. If thou preferest by omission and logically to regard it as something distinct in our mind, but not in nature or in substance derived from being or body; so that nothing be understood to exist which hath not position either finite or infinite, either corporeal or incorporeal, either as a whole or by means of his parts; and this position can finally be no other than space, and the space cannot be other than void. If then we regard this space or void as persistent, we call it the ethereal field which containeth all worlds; if we regard it as a supporting substance, we call it the space, within which is the ethereal field with the worlds; and this space cannot be conceived as existing within another space.

_Infinite Universe_ at 373.2

To the TENTH argument the reply is as to the FIFTH. For each world in the ethereal field occupieth his own space, so that one toucheth not nor thrusteth against the other; but they pursue their courses and are situate at such distance that contraries destroy not but rather comfort one another.

_Infinite Universe_ at 376.3

Since Faraday wrote exclusively in Victorian English and did not have the benefit of a university education or training in Latin or Greek and since we know precisely what he meant by "the field" and what constituted the æther in his time, and since the above translation is a fair representation of the Latin equivalent—a broad open space, vast and uncluttered, as if for tilling—there is every reason to believe that Bruno considered the "æther field" in the same way as did Faraday, namely a distinct dynamic entity that had to be denominated with a specific name. Therefore, I submit that Bruno's æther field is in every sense the same as Faraday's 4 that mandates that

### THE ÆTHER IS THE FIELD

NOTES

The relevant passages in the dual language French-Italian reprint edition [with typesetter's errors in the 1584 edition corrected] read:

1 * * * mals, que dans _le champ ethere_ le chaud et le froid, diffuses par les corpes qui sont principalement l'un ou l'autre, en viennent a se temperer mutuellemeat suivant divers degres au pont qu'ils se font principe prochain d'innombrables formes et especes d'etres.

* * * ma che per _l'etereo campo_ il caldo et il freddo diffuse da corpi principalmente tali, vegnano talmente a contemperarsi secondo diversi gradi insieme, che si fanno prossimo principio di tante forme e specie di ente.

2 * * * si nous voulons l'entendre comme une chose persistante, disons qu'il est _le champ ethere_ qui contient les mondes; si nous voulons l'entre comme une chose consistante, disons qu'il est l'espace ou se trouvent _le champ ethere_ et les mondes, qu'on ne peut concevoir alliers.

* * * il quale se vagliamo intendere come cosa persistente, diciamo essere _l'etereo campo_ che contiene gli mondi; se vogliamo concipere come cosa consistente, diciamo essere il spacio in cui e _l'etereo compo_ e mondi, e che non si puo intendere essere in altro.

3 Au onzieme argument, on repond comme au cinquieme: parce que chacun des mondes dans _le champ ethere_ occupe son espace de maniere a ce que l'un ne touche ni ne heurte l'autre; mais i1s se deplacent et sont situes a une distance telle qu'un contraire n'est pas detruit mals alimente par l'autre.

All'undecimo si risponde come al quinto: perche cossi ciascuno de mondi _nell'etereo campo_ ottiene il suo spacio, che l'uno non si tocca o urta con l'altro; ma discorreno, et son situati con distanza tale, per cui l'un contrario non si distrugga, ma si fomente per l'altro.

[Emphasis added to the critical words. JG]

I gratefully acknowledge the assistance of Nicholas Tomich, M.A., M.L.S., for confirming the "clarity of expression" and the faithfulness of Singer's English translation.

4 The Oxford English Dictionary cites Faraday as the first source under "field":

The word is freq. used as if it denoted an identifiable causal entity. 1845 FARADAY _Diary_ 10 Nov. (1933) IV. 331 Wrought with bodies between the great poles. i.e. in the magnetic field, as to their motions under the influence of magnetic force. 1850 _Ibid_. 23 July (1934), V. 325 When the opposed bodies are on opposite sides of the axis (Magnetic) then the figured forms would give fields of force in which the lines of magnetic power would vary.

I am advised by Dr. Frank James of the Royal Institution of Great Britain that there is little probability that Faraday's source for "field" was Bruno but rather Faraday's "field" in a cosmological sense evolved from his earlier work in magneto-optical effects and diamagnetism, for example, _Diary_ at November 7, 1845 (entry 7979), "when the sealing wax (7941) or paper (7953) was in the magnetic field . . . ."

**Chapter** **2.6 GALILEO**

In addition to Copernicus and Kepler, Galileo marks the transition from the Middle Ages that were dominated by Aristotelian reasoning to the modern era in which empirical evidence for the most part overrules mythotheological preconceptions about the nature of the Universe and therefore of existence itself. We must remember that Kepler (1571-1630) lived and died within Galileo's own lifetime (1564-1642) and that Newton (1642-1727) was born in the year Galileo dies. In style, Galileo continued the tradition of the Socratic dialogue although the debate was now over the Keplerian mechanical Universe that could now be reduced to simple mathematical and geometrical proportions, particularly the derivation of the rate of fall of an object in a gravitational field and the trajectory of an object in space. Integrally bound up with the new science was the analysis of the actual mechanics of putting an object in motion that had previously been at rest and the relativistic relationship between objects in motion and objects at rest before, during, and after flight. Although Galileo did not have the per se philosophical perspective of Aristotle, Aristotelian reasoning was inherent in the investigations themselves. Nonetheless one cannot say that Galileo was unaware nor incapable of observing and noting the generality of great underlying principles. In modern terms, one would say that the essence of gravity and acceleration is not that objects touch but that one exerts a pressure upon the other. Secondly, the force only continues as long as acceleration itself continues, for once acceleration becomes constant, it becomes the velocity of the combined mass. When the motion between the two contiguous bodies becomes constant they constitute a unified spacetime and as such they can no longer exert an accelerative force upon each other and therefore acceleration becomes in the nature of a gravitational force that has the appearance of holding them together. Therefore what was previously two bodies in relativistic motion becomes two bodies at rest as to each other, or in other words, one contiguous entity. Galileo precisely stated the case in operational terms:

SALV. One always feels the pressure upon his shoulder when he prevents the motion of the load resting upon him; but if one descends just as rapidly as the load would fall how can it gravitate or press upon him? Do you not see that this would be the same as trying to strike a man with a lance when he is running away from you with a speed which is equal to, or even greater, than that with which you are following him.

"The First Day," _Dialogues Concerning Two New_ _Sciences_ at 64.

But it is in the discussion of motion on the third day that Galileo recognized the equivalence of gravity and acceleration espoused in the general theory. In describing the motion of an oscillating weight or a trajectory, Galileo objectively recognized the symmetry and equivalence of time, mass, and energy between gravity and acceleration.

SAGR. From these considerations it appears to me that we may obtain a proper solution of the problem discussed by philosophers, namely, what causes the acceleration in the natural motion of heavy bodies? Since, as it seems to me, the force [virtu] impressed by the agent projecting the body upwards diminishes continuously, this force, so long as it was greater than the contrary force of gravitation, impelled the body upwards; when the two are in equilibrium the body ceases to rise and passes through the state of rest in which the impressed impetus [impeto] is not destroyed, but only its excess over the weight of the body has been consumed—the excess which caused the body to rise. Then as the diminution of the outside impetus [impeto] continues, and gravitation gains the upper hand, the fall begins, but slowly at first on account of the opposing impetus [virtu impressa], a large portion of which still remains in the body; but as this continues to diminish it also continues to be more and overcome by gravity, hence the continuous acceleration of motion.

"Third Day" at 165.

Putting aside the problem of gravity and acceleration being "interjected" into mass, unquestionably Galileo was talking about "forces" that he did not consider to any extent in a mystical or mythical sense . . . he considers force as a scientific reality, an organic part of existence that could be studied empirically and quantitatively as a general proposition applicable to all cases.

SAGR. So therefore this impressed force [virtu impressa] may exceed the resistance of gravity so slightly as to raise it only a finger-breadth; and finally the force [virtu] of the projector may be just large enough to exactly balance the resistance of gravity so that the body is not lifted at all but merely sustained. When one holds a stone in his hand does he do anything but give it a force impelling [virtu impellente] it upwards equally to the power [facoita] of gravity drawing it downwards? And do you not continuously impress this force [virtu] upon the stone as long as you hold it in the hand? Does it perhaps diminish with the time during which one holds the stone?

And what does it matter whether this support which prevents the stone from falling is furnished by one's hand or by the table or a rope from which it hangs? Certainly nothing at all. You must conclude, therefore, Simplicio, that it makes no difference whatever whether the fall of the stone is preceded by a period of rest which is long, short, or instantaneous provided only the fall does not take since so long as the stone is acted upon by the force [virtu].

SALV. The present does not seem to be the proper time to investigate the cause of the acceleration of natural motion concerning which various opinions have been expressed by various philosophers, some explaining it by attraction to the center, others to repulsion between the very small parts of the body, while still others attribute it to a certain stress in the surrounding medium which closes in behind the falling body and drives it from one of its positions to another. Now, all these fantasies, and others too, ought to be examined; but it is not really worth while. At present it is the purpose of our Author merely to investigate and to demonstrate some of the properties of accelerated motion (whatever the cause of this acceleration may be)—meaning thereby a motion, such that the momentum of its velocity [i momenti della sua velocita] goes on increasing after departure from rest, in simple proportionality to the time, which is the same as saying that in equal time-intervals the body receives equal increments of velocity; and if we find the properties [of accelerated motion] which will be demonstrated later are realized in freely falling and accelerated bodies, we may conclude that the assumed definition includes such a motion of falling bodies and that their speed [accelerazione] goes on increasing as the time and the duration of the motion.

SAGR. So far as I see at present, the definition might have been put a little more clearly perhaps without changing the fundamental idea, namely, uniformly accelerated motion is such that its speed increases in proportion to the space traversed; so that, for example, the speed acquired by a body in falling four cubits would be double that acquired in falling two cubits and this latter speed would be double that acquired in the first cubit. Because there is no doubt but that a heavy body falling from a height of six cubits has, and strikes with, a momentum [impeto] double that it had at the end of three cubits, triple that which it had at the end of one.

"Third Day" at 166.

We can recognize from the context that (1) acceleration is a direction opposite to that of gravity but including the same subjective and objective sense of relative pressure, (2) that it comes into existence only after gravity has reached the limit of zero at which moment acceleration begins, (3) acceleration is a force of propulsion rather than attraction and is the negative of gravity, and (4) that gravity and acceleration are parabolic processes. That the force increases arithmetically (double the distance over units of time) rather than geometrically (square of the distance over time) is a translational consequence when we take the actual condition as depicted in his geometric drawings. He is equally describing the primary principle. The exploration of this equivalence is succinctly stated later on the third day.

SAGR. Please allow me to interrupt the lecture for a moment in order that I may clear up an idea which just occurs to me; one which, if it involve no fallacy, suggests at least a freakish and interesting circumstance, such as often occurs in nature and in the realm of necessary consequences.

If from any point fixed in a horizontal plane, straight lines be drawn extending indefinitely in all directions, and if we imagine a point to move along each of these lines with constant speed, all starting from the fixed point at the same instant and moving with equal speeds, then it is clear that all of these moving points will lie upon the circumference of a circle which grows large and larger, always having the aforesaid fixed point as its center; this circle spreads out in precisely the same manner as the little waves do in the case of a pebble allowed to drop into quiet water, where the impact of the stone starts the motion in all directions, while the point of impact remains the center of these ever-increasing circular waves. But imagine a vertical plane from the highest point of which are drawn lines inclined at every angle and extending indefinitely; imagine also that heavy particles descend along these lines each with a naturally accelerated motion and each with a speed appropriate to the inclination of its line. If these moving particles are always visible, what will be the locus of their positions at every instant? Now the answer to this question surprises me, for I am led to the preceding theorems to believe that these particles [Figure 34] will always lie upon the circumference of a single circle, ever increasing in size as the particles recede farther and farther from the point at which their motion began. To be more definite, let A be the fixed point from which are drawn the lines AF and AH inclined at any angle whatsoever. On the perpendicular AB take any two points C and D about which, as centers, circles are described passing though the point A, and cutting the inclined lines at the points F, H, B, E, G, I. From the preceding theorems it is clear that if particles start, at the same instant, from A and descend along these lines, when one is at E another will be at G and another at I; at a later instant they will be found simultaneously at F, H, and B; these, and indeed an infinite number of other particles traveling along an infinite number of different slopes will at successive instants always lie upon a single ever-expanding circle. The two kinds of motion occurring in nature give rise therefore to two infinite series of circles, at once resembling and differing from each other; the one takes its rise in the center of an infinite number of concentric circles; the other has its origin in the contact, at their highest points, of an infinite number of eccentric circles; the former are produced by motions which are equal and uniform; the latter by motions which are neither uniform nor equal among themselves, but which vary from one to another according to the slope.

Further, if from the two points chosen as origins of motion, we draw lines not only along horizontal and vertical planes but in all directions then just as in the former cases, beginning at a single point ever-expanding circles are produced, so in the latter case an infinite number of spheres are produced about a single point, or rather a single sphere which expands in size without limit; and this in two ways, one with the origin at the center, the other on the surface of the spheres.

SALV. The idea is really beautiful and worthy of the clever mind of Sagredo.

SIMP. As for me, I understand in a general way how the two kinds of natural motions give rise to the circles and spheres; and yet as to the production of circles by accelerated motion and its proof, I am not entirely clear; but the fact that one can take the origin of motion either at the inmost center or at the very top of the sphere leads one to think that there may be some great mystery hidden in these true and wonderful results, a mystery related to the creation of the universe (which is said to be spherical in shape), and related also to the seat of the first cause [prima causa].

"Third Day" at 192.

Clearly what Galileo described was that the area generated by a body falling under the force of gravity or a body propelled outwardly by the force of propulsion (acceleration) propagates an area over unit increases of time as the gradational increases in the surfaces of a sphere is to an increases in radius, namely r. Accordingly, if we consider that what Galileo means is the distance traveled by the body, which I submit is rather clearly meant, then the distance traveled is under a constant force of gravity. The interesting thing is that in the second example of the demonstration his lines are at different angles that would clearly have the effect of making direct translations of the force of gravity over the maximum and minimum gradations of gravitational forces from a fall perpendicular to the surface (100%) to a null fall when the object would lie on a plane parallel to the surface of the line from which the object is to fall, i.e., it will actually not fall at all, and unless it is pushed to roll horizontally, it will be at rest. In both demonstrations, however, the distance through which the object travels is directly related geometrically to time, a relationship that lies at the heart of all of Newton's geometric constructions as well as the solution of problems by fluxions. Therefore distance is directly related to time, one is converted directly into the other, hence our original proposition that time and space are equivalent, or more precisely, organically fused into the same entity, spacetime.

Figure 34 Galileo's illustration of the force of gravity.

**Chapter** **2.7 NEWTON**

With the essential mechanisms of the primary principle and some of the core philosophical issues in hand, we can now move on to Newton as the pivotal figure between the physics of classical antiquity and the modern era. Certainly any view of modern physics must begin—having recognized the monumental restructuring of the Universe by Copernicus and Kepler—with either Galileo or Newton, or both. Although a review of Galileo's _Dialogues Concerning Two New Sciences_ and Newton's _Mathematical Principles_ _of Natural Philosophy_ [ _Philosophiae Naturalis Principia Mathematica_ , hereinafter the _Principia_ ], or his _Opticks: or A Treatise of the Reflections, Refractions, Inflections & Colours of Light_ on a line-by-line basis is not required or necessarily productive, I think it is important to consider the _Principia_ in some detail as it so eloquently provides an organization for the arguments of my own theory.

Even more than Galileo's _Two New Sciences_ , Newton's _Principia_ is a work that was intended to have universal application because of its exposition of gravity and its celestial perspective. The _Principia_ above all is a book whose mathematics is articulated through the medium of geometric proportions rather than the modern notational symbology or even the fluxions that provided the foundation for Newton's calculus. What was to Newton the norm of mathematical expression comes to be the very form in which the unified and pure field theories are embodied, herein further reduced to the nominalized sphere. Newton immediately draws our attention to the two forms of existence . . . mass and the space that it is in . . . the geometry of the former, and eventually the gravity that holds it together. The force of gravity attributable to mass lies at the surface of mass and therefore is a function of the radius r of the mass, which for a given mass is always equivalent and nominalized here to r, its pure spacetime, and since mass is a function of density, it is mass per unit radius.

Newton also discusses absolute time, mathematical time, absolute space, relative space, and place, 1 _Principia_ 6 et seq.,1 although it is necessary to extend his discussion to include the special theory of relativity and the relationship of time to energy. In Section II, Proposition I, Theorem I, 1 _Principia_ 40 et seq., Newton goes back to Kepler's laws of equal time:equal areas and gives time a linear measure that becomes the geometrical entity equivalent to the geometric spatial entity from which a spatial area may be measured. Time, even to Newton, is interchangeable with space and therefore has its identical geometry. Einstein extended this identity to include the interchangeability of mass with energy and in the general theory adds elasticity to time and space through his transformations. The unified field theory reunifies relativistic time and space with classical time and space into a nominalized sphere whose dimension r expands and contracts with changes in density under the dynamics of refraction. All that is necessary to update Newton's discussion is to introduce radiation pressure as the source of ponderomotive force. The rules of proportion, i.e., 3/2, are rules of proportion between the observable and unobservable, essentially the ratio between the volume of a sphere and its surface area, and therefore the volume of the density of the field at a given r with the surface area of that field at that r, having nominalized out 4/3 π as merely the spherical descriptor. As we shall see below, if the respective lines of force are translated into circular shells, the classical model is directly equivalent to the quantum mechanical one and Kepler's 3/2 relationship between the 4/3π area of the sector swept out in time reduces to the ratio of volume r to area r, when the focii of the ellipsis are converged to the center of the sphere generating the gravitational/quantum mechanical field. Time, force, distance, and area therefore are reduced to gradations of r. Essentially what Kepler discovered, if it were translated into relativistic terms, is the face of a clock! 1 _Principia_ 46, Proposition IV, Theorem IV et seq.

The essential issue addressed by both Newton and Kepler, although not expressly recognized, is that time had a "geometrical dimension" or at least could be expressed through geometrical constructions. In the _Principia_ , Newton takes distance and time and converges them into the same geometry from which volume and area may be extrapolated into gradations proportional to radius r. Since volume and area describe mass, and distance per unit time describes force, force may be described as the trajectory of mass per unit time. The movement of mass through time therefore describes motion, and conversely the geometric motion of a celestial body is a consequence of its mass under the influence of gravitational forces. The rules of proportion between mass and the field in which the mass moves are therefore embedded in the geometry that describes the motion of the mass. Geometry therefore defines the mass. The unified and pure field theory extends these concepts by advancing that the shape of the mass, i.e., its form, is itself the result of the forces of the field, and in fact, mass itself embodies the field. In other words, the "final law" of physics is

THE SHAPE OF A BODY IS THE RESULT

OF THE FORCES APPLIED TO IT

Although this is so obviously obvious, it means that the form of a spherical celestial object and its location are the result of the forces that shaped it and put it where it is. In a philosophical and operational sense, the Universe is therefore both classic and relativistic—it is simultaneously gravitational and accelerational. If that is so, as I submit it is, we not only have to consider the gravitational forces that are believed to hold the celestial body together, but we must also consider the external forces that put the body together in the first "place." That is a postulation that has heretofore not been considered or explored. It suggests that the field itself is a dynamic operative medium rather than just a place where things are and in which events occur. In Newton's Universe, time is predicated on the uniform periodicity of the rotation of the Earth so that differences in time are measured against the terrestrial base period, whether diurnal or annual, both of which may be expressed geometrically. However, although Newton is able to describe motion geometrically, he is not able to account for the mechanism underlying motion itself except that it is due to gravity. The problem is that although Newton "discovered" gravity, what he has really done is geometricized it. He has not "discovered" the underlying force that gives gravity its impetus, i.e., the mechanism by which it operates. The specter of a Universe that is constitutionally perpetually in motion presents the specter of an infinite time in which events can occur that places us on the threshold of the theory of probabilities in quantum mechanics that was so unsettling to Einstein. One may suppose, therefore, that there is something constitutional about existence itself that keeps it constantly in motion and therefore always in a state of disequilibria. Newton himself seems not to have recognized this and accordingly not to have discussed it. We will therefore have to account for **disequilibrium** in the context of a nonextinguishable force. Accordingly, I submit that

TIME [THE RIGHT-HAND RULE]

IS THE PRIMARY FORCE OF THE UNIVERSE

TIME IS MOTION

When taken from that perspective, time as a "fourth dimension" is a misnomer for it is actually one of the two elements of three-dimensional spacetime of which the field of existence is itself composed. Thus the four-dimensional Minkowskian-Einsteinian mathematical description of existence actually misdirects the reasoning that is essential to formulate a unified and pure field theory that attempts to concentrate more and more into more simple and more general formulations rather than into more complex and elaborate mathematics. It is in this sense that the present theory addresses Newton's remarks in the "Preface to the First Edition' of the _Principia_ ;

I wish we could derive the rest of the phenomena of Nature by the same kind of reasoning from mechanical principles, for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some cause hitherto unknown, are either mutually impelled toward one another, and cohere in regular figures, or are repelled and recede from one another. These forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles here laid down will afford some light either to this or some truer method of philosophy.

1 _Principia_ XVIII.

The yet unknown force underlying the phenomena of nature is to be found in Newton's own work and particularly in the _Opticks_ where space and time are unified in the various frequencies of the spectrum that he reconstituted by a second refracting prism. Notwithstanding that he refracted the spectrum into its individual components and had the intuition to see the photon as a corpuscle of matter, he did not relate sphericality to linearity or see that a sphere wound out a spiral as a photon spins out a waveform. But the _Opticks_ clearly explicates the combinatorial aspects of frequency and therefore the combinatorial aspects of time. The combinatorial aspect of frequency infers that energy can be recombined by the same mechanical means by which it may be refracted without in any way "reversing" time itself and therefore presents the proposition that energy may be condensed into mass by the same process by which it was dispersed. Accordingly, there must be something inherent in the mechanism by which matter is "broken" apart that is equally capable of putting it back together. The primary principle explicates that mechanism. The essential philosophical premise underlying classical (Newtonian) physics is that area is the common denominator of force, which is itself made manifest through time and space, for it is through area that incorporeal time is made measurable and by which force is made empirical.

By expressing the Universe geometrically Newton converted the incorporeal into the corporeal. You need only look at the drawings of Kepler, _Epitome of_ _Copernican Astronomy_ , and Newton, "The attractive forces of spherical bodies," 1 _Principia_ 183 et seq., Section xii, to recognize that the sphere and the circle are the units that describe the operations of the Universe. When we look to Newton's discussion of the pendulum, we see that the pendulum clock converts gravitational force into time as an increment of angular momentum. Force as a constituent of energy becomes equated to time, and time becomes reduced to geometry. Electromagnetism, being the result of the severance of spherical time, is the accelerational mode of gravity, its equal and opposite, the reaction to the action of the primary principle. 1 _Principia_ 158 et seq. Proposition LIII, Problem XXXV.

Brought to this point, in Book II, Proposition VII, Theorem V, 1 _Principia_ 247, Newton relates time, space, mass, and velocity. What remains is to unify time with space and mass that Newton himself nominalizes and therefore universalizes to the sphere. With the geometrization of time into the nominalized sphere, a body rotating in one place as compared to one rotating at another place is merely a relativistic variance as Newton himself explained in his discussion of "absolute space." 1 _Principia_ 1 et seq., "Definitions." in Book II, Proposition X, Problem iii, Example 1, 1 _Principia_ 262, Newton negates the possibility of negative density:

But Nature does not admit a negative density, that is, a density which accelerates the motion of bodies; and therefore it cannot naturally come to pass that a body by ascending from P should describe the quadrant PF of a circle. To produce such an effect, a body ought to be accelerated by an impelling medium, and not impeded by a resisting one.

The problem was that Newton, like his predecessors and successors, viewed Nature as predicated only on a gravitational model without regard to a Nature that could also propel things. Having recognized gravity as an aggregating phenomena Newton did not see the dispersion of forces through acceleration, although his law of action-reaction explicitly addressed it.

Newton's discussion of the density of a medium that is inversely proportional to its distance from a fixed center in relationship to the centripetal force, 1 _Principia_ 282, Book II, Section IV, Proposition XV, Theorem XII, describes a body that will degenerate in a spiral in a gravitational field as the consumption of matter makes ever decreasingly smaller the radius of the mass and therefore the volume of gravity that affects it. The reappearance of 3/2 as the ratio between the volume and density of the medium to the velocities of rotation, 1 _Principia_ 284, Cor. II, is the same Keplerian relationship between the volume of the gravitational field and the velocity of a mass in orbit around a focus. Newton recognized the relationship between compressive forces and magnetism and related centrifugal forces to densities and distances. 1 _Principia_ 300 et. seq., Book II Proposition XXIII, Theorem XVIII. But of equal importance is the postulation of a physical, and therefore a mechanical, force that operates along with centrifugal forces. In short, that repulsion and compression are inseparable correlates of each other. In the Scholium to the theorem he addresses the similarity between gravity and magnetism. You may recognize that if D becomes r, then all of the phenomena can be reduced to regular progressions of the sphere that is the fundamental shape of the gravitational body. The essence of gravity is that it is round!

By a like reasoning, if the centrifugal forces of the particles are inversely as the square of the distance between the centers, the cubes of the compressing forces will be as the fourth power of the densities. If the centrifugal forces be inversely as the third or fourth power of the distances, the cubes of the compressing forces will be as the fifth and the sixth power of the densities. And universally, if D be put for the distance, and E for the density of the compressed fluid, and the centrifugal forces be inversely as any power D of the distance, whose index is the number n, the compressing forces will be as the cube roots of the power E, whose index is the number n + 2; and conversely. All these things are to be understood of particles whose centrifugal forces terminate in those particles that are next them, or are diffused not much farther. We have an example of this in magnetic bodies. Their attractive force is terminated nearly in bodies of their own kind that are next them. The force of the magnet is reduced by the interposition of an iron plate, and is almost terminated at it: for bodies farther off are not attracted by the magnet so much as by the iron plate. If in this manner particles repel others of their own kind that lie next them, but do not exert their force on remote, particles of this kind will compose such fluids as are treated of in this Proposition. If the force of any particle diffuse itself every way _in infinitum_ , there will be required a greater force to produce an equal condensation of a greater quantity of the fluid. But whether elastic fluids do really consist of particles so repelling each other, is a physical question. We have here demonstrated mathematically the property of fluids consisting of particles of this kind, that hence philosophers may take occasion to discuss that question.

1 _Principia_ at 301-302.

The question of physical particles repelling each other is taken up here. Thus the equilibration of fluids, 1 _Principia_ 345, Book II, Proposition XXXVII, Theorem XXIX, and the motion of a body through a fluid under varying conditions of shape and density reduces to proportionality of velocities and inherently must reduce to a formulation in which time becomes a constituent in conjunction with the movement of mass in space of a noncompressible fluid. The inelasticity of the fluid under increased pressure is accommodated by the elasticity of time and space in terms of velocity. This is the type of compressibility of spacetime that is associated with the passage of light through a lens as the lens condenses and restores the coherent "phases" of the waveforms so that opolarity does not occur to generate interference.

In his discussion of the velocity of pulses, 1 _Principia_ 381, Book II, Proposition XLIX, Problem XI, Cor. I, Newton explicitly takes the relationship between the radius and circumference of a circle as a measure of time and the calculation of the velocity of the pulse.

The velocity of the pulses is equal to that which heavy bodies acquire by falling with an equally accelerated motion, and their fall describing half the altitude A. For the pulse will in the time of this fall, supposing it to move with the velocity acquired by that fall, run over a space that will be equal to the whole altitude A; and therefore in the time of one oscillation composed of one going and return will go over a space equal to the circumference of a circle described with the radius A; for the time of the fall is to the time of oscillation as the radius of a circle to its circumference.

1 _Principia_ at 381.

All that had yet to be done was to explicitly geometricize time itself rather than to just use geometry as a means of expressing it. In the immediately following proposition, 1 _Principia_ 382, Book II, Proposition L, Problem XII, Newton directly relates time to space in order to determine the distance of a wave motion and in the Scholium he extends the theory to wave motions of light and sound.

_To find the distances of the pulses_.

Let the number of the vibrations of the body, by whose tremor the pulses are produced, be found to any given time. By that number divide the space which a pulse can go over in the same time, and the part found will be the breadth of one pulse. Q.E.I.

SCHOLIUM

The last Propositions respect the motions of light and sounds, for since light is propagated in right lines, it is certain that it cannot consist in action alone (by Prop. XLI and XLII).

In Section IX, 1 _Principia_ 385, on the motion of fluids, Newton comes nearly to the identity between the r that generates the volume of the sphere with the r that generates the shape of the sphere itself, again returning to the 3/2 ratio and the motions of heavenly bodies introduced by Copernicus and extended by Kepler. Unquestionably Newton recognized the relationship between time and sphericality, and in fact, in his discussion of the spiral vortex and an embedded sphere in the vortex that itself could revolve about the central axis, he as much described celestial bodies as well as the Red Spot of Jupiter.

It is that in Book II, Section IX, Proposition LII, Theorem XL, Cor. IV, 1 _Principia_ 390, in the discussion of two bodies rotating in a common vortex, Newton recognizes that without some continuing source of motive energy, the globes would eventually "at last be carried around no longer."

Although the relationship between gravity and magnetism was known to Newton, he sees the relationship between the force of gravity and distance as the square, whereas that of magnetism to be nearly that of the cube of the distance. 2 _Principia_ 414, Book III, Proposition VI, Theorem VI, Cor. V. And yet he still recognizes the identity of the mechanism. 2 _Principia_ 415, Book III, Proposition VII, Theorem VII, Cor. 1.

Therefore the force of gravity towards any whole planet arises from, and is compounded of, the forces of gravity towards all its parts. Magnetic and electric attractions afford us examples of this; for all attraction toward the whole arises from the attractions towards the several parts.

In Book III, Proposition XVIII, Theorem XVI, 2 _Principia_ 424, Newton discusses the relationship between gravity and the origin of the sphericality of planets.

The equal gravitation of the parts on all sides would give a spherical figure to the planets. If it was not for their diurnal revolution of a circle.

Notwithstanding that gravity might adhere mass together, he does not account for the fact that planetary bodies are kept at a distance from the Sun while at the same time are held to it by gravity. For example, when the handle in Model 1 is turned quickly some of the ball bearings will dissociate themselves from the vortex and float out alone before being condensed back into the vortex. In conjunction with the other models, if an interlineating field of opolarity is generated so that the "planetary" ball bearing becomes fixed in an orbit, and other bearings are likewise propagated and fixed, a planetary system will result. Of course I do not have the means to generate a field in which all of these processes occur simultaneously, but amongst all of the models presented all of the processes can be seen individually or in various combinations so that all of the models account for all of the phenomena at issue.

In the General Scholium at the end of the mathematical principles of Book III, 2 _Principia_ 546, Newton acknowledges first that he is unable to discover the cause of the properties of gravity, and secondly, that he is unable to explain the subtle spirit that put the Universe together.

Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power. This is certain, that it must proceed from a cause that penetrates to the very centres of the sun and planets, without suffering the least diminution of its force; that operates not according to the quantity of the surfaces of the particles upon which it acts (as mechanical causes used to do), but according to the quantity of the solid matter which they contain, and propagates its virtue on all sides to immense distances, decreasing always as the inverse square of the distances. Gravitation towards the sun is made up out of the gravitations towards the several particles of which the body of the sun is composed; and in receding from the sun decreases accurately as the inverse square of the distances as far as the orbit of Saturn, as evidently appears from the quiescence of the aphelion of the planets; nay, and even to the remotest aphelion of the comets. If these aphelions are also quiescent. But hitherto I have not been able to discover the case of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypothesis, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy, in this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered.

And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea. And now we might add something concerning a certain most subtle spirit which pervades and lies hid in all gross bodies; by the force and action of which spirit the particles of bodies attract one another at near distances, and cohere, if contiguous; and electric bodies operate to greater distances, as well repelling as attracting the neighboring corpuscles; and light is emitted, reflected, refracted, inflected and heats bodies; and all sensation is excited, and the members of animal bodies move at the command of the will, namely, by the vibrations of this spirit, mutually propagated along the solid filaments of the nerves, from the outward organs of sense to the brain, and from the brain into the muscles. But these are things that cannot be explained in few words, nor are we furnished with that sufficiency of experiments which is required to an accurate determination and demonstration of the laws by which this electric and elastic spirit operates.

2 _Principia_ at 546-547.

That the propulsive energy of the Sun did not, however, go unnoticed is evidenced by Newton's discussion of the tails of comets by analogy of the ascent of smoke from a chimney. In effect he is describing the solar wind. However, there is inherent in that discussion the ponderamotive force of the solar wind that projects the tail of the comet away from the Sun at the same time that gravitational forces draw the comet to it. "The System of the World," 2 _Principia_ 611.

NOTES

1 The development of the arguments extend for the most part over several pages and often involve complex geometrical constructions far too extensive to be cited here so that I must refer you to the _Principia_ directly, except insofar as a short excerpt condenses and focuses an issue that can conveniently be incorporated here. As distinct from Faraday's _Diary_ , the _Principia_ is still in print in an inexpensive two volume paperback edition.

**Chapter** **2.8 FARADAY: GRAVITY, MAGNETISM, AND THE**

UNIFIED AND PURE FIELD THEORIES

In _Sidelights on Relativity_ , Einstein posits:

Of course it would be a great advance if we could succeed in comprehending the gravitational field and the electromagnetic field together as one unified conformation. Then for the first time the epock of theoretical physics founded by Faraday and Maxwell would reach a satisfactory conclusion. The contrast between ether and matter would fade away, and, through the general theory of relativity, the whole of physics would become a complete system of thought, like geometry, kinematics, and the theory of gravitation.

"Ether and the Theory of Relativity" at 22.

10018. Gravity (10082). Surely this force must be capable of an experimental relation to Electricity, Magnetism and the other forces, so as to bind it up with them in reciprocal action and equivalent effect. Consider for a moment how to set about touching this matter by facts and trial.

10019. What in Gravity answers to the dual or antithetical nature of the forms of force in Electricity and Magnetism? Perhaps the to and fro, that is, the ceeding to the force or approach of Gravitating bodies, and the effectual reversion of the force or separation of the bodies, quiescence being the neutral condition. Try the question experimentally on these grounds—then the following suppositions or suggestions arise.

10020. Bodies approaching by gravitation, and bodies separated by force, whilst gravitating towards each other, may shew in themselves or in surrounding matter or helices, opposite currents of electricity round the line of motion as an axis. But if not moving to or from each other, should produce no effect.

Faraday, 5 _Diary_ 150, entries for March 19, 1849.

* * * * * * *

10082. If there should be any effect of Gravity convertible into Electricity (10018)—then we might perhaps find delicate means of showing the gravitation of one body to another, and verify Cavendish's and Bally's conclusions, by comparing the action of the earth with the action of a heavy ball of lead. For the motion of the moving core (representing a gravitating body) in a horizontal instead of a vertical direction would entirely eliminate the action of the earth, and leave the bodies in the direction of the axis of motion to act on each other alone.

10083. Perhaps in that way a convenient and measurable test and indication of gravitating action of different bodies might be contrived and usefully applied.

10084. Then, under such suppositions, would the centers of gravity of two bodies, as two balls, when acted on by the earth, be also the centers when they were acting on each other i.e. considering their size and shapes? It could not well be if the shapes where extended or irregular, i.e. the center of gravity of a globe or of a solid ring of equal weight would be the same for the earth's action, but would they be the same to a near small globe in every position of the ring?

10085. If Gravity has relation or connexion (as I suppose) with electric forces, and therefore with magnetism; then it is possible that the rotation of the earth on its axis, by its counteracting gravitation in the equatorial direction, may have something to do with terrestrial magnetism and the direction of its polarity. And if so, then the rotation of a globe of copper ought to develope some magnetic effect in the direction of the axis of rotation. It should be rotated on an axis parallel to the dip, or else inductive magnelectric currents would be produced. In any case, the effect expected can only be small, and therefore interfering sources of error must be carefully excluded, and the amount of action magnified as much as possible. Astatic needles with long intermediate fibres or rods and carefully sheltered, on fixed supports, would probably be required.

10086. But gravitating force is convertible only whilst motion is being acquired or lost, then the mere rotation of a body and its tendency to expand at the equator should do nothing unless it really expands or moves. Unless indeed some other consideration is developed, like that of the moon in its orbit round the earth, where whilst moving from a to b, it may be considered as falling from a to c. (Figure 35)

10087. From the experiments (10067, etc.), it would seem just possible that there is an effect and that a current of Electricity is induced round the line of gravitating force joining two bodies together, when one of the bodies moved thrgh. If a man were falling with his face towards the earth, the electric current which would tend to form round him would be in the same direction as the hands of a watch which he should be looking at, or screw fashion. If he were to retreat from the earth, in the contrary direction. So that if he were to move face forward either to or from the earth along the line of gravity, his hands, moved as the hands of a watch or thus, would indicate the direction of the induced current. (Figure 36)

10088. Suppose all this. Then if two bodies gravitate towards each other, they ought not to induce electric currents whilst still in respect of each other, but if they approach each other they should. Now the direction of the rotation round them cannot be the same for both, according to the above law, but in contrary directions, for the two are moving in contrary directions.

10089. If we consider the magnetical result of two such induced currents, it would give for the two bodies such polarity that like poles would be towards each other.

10090. The induction must, I think, if it exists at all, be round the line of gravitating force.

10091. If the two bodies only one moved, then would that one only produce rotative current round it by induction? If so, of course either may have, as above.

(10087). Its own current with its own direction.

10092. But it is likely that the moving body should not, whilst moving under these suppositions, induce a current round itself, and yet not affect the state of the gravitating power in the still body—since the gravitation force of that quiescent body is in part the cause of its motion? Would look like a power of affecting one end of a line of gravitating force and not the other. This not likely and so is against all my suppositions, for we shall see how experiment testifies, and whether it only modifies some of my deductions and conclusions or sweeps them away altogether. Which may well be.

10093. Suppose that a body, in falling to the earth through a helix induces in that helix a given current of Electricity.

10094. Then if we send before hand such a current through the helix, that current ought to affect the fall of the body, retarding it? If we send the contrary current, it ought to facilitate (?) the fall—or the reverse? A mutual effect ought to result.

10095. The converse ought to be the case for ascent.

10096. But if the gravitating body be QUIESCENT, will a current one way or the other in the helix make it tend to ascend or descent—or must it be moving subject to gravity before it can be thus affected?

10097. If, being quiescent, it could be affected, the result would be a production of generation of gravitating force, and that is hardly possible.

10098. If a moving body were to rise or fall with different momenta under the condition and influence of a surrounding current, it would be equivalent to a generation of gravitating force of a similar kind.

10099. If an electric current could affect bodies in the line of gravitating force: then what would or could it do with a body moving at right angles to this line? Surely not affect it—or if affecting it, how?

10100. A body falling through a thick copper tube ought to fall easier than if the tube were away—and also cause currents in it and so make it even for the time magnetic. Could it affect an astatic magnetic needle?

10101. The falling body may induce currents in itself—and the induced and separated current may be a very small part of that actually set in motion at the time.

10102. Perhaps more might be separated by particular cores used as the falling body—cores of covered copper wire—of copper filings in a glass tube—or water—Sulfate of baryta—iron—Gold—Silver.

10103. Perhaps a core of solid helix covered copper wire—soaked in solution of shell lac and dried well—might be best; for the particles of the wire may act as core to the whole helix.

10104. If suppositions are true, then could not a falling river or a falling stream in a tube be converted into a Gravelectric arrangement, taking advantage of the places where the motion comes on and goes off? Now as water passes thrgh. a pipe or this shape—motion comes on from a to b and goes off from b to c. I put down all these fancies as I write, to stir up all the points of analogies, contradictions, consequences and absurdities, that I may the sooner both by experiment and reasoning settle what ground of expectation there may be in this matter, and work out the thought to the end. But the more I write the less I expect. (Figure 37)

10105. Motion of a body across the lines of gravity should produce no result.

10106. Motion downwds. in line of gravity should give result.

10107. Motion upward in line of gravity should give a contrary result.

10108. Motion downwd. in line of gravity faster than if body were falling by gravity alone, should (I think) give more effect in a given time than if falling by gravity alone: should in fact give an effect proportionate to the motion in a given time.

10109. If so, might produce the great effect of much fall in a short space for quickness of motion. Have set on for construction a trial apparatus on this principle. (10133).

10110. Then what would be the effect of a shot from the moment of quiescence up to the moment of obtaining its maximum velocity—or again, at the moment of loosing its velocity by being stopped? Could perhaps try a pistol or even a cannon shot. If there should be any truth in these vague expectations of the relation of Gravitating force, then it seems hardly possible but that there must be some extraordinary results to come out in relation to celestial mechanics—as between the earth and the moon, or the Sun and the planets, or in the great space between all gravitating bodies. Then indeed, Milton's expression of the Sun's magnetic ray would have a real meaning in addition to its poetical one. How would the compensation of centripetal force by the revolution of a secondary in its orbit work out?

10113. Supposing a Gravelectric current could be obtained, we should have to show by it the production of the electric spark,

"magnetic effect

"decomposing or electrolytic effect,

"heating effect on a wire,

"convulsions of a frog, etc. etc.

and there would probably be no difficulty in arranging so as to produce these results. The only point is, does the relation with Gravity exist as a root on which to build up these matters?

10114. Suppose a thick hollow copper tube falling vertically. If can induce a current on a helix outside of it, can it also induce a current in the helix inside of it, and in what direction should that current be? This is a serious question, affecting the whole expectation. The result, if not entirely negative, would give many variations of condition as regarding bodies passing up and down, in and by each other—of great importance.

5 _Diary_ 160 et seq., entries for August 25, 1849.

10934. In reference to Gravity (10087). Supposed that the assumed currents have relation to the line of approach (joining the gravitating bodies) and not to space generally. Hence that 2 bodies approaching or receeding would have opposite directions as to space generally, though the same as to the line of approach.

10935. Else two bodies approaching would have opposite poles in the surfaces toward each other, and tend by their approach merely to cause a force of attraction—which would lead to inconsistent consequences, for then a body between 2 others would be in instable equilibrium, for the least approach towards one would make it continue to approach that one and recede from the other.

5 _Diary_ 323, entries for July 20, 1850.

We may see in this discussion all of the essential elements underlying the convergence of two helical waveforms and the right-hand rule in entries 10087 and particularly the last sentence of 10088. The only thing that is missing is the last step of the "insight" to recognize that the two converging helices, both under unidirectional rotation (the right-hand rule), would 'intertwine" with each other into a "singularity." Thus, throughout all of Faraday's description of sparks, electrical "brushes." and so forth, he did not put "two and two together" to get "one," i.e., the mechanism by which the spark was actually generated.

The second issue that Faraday does not address is "Under what conditions does magnetism come into being?" for it is that question that unlocks the door to the relationship between gravity and magnetism, and therefore to electromagnetism. If we take the Earth as a giant spherical magnet, all magnets on its surface will align themselves along the lines of force between the poles. All of this had been known since classical antiquity and is expressly stated in Gilbert's _On the Loadstone_. The point is "What is the meaning of all this? " More simply, what is the relationship of the magnet to the Earth's own magnetism and its magnetic poles? Simply, a magnet is a segment of the Earth's magnetic circuit. Because it is a segment and has been separated from the circuit it continues to retain and maintain its polarization without completion. Thus magnetism ONLY comes into existence when the circuit is severed . . . _the_ mechanism underlying the primary principle. Such a fundamental question can ONLY be raised by a Socratic philosophical inquiry that is inherently NOT within the scope of mathematical physics. Accordingly, there is no reasonable expectation that mathematical physics would ever have come upon the primary principle, again, not because of the lack of intellect or knowledge by those who pursue it but because the inherent nature of the method of inquiry is foreign to their training and ways of thinking. What is astonishing is that this is perhaps the only question that Faraday never did ask!

In setting out to advance a new fundamental theory, three tests are generally applied:

1. The theory must leave undisturbed the successes of earlier work and not upset explanations of observations that have been used in support of earlier ideas;

2. The theory must explain in a reasonable manner new evidence that brought the previous ideas into doubt and that suggest the new hypotheses; and

3. The theory must predict new phenomena or new relationships between different phenomena that were not known or not clearly understood at the time when it was invented.

Although the present investigation did not begin with those specific propositions in mind but rather with the criteria that the theory should resolve previously conflicting views and unresolved issues through a simple, elegant, and obvious insight [once it was seen] to underlying basic principles, these criteria are equally workable from which to judge the efficacy of the proffered theories and to give clarity and structure to the discussion.

The essential question still remains "How do we define time outside the human context?" How is time defined in physical terms? Time may be defined in physical terms as the change in the size and location of mass in a mass-energy conversion system that results in the emission of electromagnetic radiation. Although the concept of circular and/or spherical time had been addressed as early as Aristotle, only Faraday actually seems to have sought to integrate it with electricity, magnetism, and motion (subsequently spacetime) into a single three-dimensional spherical geometry.

403. The mutual relation of electricity, magnetism and motion may be represented by three lines at right angles to each other, any one of which may represent any one of these points and the other two lines the other points. Then if electricity be determined in one line and motion in another, magnetism will be developed in the third; or if electricity be determined in one line and magnetism in another, motion will occur in the third. Or if magnetism be determined first then motion will produce electricity or electricity motion. Or if motion be the first point determined. Magnetism will evolve electricity or electricity magnetism. (Figure 38)

1 _Diary_ 425, entry for March 26, 1832.

As we have seen, Faraday's model adequately defines the dynamics, without revealing the primary principle, of the unified field, and as we shall see, it adequately describes pure field theory as well. If we take acceleration and gravity as demonstrated in Model 1, we can give a renewed consideration and viability to Einstein's own suggestion of what it may be like to travel at the velocity of light and look at a nearby beam of light traveling parallel to us. In his "Autobiographical Notes, " _Problems of Space and Time_ , he writes;

If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as a spatially oscillatory electromagnetic field at rest. However, there seems no such thing, whether on the basis of experience or according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, is at rest. For how, otherwise, should the first observer know, i.e., be able to determine, that he is in a state of fast uniform motion?

One sees in this paradox the germ of the special relativity theory is already contained. Today everyone knows, of course, that all attempts to clarify this paradox satisfactorily were condemned to failure as long as the axiom of the absolute character of time, viz., of simultaneity. Unrecognizably we anchored in the unconscious.

If under the general theory of relativity gravity and acceleration are variants of the same phenomena, and gravity and electromagnetism are descriptively the same, then gravity, electromagnetism and acceleration may also be descriptive of the same phenomena. Under the principle of equivalence of the general theory, a body in situ generates a gravitational field geometrically the same as one generating an electromagnetic field.

In his "On the Electrodynamics of Moving Bodies," _The Principle of Relativity,_ [hereinafter "Electrodynamics"] Einstein states that "it follows, further, that the velocity of light c cannot be altered by composition with a velocity less than that of light." However, it is possible to combine discrete frequencies of other portions of the electromagnetic spectrum all of which are traveling at the velocity of light into a coagulation of frequencies that have a mass equal to the photon as Newton demonstrated in his _Opticks_. The electromagnetic spectrum is therefore a medium that is capable of being compressed as well as diffused and this "densification and rarification," to use Newton's terms, occurs not along lines of velocity but along lines of frequency. Therefore since the velocity of light does not vary amongst all of the variant forms of radiation, we can nominalize all frequencies to the same velocity so that the time element of velocity is no longer of concern, leaving only frequency, i.e., the photoelectric effect, quanta being "nominalized", i.e., a "constant."

If an aggregate of waveforms of different frequencies and amplitudes were to converge at a locus, their constituent frequencies would converge to a mass whose energy would be a composite of the frequencies and amplitudes of the waveforms and whose density would be that of the constituent energies of the converging waves. Through the compressive force of the electromagnetic field we have a mechanism that resolves Newton's quandary about "negative gravity" and the inherent energy to compress mass at a locus. We can equally anticipate that a vortex of radiation at less than the density necessary to generate light may equally exist as a precursor to a luminous body and that itself may generate radiation at below those of the visible frequencies. On this basis we can look at non-luminous sources of radiation in the Universe as stellar precursors, proto-singularities, or "neo-entities" that are still at the early stage of condensation of a magnetic vortex and have not yet established a defined geometry at a locus. (Above at Figure 15) As the gravitational field is the result of the convergence of the electromagnetic field at a locus, and a photon is no less the product of the same process, it therefore is no less reasonable that the photon would equally be affected by a gravitational field as would any other mass, presuming we attribute mass to the photon. This of course was the _experimenta crucis_ of general relativity and is but an extension of the mechanism of the propagation of radiation that Maxwell and Hertz equated with light and that Einstein described in general terms as

All our space-time verifications invariably amount to a determination of space-time coincidences. If, for example, events consisted merely in the motion of material points, then ultimately nothing would be observable but the meetings of two or more of these points. Moreover, the results of our measurings are nothing but verifications of such meetings of the material points of our measuring instruments with other material points, coincidences between the hands of a clock and points on the clock dial, and observed point-events happening at the same place at the same time.

"The Foundation of the General Theory of Relativity," _The Principle of Relativity_ at 117.

What is presented here is that not only are we dealing with space-time coincidences but that space-time-mass-energy consists of and constitutes an inseparable, integrated unity. Of interest is Einstein's association between spacetime and the face of a clock, the ultimate device that integrates them into the same entity and demonstrates their physical and philosophical inseparability. Thus, under the present theory, there is no need to make any mechanical, physical, or philosophical distinction between gravitational fields in the general theory and electromagnetic forces, to introduce gravitational constants as postulated under the general theory, or to distinguish the gravitational field from matter and the electromagnetic field.

Under the present theory we address at least one issue left outstanding by Einstein, namely,

In particular it may remain an open question whether the theory of the electromagnetic field in conjunction with that of the gravitational field furnishes a sufficient basis for the theory of matter or not. The general postulate of relativity is unable on principle to tell us anything about this. It must remain to be seen, during the working out of the theory, whether electromagnetics and the doctrine of gravitation are able in collaboration to perform what the former by itself is unable to do.

"The Foundation of the General Theory of Relativity" at 152.

We come now to the consideration of the uniform density of matter in a finite (spherical) Universe as postulated by Einstein. First, the present theory takes the position that the Universe is infinite and since it is infinite it has no definite outer boundary. Secondly, finitude is not a requisite to make the present theory philosophically or physically nice, nor to make it operationally viable. Thirdly, there is a reasonable inference that the propagation of radiation from a spherical body propagates omnidirectional equipotential forces with equal intensity and therefore exerts uniform radiation pressure into interstellar space. The corollary inference is equally reasonable that the omnidirectional equipotential propagation of radiation operates as an omnidirectional equipotential compressive force capable of inducing mass to a locus and compacting it to a sphere. Both of these conditions are readily observable as the omnidirectional equipotential propagation of light from distant stars and as the vortices that condense solar dust into proto-stars. Although the present theory is not inconsistent with Einstein's view that space is curved the present theory expands that view to be more consistent with the electromagnetic model in which the curvature is attributable to the various gradations in the density of the lines of force around a gravitational body (nucleus) and therefore brings the general theory into harmony with quantum mechanics that Einstein held suspect because it involved inherent uncertainties too shocking to a classically trained mathematical physicist as was he.

Figure 35 Illustration associated with entry 10086.

Figure 36 Illustration associated with entry 10087.

Figure 37 Illustration associated with entry 10104.

Figure 38 Illustration associated with entry 403.

**Chapter** **2.9 MAXWELL: MOLECULAR VORTICES AND GRAVITY**

If Aristotle described what the elements of the primary principle were if they were but to be found, and Newton described the universal force of gravity, and Faraday described the universal lines of force that constitute the field, then Maxwell brings us to the threshold of the discovery of the unified field theory albeit that was not his objective on the one hand and on the other he was not oblivious that his articulation of Faraday's work in some ways suggested that deeper answers about the nature of existence may well be just beyond the limitations of his (Maxwell's) own work. We must always remember that Einstein's special theory is an explanation of the "electrodynamics of moving bodies (electrons)" and that Einstein himself was a product of classical Maxwellian electrodynamics subsequently expanded by Poisson and Lorentz. As with Aristotle, our concern is not with what Maxwell solved but rather with that which he declined to pursue and that which he failed to perceive (nonsight). It is essential to keep in mind that Maxwell recognized and explicitly acknowledged that he himself was not a principal investigator but rather a translator of Faraday's discoveries into mathematical language, and in the two areas where Maxwell did make fundamental intuitive connections—that light was an electromagnetic phenomena and that electromagnetic waves are propagated by electricity—he himself conducted no experimental work in those areas, the former essentially left to Edison and the latter to Hertz. Finally, Maxwell, notwithstanding his outstanding academic achievements and mathematical prowess, was not philosophically oriented toward discovering deep fundamental truths about the nature of existence, whereas Faraday for all of his lack of formal education had that philosophical talent . . . well actually genius!

Maxwell's major work, the _Treatise on Electricity and Magnetism,_ is divided into electrostatics and electromagnetics. Notwithstanding that he showed the mathematical unity between the two, he neither advanced nor hypothesized their underlying unity. As with Aristotle, Maxwell described the primary principle; but he did not perceive it. Accordingly, his mathematical presentation per se has little if any interest here—except for conjugates. If anything, we are returning to the simple, straightforward nonmathematical comments that occasionally appear in the _Treatise_ and that are the hallmark of Faraday's own style.

The _Treatise_ itself is divided into a "Preliminary" and four substantive parts:  
Electrostatics" (Part I), "Electrokinetics" (Part II), "Magnetics" (Part III), and "Electromagnetics" (Part IV).

PRELIMINARY

The "Preliminary" discussion addresses fundamental mathematical concepts, units of measure, and so forth, of which our interest here is primarily "force" and the "equation of continuity" that postulates the continuous existence of a particle of matter in time and space as it moves from one location or condition to another. In simple language the particle does not just "poof" appear here and "poof" appear there without moving and existing continuously between the "here" and the "there." Of the Cartesian coordinate system that lies at the heart of all his mathematical presentations we have consolidated and nominalized all of that into the unit sphere. The "lines of force" as mathematical entities have been abandoned and reinstated as empirical entities as Faraday first expressed them and demonstrated their existence by sprinkling iron filings onto a surface adjacent to a magnet. We retain Maxwell's definition of right-hand and left-hand relations in space as essential to our discussion on polarity, opolarity, unidirectional time, and the great range of other concepts that are derived therefrom, and in particular as they relate to "perversion," "inversion," and conjugate spatial relationships between juxtaposed polarized entities and fields. For our purpose, the various vector orientations—vectors directed toward an internal point (convergence) and vectors tangential to a point (rotation) are combined into a vector describing a vortex. The rest of the discussion involves integration not relevant to the presentation here.

ELECTROSTATICS

As stated above, Maxwell—even more precisely than Aristotle—describes the mechanism of the primary principle as a physical activity without recognizing the process.

27.] EXPERIMENT I. Let a piece of glass and a piece of resin, neither of which exhibits any electrical properties, be rubbed together and left with the rubbed surfaces in contact. They will still exhibit no electrical properties. Let them be separated. They will now attract each other.

If a second piece of glass be rubbed with a second piece of resin, and if the pieces be then separated and suspended in the neighbourhood of the former pieces of glass and resin, it may be observed—

(1) That the two pieces of glass repel each other.

(2) That each piece of glass attracts each piece of resin.

(3) That the two pieces of resin repel each other.

These phenomena of attraction and repulsion are called Electrical phenomena, and the bodies which exhibit them are said to be _electrified_ , or to be _charged with electricity_.

1 _Treatise on Electricity and Magnetism_ 32.

As we have set out above, the essence of establishing an electrostatic condition is not in the rubbing per se but in the mechanical "bonding" that is induced by the friction between the two entities and then the separation/severance of the induced entity thereafter. The rest of the discussion, induction, conduction, and so forth is merely the consequence of the polarity and opolarity induced into the system and the surrounding medium by the initiating severance. As to what electricity is—other than that it is always a bifurcated process involving equal amounts of "positive" and 'negative" Maxwell provides us with no clue.

35.] While admitting electricity, as we have now done, to the rank of a physical quantity, we must not too hastily assume that it is, or is not, a substance, or that it is, or is not, a form of energy, or that it belongs to any known category of physical quantities. All that we have hitherto proved is that it cannot be created or annihilated, so that if the total quantity of electricity within a closed surface is increased or diminished, the increase or diminution must have passed in or out through the closed surface.

* * * * * * *

If we ever should obtain distinct mechanical ideas of the nature of electric potential, we may combine these with the idea of energy to determine the physical category in which 'Electricity' is to be placed.

36.] In most theories on the subject, Electricity is treated as a substance, but in as much as there are two kinds of electrification which, being combined, annul each other, and since we cannot conceive of two substances annulling each other, a distinction has been drawn between Free Electricity and Combined Electricity.

1 _Treatise on Electricity and Magnetism_ 38-39.

Maxwell respectfully recognizes the two camps of electricians—those advocating the "two fluid" model (positive and negative electricity) and those advocating the "one fluid" model (one is merely ordinary matter and the other is the "electric fluid"). Clearly what has occurred is that electricity has evolved from a substance to a matter to a fluid, which is merely another semantic method of resolving the irresolvable. As to Maxwell himself

* * * For my own part, I look for additional light on the nature of electricity from a study of what takes place in the space intervening between the electrified bodies. Such is the essential character of the mode of investigation pursued by Faraday in his _Electrical Researches_ , and as we go on I intend to exhibit the results, as developed by Faraday, W. Thomson, &c., in a connected and mathematical form, so that we may perceive what phenomena are explained equally well by all the theories, and what phenomena indicate the peculiar difficulties of each theory.

1 _Treatise on Electricity and Magnetism_ 43.

Undoubtedly even Aristotle recognized that properly rubbed amber (Gk. elektron; amber, a substance that develops electricity under friction) clearly had the capacity to both attract and repel other similarly polarized entities and that pieces of magnesia could both attract and repel other pieces of magnesia, all of which were described in great detail in Gilbert's great work _On the Magnet_. Following Faraday, Maxwell elevates this phenomena to a "force" that may itself be propagated into the space adjoining a polarized entity—"the field."

_The Electric Field_.

44.] The Electric Field is the portion of space in the neighbourhood of electrified bodies, considered with reference to electric phenomena. It may be occupied by air or other bodies, or it may be a so-called vacuum, from which we have withdrawn every substance which we can act upon with the means at our disposal.

If an electrified body be placed at any part of the electric field it will, in general, produce a sensible disturbance in the electrification of the other bodies.

1 _Treatise on Electricity and Magnetism_ 47-48.

The space—the field—is itself under a state of stress or tension caused by the lines of force that emanate from an electrified entity such that other entities situated in the field will themselves become affected by the stress or tension induced into the field.

The word Tension has been used by electricians in several vague senses, and it has been attempted to adopt it in mathematical language as a synonym for Potential; but on examining the cases in which the word has been used, I think it will be consistent with usage and with mechanical analogy to understand by tension a pulling force of so many pounds weight per square inch exerted on the surface of a conductor or elsewhere. We shall find that the conception of Faraday, that this electric tension exists not only at the electrified surface but all along the lines of force, leads to a theory of electric action as a phenomenon of stress in a medium.

The significance of the electric glow, brush, and spark did not go unnoticed although unexplained. These, and many other phenomena of electrical discharge, are exceedingly important, and when they are better understood they will probably throw great light on the nature of electricity as well as on the nature of gases and of the medium pervading space. At present, however, they must be considered as outside the domain of the mathematical theory of electricity.

1 _Treatise on Electricity and Magnetism_ 51.

As advanced herein these phenomena are the indicia of the pulling apart and severance of spherical time. Since our perspective is cosmological, and the cosmos is infinite, Maxwell's effort to determine the total energy in the cosmos is Herculean. Maxwell, as postulated by Faraday, recognizes that the stress in the field that is associated with the electric tension results in a pressure perpendicular to the lines of force.

The nature of the stress is, as Faraday pointed out*, a tension along the lines of force combined with an equal pressure in all directions at right angles to these lines. The magnitude of these stresses is proportional to the energy of the electrification per unit of volume, or, in other words, to the square of the resultant electromotive intensity multiplied by the specific inductive capacity of the medium.

*Exp. Res., series xi, 1297.

1 _Treatise on Electricity and Magnetism_ 63.

Although Faraday decidedly gave the field an empirical existence, Maxwell brings it into the fold of academic mathematical physics. For our purposes, however, he does more, for he incorporates the lines of force and their pressure into a pressurized medium between bodies that is philosophically essential to prove the equation of continuity.

60.] From the hypothesis that electric action is not a direct action between bodies at a distance, but is exerted by means of the medium between the bodies, we have deduced that this medium must be in a state of stress. We have also ascertained the character of the stress, and compared it with the stresses which may occur in solid bodies. Along the lines of force there is tension, and perpendicular to them there is pressure, the numerical magnitude of these forces being equal, and each proportional to the square of the resultant intensity at the point. Having established these results, we are prepared to take another step, and to form an idea of the nature of the electric polarization of the dielectric medium.

1 _Treatise on Electricity and Magnetism_ 64.

That medium, as I have advanced above, and as Maxwell will do later in the "Magnetics," is the æther. Within the limits of his theory, Maxwell comes to the conclusion:

61.] We are thus led to a very remarkable consequence of the theory which we are examining, namely, that the motions of electricity are like those of an _incompressible_ fluid, so that the total quantity within an imaginary fixed closed surface remains always the same.

1 _Treatise on Electricity and Magnetism_ 67-68.

As we shall see, the problem of "incompressibility" lies at the heart of unified and pure field theory. Maxwell models his theory on hydrostatics, which although similar to the dynamics of the field, is really inapposite to its mechanism. A hydrostatic model does not account for the condensation and densification of mass and energy that is everywhere evident in the Universe of which we, as well as Maxwell, are the proof. But we must also recognize that his model is not predicated on an inclusive unified theory, much less cosmology!

Potential, in electrical science, has the same relation to Electricity that Pressure, in Hydrostatics, has to Fluid, or that Temperature, in Thermodynamics, has to Heat.

1 _Treatise on Electricity and Magnetism_ 79.

As with all of extant physics, the _Treatise_ is a substance-matter driven theory whose purpose is to measure and quantify electrical phenomena, of which we have no particular interest here.

Having worked through a great deal of mathematics to determine that the stress in the field surrounding an electrified entity constitutes an equipotential medium, Maxwell translates this stress to pressure, a very critical translation.

109.] The distribution of stress considered in this chapter is precisely that to which Faraday was led in his investigation of induction through dielectrics. He sums up in the following words:

'(1297) The direct inductive force, which may be conceived to be exerted in lines between the two limiting and charged conducting surfaces, is accompanied by a lateral or transverse force equivalent to a dilatation or repulsion of these representative lines (1224); or the attractive force which exists amongst the particles of the dielectric in the direction of the induction is accompanied by a repulsive or diverging force in the transverse direction.

'(1298) Induction appears to consist in a certain polarized state of the particles, into which they are thrown by the electrified body sustaining the action, the particles assuming positive and negative points or parts, which are symmetrically arranged with respect to each other and the inducting surfaces or particles. The state must be a forced one, for it is originated and sustained only by force, and sinks to the normal or quiescent state when that force is removed. It can be _continued_ only in insulators by the same portion of electricity, because they only can retain this state of the particles.'

This is an exact account of the conclusions to which we have been conducted by our mathematical investigation. At every point of the medium there is a state of stress such that there is tension along the lines of force and pressure in all directions at right angles to these lines, the numerical magnitude of the pressure being equal to that of the tension, and both varying as the square of the resultant force at the point.

1 _Treatise on Electricity and Magnetism_ 164.

However, Maxwell goes no further with the concept.

It must be carefully borne in mind that we have made only one step in the theory of the action of the medium. We have supposed it to be in a state of stress, but we have not in any way accounted for this stress, or explained how it is maintained. This step, however, seems to me to be an important one, as it explains, by the action of the consecutive parts of the medium, phenomena which were formerly supposed to be explicable only by direct action at a distance.

111.] I have not been able to make the next step, namely, to account by mechanical considerations for these stresses in the dielectric. I therefore leave the theory at this point, merely stating what are the other parts of the phenomenon of induction in dielectrics.

1 _Treatise on Electricity and Magnetism_ 165-166.

That problem has been resolved here by opolarity in which juxtaposed polarized states repel each other such that they therefore induce a pressure on the interlineating medium—the field. Thus although Maxwell recognizes that the field is in a state of stress and that that stress can be translated to pressure, and that similarly charged entities repel each other, he—nor anyone else since—relates those states such that the former in conjunction with the latter can actually produce a mechanical pressure in the medium, although the mechanical action of attraction and repulsion had been empirically known since classical antiquity. Prior to Model 1, as Maxwell himself demonstrates in Chapter VII, "Forms of the Equipotential Surfaces and Lines of Induction in Simple Cases," the lines of force always connect one entity with another, and except for the equation of continuity, the interlineating space has itself no real empirical significance per se. Of equal importance, the perspective is always "one sided," i.e., of looking from one entity to the other without ever considering the relativistic relationship between the two simultaneously, or of equal significance, of the entities in the perspective of an n-entity problem. As advanced in my introductory comments, the solution to the unified and pure field theories would not be for want of intellect but for want of insight about some fundamental deficiency in the perspective of the problem. This deficiency is explicitly made evident in Maxwell's definition of "Force" and "stress."

The word Force denotes a restricted aspect of that action between two material bodies by which their motions are rendered different from what they would have been in the absence of that action. The whole phenomenon, when both bodies are contemplated at once, is called Stress, and may be described as transference of momentum from one body to the other. When we restrict our attention to the first of the two bodies, we call the stress acting on it the Moving Force, or simply the Force on that body, and it is measured by the momentum which that body is receiving per unit of time.

The mechanical action between two charged bodies is a stress, and that on one of them is a force. The force on a small charged body is proportional to its own charge, and the force per unit of charge is called the Intensity of the force.

The word Induction was employed by Faraday to denote the mode in which the charges of electrified bodies are related to each other, every unit of positive charge being connected with a unit of negative charge by a line, the direction of which, in fluid dielectrics, coincides at every part of its course with that of the electric intensity. Such a line is often called a line of Force, but it is more correct to call it a line of Induction.

1 _Treatise on Electricity and Magnetism_ 182.

Under this scheme, A acts on B, and B on A. The n-body problem of the cumulative force that both A and B have on C . . . Z and reciprocally on each other so as to generate an interlineating equipotential field of homogeneous pressure is not raised by Maxwell nor anyone since. In Maxwellian terms, when the rotatory vector combines with the right-hand rule to converge the lines of force upon a point the vector generates a pressurized vortex that results in the "physicalization" of the vector itself—Model 1. The only aspect of Maxwell's mathematics that is of concern here, and for our purpose since this is a nonmathematical discussion, a small point at that, is his discussion of inversion, perversion, and conjugates, that he himself does not consolidate into a single concept. The combination of the three provides a means by which two right-hand waveforms converge upon each other from opposite directions so that they form a singularity, namely Figure 39. The perversion constitutes the symmetry, the inversion constitutes the 180° translation from quadrant I to III, and the conjugate _i_ (√-1) reverses the right-hand waveform in I to _another_ right-hand waveform coming back to the origin from III; or more simply it is the mathematical representation of two right-hand waveforms converging on each other. Although this would be the same as the same waveform reflected upon itself, in the unified and pure field theories it is two distinct waveforms coming from opposite directions. We should also recognize that this is the mathematical description by which attraction becomes repulsion and conversely repulsion becomes attraction that no one ever seems to have posed and therefore no one ever seems to have addressed. The empirical solution would not have been possible without the articulation of opolarity as unidirectional time that itself is embodied as the right-hand rule.

Of particular interest here, since it concerns electrical inversion and electrical images;

On Electrical Inversion.

162.] The method of electrical images leads directly to the method of transformation by which we may derive from any electrical problem of which we know the solution any number of other problems with their solutions.

1 _Treatise on Electricity and Magnetism_ 253.

is the inference that the pressure in the medium must be equipotential since all celestial objects are spherical, and the sphere is itself the result of the convergence of omnidirectional equipotential forces. In other words, the form itself evidences the forces applied to it and its trajectory evidences the lines of force that exist in the field. Although Einstein and general relativists interpret this as "curved space," that description misinterprets the dynamics of the field in the same way that it would be inappropriate to say that the quantum mechanical particle orbits according to the curved space around a nucleus.

The mathematical derivation by which Maxwell intuits that electricity propagates in waves and the extensive experiments of Hertz is superceded by one turn of the handle of Model 1.

MAGNETISM

We have previously traced magnetism and polarization to the severance of spherical unidirectional time through the primary principle so that we need not explicate Maxwell's discussion hereto.

ELECTROMAGNETISM

Notwithstanding that electrostatics may have a certain interest in meteorology and some other areas, our real concern in the present study is electromagnetism, and more particularly the permanent horseshoe magnet as the form that most conveniently demonstrates the principles with which we are concerned. The extent to which traditionally taught physicists are precluded from getting even a hint of the primary principle as the stepping stone to pure field theory is illustrated in Maxwell's "Figure 25" that shows three right-hand waveforms intersecting at the origin of the x, y, and z axes of a Cartesian coordinate system. (Figure 40) They intersect but do not converge! Since all of mathematical physics is based on the same perspective, it is constitutionally precluded from proffering a solution to unified and pure field theory. In fact, the only possible hint of such a solution lies in the esoterica √-1 whose relationship to attraction and repulsion is so far off the beaten track of both mathematics and mathematical physics that the mere attempt to give it a geometrical construction has itself remained a puzzlement, and although √-1 has found some place in alternating current theory, that area of electricity is completely devoid of even a hint of anything like opolarity as a substantive operative concept. i.e., grounded in unidirectional time and so forth. Quite obviously, the difference between the theory and construction of "Figure 25" and Model 1 are worlds apart, which ultimately makes all the difference in the world.

But a conducting circuit in which a current has been set up has the power of doing work in virtue of this current, and this power cannot be said to be something very like energy, for it is really and truly energy.

Thus, if the current be left to itself, it will continue to circulate till it is stopped by the resistance of the circuit. Before it is stopped, however, it will have generated a certain quantity of heat, and the amount of this heat in dynamical measure is equal to the energy originally existing in the current.

Again, when the current is left to itself, it may be made to do mechanical work by moving magnets, and the inductive effect of these motions will, by Lenz's law, stop the current sooner than the resistance of the circuit alone would have stopped it. In this way part of the energy of the current may be transformed into mechanical work instead of heat.

552.] It appears, therefore, that a system containing an electric current is a seat of energy of some kind; and since we can form no conception of an electric current except as a kinetic phenomenon*, its energy must be kinetic energy, that is to say, the energy which a moving body has in virtue of its motion.

We have already shewn that the electricity in the wire cannot be considered as the moving body in which we are to find this energy, for the energy of a moving body does not depend on anything external to itself, whereas the presence of other bodies near the current alters its energy.

We are therefore led to enquire whether there may not be some motion going on in the space outside the wire, which is not occupied by the electric current, but in which the electromagnetic effects of the current are manifested.

I shall not at present enter on the reasons for looking in one place rather than another for such motions, or for regarding these motions as of one kind rather than another.

What I propose now to do is to examine the consequences of the assumption that the phenomena of the electric current are those of a moving system, the motion being communicated from one part of the system to another by forces, the nature and laws of which we do not yet even attempt to define, because we can eliminate these forces from the equations of motion by the method given by Lagrange for any connected system.

*Faraday, Exp. Res. 283.

2 _Treatise on Electricity and Magnetism_ 197-198.

As advanced above, the source of the energy that moves the system and the force underlying it is unidirectional time that we perceive as the right-hand rule, polarity and its obverse opolarity.

But all that we assume here is that the electric current involves motion of some kind. That which is the cause of electric currents has been called Electromotive Force. This name has long been used with great advantage, and has never led to any inconsistency in the language of science. Electromotive force is always to be understood to act on electricity only, not on the bodies in which the electricity resides. It is never to be confounded with ordinary mechanical force, which acts on bodies only, not on the electricity in them. If we ever come to know the formal relation between electricity and ordinary matter, we shall probably also know the relation between electromotive force and ordinary force.

2 _Treatise on Electricity and Magnetism_ 212.

As Model 1 demonstrates, the electric current embodied in the lines of force are fully capable of exerting an electromotive force upon matter as well as direct mechanical action at a distance.

The action of magnets at a distance is perfectly identical with that of electric currents. We therefore endeavour to trace both to the same cause, and since we cannot explain electric currents by means of magnets, we must adopt the other alternative, and explain magnets by means of molecular electric currents.

638.] In our investigation of magnetic phenomena, in Part III of this treatise, we made no attempt to account for magnetic action at a distance, but treated this action as a fundamental fact of experience. We therefore assumed that the energy of a magnetic system is potential energy, and that this energy is _diminished_ when the parts of the system yield to the magnetic forces which act on them.

If, however, we regard magnets as deriving their properties from electric currents circulating within their molecules, their energy is kinetic, and the force between them is such that it tends to move them in a direction such that if the strengths of the currents were maintained constant the kinetic energy would _increase_.

This mode of explaining magnetism requires us also to abandon the method followed in Part III, in which we regarded the magnet as a continuous and homogeneous body, the minutest part of which has magnetic properties of the same kind as the whole.

We must now regard a magnet as containing a finite, though very great, number of electric circuits, so that it has essentially a molecular, as distinguished from a continuous structure.

2 _Treatise on Electricity and Magnetism_ 275.

In Chapter XX, "Electromagnetic Theory of Light," Maxwell introduces his hypothesis that the electromagnetic medium that exists between a sender and receiver of action at a distance is identical to the medium through which light passes from an emitter to a receiver—the luminiferous medium; in classical terms the æther. Maxwell's argument, however, is considerably different than that demonstrated in Model 1. Rather, he makes the identity through the coincidence of the velocity of light and the velocity with which an electrical disturbance is propagated in the medium.

78.] In several parts of this treatise an attempt has been made to explain electromagnetic phenomena by means of mechanical action transmitted from one body to another by means of a medium occupying the space between them. The undulatory theory of light also assumes the existence of a medium. We have now to shew that the properties of the electromagnetic medium are identical with those of the luminiferous medium.

To fill all space with a new medium whenever any new phenomenon is to be explained is by no means philosophical, but if the study of two different branches of science has independently suggested the idea of a medium, and if the properties which must be attributed to the medium in order to account for electromagnetic phenomena are of the same kind as those which we attribute to the luminiferous medium in order to account for the phenomena of light, the evidence for the physical existence of the medium will be considerably strengthened.

But the properties of bodies are capable of quantitative measurement. We therefore obtain the numerical value of some property of the medium, such as the velocity with which a disturbance is propagated through it, which can be calculated from electromagnetic experiments, and also observed directly in the case of light. If it should be found that the velocity of propagation of electromagnetic disturbances is the same as the velocity of light, and this not only in air, but in other transparent media, we shall have strong reasons for believing that light is an electromagetic phenomenon, and the combination of the optical with the electrical evidence will produce a conviction of the reality of the medium similar to that which we obtain, in the case of other kinds of matter, from the combined evidence of the senses.

2 _Treatise on Electricity and Magnetism_ 431.

Interestingly, although the present theory is not concerned with proving that light is an electromagnetic phenomena, Maxwell's argument is equally persuasive in establishing the medium as a pressurized field of radiation.

782.] When light is emitted, a certain amount of energy is expended by the luminous body, and if the light is absorbed by another body, this body becomes heated, showing that it has received energy from without. During the interval of time after the light left the first body and before it reached the second, it must have existed as energy in the intervening space.

According to the theory of emission, the transmission of energy is effected by the actual transference of light-corpuscules from the luminous to the illuminated body, carrying with them their kinetic energy, together with any other kind of energy of which they may be the receptacles.

According to the theory of undulation, there is a material medium which fills the space between the two bodies, and it is by the action of contiguous parts of this medium that the energy is passed on, from one portion to the next, till it reaches the illuminated body.

The luminiferous medium is therefore, during the passage of light through it, a receptacle of energy. In the undulatory theory, as developed by Huygens, Fresnel, Young, Green, &c, this energy is supposed to be partly potential and partly kinetic. This potential energy is supposed to be due to the distortion of the elementary portions of the medium. We must therefore regard the medium as elastic. The kinetic energy is supposed to be due to the vibratory motion of the medium. We must therefore regard the medium as having a finite density.

In the theory of electricity and magnetism adopted in this treatise, two forms of energy are recognised, the electrostatic and the electrokinetic (see Arts. 630 and 636), and these are supposed to have their seat, not merely in the electrified or magnetized bodies, but in every part of the surrounding space, where electric or magnetic force is observed to act. Hence our theory agrees with the undulatory theory in assuming the existence of a medium which is capable of becoming a receptacle of two forms of energy*.

* 'For my part, considering the relation of a vacuum to the magnetic force and the general character of magnetic phenomena external to the magnet, I am more inclined to the notion that in the transmission of the force there is such an action, external to the magnet, than that the effects are merely attraction and repulsion at a distance. Such an action may be a function of the æther; for it is not at all unlikely that, if there be an æther, it should have other uses than simply the conveyance of radiations.'—Faraday's Experimental Researches, 3075.

2 _Treatise on Electricity and Magnetism_ 432.

Our perspective and reasoning are somewhat different though it may equally be derived from the _Treatise_. We begin, as did Maxwell, with the proposition that light is transmitted from the emitter to the receiver in conformance with the equation of continuity. We also accept as a proposition that during its journey from the emitter to the receiver the corpuscle of light is propagating a polarized electromagnetic field perpendicular to the line of its trajectory, which field when juxtaposed to a like field generates opolarity identical in every respect with the space unoccupied by grains of iron sprinkled onto a surface that demonstrates the empirical existence of the lines of force. Presumptively, every luminous body emits light essentially uniformly, omnidirectionally, and perpendicularly from its surface, whether it be a photon or a star. At this point, we must reiterate that the perceiver of light perceives only that light that it perceives and that all other rays are not perceived so that the energy of the other rays perpetuates in space indefinitely until it converges at a locus. That is, the radiation generated by all n-bodies in an n-body field results in a field having an equipotential uniform radiation pressure so uniform that it can generate a sphere within the field itself. Accordingly, the æther—the interstellar medium—is the repository of all of the energy emitted by all of the mass-energy conversion processes in the Universe and is also the emitter of that energy itself, and therein lies the resolution of the outstanding issue in my answer to my nephew. Maxwell's discussion of "Plane Waves" accords with the above reasoning and with Model 1 in which the waves not only generate a magnetic force, but being polarized, generate a ponderomotive kinetic force capable of moving mass in the medium itself, whether it be a test tube or interstellar space.

In virtue of the electrokinetic state of the medium there is a tension equal to _p_ in the direction parallel to _y_ , combined with a pressure equal to _p_ in directions parallel to _x_ and _z_. See Art. 643.

Hence the combined effect of the electrostatic and electrokinetic stresses is a _pressure_ equal to _2_ _p_ in the direction of the propagation of the wave. Now _2 p_ also expresses the whole energy in unit of volume.

Hence in a medium in which waves are propagated there is a pressure in the direction normal to the waves, and numerically equal to the energy in unit of volume.

2 _Treatise on Electricity and Magnetism_ 440-441.

Whatever light is, at each point of space there is something going on, whether displacement, or rotation, or something not yet imagined, but which is certainly of the nature of a vector or directed quantity, the direction of which is normal to the direction of the ray. This is completely proved by the phenomena of interference.

2 _Treatise on Electricity and Magnetism_ 460.

Maxwell, however, is unable to detect or speculate as to any periodic frequency—wavelength—associated with a magnetic current and therefore does not proffer either a mathematical or philosophical basis for its existence. Instead, frequency implies the vorticity of electromagnetism, i.e., an electric current is only generated by magnetic forces when there is a relativistic change in the spatial relations of the components.

There is nothing, therefore, in the magnetic phenomenon which corresponds to the wave-length and the wave-propagation in the optical phenomenon. A medium in which a constant magnetic force is acting is not, in consequence of that force, filled with waves traveling in one direction, as when light is propagated through it. The only resemblance between the optical and the magnetic phenomenon is, that at each point of the medium something exists of the nature of an angular velocity about an axis in the direction of the magnetic force.

2 _Treatise on Electricity and Magnetism_ 461.

On the grand scale, however, the cumulative effect results in a series of vortices capable of rotating subatomic particles, ball bearings, celestial bodies, solar systems, and galaxies.

I think we have good evidence for the opinion that some phenomenon of rotation is going on in the magnetic field, that this rotation is performed by a great number of very small portion of matter, each rotating on its own axis, this axis being parallel to the direction of the magnetic force, and that the rotations of these different vortices are made to depend on one another by means of some kind of mechanism connecting them.

The attempt which I then made to imagine a working model of this mechanism must be taken for no more than it really is, a demonstration that mechanism may be imagined capable of producing a connexion mechanically equivalent to the actual connexion of the parts of the electromagnetic field. The problem of determining the mechanism required to establish a given species of connexion between system always admits of an infinite number of solutions. Of these, some may be more clumsy or more complex than others, but all must satisfy the conditions of mechanism in general.

2 _Treatise on Electricity and Magnetism_ 470.

As previously stated, notwithstanding all of the above, Maxwell still does not abandon the Aristotelian predilection that everything in the Universe reduces to "matter."

832.] WE have seen (Art. 380) that the action of magnets on one another can be accurately represented by the attractions and repulsions of an imaginary substance called 'magnetic matter.' We have shewn the reasons why we must not suppose this magnetic matter to move from one part of a magnet to another through a sensible distance, as at first sight it appears to do when we magnetize a bar, and we were led to Poisson's hypothesis that the magnetic matter is strictly confined to single molecules of the magnetic substance, so that a magnetized molecule is one in which the opposite kinds of magnetic matter are more or less separated toward opposite poles of the molecule, but so that no part of either can ever be actually separated from the molecule (Art. 430).

These arguments completely establish the fact, that magnetization is a phenomenon, not of large masses of iron, but of molecules, that is to say, of portions of the substance so small that we cannot by any mechanical method cut one of them into two, so as to obtain a north pole separate from a south pole. But the nature of a magnetic molecule is by no means determined without further investigation. We have seen (Art. 442) that there are strong reasons for believing that the act of magnetizing iron or steel does not consist in imparting magnetization to the molecules of which it is composed, but that these molecules are already magnetic, even in unmagnetized iron, but with their axes placed indifferently in all directions, and that the act of magnetization consists in turning the molecules so that their axes are either rendered all parallel to one direction, or at least are deflected towards that direction.

833.] Still, however, we have arrived at no explanation of the nature of a magnetic molecule, that is, we have not recognized its likeness to any other thing of which we know more. We have therefore to consider the hypothesis of Ampere, that the magnetism of the molecule is due to an electric current constantly circulating in some closed path within it.

2 _Treatise on Electricity and Magnetism_ 471-472.

Although Maxwell acknowledges that it is impossible to reduce a magnet to a single circulating molecule so that he could look at the molecule and observe the magnetic vortex itself, by the same reasoning, a large magnet is simply an n-multiple of a single molecule. If we advance the theory to the unified and pure field theory in which a single principle underlies all phenomena, then every demonstration embodies that principle—if it were but to be known.

According to Ampere's theory, therefore, all phenomena of magnetism are due to electric currents, and if we could make observations of the magnetic force in the interior of a magnetic molecule, we should find that it obeyed exactly the same laws as the force in a region surrounded by any other electric current.

834.] In treating of the force in the interior of magnets, we have supposed the measurements to be made in a small crevasse hollowed out of the substance of the magnet, Art. 395. We were thus led to consider two different quantities, the magnetic force and the magnetic induction, both of which are supposed to be observed in a space from which the magnetic matter is removed. We were not supposed to be able to penetrate into the interior of a magnetic molecule and to observe the force within it.

If we adopt Ampere's theory, we consider a magnet, not as a continuous substance, the magnetization of which varies from point to point according to some easily conceived law, but as a multitude of molecules, within each of which circulates a system of electric currents, giving rise to a distribution of magnetic force of extreme complexity, the direction of the force in the interior of a molecule being generally the reverse of that of the average force in its neighbourhood, and the magnetic potential, where it exists at all, being a function of as many degrees of multiplicity as there are molecules in the magnet.

2 _Treatise on Electricity and Magnetism_ 472-473.

As we have noted above, Maxwell considers the magnetic force like an "incompressible fluid" that does not converge.

In other words, the distribution of magnetic force is of the same nature as that of the velocity of an incompressible fluid, or, as we have expressed it in Art. 25, the magnetic force has no convergence.

2 _Treatise on Electricity and Magnetism_ 473.

865.] There appears to be, in the minds of these eminent men, some prejudice, or _a priori_ objection, against the hypothesis of a medium in which the phenomena of radiation of light and heat and the electric actions at a distance take place. It is true that at one time those who speculated as to the causes of physical phenomena were in the habit of accounting for each kind of action at a distance by means of a special æthereal fluid, whose function and property it was to produce these actions. They filled all space three and four times over with æthers of different kinds, the properties of which were invented merely to 'save apearances,' so that more rational enquirers were willing rather to accept not only Newton's definite law of attraction at a distance, but even the dogma of Cotes, that action at a distance is one of the primary properties of matter, and that no explanation can be more intelligible than this fact. Hence the undulatory theory of light has met with much opposition, directed not against its failure to explain the phenomena, but against its assumption of the existence of a medium in which light is propagated.

866.] We have seen that the mathematical expressions for electrodynamic action led, in the mind of Gauss, to the conviction that a theory of the propagation of electric action in time would be found to be a very keystone of electrodynamics. Now we are unable to conceive of propagation in time, except either as a flight of a material substance through space, or as the propagation of a condition of motion or stress in a medium already existing in space. In the theory of Neumann, the mathematical conception called Potential, which we are unable to conceive as a material substance, is supposed to be projected from one particle to another, in a manner which is quite independent of a medium, and which, as Neumann has himself pointed out, is extremely different from that of the propagation of light. In the theories of Riemann and Betti it would appear that the action is supposed to be propagated in a manner somewhat more similar to that of light.

But in all of these theories the question naturally occurs:—If something is transmitted from one particle to another at a distance, what is its condition after it has left the one particle and before it has reached the other? If this something is the potential energy of the two particles, as in Neumann's theory, how are we to conceive this energy as existing in a point of space, coinciding neither with the one particle nor with the other? In fact, whenever energy is transmitted from one body to another in time, there must be a medium or substance in which the energy exists after it leaves one body and before it reaches the other, for energy, for as Torricelli* remarked, 'is a quintessence of so subtile a nature that it cannot be contained in any vessel except the inmost substance of material things.' Hence all these theories lead to the conception of a medium in which the propagation takes place, and if we admit this medium as a hypothesis, I think it ought to occupy a prominent place in our investigations, and that we ought to endeavour to construct a mental representation of all the details of its action, and this has been my constant aim in this treatise.

* Lezioni Accademiche (Forenze. 1715), P. 25.

2 _Treatise on Electricity and Magnetism_ 492-493.

The concept of "direct action at a distance" is attributable to Cotes in his Preface to his own edition of the _Principia_ edited during Newton's lifetime, 2 [Maxwell], _Scientific Papers_ 316, not the Cajori edition cited herein.

To demonstrate the existence of that medium and articulate its properties occupies a central place in the investigations here as well.

In addition to the _Treatise_ , Maxwell wrote a substantial number of other papers that either preceded or expanded the content of the _Treatise_ or topics implicated therein, eventually collected as _The Scientific Papers of James Clerk Maxwell_ [subsequently reprinted as two volumes bound as one, herein 1 and 2 _Scientific Papers_ ]. Although the papers repeat in great part the material in the _Treatise_ , they are often more philosophically elaborate, range over different subjects, and in one particular case—his submission of an 1856 paper in response to the Adams prize for an explanation of the composition of the rings of Saturn—hypothecated by pure mathematical reasoning that they were a series of concentric rings consisting of aggregates of individual particles rather than a system of coherent solid rings. "On the Theories of the Constitution of Saturn's Rings" and "On the Stability of the Motion of Saturn's Rings," (1 _Scientific Papers_ 286-377). Interestingly, I have never seen a single mention of Maxwell's papers in view of the discoveries of the USA "Pioneer" and "Voyager 1 and 2 " space probes that reached Saturn in 1979, 1980, and 1982 respectively, that confirmed his theory.

As a "wrangler"—one who could "wrestle" and "pin" a mathematical problem to the mat—Maxwell was able to wrestle with the Universe and get a grip on some problem so tenaciously that no matter how hard Mother Nature tried, she could not shake loose his hold. Although not known as a cosmologist, it is significant to recognize that Maxwell was astutely aware of the large scale cosmological implications of the various theoretical problems associated with the electromagnetic field. For the most part, the bulk of the papers are concerned with Faraday's lines of force and the means by which those concepts are made mathematically and empirically evident.

In order to obtain physical ideas without adopting a physical theory we must make ourselves familiar with the existence of physical analogies. By a physical analogy I mean that partial similarity between the laws of one science and those of another which makes each of them illustrate the others. Thus all the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers. Passing from the most universal of all analogies to a very partial one, we find the same resemblance in mathematical form between two different phenomena giving rise to a physical theory of light.

1 _Scientific Papers_ 156.

We must recognize that Maxwell represents the maturing generation of mathematically trained physicists whereas Faraday represents the last of the generation of intuitive investigators who follow the tradition of Franklin, Ampere, and Oersted. Maxwell is quite clear and open about his place and perspective.

* * * By the method which I adopt, I hope to render it evident that I am not attempting to establish any physical theory of a science in which I have hardly made a single experiment, and that the limit of my design is to shew how, by a strict application of the ideas and methods of Faraday, the connexion of the very different orders of phenomena which he has discovered may be clearly placed before the mathematical mind. I shall therefore avoid as much as I can the introduction of anything which does not serve as a direct illustration of Faraday's methods, or of the mathematical deductions which may be made from them.

1 _Scientific Papers_ 157-158.

In adapting the analogy of a fluid Maxwell incorporates by reference its incompressibility, which as discussed later, is as much an obstacle to the solution of the problem of the singularity as is the domination of physics by gravity and matter.

* * * If we consider these curves [Faraday's lines of force. JG] not as mere lines, but as fine tubes of variable section carrying an incompressible fluid, then, since the velocity of the fluid is inversely as the section of the tube, we may make the velocity vary according to any given law, by regulating the section of the tube, and in this way we might represent the intensity of the force as well as its direction by the motion of the fluid in these tubes. This method of representing the intensity of a force by the velocity of an imaginary fluid in a tube is applicable to any conceivable system of forces, but it is capable of great simplification in the case in which the forces are such as can be explained by the hypothesis of attractions varying inversely as the square of the distance, such as those observed in electrical and magnetic phenomena.

1 _Scientific Papers_ 158-59.

I propose, then, to describe a method by which the motion of such a fluid may be clearly conceived; secondly to trace the consequences of assuming certain conditions of motion, and to point out the application of the method to some of the less complicated phenomena of electricity, magnetism, and galvanism; and lastly to shew how by an extension of these methods, and the introduction of another idea due to Faraday, the laws of the attractions and inductive actions of magnets and currents may be clearly conceived, without making any assumptions as to the physical nature of electricity, or adding anything to that which has been already proved by experiment.

By referring everything to the purely geometrical idea of the motion of an imaginary fluid, I hope to attain generality and precision, and to avoid the dangers arising from a premature theory professing to explain the cause of the phenomena. If the result of mere speculation which I have collected are found to be of any use to experimental philosophers, in arranging and interpreting their results, they will have served their purpose, and a mature theory, in which physical facts will be physically explained, will be formed by those who by interrogating Nature herself can obtain the only true solution of the questions which the mathematical theory suggests.

1 _Scientific Papers_ 159.

(1) The substance here treated of must not be assumed to possess any of the properties of ordinary fluids except those of freedom of motion and resistance to compression. It is not even a hypothetical fluid which is introduced to explain actual phenomena. It is merely a collection of imaginary properties which may be employed for establishing certain theorems in pure mathematics in a way more intelligible to many minds and more applicable to physical problems than that in which algebraic symbols alone are used. The use of the word "Fluid" will not lead us into error, if we remember that it denotes a purely imaginary substance with the following property:

The portion of fluid which at any instant occupied a given volume, will at any succeeding instant occupy an equal volume.

This law expresses the incompressibility of the fluid, and furnishes us with a convenient measure of its quantity, namely its volume. The unit of quantity of the fluid will therefore be the unit of volume.

1 _Scientific Papers_ 160.

Inherent in the analogy of an incompressible fluid confined and passing through a nonelastic tube is the generation of a force perpendicular to the direction of flow of the fluid. i.e., perpendicular against the inside wall of the tube.

(12) It is easy to see that these surfaces of equal pressure must be perpendicular to the lines of fluid motion; for if the fluid were to move in any other direction, there would be resistance to its motion which could not be balanced by any difference of pressures. (We must remember that the fluid here considered has no inertia or mass, and that its properties are those only which are formally assigned to it, so that the resistances and pressures are the only things to be considered.)

1 _Scientific Papers_ 164.

If, however, the model were expanded from a series of tubes in which there is an incompressible fluid exerting a uniform pressure perpendicularly against the inside wall of the tube to an n-body problem in which the fluid is reduced to a point out from which a uniform omnidirectional pressure is exerted, then we would have a "field" of omnidirectional pressure that is spherical and decreases in gradations in accordance with the law of inverse squares. At the same time, if we reverse and extend the argument to a field consisting of n-bodies of like constitution so situated that amongst themselves the pressure itself is equalized, then it is the pressurized field itself that causes sphericality!

(18) Let us next determine the pressure at any point of an infinite body of fluid in the centre of which a unit source is placed, the pressure at an infinite distance from the source being supposed to be zero.

The fluid will flow out from the center symmetrically, and since unity of volume flows out of every spherical surface surrounding the point in unit of time, the velocity at a distance _r_ from the source will be

1

_v_ = _________

4 π _r_ 2

The rate of decrease of pressure is therefore _kv_ for

_k_

4 π _r_ 2

and since the pressure = 0 where _r_ is infinite, the actual pressure at any point will be

k

_p_ = ________

4 π _r_

The pressure is therefore inversely proportional to the distance from the source.

1 _Scientific Papers_ 167.

Thus even though Maxwell advances the above to be mathematically true, in an n-body problem the uniformity of the pressure exerted by the distribution of the n-bodies nominalizes the consequences of the law of inverse squares so that the law no longer holds but rather reduces to a field of equalized pressure! If we extend our model of an n-body problem in which the distribution of bodies is a result of the dynamics of the forces in the field then the location of the bodies in the field is the consequence of the pressure that is generated by the bodies themselves as well as the pressure exerted on the body by the field. Thus rather than having a field in which all of the forces destroy each other they reach an aggregate cumulative effect that results in an adiabatic ambient.

In the external medium all the sources destroy one another, and we have an infinite medium without sources surrounding the internal medium. The pressure at infinity is zero, that at the surface is constant. If the pressure at the surface is positive, the motion of the fluid must be outwards from every point of the surface. If it be negative, it must flow inwards towards the surface. But it has been shown that neither of these cases is possible, because if any fluid enters the surface an equal quantity must escape, and therefore the pressure at the surface is zero in the third system.

The pressure at all points in the boundary of the internal medium in the third case is therefore zero, and there are no sources, and therefore the pressure is everywhere zero, by (16).

The pressure in the bounding surface of the internal medium is also zero, and there is no resistance, therefore it is zero throughout; but the pressure in the third case is the difference of pressures in the two given cases, therefore these are equal, and there is only one distribution of pressure which is possible, namely, that due to the imaginary distribution of sources and sinks.

1 _Scientific Papers_ 170.

If we take the "imaginary" and reconstitute it mathematically as _i_ to represent the convexity of the surface of the sphere and the concavity of the enveloping field then we have the mathematical relationship between the radiation generated by the body into the field and the opposing omnidirectional radiation of the field that generates the body. One raises the question of how a field that has been nominalized as the base level of radiation pressure and density can possibly support and sustain a body that is nominalized at the extreme opposite end of radiation pressure and density. First, we must accept as a given that it does.

### THE UNIVERSE DOES NOT HAVE TO BE PROVED!

Secondly, we must accept that the primary principle incorporates the Amperean circulating vortex, that the vortex itself is an energy generating process in which the expenditure of energy generates an omnidirectional pressure outwardly resulting in an equivalent loss of mass that proportionately reduces the radius of the vortex and therefore causes a continuously contracting spiral inwardly. Of course one can not perceive that two joined horseshoe magnets are getting smaller, but in time, contrary to Maxwell's belief, the magnetism will eventually dissipate into the ambient. It is an inherent consequence of unidirectional time! Thirdly, the radiation emitted is at the same density as the æther into which it diffuses and to which it adds its own pressure.

Although the impetus that gave rise to Model 1 was wholly outside anything in extant physics, and the closest that anyone ever came to such a model was Faraday himself, the mathematical authority for its construction is elliptically found in Maxwell's papers on Faraday's lines of force although wholly from a different perspective. In essence, Maxwell places a unit magnetic sphere at the origin of a coordinate system in a uniform field of magnetic force to describe mathematically the difference in pressure (potential) generated from within the sphere outwardly and from the surrounding field inwardly and determines the dynamics of the field by the orientation of the magnet. Maxwell then expands the argument to a coordinate system in which the magnetic field varies in magnitude and direction from one point to another so that the magnetic sphere at the center is affected by omnidirectional forces. These forces are then separated into three components representing the x, y, and z axes and the sphere itself is then considered as if it were three separate magnets each responding to the forces of the respective axis. All of this converts the process into a coordinate system that can be treated mathematically and that I have obviated by reducing the entire argument to a unit sphere. Maxwell has no intention of considering this system as empirically demonstrable.

The force impelling the sphere in the direction of _x_ is therefore dependent on the variation of the square of the intensity of (α2 \+ β2 \+ γ2), as we move along the direction of _x_ and the same is true for _y_ and _z_ , so that the law is, that the force acting on diamagnetic spheres is from places of greater to places of less intensity of magnetic force, and that in similar distributions of magnetic force it varies as the mass of the sphere and the square of the intensity.

1 _Scientific Papers_ 215.

The argument expands to two spheres in a uniform field:

Let two spheres of radius _a_ be connected together so that their centres are kept at a distance _b_ , and let them be suspended in a uniform magnetic field, then, although each sphere by itself would have been in equilibrium at any part of the field, the disturbance of the field will produce forces tending to make the balls set in a particular direction.

1 _Scientific Papers_ 215.

Let us next take the case of the same balls placed not in a uniform field but between a north and south pole, ± _M_ , distant 2c, from each other in the direction of _x_.

1 _Scientific Papers_ 216.

Maxwell then presents the equation by which the spheres are turned in the direction 0, which if propagated over each of the respective axis generates a force capable of rotating the sphere in the field. Finally—

* * * If, instead of being placed between two poles very near to each other, they had been placed in a uniform field such as that of terrestrial magnetism or that produced by a spherical electro-magnet (see Ex.VII), an elongated body would set axially whether magnetic or diamagnetic.

1 _Scientific Papers_ 217.

Without much imagination one sees that the combination of these processes mathematically describes what Model 1 demonstrates empirically, ultimately a spherical shell revolving in a magnetic field, "Spherical shell revolving in magnetic field." 1 _Scientific Papers_ 226. The same theme is subsequently taken up in "On Physical Lines of Force, Part I, The Theory of Molecular Vortices Applied to Magnetic Phenomenon," in which Maxwell "examines magnetic phenomena from a mechanical point of view, and to determine what tensions in, or motions of, a medium are capable of producing the mechanical phenomena observed." In that paper Maxwell repeats the well-known fact that poles of opposite polarity attract each other and those of the same polarity repel.

If we observe the lines of force between two magnets, as indicated by iron filings, we shall see that whenever the lines of force pass from one pole to another, there is _attraction_ between those poles; and where the lines of force from the poles avoid each other and are dispersed into space, the poles _repel_ each other, so that in both cases they are drawn in the direction of the resultant of the lines of force.

It appears therefore that the stress in the axis of a line of magnetic force is a _tension_ , like that of a rope.

If we calculate the lines of force in the neighbour-hood of two gravitating bodies, we shall find them the same in direction as those near two magnetic poles of the same name; but we know that the mechanical effect is that of attraction instead of repulsion. The lines of force in this case do not run between the bodies, but avoid each other, and are dispersed over space. In order to produce the effect of attraction, the stress along the lines of gravitating force must be a _pressure_.

Let us now suppose the phenomena of magnetism depend on the existence of a tension in the direction of the lines of force, combined with a hydrostatic pressure; or in other words, a pressure greater in the equatorial than in the axial direction; the next questions is, what mechanical explanation can we give of this inequality of pressures in a fluid or mobile medium? The explanation which most readily occurs to the mind is that the excess of pressure in the equatorial direction arises from the centrifugal force of vortices or eddies in the medium having their axes in directions parallel to the lines of force.

This explanation of the cause of the inequality of pressures at once suggests the means of representing the dipolar character of the line of force. Every vortex is essentially dipolar, the two extremities of its axis being distinguished by the direction of its revolution as observed from those points.

1 _Scientific Papers_ 454-455.

These "forces" Maxwell translates into lines of force that are allocated respectively to a three-dimensional coordinate system into which one can hypothecate the existence of "imaginary matter" capable of exerting mechanical pressure. Consistent with Faraday's experiment,

Let us first take the case of a single magnetic pole, that is, one end of a long magnet, so long that its other end is too far off to have a perceptible influence on the part of the field we are considering.

1 _Scientific Papers_ 465.

so that the effect of the opposite pole is isolated.

In Part II, "The Theory of Molecular Vortices Applied to Electric Currents," Maxwell attempts to come to grips with the mechanical aspects of the lines of force that impose a series of questions distinct from those that can be described mathematically.

We have already shown that all the forces acting between magnets, substances capable of magnetic induction, and electric currents, may be mechanically accounted for on the supposition that the surrounding medium is put into such a state that at every point the pressures are different in different directions, and the direction of least pressure being that of the observed lines of force, and the difference of greatest and least pressures being proportional to the square of the intensity of the force at that point.

Such a state of stress, if assumed to exist in the medium, and to be arranged according to the known laws regulating lines of force, will act upon the magnets, currents, &c. in the field with precisely the same resultant forces as those calculated on the ordinary hypothesis of direct action at a distance. This is true independently of any particular theory as to the _cause_ of this state of stress, or the mode in which it can be sustained in the medium. We have therefore a satisfactory answer to the question, "Is there any mechanical hypothesis as to the condition of the medium indicated by lines of force, by which the observed resultant forces may be accounted for?" The answer is, the lines of force indicate the direction of _minimum pressure_ at every point of the medium.

The second question must be "What is the mechanical cause of this difference of pressure in different directions?" We have supposed in the first part of this paper, that this difference of pressures is caused by molecular vortices, having their axes parallel to the lines of force.

We also assumed, perfectly arbitrarily, that the direction of these vortices is such that, on looking along a line of force from south to north, we should see the vortices revolving in the direction of the hands of a watch.

We found that the velocity of the circumference of each vortex must be proportional to the intensity of the magnetic force, and that the density of the substance of the vortex must be proportional to the capacity of the medium for magnetic induction.

We have as yet given no answers to the questions, "How are these vortices set in rotation?" and "Why are they arranged according to the known laws of lines of force about magnets and currents?" These questions are certainly of a higher order of difficulty than either of the former; and I wish to separate the suggestions I may offer by way of provisional answer to them, from the mechanical deductions which resolved the first question, and the hypothesis of vortices which gave a probable answer to the second.

We have, in fact, now come to inquire into the physical connexion of these vortices with electric currents, while we are still in doubt as to the nature of electricity, whether it is one substance, two substances, or not a substance at all, or in what way it differs from matter, and how it is connected with it.

We know that the lines of force are affected by electric currents, and we know the distribution of those lines about a current; so that from the force we can determine the amount of the current. Assuming that our explanation of the lines of force by molecular vortices is correct, why does a particular distribution of vortices indicate an electric current? A satisfactory answer to this question would lead us a long way towards that of a very important one, "What is an electric current?"

I have found great difficulty in conceiving of the existence of vortices in a medium, side-by-side, revolving in the same direction about parallel axes. The contiguous portions of consecutive vortices must be moving in opposite directions; and it is difficult to understand how the motion of one part of the medium can coexist with, and even produce, an opposite motion of a part in contact with it.

1 _Scientific Papers_ 467-468.

The scheme that Maxwell advances is:

The only conception which has at all aided me in conceiving of this kind of motion is that of the vortices being separated by a layer of particles, revolving each on its own axis in the opposite direction to that of the vortices, so that the contiguous surfaces of the particles and of the vortices have the same motion.

In mechanism, when two wheels are intended to revolve in the same direction, a wheel is placed between them so as to be in gear with both, and this wheel is called an "idle wheel." The hypothesis about the vortices which I have to suggest is that a layer of particles, acting as idle wheels, is interposed between each vortex and the next, so that each vortex has a tendency to make the neighbouring vortices revolve in the same direction with itself.

1 _Scientific Papers_ 468.

Notwithstanding that Maxwell has not abandoned Ampere's theory of molecular vortices, he clearly has not resolved the relationship between attraction and repulsion and the "right-hand" rule [current circulating uniformly as if in the hands of a watch] that has been resolved herein. Although he is thoroughly familiar with the history of iron filings being sprinkled onto a surface above a magnet so as to make manifest the lines of force, the actual inducement of motion into the magnet, as demonstrated in Model 1, is something that had never been done during his time or since. His model is shown as "Figure 2." (Figure 41)

It appears therefore that, according to our hypothesis, an electric current is represented by the transference of the moveable particles interposed between the neighbouring vortices. We may conceive that these particles are very small compared with the size of the vortex, and that the mass of all the particles together is inappreciable compared with that of the vortices, and that a great many vortices, with their surrounding particles, are contained in a single complete molecule of the medium. The particles must be conceived to roll without sliding between the vortices which they separate, and not to touch each other, so that, as long as they remain within the same complete molecule, there is no loss of energy by resistance. When, however, there is a general transference of particles in one direction, they must pass from one molecule to another, and in doing so, may experience resistance, so as to waste electrical energy and generate heat.

* * * * * * *

It will appear from this diagram, that if V and V' were contiguous vortices, particles placed between them would move downwards; and that if the particles were forced downwards by any cause, they would make the vortices revolve as in the figure. We have thus obtained a point of view from which we may regard the relations of an electric current to its lines of force as analogous to the relation of a toothed wheel or rack to wheels which it drives.

1 _Scientific Papers_ 471-472.

The model, however, is not without its problems in terms of the velocity of rotation, the inducement of currents, philosophical resolution between one and two fluid theories, and so forth. Having then set out a mechanical model that is consistent with Faraday's lines of force, Maxwell summarizes his findings;

* * * We may now recapitulate the assumptions we have made, and the results we have obtained:

(1) Magneto-electric phenomena are due to the existence of matter under certain conditions of motion or of pressure in every part of the magnetic field, and not to direct action at a distance between the magnets or currents. The substance producing these effects may be a certain part of ordinary matter, or it may be an æther associated with matter. Its density is greatest in iron, and least in diamagnetic substances; but it must be in all cases, except that of iron, very rare, since no other substance has a large ratio of magnetic capacity to what we call a vacuum.

(2) The condition of any part of the field, through which lines of magnetic force pass, is one of unequal pressure in different directions, the direction of the lines of force being that of least pressure, so that the lines of force may be considered lines of tension.

(3) This inequality of pressure is produced by the existence in the medium of vortices or eddies, having their axes in the direction of the lines of force, and having their direction of rotation determined by that of the lines of force.

We have supposed that the direction was that of a watch to a spectator looking from south to north. We might with equal propriety have chosen the reverse direction, as far as known facts are concerned, by supposing resinous electricity instead of vitreous to be positive. The effect of these vortices depends on their density, and on their velocity at the circumference, and is independent of their diameter. The density must be proportional to the capacity of the substance for magnetic induction, that of the vortices in air being 1. The velocity must be very great, in order to produce so powerful effects in so rare a medium.

The size of the vortices is indeterminate, but is probably very small as compared with that of a complete molecule of ordinary matter. [Footnote deleted. JG]

(4) The vortices are separated from each other by a single layer of round particles, so that a system of cells is formed, the partitions being these layers of particles, and the substance of each cell being capable of rotating as a vortex.

(5) The particles forming the layer are in _rolling contact_ with both the vortices which they separate, but do not rub against each other. They are perfectly free to roll between the vortices and so to change their place, provided they keep within one _complete molecule_ of the substance; but in passing from one molecule to another they experience resistance, and generate irregular motions, which constitute heat. These particles, in our theory, play the part of electricity. Their motion of translation constitutes an electric current, their rotation serves to transmit the motion of the vortices from one part of the field to another, and the tangential pressures thus called into play constitute electromotive force. The conception of a particle having its motion connected with that of a vortex by perfect rolling contact may appear somewhat awkward. I do not bring it forward as a mode of connexion existing in nature, or even as that which I would willingly assent to as an electrical hypothesis. It is, however, a mode of connexion which is mechanically conceivable, and easily investigated, and it serves to bring out the actual mechanical connexions between the known electro-magnetic phenomena; so that I venture to say that any one who understands the provisional and temporary character of this hypothesis, will find himself rather helped than hindered by it in his search after the true interpretation of the phenomena.

The action between the vortices and the layers of particles is in part tangential; so that if there were any slipping or differential motion between the parts in contact, there would be a loss of energy belonging to the lines of force, and a gradual transformation of that energy into heat. Now we know that the lines of force about a magnet are maintained for an indefinite time without any expenditure of energy; so that we must conclude that wherever there is tangential action between different parts of the medium, there is no motion of slipping between those parts. We must therefore conceive that the vortices and particles roll together without slipping; and that the interior strata of each vortex receive their proper velocities from the exterior stratum without slipping, that is, the angular velocity must be the same throughout each vortex.

The only process in which electro-magnetic energy is lost and transformed into heat is in the passage of electricity from one molecule to another. In all cases the energy of the vortices can only be diminished when an equivalent quantity of mechanical work is done by magnetic action.

(6) The effect of an electric current upon the surrounding medium is to make the vortices in contact with the current revolve so that the parts next to the current move in the same direction as the current. The parts furthest from the current will move in the opposite direction; and if the medium is a conductor of electricity, so that the particles are free to move in any direction, the particles touching the outside of these vortices will be moved in a direction contrary to that of the current, so that there will be an induced current in the opposite direction to the primary one.

If there were no resistance to the motion of the particles, the induced current would be equal and opposite to the primary one, and would continue as long as the primary current lasted, so that it would prevent all action of the primary current at a distance. If there is a resistance to the induced current, its particles act upon the vortices beyond them, and transmit the motion of rotation to them, till at last all the vortices in the medium are set in motion with such velocities of rotation that the particles between them have no motion except that of rotation, and do not produce currents.

In the transmission of motion from one vortex to another, there arises a force between the particles and the vortices, by which the particles are pressed in one direction and the vortices in the opposite direction. We call the force acting on the particle the electromotive force. The reaction on the vortices is equal and opposite, so that the electromotive force cannot move any part of the medium as a whole, it can only produce currents. When the primary current is stopped, the electromotive forces all act in the opposite direction.

(7) When an electric current or a magnet is moved in presence of a conductor, the velocity of rotation of the vortices in any part of the field is altered by that motion. The force by which the proper amount of rotation is transmitted to each vortex, constitutes in this case also an electromotive force, and if permitted will produce currents.

(8) When a conductor is moved in a field of magnetic force, the vortices in it and in its neighbourhood are moved out of their places, and are changed in form. The force arising from these changes constitutes the electromotive force on a moving conductor, and is found by calculation to correspond with that determined by experiment.

We have not shown in what way electro-magnetic phenomena may be imitated by an imaginary system of molecular vortices. Those who have been already inclined to adopt an hypothesis of this kind, will find here the conditions which must be fulfilled in order to give it mathematical coherence, and a comparison, so far satisfactory, between its necessary results and known facts. Those who look in a different direction for the explanation of the facts, may be able to compare this theory with that of the existence of currents flowing freely through bodies, and with that which supposes electricity to act at a distance with a force depending on its velocity, and therefore not subject to the law of conservation of energy.

1 _Scientific Papers_ 485-488.

In Part III, "The Theory of Molecular Vortices Applied to Statical Electricity," Maxwell explains:

According to our theory, the particles which form the partitions between the cells constitute the matter of electricity. The motion of these particles constitutes an electric current; the tangential force with which the particles are pressed by the matter of the cells is electromotive force, and the pressure of the particles on each other corresponds to the tension or potential of the electricity.

If we can now explain the condition of a body with respect to the surrounding medium when it is said to be "charged" with electricity, and account for the forces acting between electrified bodies, we shall have established connexion between all the principle phenomena of electrical science.

1 _Scientific Papers_ 490.

In the following investigation I have considered the relation between the displacement and the force producing it, on the supposition that the cells are spherical. The actual form of the cells probably does not differ from that of a sphere sufficiently to make much difference in the numerical result.

1 _Scientific Papers_ 492.

In Part IV, "The Theory of Molecular Vortices Applied to the Action of Magnetism on Polarized Light," Maxwell reiterates the right-handed nature of polarized light and the effect that the molecular vortices have on the advanced rotation as a consequence of it being passed through a magnetic field.

Professor Thomson has pointed out that the cause of the magnetic action on light must be a real rotation going on in the magnetic field. A _right-handed_ circularly polarized ray of light is found to travel with a different velocity according as it passes from north to south or from south to north, along a line of magnetic force. Now, whatever theory we adopt about the direction of vibrations in plane-polarized light, the geometrical arrangement of the parts of the medium during the passage of a right-handed circularly polarized ray is exactly the same whether the ray is moving north or south. The only difference is that the particles describe their circles in opposite directions. Since, therefore, the configuration is the same in the two cases, the forces acting between particles must be the same in both, and the motions due to these forces must be equal in velocity if the medium was originally at rest; but if the medium be in a state of rotation, either as a whole or in molecular vortices, the circular vibrations of light may differ in velocity according as their direction is similar or contrary to that of the vortices.

We have now to investigate whether the hypothesis developed in this paper—that magnetic force is due to the centrifugal force of small vortices, and that these vortices consist of the same matter the vibrations of which constitute light—leads to any conclusions as to the effect of magnetism on polarized light. We suppose transverse vibrations to be transmitted through a magnetized medium. How will the propagation of these vibrations be affected by the circumstance that portions of that medium are in a state of rotation?

In the following investigation, I have found that the only effect which the rotation of the vortices will have on the light will be to make the plane of polarization rotate in the same direction as the vortices, . . . .

1 _Scientific Papers_ 505-506.

In his "A Dynamical Theory of the Electromagnetic Field" Maxwell expands on what had been localized processes to a larger generalized area, again, however, retaining a matter-based theory.

(3) The theory I propose may therefore be called a theory of the _Electromagnetic Field_ , because it has to do with the space in the neighbourhood of the electric or magnetic bodies, and it may be called a _Dynamical Theory_ , because it assumes that in that space there is matter in motion, by which the observed electromagnetic phenomena are produced.

The electromagnetic field is that part of space which contains and surrounds bodies in electric or magnetic conditions.

It may be filled with any kind of matter, or we may endeavour to render it empty of all gross matter, as in the case of Geissler's tubes and other so-called vacuua.

There is always, however, enough of matter left to receive and transmit the undulations of light and heat, and it is because the transmission of these radiations is not greatly altered when transparent bodies of measurable density are substituted for the so-called vacuum, that we are obliged to admit that the undulations are those of an æthereal substance, and not of the gross matter, the presence of which merely modifies in some way the motion of the æther.

We have therefore some reason to believe, from the phenomena of light and heat, that there is an æthereal medium filling space and permeating bodies, capable of being set in motion and of transmitting that motion from one part to another, and of communicating that motion to gross matter so as to heat it and affect it in various ways.

(5) Now the energy communicated to the body in heating it must have formerly existed in the moving medium, for the undulations had left the source of heat some time before they reached the body, and during that time the energy must have been half in the form of motion of the medium and half in the form of elastic resilience. From these considerations Professor W. Thomson has argued, that the medium must have a density capable of comparison with that of gross matter, and has even assigned an inferior limit to that density.

(6) We may therefore receive, as a datum derived from a branch of science independent of that with which we have to deal, the existence of a pervading medium, of small but real density, capable of being set in motion, and of transmitting motion from one part to another with great, but not infinite, velocity.

Hence the parts of this medium must be so connected that the motion of one part depends in some way on the motion of the rest; and at the same time these connexions must be capable of a certain kind of elastic yielding, since the communication of motion is not instantaneous, but occupies time.

The medium is therefore capable of receiving and storing up two kinds of energy, namely, the "actual" energy depending on the motions of its parts, and "potential" energy, consisting of the work which the medium will do in recovering from displacement in virtue of its elasticity.

The propagation of undulations consists in the continual transformation of one of these forms of energy into the other alternately, and at any instant the amount of energy in the whole medium is equally divided, so that half is energy of motion, and half is elastic resilience.

(7) A medium having such a constitution may be capable of other kinds of motion and displacement than those which produce the phenomena of light and heat, and some of these may be of such a kind that they may be evidenced to our senses by the phenomena they produce.

(8) Now we know that the luminiferous medium is in certain cases acted on by magnetism; for Faraday* discovered that when a plane polarized ray traverses a transparent diamagnetic medium in the direction of the lines of magnetic force produced by magnets or currents in the neighbourhood, the plane of polarization is caused to rotate.

This rotation is always in the direction in which positive electricity must be carried round the diamagnetic body in order to produce the actual magnetization of the field.

*Experimental Researches, Series xix.

1 _Scientific Papers_ 527-529.

Of considerable importance to our discussion regarding redshift is Maxwell's recognition of the relationship amongst magnetic effects, light, and the æther.

It is true that the rotation by magnetism of the plane of polarization has been observed only in media of considerable density; but the properties of the magnetic field are not so much altered by the substitution of one medium for another, or for a vacuum, as to allow us to suppose that the dense medium does anything more than merely modify the motion of the ether. We have therefore warrantable grounds for inquiring whether there may not be a motion of the ethereal medium going on wherever magnetic effects are observed, and we have some reason to suppose that this motion is one of rotation, having the direction of the magnetic force as its axis.

1 _Scientific Papers_ 529-530.

As with Faraday, although from a considerably more mathematical level based on his own investigations of the electrified field, Maxwell is equally "attracted" to the coincidence between the mathematical laws that describe gravity with those that describe the laws of attraction between electrified entitles. In his "Note on the Attraction of Gravity," he sets out what he has learned and the fact that he himself cannot go further to solve the problem.

Note on the Attraction of Gravitation

(82) After tracing to the action of the surrounding medium both the magnetic and the electric attractions and repulsions, and finding them to depend on the inverse square of the distance, we are naturally led to inquire whether the attraction of gravitation, which follows the same law of the distance, is not also traceable to the action of a surrounding medium.

Gravitation differs from magnetism and electricity in this; that the bodies concerned are all of the same kind, instead of being of opposite signs, like magnetic poles and electrified bodies, and that the force between these bodies is an attraction and not a repulsion, as is the case between like electric and magnetic bodies.

The lines of gravitating force near two dense bodies are exactly of the same form as the lines of magnetic force near two poles of the same name; but whereas the poles are repelled the bodies are attracted.

* * * * * * *

As energy is essentially positive, it is impossible for any part of space to have negative intrinsic energy. Hence those parts of space in which there is no resultant force, such as the points of equilibrium in the space between the different bodies of a system, and within the substance of such body, . . . .

The assumption, therefore, that gravitation arises from the action of the surrounding medium in the way pointed out, leads to the conclusion that every part of this medium possesses, when undisturbed, an enormous intrinsic energy, and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction.

As I am unable to understand in what way a medium can possess such properties, I cannot go any further in this direction in searching for the cause of gravitation.

1 _Scientific Papers_ 570-571.

If we go to Cavendish, we learn that all mass has an inherent attractive gravitational force, and that this force, as advanced here, is the result of the circularity of the electromotive force about a center. The problem lies in Maxwell's framing of the issue, namely, that gravitation is the result of external forces in the æther, whereas it is the body that determines the conditions of the surrounding medium. Under the unified and pure field theory the æther and the converging waveforms cause the entification of the body and those forces themselves are molecular vortices that bring about an entity having one set of N-S poles. In "On the Equilibrium of a Spherical Envelope" Maxwell continues his exploration of the reciprocal relationship between the internal and external stresses and pressures on the same surface considered as an infinitely thin spherical sheet.

I propose to determine the distribution of stress in an indefinitely thin and inextensible spherical sheet, arising from the action of external forces applied to it at any number of points on its surface.

2 _Scientific Papers_ 86.

Maxwell introduces a "twist" (spiral) to the forces existing between two points on the surface of the sphere. In the unified and pure field theories, the "twist" is replaced by the right-hand rule that is constitutional with all electromagnetic radiation as a waveform, and when the handle in Model 1 is turned that waveform is induced into the field to induce the molecular vortex.

The final three papers with which we are concerned, "On Action at a Distance," "Attraction," and "Ether," the latter two for the _Encyclopoedia Britannica_ , essentially bring to a close the state of the art up to and through the Michelson-Morley experiment [which did not explain anything about the nature or existence of the æther] and brings us to the eve of the special theory. After Einstein's special theory no one talks about the æther anymore or at least that it has any empirical existence to which one should pay any significant attention in terms of being an operative force in the cosmos and particularly as a source of radiation that might provide a pressurized medium that would cause the "red shift." See particularly Eddington, _New Pathway in Science_ at 36 to 49 and elsewhere throughout. Nonetheless, as we now open the 21st Century and fourth millennium since the idea of an æther was first formulated, the æther [although now reconstituted as dark matter amongst many other theories] remains the unresolved problem, for it implicates the redshift, that implicates the big bang, that ultimately implicates the singularity.

The question is that of the transmission of force. We see that two bodies at a distance from each other exert a mutual influence on each other's motion. Does this mutual action depend on the existence of some third thing, some medium of communication, occupying the space between the bodies, or do the bodies act on each other immediately, without the intervention of anything else?

2 _Scientific Papers_ 311.

In "Action at a Distance" Maxwell reviews the history of action at a distance beginning essentially with Newton's _Principia_ and the "Queries" in the _Opticks_.

Newton himself, with that wise moderation which is characteristic of all his speculations, answered that he made no pretence of explaining the mechanism by which the heavenly bodies act on each other. To determine the mode in which their mutual action depends on their relative position was a great step in science, and this step Newton asserted that he had made. To explain the process by which this action is effected was a quite distinct step, and this step Newton, in his _Principia_ , does not attempt to make.

But so far was Newton from asserting that bodies really do act on one another at a distance, independently of anything between them, that in a letter to Bentley, which has been quoted by Faraday in this place, he says:—

"It is inconceivable that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact, as it must do if gravitation, sense of Epicurus, be essential and inherent in it . . . .

That gravity should be innate, inherent, and essential to matter, so that one body can act upon another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it."

Accordingly, we find in his _Optical Queries_ , and in his letters to Boyle, that Newton had very early made the attempt to account for gravitation by means of the pressure of a medium, and that the reason he did not publish these investigations "proceeded from hence only, that he found he was not able, from experiment and observation, to give a satisfactory account of this medium, and the manner of its operation in producing the chief phenomena of nature. "

2 _Scientific Papers_ 315-316.

The work of Cavendish, Coulomb, and Poisson essentially "skip over the problem" by turning their attention directly to the action that is observed at a distance without regard to the existential nature of the intervening space through which the action is perceived to travel. Oersted's observation of the turning of a compass in the vicinity of a wire through which an electric current was passed provides the first demonstrable evidence of the causal relationship between two entities separated by a distance through which action could be effectuated. Ampere directly related attraction and repulsion to electrical current and orientation of iron filings sprinkled in the presence of a magnet became a system of defined forces—lines of force—that made manifest the physical embodiment of a very real empirical entity—the field. Faraday then moved on to demonstrate the physicality and polarity of light by passing it through a strong magnetic field and Maxwell is not oblivious to the cosmological implications of Faraday's discovery and its relation to galactic space and the continuity of existence.

The vast interplanetary and interstellar regions will no longer be regarded as waste places in the universe, which the Creator has not seen fit to fill with the symbols of the manifold order of His kingdom. We shall find them to be already full of this wonderful medium; so full, that no human power can remove it from the smallest portion of space, or produce the slightest flaw in its infinite continuity. It extends unbroken from star to star; and when a molecule of hydrogen vibrates in the dog-star, the medium receives the impulses of these vibrations; and after carrying them in its immense bosom for three years, delivers them in due course, regular order, and full tale into the spectroscope of Mr. Huggins, at Tulse Hill.

But the medium has other functions and operations besides bearing light from man to man, and from world to world, and giving evidence of the absolute unity of the metric system of the universe. Its minute parts may have rotatory as well as vibratory motions, and the axes of rotation form those lines of magnetic force which extend in unbroken continuity into regions which no eye has seen, and which, by their action on our magnets, are telling us in language not yet interpreted, what is going on in the hidden underworld from minute to minute and from century to century.

And these lines must not be regarded as mere mathematical abstractions. They are the directions in which the medium is exerting a tension like that of a rope, or rather, like that of our own muscles. The tension of the medium in the directions of the earth's magnetic force is in this country one grain weight on eight square feet. in some of Dr Joule's experiments, the medium has exerted a tension of 200 lbs. weight per square inch.

But the medium, in virtue of the very same elasticity by which it is able to transmit the undulations of light, is also able to act as a spring. When properly wound up, it exerts a tension, different from the magnetic tension, by which it draws oppositely electrified bodies together, produces effects through the length of telegraph wires, and when of sufficient intensity, leads to the rupture and explosion called lightning.

These are some of the already discovered properties of that which has often been called vacuum, or nothing at all. They enable us to resolve several kinds of action at a distance into actions between contiguous parts of a continuous substance. Whether this resolution is of the nature of explication or complication, I must leave to the metaphysicians.

2 _Scientific Papers_ 323-323.

This may be the first, and perhaps _only_ , hypothecation of the continuity of the æther as well as light throughout the cosmos.

In "Attraction," Maxwell again reiterates the issue of action at a distance with a short review of the subject from Newton to Faraday and a transformation of the pressure perpendicular to the lines of force into the pressure associated with gravitation.

The force of gravitation is also inversely as the square of the distance, but it differs from the electric and magnetic forces in this respect, that the bodies between which it acts cannot be divided into two opposite kinds, one positive and the other negative, but are in respect of gravitation all of the same kind, and that the force between them is in every case attractive. To account for such a force by means of stress in an intervening medium, on the plan adopted for electric and magnetic forces, we must assume a stress of an opposite kind from that already mentioned. We must suppose that there is a pressure in the direction of the lines of force, combined with a tension in all directions at right angles to the lines of force. Such a state of stress would, no doubt, account for the observed effects of gravitation. We have not, however, been able hitherto to imagine any physical cause for such a state of stress. It is easy to calculate the amount of this stress which would be required to account for the actual effects of gravity at the surface of the earth. It would require a pressure of 37,000 tons weight on the square inch in a vertical direction, combined with a tension of the same numerical value in the horizontal directions. The state of stress, therefore, which we must suppose to exist in the invisible medium is 3000 time greater than that which the strongest steel could support.

2 _Scientific Papers_ 488-489.

If this were the case, then under no stretch of the imagination is interstellar space a void, and if we were to apply these calculations to the æther as the reservoir of this force, notwithstanding that it may be imperceptible, it certainly is not insubstantial―

ALL CELESTIAL BODIES ARE SUSPENDED IN IT!!!!!!

In the remainder of the article Maxwell recognizes the theories of William Thomson, Robert Cooke, and others who advanced an adiabatic universe in which bodies were constantly giving off energy while others were absorbing it so that the average pressure was maintained. To these he concludes:

According to such hypotheses we must regard the processes of nature not as illustrations of the great principle of the conservation of energy, but as instances in which, by a nice adjustment of powerful agencies not subject to this principle, an apparent conservation of energy is maintained. Hence, we are forced to conclude that the explanation of the cause of gravitation is not to be found in any of these hypotheses.

2 _Scientific Papers_ 491.

These hypotheses, putting aside the nuances of the articulation and the mechanism by which the pressure is maintained, turn out as advanced here, to be correct. But as with Einstein and other modern theoreticians, postulating a force other than gravity has alluded them all. Such a force and mechanism—opolarity—is simply Maxwell's pressure. Finally, in the "Ether" Maxwell brings together the state of the art as it existed at the end of the 19th Century prior to Michelson-Morley. Having established that light travels at a finite, albeit great, velocity, there was no longer any doubt that it did not travel instantaneously. The issue therefore is what supports the light and through what does it pass on its journey from the dog-star to Earth. Terrestrially, the phenomena of interference had by then been recognized as a light phenomena associated with wave characteristics, although the actual dynamics of the phenomenon had not been resolved, herein by unidirectionality and opolarity. Interference is merely the juxtaposition of two waveforms in opolarity to each other which, because of the pressure perpendicular to the longitudinal direction of the wave, operates as a boundary that confines the light to respective lines of force and prevents it from diffusing into the interlineating space. Instead of lines of force, lines of iron filings, we have lines of light between alternating lines of non-light (darkness). Although the iron filings orient themselves in distinct patterns, the interlineating space has itself never been given any empirical attention other than Maxwell's mechanical paradigm. To Maxwell, light itself is a phenomenon in the æther rather than a substance so that inferentially he rejects Newton's corpuscular theory.

That light is not itself a substance may be proved from the phenomenon of interference. A beam of light from a single source is divided by certain optical methods into two parts, and these, after traveling by different paths, are made to reunite and fall upon a screen. If either half of the beam is stopped, the other falls on the screen and illuminates it, but if both are allowed to pass, the screen in certain places becomes dark, and thus shows that the two portions of light have destroyed each other.

Now, we cannot suppose that two bodies when put together can annihilate each other; therefore light cannot be a substance. What we have proved is that one portion of light can be the exact opposite of another portion, just as + _a_ is the exact opposite of - _a_ , whatever _a_ may be. Among physical quantities we find some which are capable of having their signs reversed, and others which are not. Thus a displacement in one direction is the exact opposite of an equal displacement in the opposite direction. Such quantities are the measures, not of substances, but always of processes taking place in a substance. We therefore conclude that light is not a substance but a process going on in a substance, the process going on in the first portion of light being always the exact opposite of the process going on in the other at the same instant, so that when the two portions are combined no process goes on at all. To determine the nature of the process in which the radiation of light consists, we alter the length of the path of one or both of the two portions of the beam, and we find that the light is extinguished when the difference of the length of the paths is an odd multiple of a certain small distance called a half wave-length. In all other cases there is more or less light; and when the paths are equal, or when their difference is a multiple of a whole wave-length, the screen appears four times as bright as when one portion of the beam falls on it. In the ordinary form of the experiment these different cases are exhibited simultaneously at different points of the screen, so that we see on the screen a set of fringes consisting of dark lines at equal intervals, with bright bands of graduated intensity between them.

If we consider what is going on at different points in the axis of a beam of light at the same instant, we shall find that if the distance between the points is a multiple of a wave-length the same process is going on at the two points at the same instant, but if the distance is an odd multiple of half a wave-length the process going on at one point is the exact opposite of the process going on at the other.

2 _Scientific Papers_ 764-765.

Notwithstanding that it had been known since classical antiquity that the same poles of a magnet repel each other, that Faraday had conclusively proved the polarization of light, and Maxwell himself had proffered that light was an electromagnetic phenomena akin to all other such phenomena, no one had ever (a) given the interlineating space between the lines of force any empirical significance, (b) equated Faraday's lines of force with interference, and (c) concluded that if light were a polar phenomena that it would act and react in the same way to another like juxtaposed polarized medium in the same way as a magnet acts and reacts by repelling itself from a pole of the same polarity—opolarity.

We have determined nothing as to the nature of the process. It may be a displacement, or a rotation, or an electrical disturbance, or indeed any physical quantity which is capable of assuming negative as well as positive values. * * *

2 _Scientific Papers_ 765-766.

Accordingly,

_Elasticity, tenacity, and density of the æther_.―Having so far determined the geometrical character of the process, we must now turn our attention to the medium in which it takes place. We may use the term æther to denote this medium, whatever it may be.

2 _Scientific Papers_ 767.

First, the æther is not a void but rather something in the nature of a corporeal entity; secondly. it has the capacity to transmit, store, and expend energy that infers elasticity; and thirdly, it therefore has density.

In the first place, it is capable of transmitting energy. The radiations which it transmits are able not only to act on our senses, which of itself is evidence of work done, but to heat bodies which absorb them; and by measuring the heat communicated to such bodies, the energy of the radiation may be calculated.

In the next place this energy is not transmitted instantaneously from the radiating body to the absorbing body, but exists for a certain time in the medium.

If we adopt either Fresnel's or Maccullagh's form of the undulatory theory, half of this energy is in the form of potential energy, due to the distortion of elementary portions of the medium, and half in the form of kinetic energy, due to the motion of the medium. We must therefore regard the æther as possessing elasticity similar to that of a solid body, and also as having a finite density.

2 _Scientific Papers_ 767.

If the temperature of the atmosphere were everywhere 0° C, and if it were in equilibrium about the earth supposed at rest, its density at an infinite distance from the earth would be 3x10-346 which is about 1.8x10327 times less than the estimated density of the æther. In the regions of interplanetary space the density of the æther is therefore very great compared with that of the attentuated atmosphere of interplanetary space, but the whole mass of æther within a sphere whose radius is that of the most distant planet is very small compared with that of the planets themselves.*

*[Footnote omitted. JG]

2 _Scientific Papers_ 768.

To differentiate the light that passes through the æther from the motion of the æther itself he suggests an experiment that ultimately became the basis for Michelson-Morley.

_Relative motion of the æther._ —We must therefore consider the æther within dense bodies as somewhat loosely connected with the dense bodies, and we have next to inquire whether, when these dense bodies are in motion through the great ocean of æther, they carry along with them the æther they contain, or whether the æther passes through them as the water of the sea passes through the meshes of a net when it is towed along by a boat. If it were possible to determine the velocity of light by observing the time it takes to travel between one station and another on the earth's surface, we might, by comparing the observed velocities in opposite directions, determine the velocity of the æther with respect to these terrestrial stations. All methods, however, by which it is practicable to determine the velocity of light from terrestrial experiments depend on the measurement of the time required for the double journey from one station to the other and back again, and the increase of this time on account of a relative velocity of the æther equal to that of the earth in its orbit would be about one hundred millionth part of the whole time of transmission, and would therefore be quite insensible.

2 _Scientific Papers_ 768-769.

The purpose of that work would be to determine the velocity of the æther, and Maxwell himself conducted experiments to that effect, coincidentally possibly even revealing redshift.

The only practical method of determining directly the relative velocity of the æther with respect to the solar system is to compare the values of the velocity of light deduced from the observation of the eclipses of Jupiter's satellites when Jupiter is seen from the earth at nearly opposite points of the ecliptic.

Arago proposed to compare the deviation produced in the light of a star after passing through an achromatic prism when the direction of the ray within the prism formed different angles with the direction of motion of the earth in its orbit. If the æther were moving swiftly through the prism, the deviation might be expected to be different when the direction of the light was the same as that of the æther, and when these directions were opposite.

The present writer* arranged the experiment in a more practicable manner by using an ordinary spectroscope, in which a plane mirror was substituted for the slit of the collimator. The cross wires of the observing telescope were illuminated. The light from any point of the wire passed through the object-glass and then through the prisms as a parallel pencil till it fell on the object-glass of the collimator, and came to a focus at the mirror, where it was reflected, and after passing again through the object-glass it formed a pencil passing through each of the prisms parallel to its original direction, so that the object-glass of the observing telescope brought it to a focus coinciding with the point of the cross wires from which it originally proceeded. Since the image coincided with the object, it could now be observed directly, but by diverting the pencil by partial reflection at a plane surface of glass, it was found that the image of the finest spider line could be distinctly seen, though the light which formed the image had passed twice through three prisms of 60°. The apparatus was first turned so that the direction of the light in first passing through the second prism was that of the earth's motion in its orbit. The apparatus was afterwards placed so that the direction of the light was opposite to that of the earth's motion. If the deviation of the ray by the prisms was increased or diminished by this reason in the first journey, it would be diminished or increased in the return journey, and the image would appear on one side of the object. When the apparatus was turned round it would appear on the other side. The experiment was tried at different times of the year, but only negative results were obtained. We cannot, however, conclude absolutely from this experiment that the æther near the surface of the earth is carried along with the earth in its orbit, for it has been shown by Professor Stokes* that according to Fresnel's hypothesis the relative velocity of the æther within the prism would be to that of the æther outside inversely as the square of the index of refraction, and that in this case the deviation would not be sensibly altered on account of the motion of the prism through the æther.

* Phil[osophical]. Trans[actions] [of the Royal Society], CLVIII (1868), p. 532. [Communicated by Prof. Maxwell to Dr Huggins and included by him in his paper on the spectra of some of the stars and nebulae.]*

* Phil. Mag., 1846, p. 53.

2 _Scientific Papers_ 769-770.

Taken from the perspective advanced here if the æther in fact moves the earth. i.e., the river moves the boat, any experiment attempting to differentiate the velocity between the two would always produce a null result.

By recognizing the near equivalence between the velocity of light and the velocity of the propagation of electromagnetic phenomena in the æther, Maxwell deduces that the æther, the luminiferous medium through which light passes, electromagnetic radiation, and light itself are one and the same.

_Electromagnetic Theory of Light_.—The properties of the electromagnetic medium are therefore as far as we have gone similar to those of the luminiferous medium, but the best way to compare them is to determine the velocity with which an electromagnetic disturbance would be propagated through the medium. If this should be equal to the velocity of light, we would have strong reason to believe that the two media, occupying as they do the same space, are really identical.

* * * * * * *

The undulatory theory in the form which treats the phenomena of light as the motion of an elastic solid, is still encumbered with several difficulties.[Footnote omitted. JG]

The first and most important of these is that the theory indicates the possibility of undulations consisting of vibrations normal to the surface of the wave. The only way of accounting for the fact that the optical phenomena which would arise from these waves do not take place is to assume that the æther is incompressible.

2 _Scientific Papers_ 771-772.

The issue then is what constitutes "compressibility." Compressiblity invariably involves "synchronicity" of the converging waveforms such that volume is reduced without the attendant loss of mass, addressed more fully below.

Although Maxwell retains Ampere and Thomson's theories of molecular vortices, the problem arises as to the size and dynamics of the vortices, and ultimately the energy necessary to maintain the angular velocity of the vortex. The problem, as Maxwell recognizes, is that if the magnet were taken to be an archtypical vortex, there appears to be no diminution in energy over the life of the magnet inferring that the vortex is capable of maintaining its velocity indefinitely that itself poses philosophical and cosmological anomalies, ultimately, although not stated, of perpetual motion itself.

It is often asserted that the mere fact that a medium is elastic or compressible is a proof that the medium is not continuous, but is composed of separate parts having void spaces between them. But there is nothing inconsistent with experience in supposing elasticity or compressibility to be properties of every portion, however small, into which the medium can be conceived to be divided, in which case the medium would be strictly continuous. A medium, however, though homogeneous and continuous as regards its density, may be rendered heterogeneous by its motion, as in Sir W. Thomson's hypothesis of vortex-molecules in a perfect Liquid (see Art. ATOM)* . [Footnote omitted here. JG]

* * * * * * *

Whatever difficulties we may have in forming a consistent idea of the constitution of the æther, there can be no doubt that the interplanetary and interstellar spaces are not empty, but are occupied by a material substance or body, which is certainly the largest, and probably the most uniform body of which we have any knowledge.

Whether this vast homogeneous expanse of isotropic matter is fitted not only to be a medium of physical interaction between distant bodies, and to fulfil other physical functions of which, perhaps, we have as yet no conception, but also, as the authors of the _Unseen Universe_ [Balfour Stewart] seem to suggest, to constitute the material organism of being exercising functions of life and mind as high or higher than ours are at present, is a question transcending the limits of physical speculation.

2 _Scientific Papers_ 775.

In _Matter and Motion_ Maxwell brings together this material in a nontechnical book for laypersons, which even within the style of the present work is too thinned down to require discussion here except for the clear and concise explanation of what it means to be "at rest" and contrariwise to be "in motion,' under the distinction of which lies buried the primary principle of the Universe and through which everything is simultaneously both together and apart, i.e., "pure spacetime" and 'relative spacetime" above.

30. MEANING OF THE PHRASE "AT REST"

It is true that when we say that a body is at rest we use a form of words which appears to assert something about that body considered in itself, and we might imagine that the velocity of another body, if reckoned with respect to a body at rest, would be its true and only absolute velocity. But the phrase "at rest" means in ordinary language "having no velocity with respect to that on which the body stands," as, for instance, the surface of the earth or the deck of a ship. It cannot be made to mean more than this.

It is therefore unscientific to distinguish between rest and motion, as between two different states of a body in itself, since it is impossible to speak of a body being at rest or in motion except with reference, expressed or implied, to some other body.

_Matter and Motion_ at 22.

Figure 39 Convergence of "right-hand rule" waveforms at locus.

Figure 40 Maxwell's "Fig. 25," _A Treatise on Electricity & Magnetism_,Volume 2, page 156, illustrating three right-hand waveforms on the respective x, y, and z axes intersecting at the origin.

Figure 41 Maxwell's "Fig. 2,' "On Physical Lines of Force: Part IV, The Theory of Molecular Vortices applied to the Action of Magnetism on Polarized Light," _The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science_ , Series 4, Volume 21, Plate V.

**Chapter** **2.10 EINSTEIN**

The final word in this historical discussion of unified and pure field theory **MUST GO TO** Einstein who is responsible for bringing the issue at least to the doorstep if not the first step through the threshold of its solution. Like those who preceded him, and it is difficult to say whether Aristotle himself might not have solved the problem for ages to come in perceiving that the Sun and Moon, and inferentially even the Earth itself were if not spherical, then certainly "round" from which in conjunction with a drop of water (recall Archimedes!!) suspended as a sphere at its apogee, could have surmised that possibly all celestial bodies where likewise spheres. Apparently no one before had ever considered the fact that the Moon was spherical and that now that man has set foot on it and traveled 'round it that that fact had any metaphysical significance to current cosmologists. Even "the man in the Moon" has remained moot from his first appearance eons ago!!

Notwithstanding Einstein's apparent interest in various philosophical, moral, and ethical issues, as for example those collected in the essays in _Out of My Later Years_ , his empirical view of the nature of the physical world was decidedly not philosophical or metaphysical. His view of the physical world had decipherable meaning only when it could be or was actually reduced to a mathematical equation, and that always within the limits of the "philosophy" of mathematics that dominated the "mathematical physics" to which he had taken an oath of fealty and that discipline was philosophically wanting. Ultimately, that oath precluded him from perceiving the underlying principle of the Universe and the unified and pure field theories that he himself broached. The truth of that proposition is exemplified in the three simple drawings that he proffered in the short essay "An Elementary Derivation of the Equivalence of Mass and Energy" in his _Essays in Physics_. The drawings and associated text are:

The following derivation of the law of equivalence, which has not been published before, has two advantages. Although it makes use of the principle of special relativity, it does not presume the formal machinery of the theory but uses only three previously known laws:

(1) The law of the conservation of momentum.

(2) The expression for the pressure of radiation; that is, the momentum of

a complex of radiation moving in a fixed direction.

(3) The well known expression for the aberration of light (influence of the

motion of the earth on the apparent location of fixed stars—Bradley).

We now consider the following system. Let the body B rest freely in space with respect to the system Ko. Two

complexes of radiation S, S' each of energy move in the positive and negative xo direction respectively and are eventually absorbed by B. With this absorption the energy of B increases by E. The body B stays at rest with respect to Ko by reasons of symmetry.

Now we consider this same process with respect to the system K, which moves with respect to Ko with the constant velocity v in the negative Zo direction. With respect to K the description of the process is as follows.

The body B moves in the positive Z direction with velocity v. The two complexes of radiation now have directions with respect to K which make an angle  with the x axis. The law of aberration states that in the first approximation  = , where c is the velocity of light. From the considerations with respect to Ko we know that the velocity of v of B remains unchanged by the absorption of S and S'.

When all of this is taken individually and as an integrated whole, one may see, but for some small but monumental differences, all that underlies the unified and pure field theory. The parsing begins, as it must, with the presumption of the "three previously known laws."

As to the first, "the law of conservation of momentum," one may readily deduce from the discussion and the drawings that notwithstanding the outward appearance of what I have designated as Figure 39, the body "B" is not one that is considered to remain in situ for purposes of the exposition but of necessity within the context of the theory of special and even general relativity is one "in motion." Hence, the phrase "conservation of momentum" perforce applies to bodies in motion and not bodies that in the vernacular would be "at rest." Accordingly, Einstein's view of the process—and here I distinctly use the word "process" as distinct from "Einstein's view of the theory of relativity" as the latter is inherently based on bodies in motion, i.e., "On the Electrodynamics of **Moving** Bodies," that is predicated as a start with a Universe in which everything is "in motion." As a result, he has disqualified both himself and his theories from taking into consideration bodies "at rest." The problem with that position is that he has created an inherent incongruity between everything that would be nominally in the center of an orbital system as distinct from the entities in orbit. That premise ultimately, like Aristotle before him, precludes him from seeing the continuity of existence that is itself merely predicated on the concept of orders of magnitude, i.e., "gradations of r." That is the first problem.

The second problem, although one might see it as miniscule, turns out to be in relation to the theory advanced here, not the "gravitational constant' as being what he considered as his "biggest mistake," but rather that he drew B as a rectangle rather than a circle. Although parenthetically he drew the two "complexes of radiation, S, S'" as circles, again he did not perceive what he himself drew in terms of the larger context of the drawing even when he was working on unified and pure field theory at the time the collection of essays were being put together. Had it possibly even been the other way around, i.e., B being the circle and S and S" being squares, there might have been the possibility—though remote—that he would have "stubbed his toe on a stone" that would have resulted with a "Oh meine gott, dat est." But he didn't. One must also recognize that it is this very "expression of pressure of radiation" that was the outstanding issue in my response to my nephew.

The third is that as advanced here, had his diagram been a circle it might have raised a potential inference of an omnidirectional equipotential "pressure of radiation" that would have **of itself had the capacity to generate the circle itself** but that would have led him to perceive the association of radiation pressure as being but another manifestation of the same type of pressure exemplified in Model 1 and opolarity. But apparently, quite "Franckly," that was outside his capacity to perceive as he had no real experience with the experimental world of which **Faraday was the master** but rather Einstein conducted all of his experiments in his head—the famous "thought experiments" of which **he was the master.**

As a quantum photonist, he was never especially enamored by wave mechanics and all of its implications for "quantum mechanics" and therefore apparently did not consider the application of the "right hand rule" as it applied to his model as that model does not seem to have any consideration of the underlying "mechanics" of the phenomenon that he was in fact depicting. Thus it was one thing to perceive "pressure of radiation" as a pressure exerted on an entity that will be absorbed by the entity and quite another to see that the pressure of radiation was in fact a pressure that results from electromagnetic radiation and therefore has a polarity to it, all of which had been clearly drawn in Maxwell's Figure 25. However, neither Maxwell himself and certainly not Einstein perceived the particular significance of two right-hand waveforms colliding, i.e., into a spark, although Maxwell's model attempts to articulate it, but not quite correctly. Einstein had all of the elements in place had he changed the square into a circle so that the two "complexes of radiation" collided with each other and their combined energy would have resulted in the primary singularity or some gradation thereof.

Finally, when S and S' converge into the singularity, the conservation of momentum is conserved but it is now converted into the angular velocity of an entity rotating at velocity c about a fixed point so that it appears to be a body "at rest." This is exactly the _Aristotlespeak_ that Aristotle himself could not extricated himself from as the quagmire of semantics could not have the **same** body simultaneously in motion and still be at rest. Well, quite simple, all of us sitting here reading this page as the "world turns."

The statement of the relationship between energy and mass therefore is a statement about the condensation and convergence of the pressure of radiation, i.e., the electromagnetic radiation that constitutes "the field" at a point locus, an entity, a singularity.

The final word, therefore, must be reserved for the problem underlying the "philosophy of mathematics," namely, the equation for describing the convergence of the pressure of radiation not into a body B but into each other, i.e.,

S   S'

What is the equation of the convergence of two right-hand waveforms into each other? Well, the complexities of that anomaly are set out above in the "The Primary Equation" and were buried so deep in the underlying "philosophy" of _i_ (√-1) and how it could be emulated in the modern context of "mathematical physics." I submit, except as postulated here it could not! And there we have it!

One must recognize that Einstein presents the paradox of one who devoted essentially one-half of his life in the search for a/the unified and pure field theory/ies and yet was psychologically precluded from finding it/them because of his premise that "god does not play dice," i.e., that physics does not include the laws of probability. First, there is the deification of the Universe that (a) presents its own set of problems that go back to Bruno and the unwillingness to accept that the Universe is everything and the only thing and (b) that the laws of causality, if there were any, are themselves deified. If that were the case, Einstein should have stopped there. But being an advocate in his defense against being excommunicated that would not have applied to him because of his own religious background or contrary to the first Amendment to the Federal Constitution or being burned at the stake that would constitute aggravated arson under the criminal law of New Jersey where he lived, we can not take the position that it was simply a theatrical statement to placate those who were antithetical to atheists or agnostics. However, even putting that aside, we are still left with the problem of probabilities to which we all owe our own existence and the infinity of space and time where the laws of probability open a view to existence beyond that of classical mathematical physics to which he had taken an oath of fealty. Simply put, he could not conceive that the physical Universe itself had any evidential value and that physics ultimately was still but a branch of natural philosophy going back to classical antiquity, namely, the truths or principles underlying all knowledge, being, and reality. Better than that I do not know how it can be stated, at least by me, nor, so far as I have perceived to date, by anyone else.

**Chapter** **2.11 MODEL 3**

Model 3 begins with focusing magnetic lines of force to a locus of convergence as shown in Figure 42. The experiment was conducted by placing four horseshoe magnets (See Models 1, 2A and 2B) in a nonmagnetic square wooden frame to which the magnets were held in fixed positions by bolts and nuts through the orifices in the arch of the magnets. In the top configuration, the magnets were placed in N-S-N-S-N-S-N-S orientation in relation to each other and iron filings were sprinkled onto a clear plastic sheet (not shown) that was placed over the magnets and the sheet given "Faraday-like" taps that caused the iron filings to align themselves along the magnetic lines of force emanating from the magnets.

The middle figure shows the rearrangement of the filings as the magnets were partially rotated from a N-S-N-S relationship to the fully rotated relationship of N-N-S-S-N-N-S-S orientation of opolarity in the bottom figure in which the magnetic lines of force are focused to a locus of convergence.

As a result of the radiation pressure (magnetic lines of force) directed to the locus of convergence, the filings are expelled outwardly as if they were subjected to four jets of water directed to the locus causing the water to be sprayed outwardly. If the pressure were uniform and omnidirectionally focused to the locus of convergence at the center, the filings would have been compacted there as a sphere. From what little that I know of the mechanism of the atomic bomb, and that being virtually nothing, the fissionable material was focused and compacted by simultaneous explosions around the critical mass to the point of E = mc2. Here only a portion of that convergence can be executed into the essentially geometrically perfect circular center that however is duplicated in "atomic bomb" kind shown in Figure 12 of Model 1 had the configuration been further modified by other magnetic lines of force (radiation pressure) omnidirectionally around the configuration in Figure 42, the filings then being prevented from being expelled from the locus of convergence.

When the filings are removed and an incandescent light bulb is placed at the locus of convergence Model 3 demonstrates the direct effect of the radiation pressure upon light itself as shown in Figure 43. When the frame is placed over the unlit bulb there is no effect upon the filament. When the frame is placed over a lit bulb, the filament will instantaneously begin to vibrate and the luminosity will instantaneously increase such that most bulbs will burn out essentially instantaneously beyond their thermal/luminosity threshold. Within the limits of manufacturing variations, a few bulbs will be able to continue to "burn" without destruction. See also the discussion below at Section 3.1, Redshift.

When all of these demonstrations and principles are taken together, the inference—at least as far as I am concerned and convinced—is an empirical _dis_ proof of the concept of a "black hole," namely a cosmological phenomenon in which the gravitational forces are so great that even light itself (a photon) cannot escape the intensity of the gravitational field generated by the entity, since as advanced herein, the Universe is **more** than gravitational.

We begin with the proposition that the concept of a "black hole" is predicated on **mathematical** presumptions about a cosmos in which **gravity is the only known cosmological force** whereas I submit that I have here consistently demonstrated that there is an _equal and opposite_ force that exists concurrently with gravity. Secondly, my models demonstrate that opolarity is fully capable of moving, aggregating, and levitating mass to and at a locus in a manner that is indistinguishable from a process that would otherwise be attributable to gravity or interstellar space alone. There is nothing about the "curvature of space" implicated in any of these models—at least as I consider the models and the demonstrations and experiments and the theory upon which they are built and the demonstrations produced. Finally, the lines of force that aggregate and compress mass to a locus concurrently come into opposition with themselves to effluviate themselves outwardly from the locus, or more simply, result in the concurrent outward generation of electromagnetic radiation thereby demonstrating that no matter how powerful the force that compresses the mass together at the locus there is an equal and opposite effluvium of forces outwardly from that locus under the "pressure" of unidirectional time. Accordingly, no phenomenon, whether it be cosmological or quantum or wave mechanical, can have a gravitational force so intense that even the radiation generated by the phenomenon itself cannot escape its own gravitational field. As the above figures demonstrate such a conclusion is a contradiction in terms. Ask any volcano!!

Finally, having set out what I believe to be the empirical demonstration of the molecular vortex that returns us to the initiation of the issue by Ampere, I submit that the resolution of that issue also resolves the issue of "What is gravity?"

GRAVITY IS THE OUTWARD MANIFESTATION

OF THE LINES OF FORCE THAT CONVERGE

TOWARD THE CENTER OF THE MOLECULAR VORTEX

Since the mass agglomerated at the center of the molecular vortex is itself a consequence of the compactive pressure of the field that generates the molecular vortex, the mass constitutionally embodies the convergent lines of force that generate the mass and therefore the mass embodies the electromagnetism that is a constituent element of its existence. Thus the dynamic lines of force in Model 1 that aggregate the ball bearings into the vortex remain "embedded" in the mass that the lines of force themselves aggregated. Accordingly, gravity, magnetism, and electromagnetism are unified. Q.E.D.

Having come this far, what can be said about a "line of force" and the best that I can come up with is that it is a "single thread of unidirectional time" the precise length and breadth of which is determinable only to the extend that it can be made perceptible by fine iron filings and yet without them its force is nonetheless empirically perceptible because of their absence and therefore their individuality is not perceptible as shown for example in Figures 14, 42, and 43. Beyond that I cannot go nor do I think that it is possible to go. But that the Earth, Moon, Sun, and other planets and their satellites, Jupiter and its moons for example, are spherical can not be denied and that all of the Universe and therefore existence is afloat in it can also not be denied by anyone who has the will and capacity to see. He who believes he is getting younger is beyond redemption even to his dying day.

To finish it off, as a **matter** of fact, there is nothing **dark** about the forces that compress the **matter** into the essentially spherical shape in Figures 12 and 14 nor the perfectly circular (spherical) shape in the bottom configuration in Figure 42 and yet there it is for all to see in the very light of day to put an end to the search for dark matter in the Universe.

Figure 42 Magnetic lines of force of four magnets being configured to generate a field in opolarity focused to a locus of convergence.

Figure 43 Model 3—Demonstration of the direct affect of the "invisible" magnetic lines of force of magnets in opolarity on a 4-watt incandescent bulb at the locus of convergence at which the filament either spontaneously increases luminosity or spontaneously "burns out" because of the densification of the energy in the pressurized æther that exceeds the manufacturing limits of the filament.

**Chapter** **3. TOPICAL DISCUSSION**

**Chapter** **3.1 REDSHIFT**

In an _infinite_ Universe, the determination of cosmological distances per se adds nothing to unified or pure field theory for the processes discussed herein exist uniformly throughout the cosmos (Universe) and the present theories explicitly reject the "big bang" model. To detect an entity at cosmological distances only raises the inference that there are omnidirectional equipotential forces beyond that entity that exert radiation pressure to place that entity where it is. Hubble himself recognized the problems with using redshift as a measuring stick in his discussion of "The Exploration of Space" in _The_ _Realm of the Nebulæ_ (reprinted in part in Munitz, _Theories of the_ _Universe_ ). We begin with the empirical findings because of their importance to a fundamental issue in unified and pure field theory. I quote at length:

When large regions of the sky, or large volumes of space, are compared, the irregularities average out and the large-scale distribution is sensibly uniform. The distribution over the sky is derived by comparing the numbers of nebulæ brighter than a specified limit of apparent faintness, in sample areas scattered at regular intervals.

The true distribution is confused by local obscuration. No nebulæ are seen within the Milky Way, and very few along the borders. Moreover, the apparent distribution thins out, slightly but systematically, from the poles to the borders of the Milky Way. The explanation is found in the great clouds of dust and gas which are scattered throughout the stellar system, largely in the galactic plane. These clouds hide the more distant stars and nebulæ. Moreover, the sun is embedded in a tenuous medium which behaves like a uniform layer extending more or less indefinitely along the galactic plane. Light from nebulæ near the galactic poles is reduced about one fourth by the obscuring layer, but in the lower latitudes, where the light-paths through the medium are longer, the absorption is correspondingly greater. It is only when these various effects of galactic obscuration are evaluated and removed, that the nebular distribution over the sky is revealed as uniform, or isotropic (the same in all directions).

The distribution in depth is found by comparing the numbers of nebulæ brighter than successive limits of apparent faintness, that is to say, the numbers within successive limits of distance. The comparison is effectively between numbers of nebulæ and the volumes of space which they occupy. Since the numbers increase directly with the volumes (certainly as far as the surveys have been carried, probably as far as telescopes will reach), the distribution of the nebulæ must be uniform. In this problem, also, certain corrections must be applied to the apparent distribution in order to derive the true distribution. These corrections are indicated by the velocity-distance relations, and their observed values contribute to the interpretation of that strange phenomenon.

Thus the observable region is not only isotropic but homogeneous as well—it is much the same everywhere and in all directions. The nebulæ are scattered at average intervals of the order of two million light-years or perhaps two hundred times the mean diameters. The pattern might be represented by tennis balls fifty feet apart.

_The Realm of the Nebulæ_ at 30-31.

He next addresses the red shift analogous to a prism.

When a ray of light passes through a glass prism (or other suitable device) the various colors of which the light is composed are spread out in an ordered sequence called a spectrum. The rainbow is, of course, a familiar example. The sequence never varies. The spectrum may be long or short, depending on the apparatus employed, but the order of the colors remains unchanged. Position in the spectrum is measured roughly by colors, and more precisely by wave-lengths, for each color represents light of a particular wave-length? From the short waves of the violet, they steadily lengthen to the long waves of the red.

* * * * * * *

Nebular spectra are peculiar in that the lines are not in the usual positions found in nearby light sources. They are displaced toward the red of their normal position, as indicated by suitable comparison spectra. The displacements, called red-shifts, increase, on the average, with the apparent faintness of the nebula that is observed. Since apparent faintness measures distance, it follows that red-shifts increase with distance. Detailed investigation shows that the relation is linear.

Small microscopic shift, either to the red or to the violet, have long been known in the spectra of astronomical bodies other than nebulæ. These displacements are confidently interpreted as the results of motion in the line of sight—radial velocities of recession (red-shifts) or of approach (violet-shifts). The same interpretation is frequently applied to the red-shifts in nebular spectra and has led to the term "velocity-distance" relation for the observed relation between red-shifts and apparent faintness. On this assumption, the nebulæ are supposed to be rushing away from our region of space, with velocities that increase directly with distance.

Although no other plausible explanation of red-shifts has been found, the interpretation as velocity-shifts may be considered as a theory still to be tested by actual observations. Critical tests can probably be made with existing instruments. Rapidly receding light sources should appear fainter than stationary sources at the same distances, and near the limits of telescope the "apparent" velocities are so great that the effects should be appreciable.

The Observable Region as a Sample of the Universe

A completely satisfactory interpretation of red-shifts is a question of great importance, for the velocity-distance relation is a property of the observable region as a whole. The only other property that is known is the uniform distribution of nebulæ. Now the observable region is our sample of the universe. If the sample is fair its observed characteristics will determine the physical nature of the universe as a whole.

And the sample may be fair. As long as explorations were confined to the stellar system, the possibility did not exist. The system was known to be isolated. Beyond lay a region, unknown, but necessarily different from the star-strewn space within the system. We now observe that region—a vast sphere, through which comparable stellar systems are uniformly distributed. There is no evidence of a thinning-out, no trace of a physical boundary. There is not the slightest suggestion of a supersystem of nebulæ isolated in a larger world. Thus, for purposes of speculation, we may apply the principle of uniformity, and suppose that any other equal portion of the universe, selected at random, is much the same as the observable region. We may assume that the realm of the nebulæ is the universe and that the observable region is a fair sample.

The conclusion, in a sense, summarizes the results of empirical investigations and offers a promising point of departure for the realm of speculation. That realm dominated by cosmological theory, will not be entered in the present summary. The discussions will be largely restricted to the empirical data—reports of actual explorations—and their immediate interpretations.

Yet observation and theory are woven together, and it is futile to attempt their complete separation. Observations always involve theory. Pure theory may be found in mathematics but seldom in science. Mathematics, it has been said, deals with possible worlds—logically consistent systems. Science attempts to discover the actual world we inhabit. So in cosmology, theory presents an infinite array of possible universes, and observation is eliminating them, class by class, until now the different types among which our particular universe must be included have become increasingly comprehensible.

The reconnaissance of the observable region has contributed very materially to this process of elimination. It has described a large sample of the universe, and the sample may be fair. To this extent the study of the structure of the universe may be said to have entered the field of empirical investigation.

_Realm of the Nebulæ_ at 32-35.

The issue of redshift invariably is tied to the metrification of an infinite and adiabatic Universe. The problem that arises with redshift is the resolution of an expanding Universe with a cosmological model predicated on gravity. If we accept that the Universe is held together by gravity, does an expanding Universe imply that gravitational forces also dissipate as the Universe expands? Does that diminution also apply to electrostatics and electromagnetics. On the other hand, do electrostatics, electromagnetics, and gravity already incorporate redshift that is empirically not perceptible in the inertial system of our solar system or galaxy because of the relatively short distances at issue? Or is there another yet undisclosed relationship between the attractive force of gravity and the suggested expanding Universe? Looked at from another perspective, can we say that not only does gravity keep a solar system or local group together, but that conversely, the local group is also gravitationally attracted to other constellations. Thus, a gravitational force directed toward an internally focused point would be equally attracted by an equal and opposite force to an externally focused point. The problem arises whether the attractive force toward an external object can be converted to an equivalent repulsive force in the same way that the concept of polarity can by axial rotation be converted into opolarity. Notwithstanding that the problem can be reduced to a mathematical inversion by a simple change of sign, empirically the change is not so simple. The larger problem is when we try to predicate a unified and pure field theory on an expansionary Universe we have to account for nongravitational cosmic processes that would ultimately condense the Universe back together. Invariably this implicates time, an upper limit of gravitational forces, and a mechanism for condensing the Universe. We also have to consider whether these processes exist simultaneously, concurrently, cyclically, or successively, and whether they are detectible by a process that is itself part of the process. Ultimately, a unified and pure field theory must account for all phenomena as well as all apparent disparities.

As Hubble himself states, a beam of light is refracted into its spectrum by passing it through a densified prism and to no less an extent does the densified æther act as a prism to refract interstellar light. Thus the nature of the æther left unresolved at the close of the 19th Century is the central issue in cosmology at the beginning of the 21st! Accordingly, the resolution of redshift lies in the homogeneity of the pressurized interstellar medium, the æther, that operates exactly _as if it were a uniform refracting prism across the uniform infinity of space_. Model 1 demonstrates that a pressurized field can compress, suspend, and move mass at a distance without any perceptible mechanical device. Faraday showed that a densified field could directly affect the rotation and therefore frequency of a beam of light. Model 3 demonstrates that a field in opolarity can directly affect light—or at least a filament sufficiently energized to generate light or at least electromagnetic radiation, which as Maxwell intuited are the same thing. To that end I conducted a series of experiments in an attempt to duplicate redshift at ambient. On or around January 1, 1994 my first version of the experiment was to take a small metal can and punch a pinhole in the side. I placed a small 4-watt incandescent bulb inside the can. (See Model 3) At the outside of the pinhole I held two magnets in opolarity in an attempt to see if I could affect the interference pattern as the light was projected onto a wall. Figure 44 is my sketch of the apparatus. But I never got that far. Instead of getting a nice collimated light, what I made was a pinhole camera that projected an extremely clear inverted image of the filament of the bulb when the can was at the precise focal length from the wall. Additionally the magnet went directly to the metal can! After about two hours of frustration until I recognized what I had done, I threw out the can, put the bulb back into a drawer, the magnets back into a storage box, and that was that.

Sometime around the late summer or fall of 1996 I began to rethink the experiment and the first thing that I had to do was get a steady source of collimated light, and a pinhole in a shutter was not a feasible setup. After researching the cost and feasibility of making a beam collimator, I just went out and bought a used 8 mm motion picture projector for $30 as the source for a steady collimated beam. Next, it was necessary to confine the beam to as narrow a pencil as possible so that I fabricated an extended column to the lens holder and fitted a pinhole aperture to the end to further reduce the pencil. With this apparatus, on or about February 23, 1997 I began the experiments by focusing the beam through a narrow opening between two 1-ton electromagnets whose fields could be turned on and off and reversed. The first arrangement (Figure 45) had the beam pass through the pinhole to create Fraunhofer diffraction rings on the screen and by switching the field on and off in the different modes I looked through a magnifying glass in an attempt to see any shifting in the rings. No perceptible difference. As shown, it was necessary to build a heavy wooden frame around the magnets to keep them in a fixed position when the field current was turned on. A c-clamp was also used to hold the top of the magnets, removed in Figure 45 but shown in Figure 46.

In Figure 46 I reduced the distance between the magnets and passed the beam over a small nail that created diffraction patterns to again attempt to observe any shifting in the patterns, since we are talking about wavelength variations that might be noticeable at ambient. No perceptible difference.

In Figure 47 I passed the beam through the gap and reflected it off a refraction grating onto a screen to produce a spectrum. No perceptible difference.

In Figure 48, per Faraday, I attached a rotatable polarized filter to the end of the extended tube and used a pair of polarized sunglasses to see if there was any change in the angle of polarization. No perceptible difference.

In Figure 49 I passed the beam through a 50% beam splitter, one-half passing directly through two 2-ton electromagnets and the other half reflected to the left to a mirror and then focused to be superimposed on the first beam as an optical comparison. No detectible difference.

In Figure 50 I passed the beam through the beam splitter with one-half going through the 2-ton electromagnets through a refracting prism onto a screen and the other half reflected to a second prism whose spectrum was then reflected to be superimposed on the first. No perceptible difference.

At this point, having tried these various configurations over the period between February 23 to March 30, 1997, it was time to go back to the beginning and try something different. The first question was "Whether the densified field in opolarity has any affect on light at all?" Accordingly, I got the 4-watt incandescent bulb out again and built a small wooden frame into which I fitted my four magnets in opolarity. Subsequently Model 3 above. (Figure 51) The bulb was placed in the center of the magnets and with the light off there was no motion of the filament. When the light was turned on the filament vibrated so vigorously that it "blew out." I replaced the bulb and switched it on and off and unquestionably the energized filament is affected by the field in opolarity. I then reoriented the magnets N-S-N-S and switched on the light, no affect. Unquestionably the densified field has a direct affect on the luminous filament. i.e., radiation.

The issue is whether this could be applied to a beam of light and redshift. Accordingly I refitted the projector with an elongated piece of plastic pipe through which I could confine the collimated light over a thin target to create diffraction patterns. (Figure 52) No perceptible difference.

In the final series I used a spectroscope. I placed two pieces of black tape over the aperture of the spectroscope so that they converged into a fine point at the top of the aperture to create spikes at the peaks of the spectrum that was projected onto the scale on the inside of the spectroscope. A fluorescent bulb was used because it has a selective spectrum rather than the more continuous spectrum of a standard incandescent bulb. Thus if there were any shift in the spectrum the point on the scale would make it more easily discernible than a shift in the continuous spectrum of the incandescent bulb. Figure 53 shows the configuration with the two 2-ton electromagnets. No perceptible shift. Figure 54 shows the setup using the permanent horseshoe magnets in opolarity. Figure 55 shows the setup with the fluorescent bulb behind the coil of a 1-ton electromagnet, and Figure 56 shows the bulb inside the coil itself. The orientation of the coil in respect to the spectroscope was also reversed. No perceptible shift.

Although I was not able to detect any shift, these experiments can not be totally written off as failures for a variety of reasons. First, as shown in Figure 57, the field generated by an electromagnet with an iron core can not be focused to a point as the lines of force are propagated omnidirectionally around the core rather than from pole to pole Secondly, with the iron core removed, the lines of force are concentrated inside the coil, but not in opolarity. (Figure 58) Thirdly, since the redshift itself is only a few angstroms per 10-million light-years, these experiments are undoubtedly well below the density that approaches that of interstellar space at those distances. Fourthly, the experiments even in their simplicity are not done with camera attachments or microscopes so that if there were in fact any redshift, I do not have the precise lines whose position could be checked against several successive photographs.

Additionally, **all of the apparatus itself must be within the pressurized field** **when the experiment is conducted** otherwise the pressure of the field will be eliminated once the photons (beam of light) leaves the "resistance" created by the field in which the redshift occurs and returns to the ambient "unpressurized" æther outside the experimental apparatus. One must recognize that as to Hubble the Earth is **itself** in the surrounding pressurized æther when the light from the distant star is perceived and redshift detected. That is not the same when an artificial pressurized field is created in a laboratory in which the emitting and "interstellar" medium is in the pressurized field and the detecting equipment is not! and that makes all the experimental and philosophical difference.

It is also reasonable to hypothecate that a correlation coefficient can be derived between the uniform interstellar pressure (Penzias and Wilson) and other schemes involving uniform densified medium that replicate the essentially linear graph derived by Hubble in his Figure 1 ("A Relation Between Distance and Radial Velocity Among Extra-Galactic Nebulae," at 168). For example, a spectroscope and light source could be placed in a hyperbaric chamber in which the air pressure is gradually increased with the result that redshift is detected with increased density of the air pressure. A second scheme would be to pass a beam of light through a vessel filled with distilled water from various distances from a spectroscope to which a camera has been attached in order to detect redshift having an essentially linear correlation comparable to the passage of light through the uniform æther at comparable lightyear gradations. A third scheme would be to pass a sound wave through a similar column of water, or even better, to use the sonar system of a submarine to conduct comparable experiments at exceedingly longer distances between the source of the signal and its reception to derive an equally linear coefficient of correlation between density of a uniform medium and distance all to dispel the underlying premise that "redshift" is a result of radial velocity rather than resistance of the interlineating medium. There are undoubtedly other schemes that a clever researcher can come up with while still faithful to the underlying theory.

Finally, it may well be that some or all of the elements of these experiments in proper combination do or could show redshift if the apparatus were bigger, more elaborate, and more precise than my "tabletop" laboratory setup, i.e., a $10.00 plastic spectroscope without camera attachment!

Beyond this I cannot go and as much as I am disinclined to, I must leave this work to others who have the facilities to try it. Certainly a detectible redshift will be directly proportional to the density of the field that if found, would duplicate Hubble's scale and thereby disprove the big bang theory in favor of the one advanced here. The reinterpretation of Hubble's findings and several possible research setups based on light from existing distance light sources are shown in Figure 59.

**Chapter** **3.2 UNIDIRECTIONAL TIME**

The issue presents itself as to how to determine the "right" way to paint the directional arrows on the magnets, i.e., the "direction of time." This issue has great philosophical, theoretical, and physical importance for it implicates the "non-sense" of time reversal and other related theories in modern physics and cosmology. Without belaboring the point, it makes no difference which way the first set of arrows are painted on the magnets just as long as they uniformly point in the same direction in relationship to each other. If you start with counterclockwise arrows you will see that on the other side of the magnet the arrows will be clockwise or vice versa! Simply put. it is impossible and wholly irrelevant to even attempt to know which way the "current" (time) runs in any given pair of magnets. The proof is that if you followed my directions and rotated the magnets, one pair will point away from each other and the other pair will point toward each other and yet both pairs are in opolarity. More than that one cannot do except that I am unaware of anyone giving birth to an elderly person who over the course of a lifetime progressively gets younger and ultimately expires as an infant or that walking backwards or putting a car in reverse will work any better. Simply put, all empirical evidence and the inferences that can reasonably be drawn therefrom suggest that time invariably moves "forward," i.e., it is "unidirectional" and that means in simplest terms that you cannot drink the same glass of water twice or the earlier version that "you cannot step into the same river twice." It is

### THE PRIMARY FORCE OF

### EXISTENCE FROM WHICH

### NOTHING IS IMMUNE

**Chapter** **3.3 THE METRIFICATION OF THE COSMOS**

By advancing the proposition that all celestial bodies are spherical,* we infer that the shape of a body is the consequence of an omnidirectional equipotential pressurized (æther) field that surrounds that body. At the limits of the perceptual Universe from that body at which may be perceived another celestial body one infers in like manner that that celestial body is also surrounded in like manner by an equally uniform omnidirectional equipotential field and so forth and so on ad infinitum. This does **NOT** mean that the _cosmos_ itself is spherical! It only means that the extend of the _perceptible_ cosmos (Universe) **ALWAYS** raises the inference that the Universe is

ALWAYS

at least twice as large as the distance between the furthest perceptible object since the observed object itself could only be supported and suspended by a comparably omnidirectional equipotential field. (Figure 60) Therefore, we reach an empirical proof of Bruno's postulate that there must be that which is beyond that which is perceptible in order to support in space that which is at the limit of perception. Simply put, at _n_ \+ _p_ there is always another _n_! One must eventually psychologically accept the proposition that the measurable limit of infinity cannot inherently be known as that is the essence of infinity itself. However, that does not mean that infinity cannot be known and accepted conceptually as a result of the reasonable inferences that can be drawn from that which is empirical. To conceive of an empirical infinity is no small accomplishment epistemologically or cosmologically.

_________

* I am categorically excluding such objects as meteors, asteroids, and even individual objects such as the rings of Saturn, although of course the rings of Saturn albeit not spherical are certainly circular.

**Chapter** **3.4 THE SPARK: THE PRIMARY SINGULARITY**

Interestingly, although the "spark" occurs often in Faraday and Maxwell, and putting aside that it constituted for Hertz the proof of the existence of the propagation of electromagnetic waves, no one ever says that a "spark is light," although overwhelmingly obvious, and therefore those conditions where a spark is generated have in common a great underlying premise perhaps applicable to all existence, and if so, perhaps a great unifying truth about existence itself. The "spark," I submit, is the primary singularity that makes manifest the primary principle at ambient. Accordingly,

THE SPARK IS THE PRIMARY POINT

from which every point in the Universe can be metrified and therefore

4303. I think time is concerned in the passing of a spark; but when simple and direct, as between metal balls, I should rather look for it as continuing the time of the whole spark, not as giving existence first at the balls and then in the middle. If a spark be thus with stationary balls or with a steady image, I think Wheatstone's apparatus ought not to shew it thus, as at b, but thicker, rather as at c, the time being employed in continuing the whole spark, not in giving existence to one part before the other. I think this is the case in Wheatstone's middle spark.

4304. Still, in a brushy spark, it is possible that time might be discovered, affecting the prior existence of one part to another, for it is quite clear that in discharge to air, the induction of different parts may be let down gradually or even in separate portions. I must send out a straight constant brush, and then by analysing it by movg. the eye in different directions across it, see whether I can give it a general curve first one way and then the other. Is very likely.

Faraday, 3 _Diary_ 230, entries for December 16, 1837.

**Chapter** **3.5 THE LIMIT OF ZERO (0)**

In order to fully understand the extent of the limits of mathematical physics as a discipline amendable to the formulation of a unified and pure field theory as distinct from natural philosophy we must consider the philosophical and operational aspect of zero (0) as a limit related as it is to infinity itself. Our concern is not so much with the problem of reducing instantaneous velocity to a single number but rather with the conceptualization of the mechanics of a severance of a unified body and the unification of converging bodies into a unified entity. In order for a unified inertial system to be bifurcated, the subentities must separate from the inertial system at some rate of velocity (acceleration) greater than the velocity of the inertial system itself, that to itself is always zero.

Stated operationally, while you are sitting in your chair reading this sentence you have no relativistic velocity to the chair that sits on the floor that is attached to the Earth, i.e., you move as the chair moves, etc. Simply put, you are "at rest" and hopefully so. If you move from the chair you sever yourself from the inertial motion of the Earth (and incidentally prove the primary principle by inducing an electrostatic charge into yourself) and thereby become yourself an inertial subsystem as to yourself. However, you cannot go instantly from rest to your terminal velocity without going through an ordered series of increases in the rate of velocity, i.e., acceleration. On the other hand, you cannot accelerate indefinitely since the upper limit is the velocity of light, c., if you can reach it! hence you cannot accelerate beyond the velocity of light, that is a constant. Therefore, the limit of velocity, i.e., acceleration, and therefore of time, is between a minimum of zero (0) when you are at rest and c. However, no object in the Universe is truly at rest, so that zero is a _perceptual_ relativistic concept that does not exist in unified and pure field theory. On the other hand, when waveforms converge into a singularity the linear velocity of radiation, c, is changed into the angular velocity of the singularity that has no velocity as to itself and is therefore "at rest," "0." Accordingly, in the unified and pure field theories the Universe, in Bruno's terms, is simultaneously in motion and simultaneously at rest, which in Aristotelian reasoning and mathematical physics is impossible but nonetheless true. All of this will, of course, become shockingly undeniable when you discharge the static electricity that you have induced into yourself when you touch the door knob on your way out, and if all goes well will "shock" you into that "spark" of insight that proves how all of this fits into one big theory even when it only comes down to you and the door knob. It 's not a "big bang" but hopefully big enough to turn your mind around to another point of view and that is all that I ever asked of you at the start.

**Chapter** **3.6 THE NON-EUCLIDEAN UNIVERSE**

Although not expressly stated in my earlier footnote on projective geometry, everything here advances a non-Euclidean Universe that establishes the unity between geometry and physics. For example, the nominalizatlon of all entities to a sphere is consistent with the main discussion of Bonola, _Non-Euclidean Geometry; A Critical and_ _Historical Study of its Development_ , and those of Lobachevski and Bolyai. As to the latter, no two rays of light are propogated simultaneously and parallel from the same place at the same time, and since the rays are propagated omnidirectionally and perpendicularly from the surface of a sphere they cannot be parallel, recalling that it was the challenge to the theory of parallel lines that launched non-Euclidean geometry. The sequential propagation of quanta from celestial bodies incorporates by reference the fact that the body is itself moving so that successive quanta are always in trajectories that "fan out" from the immediate predecessor quanta and from the celestial body itself. The concept of absolute parallelism therefore has no basis in physical reality. See for example, Kepler's laws of equal times in Section 41 of Bolyai's "The Science Absolute of Space," appended to Bonola, _Non-Euclidean Geometry_ ; see also selections in Smith, _A_ _Source Book in Mathematics_ at 375.

**Chapter** **3.7 COMPRESSIBILITY**

The concept of the æther being condensed matter was postulated by Newton and revisited by Poincare.

For this, let us bear in mind that it is not enough to be content with the ordinary matter of which we are aware by means of our senses, and the movements of which we observe directly. We may conceive of ordinary matter as either composed of atoms, whose internal movements escape us, our senses being able to estimate only the displacement of the whole; or we may imagine one of those subtle fluids, which under the name of ether or other names, have from all time placed so important a role in physical theories. Often we go further, and regard the ether as the only primative, or even as the only true matter. The more moderate consider ordinary matter to be condensed ether, and there is nothing startling in this conception; but others only reduce its importance still further, and see in matter nothing more than the geometrical locus of singularities in the ether. Lord Kelvin, for instance, holds what we call matter to be only the locus of those points at which the ether is animated by vortex motions. Riemann believes it to be locus of those points at which ether is constantly destroyed; to Wiechert or Larmor, it is the locus of the points at which the ether has undergone a kind of torsion of a very particular kind. Taking any one of these points of view, I ask by what right do we apply to the ether the mechanical properties observed in ordinary matter, which is but false matter? The ancient fluids, caloric, electricity, etc., were abandoned where it was seen that heat is not indestructible. But they were also laid aside for another reason. In materializing them, their individuality was, so to speak, emphasized—gaps were opened between them; and these gaps had to be filled in when the sentiment of the unity of Nature became stronger; and when the intimate relations which connect all the parts were perceived. In multiplying the fluids, not only did the ancient physicists create unnecessary entities, but they destroyed real ties. It is not enough for a theory not to affirm false relations; it must not conceal true relations.

_Science and Hypothesis_ at 168-169.

The question arises in pure field theory of what is the device that operates in interstellar space to condense the field into mass. Interestingly, it is all of those celestial bodies generating the field itself. i.e., mass. Since only mass has a density greater than the surrounding æther and since only mass generates radiation, only mass can increase the radiation pressure of the field.

Accordingly we return to investigate the mechanism of compressibility. Historically, as we have seen, electricity and the field have been considered as if they were incompressible fluids, which analogy would never lead to a unified and pure field theory and therefore a solution to the problem of the singularity, for the singularity requires a fortiori the condensation of the field itself. Quite clearly Newton had already demonstrated the condensation of the field by recombining the spectrum back into a beam of corpuscles. For our purposes that demonstrates the compressibility of electromagnetic radiation, but it does not demonstrate or explain the principle.

Figure 61 shows three identical stampings with teeth around the periphery and in the center of the left stamping is a solid metal disk that shows tool marks as concentric rings and a raised portion in the center. The center stamping is a single waveform constituting a spiral that is the mass removed from the disk on the left. Note that the teeth of the left stamping and middle stamping do not "mesh" whereas the teeth on the center stamping and right stamping do mesh. Accordingly, the distance between the center of the left stamping and the center of the center stamping can not be reduced whereas the distance between the center stamping and the right stamping has been reduced by an amount equal to the depth of the teeth, i.e., the space has been compressed and therefore the density increased without any attendant loss of mass.

At the bottom of Figure 61 are our generic waveforms, which start from the right as a single waveform that "screws" into a second waveform of the same frequency, then a third and so on, so that each in turn adds its own density to the aggregate waveform that approaches a solid as a limit just as the concentric waveform in the center stamping approaches as a limit the original disk from which it was derived. This, of course, is where I began my study in 1987 in reconstituting the steel plate. Compressibility therefore implies synchronicity. More simply, if two waveforms are synchronous with each other they do not generate opolarity (interference) and therefore can interlineate each other into a single waveform whose density is the aggregate of both. At the superconducting temperatures of interstellar space, the "molecular vortex" of a spinning subatomic particle is virtually at a stand still so that opolarity is minimized for the convergence of waveforms into stellar precursors and then to singularities. Accordingly, in conjunction with the other propositions advanced elsewhere herein,

### THE FIELD COMPRESSES ITSELF

**Chapter** **3.8 THE PRIMARY EQUATION**

Another reason that classical mathematical physics itself alone would not lead to a/the unified and pure field theory/ies lies in its failure to perceive, articulate, and reconcile the mathematical relationship between the attractive force of gravity and repulsive force of acceleration to the/an identical attractive force of two magnets when poles of opposite magnetic polarity (N-S-N-S) face each other and the repulsive force when poles of the same magnetic polarity (N-N-S-S) face each other―opolarity―that leads to the relationship between gravity and electromagnetism and eventually the conflict between Einstein and the quantum mechanicists. The problem lies in discounting and not fully comprehending the significance of negative roots and "imaginary" numbers in mathematical physics. The mathematics necessary to describe the symmetry of the primary principle requires that we revisit Gauss's discovery of the fundamental theorem of algebra that "every complex polynomial has a complex zero" and ultimately its importance in conjugate zeros as they apply to symmetry. The implications of _i_ (√–1) become critical in revealing the relationship between the real and the imaginary, the corporeal and the incorporeal, since it can generate both symmetrical and chiral forms that can mathematically converge to both 0 and " –1 simultaneously. Thus any equation replicated on one side of the equal sign and multiplied by _i_ will produce a mirrored form of itself whose characteristics will be equal, opposite, symmetrical, and _inverted_ to the real object, namely the 180° axial inversion of the primary principle.

At this point, three problems occur mathematically. First, by discarding the imaginary root the baby is thrown out with the bath water and out goes the correlative converging waveforms. The second problem is that with the introduction of a positive number that equals a negative number we introduce the topological problem of a closed surface with a negative curvature that describes a spherical hole that has no empirical meaning and therefore leads to the hypothecation of such things as "black holes." The third problem is the anomaly that results when a negative number is transposed from one side of the equal sign to the other side and becomes a positive number so that instead of getting one entity we get 2, i.e., a = -a becomes a + a = 2 not 1, when what actually happens is +½ + (-½) = 1. However, if we remove the parenthesis we get +½ - ½ = 0! That, however, raises the problem in quantum mechanics of seeing one-half of a mass as a singularity, or even a singularity with spin. In fact, ½ is both a singularity and spin! Accordingly, the fundamental equation of the unified and pure field theory is actually

repulsion = _i_ attraction

attraction = _i_ repulsion

or in Newtonian or Einsteinian terms

gravity = _i_ acceleration

acceleration = _i_ gravity

One may see that this is none other than Einstein's equivalence principle that was there all along had he simply rotated one of two horseshoe magnets 180° as to the other converting "attraction [gravity]" into "repulsion [acceleration]." His "gravitational constant" is unidirectional time, an [undisclosed] force that "keeps the engine running." The problem, therefore, is that the mathematical conventions mask the underlying difference between inertial systems that are coming together from those that are separating although the "feel" is the same. It was beyond his ken to contemplate such a simple thing that any school boy knows how to do. It is empirical and therefore falls to the lot of the experimentalists, the Faradays who are not so mathematically trained but who are philosophically tuned.

Finally, we may now see that the primary equation answers Newton's mathematical dilemma about "negative density" when we consider that the addition of gravity with negative acceleration results in equipoise, a body suspended in space that when translated into geometry constitutes an omnidirectional equipotential field that will generate a sphere of constant positive curvature in a field of constant negative curvature. When this is applied to converging fields at a locus, the converging fields will generate a singularity, either the mass in Model 1 (Figure 11) (classical) or our generic spark (quantum mechanical). Since time (magnetic lines of force) is unidirectional the juxtaposition of unidirectional times results not in time reversal but in the repulsion made manifest by opolarity, e.g., as to light, interference patterns and so forth. Generically, the primary equation reduces to

(any phenomena) = _i_ (itself in order to be repeated)

In short, one cannot clap one's hands [gravity/attraction] twice in a row without separating one's hands [acceleration/repulsion] after the first clap in order to effectuate the second and so forth and so one throughout all of existence.

NOTES

1 But see Eddington, _New Pathways in Science_ at 51.

2 For a generalization of the relationship between electrical and magnetic components in the context of unified field theory expressed in (parenthetical form) but without recognizing the underlying structural identity, even within the context of "physics as geometry," see especially equation (39) and the inversion of equation (245) and the associated discussions in Misner and Wheeler, "Classical Physics as Geometry" at 544 and 593. For a model "intimating" "converging" fields but at the same time impliedly discounting their existence, review the especially terse discussion under "Relation to Geons" and "Equations of Motion" also in Misner and Wheeler, "Classical Physics as Geometry" at 595-596 for an evaluation of the extent to which the Newtonian gravitational view of cohesiveness of the universe continues to dominate contemporary "mathematical physics." See also the many equations thereafter embracing the "fundamental formula" but without recognizing the underlying unity between electrical and magnetical fields as well as the suggestions of converging wave mechanics underlying much of the discussion throughout. Of particular interest is the comment in view of the previously set out series of equations:

Now we turn from the question of the best formulation of the field equations to the problem how best to deal with the initial value requirements. For the case of pure electromagnetism one has long ago learned to satisfy automatically the requirement div **h** = - **dh** = 0 on the initial hypersurface by introducing as the primary data, not **h** itself, but a 3-potential a that generates an acceptable **h**. In the case of the coupled equations of geometrodynamics, we meet nonlinear initial value requirements (224) and (225) on the measures, P., of the time derivative of the metric. Does there exist any kind of freely choosable superpotential, analogous to a, which will generate a tensor Pij, which in turn will automatically satisfy (224) and (225)? If so, the properties of such a superpotential should reveal much about the truly independent variable of geometrodynamics. To clarify this point is essential for the understanding of already unified theory, for its most efficient application and for illumination on what it means to quantitize it.

Misner and Wheeler, "Classical Physics as Geometry," 599.

**Chapter** **3.9 THE CONTINUOUS, THE SIMULTANEOUS, AND THE INSTANTANEOUS**

Although we have made some comments about motion and rest, it is appropriate to propose that the horseshoe magnet (because of its hemispherical shape) represents the quintessential "nominalized" embodiment of the smallest "entity," i.e., "matter," of existence at ambient, so small and going so fast that it is unable to catch up with itself to become spherical. It is what would be found if time could be made to stand still at the moment when the vortex of the field had not become a full circle, when energy was neither linear nor circular, when gravity and acceleration were indistinct. It is the infinitesimal moment when time marks the line between past, present, and future, the "now." But even in that moment it is not a monopole, i.e., it still has tense, "north" and "south," as the past races into the future. "Time" remains for that moment "frozen."

In _Sidelights on Relativity_ , Einstein states:

If two ideal clocks are going at the same rate at any time and at any place (being then in immediate proximity to each other) they will always go at the same rate, no matter where and when they are again compared with each other at one place.

"Geometry and Experience" at 39.

If we take this statement in pieces, first, as we have unified the processes of the Universe into the same geometry we have made physics itself geometry. Secondly, two bodies moving at the same velocity with respect to each other and without reference to a third body will perceive each other as standing still as if time stood still. Accordingly, time itself requires a disparity between spacetimes to be evidential, for a face of a clock that rotates with the hands does not tell time. But there is an operational aspect of this situation that I think has gone completely unnoticed. The light that we see from a distant star we only see at the moment of its arrival irrespective of when or where it started or came from, but the unidirectional radiation that was emitted from that distant object has continued to retain its integrity from the past into the present, and although it is not a fixed rod, it is nonetheless an entity capable of existential consequences, notwithstanding that the initiating star may no longer be "in existence," i.e., dissipated itself into the æther. That beam of light preserves the continuity of existence over the passage of time itself, and the radiation generated by the light that we do not see continues to exert its pressure as the æther over the continuity of time.

Finally, the process by which that light came into existence is commensurate with the processes under which it is seen.

In the first place, what are the properties of space properly so called? I mean of that space which is the object of geometry, and which I shall call geometrical space. The following are some of the more essential:—

1st, it is continuous; 2nd, it is infinite; 3rd, it is of three dimensions; 4th, it is homogeneous—that is to say, all its points are identical one with another; 5th it is isotropic.

_Science and Hypothesis_ at 52.

that leads us to our closing thoughts on "time." We take as a given that the velocity of light is invariant in the Universe and therefore all of existence is unified by that velocity. If that is the case, then no part of existence goes any faster or any slower than any other part of existence notwithstanding the surface perception of bodies at rest and bodies in motion that we have resolved by the transformation of linear velocity and angular velocity into each other. Therefore no part of existence ever gets ahead of any other part nor does any part fall behind any other part. Therefore all of existence moves at the same time and therefore

### ALL EXISTENCE IS SIMULTANEOUS WITH ITSELF

The physical concept of time, therefore, as Bruno advanced, is meaningless since there can be no difference in time on the omnidirectional continuum that is unified by the velocity of light. Since we have reduced everything to the principle of synchronicity, the absolute value of the velocity of light is irrelevant as it is merely an arbitrary point on the spectrum of continuity within the Universe and therefore within the pure field theory itself. Thus the proposition that looking at a distant star is the same as looking back in time is false in the same way that looking at a baby picture will give some indication of either the mechanism by which that baby came into existence or will make the adult younger. Although the simultaneous and the continuous mean that all of existence moves uniformly together in unidirectional time, it does not mean that all events are so joined that they occur experientially with each other, which is the real issue that Einstein addressed in the special theory and which is addressed more precisely here by the primary principle and is a consequence of his failure to distinguish simultaneity and causality at a local level and simultaneity and causality at the cosmic level. In the unified and pure field theories existence is simultaneous whereas only events are "instantaneous" when there is a causal connection between the entities, namely when the primary principle is involved.

The resolution of the ultimate philosophical paradox of logical reasoning is therefore that there is no place where existence does not exist and therefore

### THE UNIVERSE IS EVERYTHING

### AND

### THE ONLY THING!

### IT IS THAT IT IS

Figure 44 Sketch for "redshift" experiment (January 16, 1994).

Figure 45 Model with opposing electromagnets.

Figure 46 Model attempting to detect shift in interference patterns.

Figure 47 Model attempting to detect shift in spectrum.

Figure 48 Model attempting to detect angle of polarization.

Figure 49 Model with beam splitter attempting to detect shift by compare of superimposed interference patterns.

Figure 50 Model attempting to compare spectrum.

Figure 51 Model with magnets in opolarity around incandescent bulb.

Figure 52 Model with magnets in opolarity with beam confined to plastic tube attempting to detect in interference patterns.

Figure 53 Model with spectroscope, -electromagnets, and fluorescent bulb

Figure 54 Model with spectroscope, permanent magnets in opolarity, and fluorescent bulb.

Figure 55 Model with spectroscope, coil of electromagnets, and bulb outside coil.

Figure 56 Model with bulb inside coil of outside coil.

Figure 57 Lines of force projected from face of 1-ton electromagnet.

Figure 58 Lines of force projected from coil of electromagnet.

Refractive index of interstellar space

K = nλ/1010 /10 parsecs

(3ok, 21 cmλ)

Figure 59 Reinterpretation of Hubble's graph for redshift as a result of interstellar space considered as a field of uniform radiation pressure (opolarity) and suggested simplified experimental schemes. (Somewhat rearticulated from original hand drawn sketch.)

   ∞

∞

L    ocation of Observer

∞

I   nference of spheres of æther surrounding further observable objects and so forth and so on to

i  nfinity

Figure 60 Metrification of the perceptible universe.

Figure 61 Compressibility.

Chapter 4. SPECULATIVE HYPOTHESIS

Having set out the primary principle and the unified and pure field theories, two subjects came up during the progress of the work to which this investigation may provide some insight. I offer these as "speculative hypotheses."

Chapter 4.1 DNA

The first speculative hypotheses concerns the mechanism by which the long-chain DNA molecule assumes its double-helix and self-replicating properties. We begin with the simple modification of Model 1. At several inches from the end of an approximately one-foot piece of wooden dowel (a chopstick works nicely) whose diameter is smaller than the hole in a horseshoe magnet, wrap a rubber band tightly around the dowel so as to create a "wad or blockage" such that the magnet will not come off the end. With the poles of the magnet facing the short end, slide the magnet onto the dowel up to the rubber band and lightly press the inside curve of the magnet against the rubber band with the knuckle of your thumb against the outside curve as you grab the dowel firmly in a horizontal position. Take a second magnet in your other hand and wave it like a wand up and down perpendicular to the faces of the first magnet to induce a constantly changing field in opolarity to drive the first magnet around the dowel. If this is done in a very quiet area where you are undisturbed you will note the synchronous attraction and repulsion of the action with your own breathing. I submit that this embodiment of the primary principle that neither fully separates nor fully joins is the mechanism of the vital force of biological existence. It is essentially predicated on the elasticity of the long-chain hydrocarbon molecule that accommodates torsion and release without severance.

On close observation of the dynamics of the ball bearings in Model 1 you will recognize their helical alignment across the vortex. Given "world enough and time" the helicity of the terrestrial lines of force—the right-hand rule—became the mechanism that induced long-chain organometallic molecules into the double helix of the DNA molecule. One must recognize that "blood," at least mammalian blood (horseshoe crab is copper based), is a ferrous-carbonate solution and that iron is the most magnetically susceptible of all elements and that carbon the most amorphous of all elements for purposes of mutation. Just as the little spiral pirouettes in Model 2 became self-induced when they were subjected to the lines of force, so the lines of force of the terrestrial magnetic field induced into long-chain molecules a polarity that became embedded in the molecule itself. The molecule became polarized along its longitudinal axis that under the primary principle severs the molecule into two symmetrical halves, each half itself likewise polarized and able to attract an oppositely polarized chiral helix as done artificially in DNA recombinant analysis in which the requisite compounds become available in the "primordial soup" and are attracted to and bond to various sites in the sample. (Figures 62)

An extensive amount of research has attempted to generate self-replicating molecules. These experiments, however, have assumed that the "spark" of biological existence is the result of lightning or other like-kind atmospheric electrostatic discharges. I do not think that that was the evolutionary model. An electrostatic model, although dramatic, is an essentially spontaneous sporadic process that is predicated on a great many unstable, short-term climatologically and meteorological forces. It is neither constant nor pervasive as are the terrestrial electromagnetic lines of force of the Earth's magnetic field that would have come into existence with the formation of the Earth itself. Rather, a model that incorporates the structure of Model 1 would have the capacity to induce both a double helix into a long-chain molecule as well as to induce an electromagnetic polarity into the molecule itself.

In my model, see the appendix for my patent "Apparatus and Methods for Processing Material in a Magnetic Vortex," the organometallic substance would be contained in a vessel located at the locus of converging lines of force similar to the way in which the ball bearings were located in Model 1 and the organometallic substance inside the vessel would be continuously subjected to the "molecular vortex" generated by the magnets in opolarity so as to ultimately compact, twist, and polarize the long-chain molecule. The turbidity of the action would result in a certain upper limit of length and density of polarity at which the molecule would spontaneously divide itself and thereby combine with other elements in the solution and become self-replicating. Because of the turbidity of the motion, the quantum and wave mechanical effects would "call on the law of probabilities" involved in all of these multiplicity of events to give rise to "mutations" that themselves would become replicated.

Chapter 4.2 REVERSAL OF THE EARTH'S MAGNETIC FIELD

(DIRECTION OF POLARITY)

In the mid-1950's extensive work began in paleomagnetism and the study of the magnetic direction of ancient rocks, and primarily the symmetrical alteration of the lines of magnetic direction along the various mid-ocean ridges found throughout the oceans of the world. On the basis of this work it was hypothecated that the Earth has undergone a series of repeated reversals of the direction of its polarity. I submit, on the other hand, that the phenomena is the result of the severance of localized "molecular vortices" that are induced by the constant and prevailing terrestrial N-S polar axis into the molten magma as it is pushed to the surface and becomes solidified and severed into symmetrical halves at the various mid-ocean ridges. In the molten state, the magma has no discernible magnetic direction, but as it upwells and cools it becomes circularly polarized with the next uppermost layer the same as if the layers were a series of elongated horseshoe magnets that are constantly in the process of forming and being severed as they rise to the ocean floor in a series of alternating N-S-N-S orientations. The uppermost layer is then severed symmetrically at the ridge with one-half going to the left and the other half going to the right, and so forth. Each successive upwelling therefore is oppositely polarized to that to which it is juxtaposed as the vertical lines of polarity become horizontal bands thus giving the impression that terrestrial polarity has gone through a continuous series of reversals, whereas, I submit, that the polar axis has remained constant since the solidification of the Earth itself. (Figure 63)

Figure 62 Close-up of Model 1 showing two adjacent helical strands (DNA) levitated in the field in opolarity.

Figure 63 Reconsideration of mechanism of formation of symmetrical sections of reversed polarity along mid-ocean ridges.

Chapter 5. AFTERWORD

The search for a unified and pure field theory raises many profound philosophical questions about the nature of existence far beyond those within the traditional scope of mathematical physics. Understandably, a bona fide search must presuppose that the Universe is unified, that everything is part of a consistent whole, and that a single theory can account for all that is, was, and will be.

The search began when Aristotle described the elements of the answer but not what it was. Bruno defined the fundamental propositions of an infinite unified Universe and the inferences that could reasonably be drawn therefrom. Newton discovered the laws of gravity of the mechanical Universe and left unresolved a first principle that was not mechanical. Faraday discovered the field and a nonmechanical ponderomotive force and then sought the relationship between gravity, electromagnetism, and time. Maxwell unified light with electromagnetism and broached a primary principle without perceiving it and hypothecated the molecular vortex that underlies the compression of the field into a singularity. Einstein discovered the unity between space and time, the corporeal and the incorporeal, and began the search for a unified field theory and the possibility of a pure field theory beyond that. I took up the problem with the question of "whether energy could be recycled" and my answer is that there is no such thing as "recycling of energy" for that is a pure anthropomorphic misnomer and misperception about an ephemeral view of a process that is inherent in the continuity of existence itself under the imperative of unidirectional time. Simply put, nothing is ever truly "recycled." Nothing gets done without the expenditure of energy and that energy―radiation―is lost forever on its return to the æther from which it came eons ago when condensed into mass.

Wherefore we here bring to an end and conclusion our arguments and experiments magnetical.

Gilbert, _On the Loadstone_ at 121.1

A FINAL NOTE

1 As a final note, if you are still unconvinced that what I have set out above is not embodied and embedded throughout all of existence down to your very own being as to the primary principle underlying the unified and pure field theories ask any obstetrician. Alternatively, you can always strike two things together to make a spark to confirm the same process preferably not near something combustible without the consequences of parenthood, or snap your fingers, or clap your hands, or blink your eyes and so forth and so on. Beyond that, you're on your own. More than that I cannot do to prove my case except perhaps to continue my invitation that you should continue to gaze at the Moon until it finally "sinks in." If not, then all that I have left is "hope" and that amount of disappointment that comes to one who "did the best he could but it just wasn't good enough" that falls to the great lot of the rest of humanity in the passage through this but one ephemeral life given to us all. Thank you for getting this far. Have a nice day.

Chapter 6. SELECTED BIBLIOGRAPHY

As stated in the introductory materials, I readily admit that I have not read everything that could possibly have a bearing on the discovery and explanation of the fundamental principle of the Universe, and accordingly I cannot offer a bibliography that will lead you to that result either. The best that I can do is offer you some of what I have read in the belief that it may help you place this work in perspective or that it will guide your own autodidactic course of study. I cannot assure you that if you read through all of the following material that you will be convinced of the theory that I have proffered, but I can assure you that there is nothing else that I could do to help you reach that objective. Some of the material in the bibliography will have only pedagogical interest, some historical interest, and some little or no interest other than a presentation of what others have written about the subject and related matters. For the academically trained scientist this list is superfluous and for the layman without any scientific training there are many non-technical selections included. If you are as slow (the old "read as you speak" model) a reader as I am and cannot work at it day and night as I could not, there is enough here to keep you busy for several years and hopefully give you the sense of when you have cycled back on the major sources that are available in English, the major investigators in the various disciplines, the variety of theories that have been proffered, and the problems that have to be addressed in the ultimately successful theory if in fact there is one. Most of the selections are themselves buttressed with extensive bibliographies that lead to other works with extensive bibliographies and so forth. Many of the works were not in print at the time of this writing and were obtained through the interlibrary loan services of the Elizabeth Public Library and its cooperating libraries, to whose collective staffs I owe a special note of thanks for their diligence and courtesy in obtaining materials that are fairly well off the beaten path for the general reading public. Above all, this work attests to the enduring wisdom of our founding father Benjamin Franklin who advanced that the free public library is the common man's university. In that spirit, the following is a reading list for the doctoral degree in theoretical physics, philosophy, ontology and whatever else is "out there."

Abbott, Larry, "The Mystery of the Cosmological Constant," _Scientific American_ , 258:105 (No. 5, May 1988).

Abragam, A., and B. Binaney, _Electron Paramagnetic Resonance of Transition Ions_ , New York: Dover Publications, 1986.

Abrikosov, A.A., L.P.Gorkov, and I.E. Dzyaloshinski, _Methods of Quantum Field Theory in Statistical Physics_ , New York: Dover Publications, 1975.

Adams, George P., J. Loewenberg, and Stephen C. Pepper, _The Problem of Time_ , University of California Publications in Philosophy, Volume 18, New York: Johnson Reprints, 1969.

Aharoni, J., _The Special Theory of Relativity_ , New York: Dover Publications, 1985.

Allen, L[eslie], and J.H. Eberly, _Optical Resonance and Two-Level Atoms_ , New York: Dover Publications, 1987.

Anonymous, "You need cosmology and GUT'S to find monopoles," _New Scientist_ , 100:495 (November 17, 1983).

Anthony, Simon, "The Rare Attraction of the Magnetic Monopole," _New Scientist_ , 112:53 (October 16, 1966).

Aristotle, _The Complete Works_ , Two Volumes, Princeton: Princeton University Press, 1985.

Barnett, Lincoln, _The Universe and Dr. Einstein_ , Mattituck, New York: Rivercity Press, 1950. [This is the book with which I and many, many others, began our investigations into this most fascinating of all inquiries into the fundamental principle[s] of the universe.]

Baron, Margaret E., _The Origins of the Infinitesimal Calculus_ , New York: Dover Publications, 1987.

Barut, A.0., _Electrodynamics and Classical Theory of Fields and Particles_ , New York: Dover Publications, 1980.

Backer, Richard, _Electromagnetic Fields and Interactions_ , New York: Dover Publications, 1982.

Benecerraf, Paul, and Hilary Putnam, eds., _Philosophy of Mathematics; Selected Readings_ , Second Edition, New York: Cambridge University Press, 1983.

Bergmann, P[eter] G[abriel], _Introduction to the Theory of Relativity_ , New York: Dover Publications, 1976.

——— _The Riddle of Gravitation_ , New York: Charles Scribner's Sons, 1987.

———and Venzo De Sabbata, eds. _Cosmology and Gravitation: Spin, Torsion, Rotation, and Supergravity_ , New York: Plenum Press, 1980.

———and Venzo De Sabbata, _Topological Properties and Global Structure of Space-Time_ , New York: Plenum Press, 1986.

Blau, Steven K., and Alan H. Guth, "Inflationary Cosmology," in Hawking, _300 Years of Gravitation_ , 524-603.

Bohr, Niels, "On the Constitution of Atoms and Molecules," _The London. Edinburg, and Dublin Philosophical Magazine and Journal of Science_ , Sixth Series, 26:1 (Part I, No. 151, July 1913); 26:476 (Part II, No. 153, September 1913); 26:857 (Part III, No. 155, November 1913).

———"On the Effect of Electric and Magnetic Fields of Spectral Lines," _The London, Edinburg, and Dublin Philosophical Magazine and Journal of Science_ , Sixth Series, 27:506 (January-June 1914).

——— _The Philosophical Writings of Niels Bohr_ , Woodbridge, Conn.: Ox Bow Press, 1987: Volume I: _Atomic Theory and the Description of Nature_ ; Volume II: _Essays 1932-1957 on Atomic Physics and Human Knowledge_ ; Volume III: _Essays 1958-1962 on Atomic Physics and Human Knowledge_.

Bold, Benjamin, _Famous Problems of Geometry and How to Solve Them_ , New York: Dover Publications, 1982.

Bondi, Hermann, _Relativity and Common Sense: A New Approach to Einstein_ , New York: Dover Publications, 1980.

Bonola, Roberto, _Non-Euclidean Geometry: A Critical and Historical Study of Its Development_ , contains the English translations of Bolyai's "The Science of Absolute Space," and Lobachevski's "The Theory of Parallels," New York: Dover Publications, 1955.

Boole, George _, An Investigation of the Laws of Thought of Which Are Founded the Mathematical Theories of Logic and Probabilities_ , New York: Dover Publications, 1958.

Born, Max, _Atomic Physics_ , Eighth Edition, New York: Dover Publications,1989.

——— _Einstein's Theory of Relativity_ , New York: Dover Publications, 1965.

——— _Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light_ , Sixth Corrected Edition, New York: Pergamon Press, 1989.

——— _The Restless Universe_ , New York: Dover Publications, 1951.

———and L[eopold] Infeld, "Foundations of the New Field Theory," _Proceedings of the Royal Society of London, Series A Containing Papers of a Mathematical and Physical Nature_ , 144 (CXLIV):425 (May 1934), London: Harrison and Sons, 1934.

Botto, I.D., "Note on the Application of Electro-Magnetism as a Mechanical Power," in Robert Taylor, ed., _Scientific Memoirs, Selected from the Transactions of Foreign Academies of Science and Learned Societies_ , Volume I, 1837, 532-534, New York: Johnson Reprints, 1966.

Bouchiat, Marie-Anne, and Lionel Pettier, "Optical Experiments and Weak Interactions," _Science_ , 234:1203 (December 5, 1986)

Boyce, William E., and Richard C. DiPrima, _Elementary Differential Equations_ , Fourth Edition, New York: John Wiley & Sons, 1986.

Boyer, Carl B., _The History of the Calculus and Its Conceptual Development_ , New York: Dover Publications, 1959.

Boys, C.V., _Soap Bubbles; Their Colors and Forces Which Mold Them_ , New York: Dover Publications, 1958.

Bridgman, P.W., _A Sophisticate's Primer of Relativity_. Second Edition, Middletown, Conn.: Wesleyan University Press, 1983.

Brillouin, Lion, _Relativity Reexamined_ , New York: Academic Press, 1970.

Bruno, Giordano, _Oeuvres Completes_ , Paris: Les Belles Lettres, 1995, Volume IV.

——— _His Life and Thought with Annotated Translation of His Work On the Infinite Universe and Worlds_ , trans. Dorthea Waley Singer, New York: Henry Schuman, 1950.

——— _The Infinite in Giordano Bruno with a Translation of His Dialogue "Concerning the Cause, Principle, and One,"_ trans. Sidney Greenberg, New York: King's Crown Press, 1950.

Bunt, Lucas N.H., Phillip S. Jones, and Jack D. Bedient, _The Historical Roots of Elementary Mathematics_ , New York: Dover Publications, 1988.

Burbridge, G., "Arguments and Evidence Concerning Non-Cosmological Redshifts—A Partial Summary," _The Evolution of Galaxies and Its Cosmological Implications_ , No. 263, Paris International Center for Scientific Research, 1977.

Bureau of Naval Personnel, _Basic Electricity_ , New York: Dover Publications, 1970.

Cantor, G.N., and M.J.S. Hodge, _Conceptions of Ether; Studies in the History of Ether Theories 1740-1900_ , Cambridge: Cambridge University Press, 1981.

Cantor, Georg _, Contributions to the Founding of the Theory of Transfinite Numbers_ , New York: Dover Publications, 1955.

Capek, Milic, _The Concepts of Space and Time; Their Structure and Their Development_ , Boston: R. Reidel Publishing, 1976.

Carnap, Rudolf, _Introduction to Symbolic Logic and Its Applications_ , New York: Dover Publications, 1958.

——— _Philosophical Foundations of Physics; An Introduction to the Philosophy of Science_ , New York: Basic Books, 1966.

Cartan, Elie, _The Theory of Spinors_ , New York: Dover Publications, 1981.

Chados, Alan, "Marginalia: String Fever," _American Scientist_ , 74:253 (May-June 1986).

———"Marginalia: The Fifth Force," _American Scientist_ , 74:619 (November-December 1986).

Chandresekhar, S., _An Introduction to the Study of Stellar Structure_ , New York: Dover Publications, 1958.

Chyba, Christopher F., "Kaluza-Klein Unified Field Theory and Apparent Four-Dimensional Space-Time," _American Journal of Physics_ , 53:863 (No. 9, September 1985).

Clifford, William Kingdon, _The Common Sense of the Exact Sciences_ , New York: Alfred A. Knopf, 1946.

Cohen, Martin, _In Darkness Born: The Story of Star Formation_ , New York: Cambridge University Press, 1988.

Cohn, Harvey, _Advanced Number Theory_ , New York: Dover Publications, 1980.

——— _Conformal Mapping on Reimann Surfaces_ , New York: Dover Publications, 1980.

Copernicus, Nicolaus, _On the Revolutions of the Heavenly Spheres,_ in _Ptolemy, Copernicus, Kepler_ , Great Books of the Western World, Volume 16, Chicago: Encyclopaedia Britannica, 1984.

——— _Three Copernican Treatises: The Commentariolus, Letter to Werner, and Narratio Prima of Rheticus_ , trans. Edward Rosen, New York: Octagon Books, 1971.

D'Abro, A., _The Rise of the New Physics: Its Mathematical and Physical Theories_ , New York: Dover Publications, 1952: Volume One: _Classical Physics_ ; Volume Two; _Quantum Theory_.

Darwin, C. G., "Collision of a Particles with Light Atoms," _The London, Edinburg, and Dublin Philosophical Magazine and Journal of Science_ , Sixth Series, 27:499 (January-June 1914).

Davenport, H., _The Higher Arithmetic: An Introduction to the Theory of Numbers_ , New York: Dover Publications, 1983.

Davies, Paul [C. W.], _Superforce; The Search for a Grand Unified Theory of Nature_ , New York: Simon and Schuster, 1984.

——— _The Forces of Nature_ , Second Edition, Cambridge: Cambridge University Press, 1986.

DeBroglie, Louis, _The Revolution in Physics: A Non-mathematical Survey of Quanta_ , New York: The Noonday Press, 1953.

Dedekind, Richard, _Essays on the Theory of Numbers_ , New York: Dover Publications, 1963.

Descartes, Rene, _The Geometry_ , New York: Dover Publications, 1954.

——— _Principles of Philosophy_ , Boston: D. Reidel Publishing, 1983.

Dibner, Bern, _Oersted and the Discovery of Electromagnetism_ , New York: Blaisdell Publishing, 1962.

Digges, Thomas, "A PERFIT DESCRIPTION OF THE CAELESTIAL Orbes according to the most aunciente doctrine of the PYTHEGOREANS, lately reuiued by COPERNICVS and by Geometricall Demonstrations approued," in "Thomas Digges, The Copernican System, and the Idea of Infinity of the Universe in 1576," Francis R. Johnson and Sanford V. Larkey, _The Huntington Library Bulletin_ , No. 5: 69 (April 1934), Cambridge: Harvard University Press, 1934.

Dijksterhuis, E.J., _Archimedes_ , Princeton: Princeton University Press, 1987.

Dirac, Paul A. M., "The Evolution of the Physicist's Picture of Nature," _Scientific American_ , 208:45 (No. 5, May 1963).

Ditchburn, R. W., _Light_ , New York: Dover Publications, 1991.

Duff, Michael, and Christine Sutton, "The Membrane at the End of the Universe," _New Scientist_ , 118:67 (June 30, 1988).

Duffin, W. J., _Electricity and Magnetism_ , Third Edition, New York: McGraw-Hill, 1980.

Dugas, Rene, _A History of Mechanics_ , New York: Dover Publications, 1988.

Eddington, A[rthur] S., _New Pathways in Sciences,_ New York, The Macmillan Company, 1935.

――― _The Mathematical Theory of Relativity_ , New York: Chelsea Publishing Co., 1975.

Ehrenfest, Paul and Tatinna, _The Conceptual Foundations of the Statistical Approach in Mechanics_ , New York: Dover Publications, 1990.

Einstein, Albert, _Essay in Physics_ , New York: Philosophical Library, 1950.

——— _Essays in Science_ , New York: Philosophical Library, 1934.

——— _Investigations on the Theory of the Brownian Movement_ , New York: Dover Publications, 1956.

——— _Relativity; The Special and the General Theory_ , New York: Crown Publishers, 1959.

——— _Sidelights on Relativity_ , New York: Dover Publications, 1983.

——— _The Meaning of Relativity_ , Fifth Edition, Princeton: Princeton University Press, 1974.

———and Leopold Infeld, _The Evolution of Physics; From Early Concepts to Relativity and Quanta_ , New York: Simon & Schuster, 1966.

——— and H[enrick] A[ntoon] Lorentz, H[ermann] Weyl, H[ermann] Minkowski, _The Principle of Relativity; Collection of Original Papers on the Special and General Theory of Relativity_ , New York: Dover Publications, 1952.

———and Erwin Schrödinger, Max Planck, Henrick Lorentz, _Letters on Wave Mechanics; Schrödinger, Planck, Einstein, Lorentz_ , New York: Philosophical Library, 1967.

———"On Gravitational Waves," _Journal of the Franklin Institute_ , 223:43 (Nos. 1333-1338, January-June 1937).

———"On the Generalized Theory of Gravitation," _Scientific American_ , 182:13 (No. 4, April 1950).

———and W. DeSitter, "On the Relation Between the Expansion and the Mean Density of the Universe," _Proceedings of the National Academy of Sciences_ , 18:213 (No. 3, March 15, 1932).

———"The Particle Problem in the General Theory of Relativity," _Physical Review_ , Second Series, 48:73 (No. I, July 1, 1935).

Ekspong, Gosta, _Nobel Lectures in Physics; 1981-1990_ , New York: Elsevier Publishing Co., 1993.

_Encyclopaedia Britannica_ , and particularly the extensive articles in the _Encyclopaedia Macropaedia_ are excellent sources to start a fuller study. Particularly see in the _Macropaedia_ : Analysis, Analysis, Abstract, Analysis, Complex, Analytic Geometry, Atmosphere, Atoms, Color, Cosmos, Electricity and Magnetism, Electromagnetic Radiation, Energy, The Concept of Ether (in Physics), Fields, Theory of, in Physics, Force, Galaxies, Geometry, Gravitation, Light, Mathematics, Matter, Mechanics, Molecules, Nebula, Optics, Physical Principles and Concepts, Physics (articles on), Physics: General Survey, Physical Sciences, Quantum Theory [by Einstein], Radiation, Relativity, Solar System, Sound, Space-Time, Spectroscopy, Time, Stars and Star Clusters, Subatomic Particles, Thermodynamics, Unified Field Theory.

Euclid, _The Thirteen Books of the Elements_ , Three Volumes, New York: Dover Publications, 1956.

Faraday, Michael, _Experimental Researches in Chemistry and Physics_ , London: Richard Taylor and William Francis, 1859.

——— _Experimental Researches in Electricity_ , Two Volumes, New

York: Dover Publications, 1965.

——— _Faraday's Diary: Being the Various Philosophical Notes of Experimental Investigation Made by—,_ Seven Volumes, London: G. Bell and Sons, 1932.

Fermi, Enrico, _Thermodynamics_ , New York: Dover Publications, 1956.

Feshbach, Herman, "The Road to Four Dimensions," _Physics Today_ , 39:7 (December 1986).

Feynman, Richard, _The Character of Physical Law_ , Cambridge, Mass.: The M.I.T. Press, 1989.

———Leighton, Robert B., and Matthew Sands, _The Feynman Lectures on Physics_ , Reading, Mass.: Addison-Wesley Publishing, 1963: Volume I: _Mainly Mechanics, Radiation, and Heat_ ; Volume II: _Mainly Electromagnetism and Matter_ ; Volume III: _Quantum Mechanics_.

Field, George B., Halton Arp, and John N. Bahcall, _The Redshift Controversy_ , Reading, Mass.: W.A. Benjamin Inc., 1973.

Fitzgerald, George Francis, _The Scientific Writing of—_ , London: Longmans, Green & Co., 1902.

Frank, Philipp, _Foundations of Physics_ , Chicago, University of Chicago Press, 1946.

Fraser, J.T., _The Genesis and Evolution of Time_ , Sussex, England: The Harvester Press, 1982.

——— _The Voices of Time; A Cooperative Survey of Man's Views of Time as Expressed by the Sciences and by the Humanities_ , Amherst, Mass.: The University of Massachusetts Press, 1981.

———and N. Lawrence, and D. Park, _The Study of Time I—Berlin: Proceedings of the First Conference of the International Society for the Study of Time_ , Berlin: Springer-Verlag, 1972.

——— _The Study of Time II—Japan; Proceedings of the Second Conference of the International Society for the Study of Time_ , Berlin: Springer-Verlag, 1973.

——— _The Study of Time III—Austria; Proceedings of the Third Conference of the International Society for the Study of Time_ , Berlin: Springer-Verlag, 1978.

Freedman, Daniel Z., and Peter van Nieuweahuizen, "The Hidden Dimensions of Spacetime," _Scientific American_ , 252:74 (March 1985).

Galilei, Galileo, _Dialogues Concerning Two New Sciences_ , New York: Dover Publications, 1954.

Gamow, George, _The Great Physicists from Galileo to Einstein_ , New York: Dover Publications, 1961.

Gardner, M[artin], _The Ambidextrous Universe_ , New York: Basic Books, 1964.

Gauss, Karl Friedrich, _General Investigations of Curved Surfaces; The Paper of 1827_ , Hewlett, New York: Raven Press, 1965.

Geroch, Robert, "What is a Singularity in General Relativity," _Annals of Physics_ , 48:526 (1968).

Gibbs, J. Willard, _Elementary Principles in Statistical Mechanics_ , Woodbridge, Conn.: Ox Bow Press, 1981.

Gilbert, William, _On the Loadstone and Magnetic Bodies_ , Chicago: Encyclopedia Britannica, 1952; also Dover Publications, New York, 1993.

Gold, T., "The Arrow to Time," _American Journal of Physics_ , 30:403 (1962).

———and D. L. Schumacher, _The Nature of Time_ , Ithaca, New York: Cornell University Press, 1967.

Goldberg, Samuel I., _Curvature and Homology_ , New York: Dover Publications, 1982.

Goodstein, David L., _States of Matter_ , New York: Dover Publications, 1985.

Greenhouse, Carol J., "Just in Time: Temporality and the Cultural Legitimation of Law," _The Yale Law Journal_ , 98:1631 (1989) as reprinted in Sack and Aleck, _Law and Anthropology_ , New York: New York University Press, 1992. This article, much less a book, lies buried in a collection of articles on anthropology and law and is the only instance of which I am aware in which the concept of "linear" time and 'cyclic' time are even ever mentioned with some sense of conceptual exploration, notwithstanding its context outside academic, experimental, or theoretical physics and therefore its extension into the nature of the physical Universe as a fundamental principle activating force of existence itself. The article, therefore, unfortunately constitutes a "beginning" on the one hand and an "ending' on the other. In short, it constituted simultaneously both the 'first and the last" step toward something of greater scope of which one would have wanted to know more. Those further steps are taken up here.

Greenstein, Jesse L., and Thomas Matthews, "Red-Shift of the Unusual Radio Source," _Nature_ , 197:1041 (March 16, 1963).

Gribbin, John, "Precise Measurements of Nothing Pin Down the Universe," _New Scientist_ , 100:814 (December 15, 1983).

Gross, David J., "Can We Scale the Planck Scale?" _Physics Today_ , 42:9 (June 1989).

Hadamard, Jacques, _The Psychology of Invention in the Mathematical Field_ , New York: Dover Publications, 1954.

Hamilton, William Rowan, _A Collection of Papers in Memory of—,_ New York: Scripta Mathematica, 1945.

——— _Theory of Conjugate Functions or Algebraic Couples; With An Elementary Essay of Algebra as the Science of Pure Time_ , Dublin: Philip Dixon Hardy, 1835. [Based on the similarity of title, date, and errata sheet whose pages correspond to the folio and signatures bearing the imprint "Volume XVIII" and date of delivery, November 4, 1833, and June 1, 1835, this is apparently a reprint of the papers printed in the _Transactions of the Royal Irish Academy_ , Volume XVIII, Part 2, pp. 293-422, Dublin, 1835, an original copy of which I was unable to obtain. The only extant circulating copy in the United States that I was able to obtain is at the Kresge Library, Dartmouth College. Interestingly, the work is about the sequence of numbers, which of course is what numbers are all about, and has really nothing to do with "time" in the physical sense as herein presented, and accordingly is hardly worth the effort of an interlibrary loan request notwithstanding the seductiveness of the title. See the above discussion on Plato and Aristotle. JG]

Harrison, Edward, _Darkness at Night; A Riddle of the Universe_ , Cambridge: Harvard University Press, 1987.

Hawking, Stephen W., _A Brief History of Time: Updated and Expanded 10_ th _Anniversary Edition_ , New York: Bantam Books, 1996.

———"Quantum Cosmology," in Hawking, _300 Years of Gravitation_ , 631-651.

———and W. Israel, eds., _General Relativity; An Einstein Centenary Survey_ , Cambridge: Cambridge University Press, 1979.

———and Leonard Mlodinow, _Grand Design_ , New York: Bantam Books, 2010.

———and W. Israel, eds. _300 Years of Gravitation_ , Cambridge: Cambridge University Press, 1987.

———and George W. Ellis, _The Large Scale Structure of Space-Time_ , Cambridge: Cambridge University Press, 1973.

Heathcote, Niels, _Nobel Prize Winners in Physics 1901-1950_ , Freeport, New York: Books for Libraries Press, [1971, © 1953].

Heaviside, Oliver, _Electrical Papers_ , Two Volumes, London: Macmillan and Co., 1892.

Helibron, J.L., _Electricity in the 17th and 18th Centuries; A Study in Early Modern Physics_ , Berkeley: University of California Press, 1979.

Heisenberg, Werner, _Philosophical Problems of Quantum Physics_ , Woodbridge, Conn.: Ox Bow Press, 1979.

——— _The Physical Principles of the Quantum Theory_ , New York: Dover Publications, 1949.

Hettler, W., _The Quantum Theory of Radiation_ , New York: Dover Publications, 1984.

Helmholtz, Hermann, _Popular Lectures on Scientific Subjects_ , New York: D. Appleton and Company, 1900.

——— _Selected Writings of —_ , ed. Russell Kahl, Middletown, Conn.: Wesleyan University Press, 1971.

Henry, [Joseph], "On the Influence of a Spiral Conductor in Increasing the Intensity of Electricity from a Galvanic Arrangement of a Single Pair, &e," in Robert Taylor, ed., _Scientific Memoirs, Selected From the Transactions of Foreign Academies of Science and Learned Societies_ , Volume I, 1837, 541-547, New York: Johnson Reprints, 1966.

Herzberg, Gerhard, _Atomic Spectra and Atomic Structure_ , New York: Dover Publications, 1945.

Hertz, Heinrich, _Electric Waves Being Researches on the Propagation on Electric Action with Finite Velocity Through Space_ , New York: Dover Publications, 1962.

——— _The Principles of Mechanics Presented in a New Form_ , New York: Dover Publications, 1956.

Hilbert, David, _Foundations of Geometry_ , La Salle, Illinois: Open Court, 1971.

———and S. Cohn-Vossen, _Geometry and the Imagination_ , New York: Chelsea Publications, 1952.

Hinton, Charles H. _Speculations on the Fourth Dimension_ , New York: Dover Publications, 1980.

Hochstadt, Harry, _The Functions of Mathematical Physics_ , New York: Dover Publications, 1986.

Hoffman, James R., _Andre-Marie Ampere_ , Cambridge: The University Press, 1995.

Hubble, Edwin, _The Realm of the Nebulæ_ , New Haven: Yale University Press, 1936.

———"A Relation Between Distance and Radial Velocity Among Extra-Galactic Nebulae," _Proceedings of the National Academy of Sciences_ , 15:168 (No. 5, March 15, 1929).

Huff, Douglas, and Omer Prewett, eds _., The Nature of the Physical Universe:1976 Nobel Conference_ , New York: John Wiley & Sons, 1979.

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Jacobi, H.H., "On the Application of Electro-Magnetism to the Movement of Machines," in

Robert Taylor, ed.. _Scientific Memoirs, Selected from the Transactions of Foreign_

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Johnson Reprints, 1966.

Jammer, Max, _Concepts of Force; A Study of the Foundations of Dynamics_ , Cambridge: Harvard University Press, 1957.

——— _Concepts of Mass in Classical and Modern Physics_ , Cambridge: Harvard University Press, 1961.

——— _Concepts of Space: The History of Theories of Space in Physics_ , Cambridge: Harvard University Press, 1954.

Jeans, Sir James, _Physics and Philosophy_ , New York: Dover Publications, 1981.

Jespersen, James, and Jane Fritz-Randolph, _From Sundials to Atomic Clocks; Understanding Time and Frequency_ , New York: Dover Publications, 1982.

Johnson, Charles S., Jr., and Lee G. Pedersen, _Problems and Solutions in Quantum Chemistry and Physics_ , New York: Dover Publications, 1986.

Jones, Henry Bence, _The Life of Faraday_ , London: Longmans, Green and Co., 1870.

Jones, Tegid Wyn, "Do Protons Decay?" _New Scientist_ , 105:48 (February 14, 1985).

Joos, Georg, and Ira M. Freeman, _Theoretical Physics_ , Third Edition, New York: Dover Publications, 1986.

Kaufmann, William J. III., _Universe_ , Third Edition, New York: W.H. Freeman, 1991.

Kelvin, Lord, See William Thomson.

Kepler, Johannes, _Epitome of Copernican Astronomy, IV and V; The Harmonies of the World: V_ , in _Ptolemy, Copernicus, Kepler_ , Great Books of the Western World, Volume 16, Chicago: Encyclopaedia Britannica, 1984.

——— _Kepler's Conversation with Galileo's Sidereal Messenger_ , trans. Edward Rosen, New York: No. 5, _The Sources of Science_ , Johnson Reprint Corporation, 1965.

Klein, Oscar, "The Atomicity of Electricity as a Quantum Theory Law," _Nature_ , 118:516 (October 9, 1926).

Kline, Morris, _Mathematics for the Nonmathematician_ , New York: Dover Publications, 1967.

Kolb, Edward, et al., eds., _Inner Space/Outer Space; The Interface Between Cosmology and Particle Physics_ , Chicago: University of Chicago Press, 1986.

Konuma, M., and T. Mashawa, _Grand Unified Theories and Related Topics_ , River Edge, New Jersey: World Scientific, 1981.

Kormendy, J., and G.R. Knapp, eds., _Dark Matter in the Universe_ , Boston: Reidel Publishing, 1985.

Koraar, Stephan, _The Philosophy of Mathematics; An Introductory Essay_ , New York: Dover Publications, 1986.

Krause, Eugene F., _Taxicab Geometry; An Adventure in Non-Euclidean Geometry_ , New York: Dover Publications, 1986.

Kuhn, Thomas W., _The Copernican Revolution; Planetary Astronomy in the Development of Western Thought_ , Cambridge: Harvard University Press, 1957.

——— _The Structure of Scientific Revolutions_ , Chicago: The University of Chicago Press, 1962.

Laertius, Diogenes, "Melissus," 'Epicurus," _The Lives and Opinions of Eminent Philosophers_ , London: George Bell and Sons, 1905.

Lanezos, Cornelius, _Albert Einstein and the Cosmic World Order_ , New York: John Wiley & Sons, 1965.

Larmor, Joseph, _Aether and Matter; A Development of the Dynamical Relations of the Aether to Material Systems on the Basis of the Atomic Constitution of Matter_ , Cambridge: Cambridge University Press, 1900.

Lebedav, N.N., I.P. Skalskaya, and Y.S. Uflyand, _Worked Problems in Applied Mathematics_ , New York: Dover Publications, 1979.

Lederman, L., "1986 Richtmyer Lecture: Unification, Grand Unification, and the Unity of Physics," _American Journal of Physics_ , 54(7):594 (July 1986).

Lee, E.W., _Magnetism; An Introductory Survey_ , New York: Dover Publications, 1970.

Lee, T. D., and C. N. Yang, "Questions of Parity Conservation in Weak Interactions," _Physical Review_ , 104:254 (No. 1, October 1, 1956).

Lenz, E., "On the Laws According to Which the Magnet Acts Upon a Spiral When It Is Suddenly Approached to or Removed From It; and on the Most Advantageous Mode of Constructing Spirals for Magneto-electrical Purposes," in Robert Taylor, ed., _Scientific Memoirs, Selected from the Transactions of Foreign Academies of Science and Learned Societies_ , Volume I, 1837, 608-630, New York: Johnson Reprints, 1966.

LePage, Wilbur R., _Complex Variables and The Laplace Transform for Engineers_ , New York: Dover Publications, 1980.

Levi, Howard, _Topics in Geometry_ , Huntington, New York: Robert E. Krieger Publishing, 1975.

Levi-Civita, Tullio, _The Absolute Differential Calculus_ , New York: Dover Publications, 1977.

Levinson, Horace C., and Ernest Bloomfield Zeisler, _The Law of Gravitation in Relativity_ , Second Edition, Chicago: University of Chicago Press, 1931.

Lieber, Lillian R., _The Einstein Theory of Relativity_ , New York: Holt, Rinehart and Winston, 1945.

Linde, Andrel, "Inflation and Quantum Cosmology," in Hawking, _300 Years of Gravitation_ , 604-630.

———"Particle Physics and Inflationary Cosmology," _Physics Today_ , 40:61 (September 1987).

Lindsay, Robert Bruce, and Henry Margenau, _Foundations of Physics_ , Woodbridge, Conn.: Ox Bow Press, 1981.

Loeaen, J.H.M.M., _Parmenides, Melissus, Gorgias: A Reinterpretation of Eleatic Philosophy_ , Assea, Netherlands: Royal VanGorcum Ltd., 1959

Lorentz, H[enrick] A[atoon], _The Theory of Electrons and Its Application to the Phenomena of Light and Radiant Energy_ , New York: Dover Publications, 1952.

——— et al.. _Letters on Wave Mechanics_ , See Einstein.

Lotka, Alfred J., _Elements of Mathematical Biology_ , New York: Dover Publications, 1956.

Lucretius, [Tullius Caius], _On the Nature of Things_ , Rosyln, New York: Walter J. Black, 1946.

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Mach, Ernst, _Space and Geometry in Light of Physiological, Psychological and Physical Inquiry_ , LaSalle, Illinois: The Open Court Publishing Co, 1906 (reprint 1988).

——— _The Science of Mechanics; A Critical and Historical Account of Its Development_ , Sixth Edition, LaSalle, Illinois: Open Court, 1960.

Manning, Henry, _The Fourth Dimension Simply Explained_ , New York: Dover Publications, 1960.

Maxwell, James Clerk, _A Commemorative Volume: 1831-1931_. New York: The Macmillan Company, 1931.

——— _Scientific Papers_ , New York: Dover Publications, 1965.

——— _A Treatise on Electricity & Magnetism_, Two Volumes, New York: Dover Publications, 1954.

——— _Matter and Motion_ , New York: Dover Publications, 1991.

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——— _Mathematical Physics_ , New York: Dover Publications, 1961.

——— _Selected Papers on Physical Processes In Ionized Plasmas_ , New York: Dover Publications, 1962.

——— and Fred L. Whipple, and Gerard de Vaucouleurs, _Survey of the Universe_ , Englewood Cliff, New Jersey: Prentice-Hall, 1970.

Miller, Kenneth S., _Advanced Real Calculus_ , Huntington, New York: Robert E. Krieger Publishing, 1975.

———and J. B. Walsh, _Advanced Trigonometry_ , Huntington, New York: Robert E. Krieger Publishing, 1977.

——— _Elements of Modern Abstract Algebra_ , Huntington, New York: Robert E. Krieger Publishing, 1975.

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