 
### Objective Reality

A Mentally Picturable Resolution of Physics' Wave-Particle Paradox

Second Edition

Donald R. Miklich, Ph.D.

"Only he who attempts the absurd is capable of achieving the impossible."

Miguel de Unamuno, _La Vida de Don Quijote y Sancho._
Für Itha

### Table of Contents

### Preface and Purpose

### A Note on Notes

### Part I: The Mystery

### Introduction

### Orientation

### The Quantum Mechanics Story

### Two Slit Data

### Ambiguous Data

### Quantum Interpretations: Copenhagen

### Two Other Quantum Interpretations

Many-Worlds

Pilot-Wave

### Part II: A Possible Solution

### Fundamental Assumptions

### A Realistic Quantum Interpretation: Basic Idea

### Some Paradoxes and Puzzles Explained

Schrödinger's Cat

Diffraction

Mini-solar-system atom

Quantum jumps

Radioactive decay

Chamber paths

Inertia and acceleration

Tunneling

Nonlocality

Particle detection

Time backward causality

Polarization

### Believability

### Part III: Foundational Premise and Extension

### Hidden Variables

### Hoist with His Own Petard

Special relativity background

Einstein's approach

The Hafele-Keating study

Special relativity wrap-up

### Membrane Model Resolution

Time dilation

Location in space

Size contraction

### Conclusion

### Final Thoughts

### Dear Reader:

### Appendix

### References

Preface and Purpose

Quantum phenomena are the invisible micro processes underlying and causing all physical events. Quantum mechanics is the scientific theory of these phenomena. It is precisely accurate and enormously useful, one of science's best tools. Nevertheless, it provides no description of quantum entities, nor does it provide any explanation of how they work. Its greatest shortcoming, however, is its inability to resolve the mystery of the manifestly self-contradictory data upon which it is based, the wave-particle paradox. Thus, though quantum mechanics is a superb engineering tool, it affords no understanding of the essentials of quantum phenomena.

Attempting to rectify this failure, physicists have invented many, many different quantum interpretations. An impartial judge must conclude that, though they are different, all are unrealistic. Indeed, most add logical inconsistencies and paradoxes of their own. Because these interpretations are the inventions of scientists, the public may consider them scientific conclusions. They are not. Since all go beyond the scientific evidence, all are merely metaphysical guesses. Nevertheless, most are constructed in terms of the variables and processes of classical physics. Unfortunately, this merely muddles the matter because the quantum data are conspicuously inconsistent with these variables and processes. What is worse, many of these quantum interpretations are tinged with, and some are immersed in antiscientific mysticism and subjectivism. As such these interpretations only compound the mystery. At best, they are unconvincing. At worst, they are unbelievable.

The present book offers an alternative. It also goes beyond the scientific evidence, so it also is a metaphysical guess. But this interpretation can not only explain the wave-particle paradox, it can explain many other aspects of the quantum mystery. Indeed, its explanation is so simple one can form mental pictures to see what it suggests. Above all, its explanation is completely objective and nonmystical. However, since it is a metaphysical proposal, not a scientific conclusion, like all other quantum interpretations it is beyond empirical proof. Therefore, everyone must determine for one's self whether it is believable. Accordingly, this book submits the interpretation to your judgment.

**Part I** presents a very brief, totally nontechnical and, in particular, a completely nonmathematical description of the wave-particle paradox and the history of this quantum mystery. It describes and critiques three of the most popular quantum interpretations.

**Part II** suggests a realistic and objective alternative, a mentally picturable, nonmathematical, nonmystical interpretation. Understanding it requires no knowledge whatsoever of math nor of quantum mechanics. This interpretation is based on Einstein's contention that the quantum mystery is due to something hidden from scientific observation. Thus, because the operative process is hidden, the interpretation can not be scientifically proven. Nevertheless, it is directly based on quantum data, so it is a plausible, evidence consistent speculation.

**Part III** considers the suitability of hidden processes such as underlie the quantum interpretation suggested in **Part II**. In particular it examines the claim of a science philosophy holding hidden processes to be meaningless. It shows such processes are common in science theories. It illustrates this in detail with respect to special relativity, a theory specifically developed to avoid hidden variables. In so doing it shows that the quantum interpretation developed in **Part II** to explain the quantum mysteries can, without modification, also explain the two great mysteries of special relativity, size contraction and time dilation. This is a finding of the utmost significance, for special relativity is entirely different from and apparently unrelated to the quantum problem. The fact, therefore, that an interpretation invented to explain one mystery can, without any alteration whatsoever, also explain a completely separate and independent one strongly supports the interpretation's believability.
A Note on Notes

Footnotes are the bane of expository writing. If a reader attends to them they break up the continuity of the material presented, requiring one to backtrack, often extensively, in order to get back into the flow of the discussion. But a reader who does not read them looses some, occasionally much of the material being presented. This latter problem is made more frequent by the typesetting practice of signifying footnotes with a small superscript, something easily overlooked. When they come to the bottom of a page, readers who have missed one of these tiny superscripts must either ignore the footnote and forego the information it conveys, or reread the entire page in an attempt to discover the material to which it pertains. For these reasons there are no footnotes in this book. If material deserves presentation it will be worked into the text. Matters which are unequivocally parenthetical will be enclosed in parentheses at the relevant location in the text.

The small superscripts problem also occurs with references. Therefore they are not used here. Instead, the practice common in scientific writing is followed. When the author of a referenced work is mentioned in the text, the date of the referenced work is placed in parentheses following the author's name. Thus: "Herbert (1985) uses the Airy pattern to show the wave aspect of electrons". But if an author is not named in the text, then his/her name and date will be given in parentheses at the relevant point of the text. Thus: "Quantum mechanics has been called the language of nature (Pagels, 1983)". More specific references will list appendix, chapter, page or section. Thus: "Feynman (1965, pgs. 129 30) says the two slit demonstration conveys the whole quantum mystery." With an author's name and the date of the referenced work an interested reader need only go to the **References** to identify it.

Another point about references must be made. This book is an expository essay, an opinion piece, if you will. It is neither a scholarly tome nor a scientific report. And it most unequivocally is not a text. It is addressed to educated lay persons, not scientists. Therefore (and for other reasons explained in the **Orientation** chapter) the kind of exhaustive referencing appropriate for a scholarly work is not followed. While all vital physical points are referenced, many historical points are not. And because this is a completely nontechnical essay addressed to a popular audience, I have tried to reference only similar works. In keeping with this popular orientation, if I know of a quote by a competent scholar or scientist, I will reference it rather than dig out the original from the scientific literature.

One other convention followed here must be mentioned. In reading a preliminary draft I became aware of a frequent redundant usage, "the physicist" followed by a name. This is redundant because almost every person mentioned in the text is a physicist of one kind or another. Therefore, I have dropped the "the physicist" identifier. If a person (celebrities excepted) is named without being otherwise categorized, you may assume he/she is a physicist of some kind.
These conventions and considerations having been noted, let's get on with the description of a realistic, objective, non-mystical, non-mathematical, intuitively comprehensible, mentally picturable, logic and evidence consistent, reality conception capable of explaining the quantum mystery, the special relativity mysteries and, especially, the wave-particle paradox.

DRM

Denver, Colorado

2020

### Part I: The Mystery

Introduction

Albert Einstein was a Jew; ethnically. But not religiously. In his definitive Einstein biography Abraham Pais (1982) says, "Albert's father was proud of the fact that Jewish rites were not practiced in his home." The family, he states, had an "assimilationist disposition". Many Jews dislike the term assimilation. (A flavor of this is enjoyably conveyed by the "I am easily assimilated" aria of the Old Lady With One Hip in Leonard Bernstein's _Candide_ ; lyrics by Bernstein himself and his wife Felicia.) So the fact that Pais, himself a Jew, used the term to describe the Einstein family may fairly be taken as indicating the depth of the family's separation from the religion of their ancestors. Pais emphasizes that Einstein's upbringing left an indelible nonreligious imprint on him by noting that he "did not become _bar mitzvah_ ", that is, he never was consecrated to Judaism as religious Jewish men, usually when teenagers, are. Also Pais reports Einstein "never mastered Hebrew", the language of Jewish rites.

This secular disposition notwithstanding, at one time in his boyhood Einstein became deeply interested in and committed to matters religious. Although this interest was intense, it did not last long, being replaced by an equally intense interest in science. This incident could be viewed as simply an incidental growth event, a child's sampling of various life orientations until one is found which fits. But I think a better interpretation sees it as evidence of the essence of Einstein's fundamental lifelong goal. Let me consider this a bit in order to show exactly what I mean.

At first glance Einstein's boyhood interest in religion would seem antithetical to his eventual career as a scientist. This is so because religion and science are usually seen as opposites, and indeed there is much to justify this opinion. The essence of religion is unquestioning acceptance of, _i.e._ , faith in, the tenets of one's particular religion, be they based on intuition, tradition, sacred writings, or religious authorities. However, evidence based reason is supposed to be the only authority in science. And since we can never have all the evidence, science therefore demands eternal doubt. The most well established scientific conclusions are supposed to be tentative, perpetually vulnerable to modification or replacement in the light of better reasoning and/or further evidence.

In truth, however, the opposite practices of religion and science are overblown. For example, Christian fundamentalists correctly insist a literal reading of the Bible contradicts the scientific fact of evolution. But many millions of other Christians, sincere, practicing, faithful and devout other Christians, interpret the Bible in an allegorical manner which removes this contradiction. An excellent illustration of this is the Roman Catholic priest (whose identity I regret I do not know) who once said the Bible is certainly divinely inspired, but not a divinely inspired biology text.

Nor is there any lack among scientists of blind dogmatism, unwillingness to abandon or even consider alternatives to scientific conclusions which have been rendered suspect, or even disproved by changed reason and/or further evidence. As Max Planck, the father of quantum theory, once observed: Science does not progress by new evidence and reason changing scientists' minds, but rather because younger scientists are trained in the new conclusions while the unconvinced older ones eventually die.

An excellent exposé of scientific dogmatism is the recent book by Adam Becker (2018). The issue he addresses is the same one addressed in the present book, the nature of the reality underlying quantum phenomena. But the generally accepted interpretation of quantum mechanics, the Copenhagen interpretation, claims this issue is a fantasy. Niels Bohr, one of the founders of quantum mechanics and the father of this interpretation, once famously said there is no quantum reality, only a quantum description (Bell, 1987, pg. 142). As Becker shows, those young physicists who questioned this and sought a meaningful, realistic interpretation did so at risk of, and sometimes at a cost to their professional careers. Thus, according to Becker, the general body of physicists did not, and still do not treat the Copenhagen interpretation as necessarily tentative, but rather as a dogma as unquestionable to them as creationism is to religious fundamentalists.

And it is precisely this issue of realistic understanding of quantum mechanics which, I believe, demonstrates the identical goal underlying Einstein's religious and scientific periods. Einstein never accepted Copenhagen's claim of the impossibility of any realistic quantum mechanics interpretation. He wanted to understand reality, and until quantum mechanics could provide such understanding he considered it self-evidently incomplete. He once said: "I want to know how God created this world. I am not interested in this or that phenomenon, ... I want to know his thoughts, the rest are details." (Herbert, 1985, pg. 177)

(When speaking of reality Einstein often referenced God. To my knowledge, he never explained this usage. However, since after his brief childhood episode he never practiced any religion it is presumed he used the word God as a metaphor for nature, which would be consistent with the pantheism of the philosopher Spinoza which he once endorsed.)

Knowledge of how the world was created is something most people seek in religion. We may presume it is what the young Einstein also sought there. But, as he states in his autobiographical note (Schlipp, 1949, Sec. I), at age twelve he abandoned religion because he became convinced many of the Bible stories could not be true. Thus, he changed his orientation not because his life goal changed. He still intensely wanted a complete understanding of reality, but he concluded science was a more trustworthy route to it.

Quite obviously, therefore, Einstein's pursuit of complete understanding would place him at loggerheads with Copenhagen's insistence that such understanding is impossible. But though other physicists respect him, indeed, for many this respect amounts to veneration, apparently most accept some version of Copenhagen. (There are different versions. However, all agree no realistic, objective, picturable understanding of quantum phenomena is scientifically possible.) Whether or not they believe there is a reality underlying quantum mechanics, most physicists consider it scientifically unfathomable. And they consider Einstein's goal to be as illusory as the quest for the legendary Holy Grail.

But Copenhagen, while it may be believed and taught dogmatically, most certainly was not developed dogmatically. Different persons may define it differently, but basically the interpretation is accepted because the evidence does not reveal the nature of any reality underlying quantum phenomena, and there is compelling reason to believe no more fundamental evidence is possible. The data themselves so suggest. Many physicists, I suspect, do not accept Bohr's contention of no quantum reality. I think many, if not most, are sure there is such. Indeed, no matter what he once said, even Bohr himself, some scholars have argued, really believed there existed a quantum reality. But physicists generally (and Bohr too, if he really believed in a quantum reality) are convinced no evidence can exist to reveal its nature. With abundant good reason they believe any meaningful, realistic understanding is scientifically inaccessible. So many resign themselves to one or another version of the Copenhagen interpretation. It provides a philosophical _modus vivendi_ , something philosophers, and physicists in their philosophic moments, may argue about. But for those not interested in philosophizing, it justifies their turning from quantum mechanics' reality ambiguities to the cookbook use of it as the superb engineering tool it is.

Quantum mechanics is widely considered to be the greatest, most precisely accurate of all science theories. As Tony Rothman and George Sudarshan (1998, pg. 116) have said, "Quantum mechanics ... is as close to true as science gets." Nevertheless, fundamental quantum phenomena are simply incomprehensible. This has probably best been stated by Richard Feynman (1965, pg. 129). He said, "I think I can safely say that nobody understands quantum mechanics." And he gave this advice, advice which doesn't endorse Copenhagen specifically, but which implicitly concedes something like it must be accepted because the quantum data themselves preclude any scientific explanation. Feynman's advice was: "Do not keep saying to yourself, if you can possibly avoid it, 'But how can it be like that?' because you will get 'down the drain', into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that."

As is clear from the title of the book containing these quotes, _The Character of Physical Law_ , Feynman was speaking as a physicist, a scientist. Thus, when he said "nobody knows", the knowledge he referenced was scientific knowledge. As such his claim has never been challenged. But there are other kinds of knowledge. The religious knowledge which preoccupied the boy Einstein is an obvious example. Conceivably a different, non-scientific kind of knowledge may explain "how it can be like that".

Presenting a possible such explanation is the purpose of this book. In no way does it seek nor presume to improve or complete quantum mechanics. Quantum mechanics is considered scientifically valid and essentially complete. But, as everyone agrees, it is profoundly puzzling. All this book seeks to do is present an objective interpretation of quantum phenomena which makes intuitive sense. This interpretation suggests a non-mystical, non-mathematical, easily comprehensible, completely objective and realistic but beyond science mental image, a picture anyone can understand, a picture which resolves the quantum mystery.

The kind of knowledge to be presented here is metaphysical. In the past several years this word has taken on many new meanings and implications. This is normal. Except where a particular profession may use particular words with precisely prescribed definitions, words do not have fixed meanings. In ordinary usage words' meanings grow, change and evolve. Though some object to this, considering such changes to be dysfunctional, if not sinful, these objections are rather like objecting to gravity. Whether it is a force or inertia in curved spacetime, gravity exists. Thus, if you don't want something to fall, support it. Similarly, the meanings of nontechnical words often change. Thus, if you don't want yours to be ambiguous, define them. So let me so do.

The metaphysics in this book is the classical kind. It does not in any way involve, for example, persons who dress and act unconventionally. There is nothing, paranormal, supernatural, mystical, magical or occult about the metaphysics presented here. Indeed, the major goal of the present metaphysics is to escape the flagrantly paranormal, supernatural, mystical, magical and occult characteristics of most existing quantum mechanics interpretations. For example, the mystical interpretations of the quantum mystery have been taken as analogous to some premises of far eastern religions (Capra, 2010). Another mystical opinion sees the quantum mystery as evidence that reality is not preexistent and objective but rather is subjective and partly created in the minds of those who know it ( _e.g._ , Nadeau & Kafatos, 1999). Such subjectivism is a fundamental characteristic of the Copenhagen interpretation, and subjectivism is the main thing the interpretation offered here seeks to escape.

The quantum explanation presented in **Part II** , though metaphysical rather than scientific, has no relationship whatsoever with subjective mysticism. Rather, it is reasoned speculation based upon the quantum data and evidence. Unlike the occult interpretations, the one offered here firmly adheres to science's, and Einstein's, fundamental assumption of a preexisting objective reality. But it ventures beyond science to achieve a realistic intuitive image of this presumed quantum reality and a realistic, visualizable, mechanical explanation of how it functions.

The essence of science is its public, collective nature. Science is a social activity, and scientific knowledge is a shared amalgam of the work and thinking of many persons. There neither is nor can there be science for one person only. But there can be individual metaphysics. Indeed, ultimately every metaphysics is individual. This is shown by the existence of abundantly many quantum mechanics interpretations. Wikipedia lists more than a dozen, each a different metaphysical understanding. Herbert (1985) discusses eight, two versions of Copenhagen and six others. Doubtlessly, if several advocates of one of these eight were carefully quizzed we would discover slight variations of their particular takes on their particular interpretation. This is inevitable. It is because there is no ultimate authority for any metaphysical explanation except one's self. Your metaphysical understanding of anything may make no sense to any other person in the world. It need not. It need only make sense to you.

And that's what this book offers, not science, but one person's beyond science intuitive, nontechnical, nonmathematical interpretation of quantum reality. It differs from most current interpretations by providing a realistic, objective, picturable, mechanical, easily understood explanation of "how it can be like that". With it in mind I no longer am bothered by Feynman's specter. Without going "down the drain" I can form a comprehensible realistic mental image of how the apparently incomprehensible quantum phenomena could happen. But even more importantly, with this realistic metaphysical interpretation I can dismiss the mystical metaphysics characteristic of almost every other quantum mechanics interpretation, magical notions which, like Einstein, I consider preposterous. For example, the usual Copenhagen interpretation claims nothing exists unless it is being measured. Advocates of this view are unapologetic about the absolutely bizarre, illogical nature of this claim. They concede, indeed, they insist it means exactly what it says. From this measurement claim they conclude the moon, for example, really exists only when it is being viewed, which viewing they reckon as a kind of measurement. (Einstein once facetiously asked if the glance of a rodent could make the moon real.) The alternative objective metaphysical interpretation presented in **Part II** justifies my dismissing this "viewing makes the moon real" and other even more egregiously outlandish and unrealistic wild-eyed notions. If you find it believable, it can do the same for you. Even if you do not find it believable, at least it shows the possibility of other than the usual mystical quantum interpretations. And perhaps it will help you invent your own realistic one. But in any case, I think you will find it interesting.

At its most general level the issue of the meaning of quantum phenomena may be meaningfully considered a disagreement between Bohr, the father of the Copenhagen interpretation, and Einstein. Although different in detail, the interpretation offered in this book follows Einstein. Most fundamentally, like the great theorist, this interpretation assumes an objective reality. It firmly rejects the notion that fundamental reality is created by those who study it. But this is not the only agreement.

Einstein once said the quantum explanation he sought, if removed from its mathematics, would be so simple it could be understood by a child. The realistic metaphysical quantum explanation suggested in **Part II** is precisely such. It involves no math whatsoever, not even elementary arithmetic. Rather, it proposes a mechanical quantum entity and quantum process, which, while neither could ever be seen or measured, nevertheless can be mentally pictured. And this mental image can readily be grasped by a child. Indeed, because they have not yet learned to see reality through the constructs of classical physics, children will have less difficulty understanding and accepting this quantum explanation than will trained physicists. (The surest way to think outside the box is by never having been inside it.)

This metaphysics is also like the explanation Einstein sought in another major way. It is causal. Quantum mechanics is not. Quantum mechanics identifies no cause of quantum phenomena. Therefore most physicists conclude there is none. They say quantum events just spontaneously, randomly happen. Indeed, one of the developers of the matrix algebra version of quantum mechanics, Pascual Jordan, once said an electron decides for itself where to assume a definite position (Bell, 1987, pg. 142). Einstein thought such ideas a "soft pillow" of self deceiving pseudo knowledge. I agree. To accept Jordan's claim one must surrender to the most flagrantly mystical kind of metaphysics. Einstein insisted quantum events must have a cause, and that quantum mechanics is demonstrably incomplete precisely because it identifies none. His position is called the hidden variable assumption. It means an electron, for example, does not spontaneously assume a position nor does it decide its position for itself. Rather, it has an empirically non-detectible, _i.e._ , hidden but determinate, characteristic which eventually leads it to assume a particular position.

At one time the hidden variable idea was thought to have been disproved by the mathematician John von Neumann. However, his disproof has been shown to be in error (Gribbin, 1995, pgs. 152-6. For those whose math is better than mine, Bell, 1987, Chpt. 1.). Soon after it was published, von Neumann's error was exposed by a lady mathematician, Grete Hermann. But the physics community ignored her. Feminists may suspect it was because Hermann was female, which may be partly true. But I think the main reason is that anything hidden is, by that very fact, incapable of producing evidence. So most scientists probably never checked out von Neumann's claim because they thought it irrelevant. They probably thought Einstein's hidden variable idea scientifically useless even were it correct, for without evidence there is no way to apply reason to evidence, the paradigm of science, in order to discover and characterize the hidden thing. And indeed, as will be shown in **Part III** , Einstein forthrightly admitted that, for him, reason was more powerful than evidence, and that a reason based fundamental theory, the unified field theory he long sought to develop, would uncover the operative variable even though it was hidden.

On this point I disagree completely with Einstein. Like the majority of scientists, evidence, I firmly believe, is the essence of science. So while the realistic quantum interpretation suggested below is similar to Einstein's view inasmuch as it proposes a hidden process, this idea is proposed as a metaphysical speculation, not as science. It also differs in that, while Einstein thought a quantum entity such as an electron had a hidden but determined characteristic, this book's idea says there is a hidden indeterminate cause. (An indeterminate cause sounds contradictory, but the apparent contradiction is explained in **Part II**.)

However, there is one way in which this book's explanation of the wave-particle paradox definitely would not have appealed to Einstein. It is nonlocal. Nonlocality refers to events where something occurring at one place in space has an immediate effect elsewhere, maybe all the way across the cosmos. Einstein called nonlocality "spooky action at a distance". He insisted it is an impossibility, something no reasonable person could accept. In fact, it was Einstein with the aid of two junior colleagues, Boris Podolsky and Nathan Rosen, who pointed out the implied nonlocality in some quantum mechanics predictions, an implication which he took as proof of the theory's incompleteness. (The paper which presented this argument and the argument itself are universally identified by the authors' initials, EPR.) At first Einstein's identification of quantum nonlocality was smothered by Bohr with Copenhagen gobbledygook and ignored by the physics community. But eventually a brilliant nonconformist, John Stewart Bell, who also was one of those who demonstrated and brought to general attention the math error in von Neumann's hidden variable impossibility proof, deduced a theorem which led to research proving Einstein both right and wrong. He was right when he said quantum mechanics predicts nonlocal phenomena. He was wrong when he said nonlocality is impossible. Today it is an empirically established fact that if there is an objective reality underlying quantum mechanics, then such reality has nonlocal phenomena. (Aczel, 2001; Becker, 2018; Crease & Goldhaber, 2014; Gribbin, 1995; Gilder, 2008; Kumar, 2008; Peacock, 2008; Squires, 1994. Look in the index of these and/or any other work concerning modern quantum mechanics under topics such as Alain Aspect, EPR, entanglement, locality, and of course nonlocality.) Since the metaphysical interpretation offered in **Part II** presumes an objective reality, as of course did Einstein, it accepts nonlocality. Indeed, it provides a mental image of precisely how nonlocality can occur. Insofar as I know, it is the only interpretation yet suggested which offers any nonlocality explanation.
Orientation

The above **Introduction** chapter tells the purpose of this book, where it is heading. But you need know more. You also need to know where it's coming from. This is so because it is coming from an unusual source. Though I am a retired scientist, I am not a physicist, and I know no quantum mechanics. (My doctoral training was as a social and experimental psychologist, but I spent the bulk of my career in behavioral and medical research.) If you have assumed this book is about quantum mechanics, an eminently reasonable inference, my ignorance would seem disqualifying. Certainly it would be if your assumption were the case. But it's not. This book is not about quantum mechanics. It's about the wave-particle paradox, _i.e._ , the quantum mystery. And the highest authority provides this assurance: One need know no quantum mechanics whatsoever in order to grasp this mystery.

The authority for this claim is the already quoted Richard Feynman. For readers who may be unfamiliar with the history of physics, Feynman was one of the outstanding physicists of the second half of the twentieth century. The 1999 Standard Edition CD _Encyclopædia Britannica_ calls him "probably the most brilliant" theoretical physicist of the post-World War II era. Not only did he receive the Nobel Prize, he received it for being one of the creators of the most advanced form of quantum mechanics, quantum electrodynamics (usually abbreviated QED). So on questions concerning quantum mechanics he is indeed a high authority.

No technical knowledge is needed to consider the quantum mystery because it does not originate in quantum mechanics. It comes from the wave-particle paradox which is conspicuous in the quantum data itself. Anyone can see, literally, the paradox. There is a very simple demonstration of it, the two hole or two slit demonstration. Not only is it so obvious anyone can understand what it illustrates, persons with the inclination can, with a little effort, build such device and see the mystery for themselves. Feynman (1965, pg. 130) said this device reveals "all of the mystery of quantum mechanics." I have often seen this claim repeated and reaffirmed by other physicists. I have never seen it questioned. The present book considers the data from the two slit apparatus, considers why these data are paradoxical, then suggests a realistic, objective and mechanical explanation of them. To do this there is no need for either the author or readers to know even the tiniest bit about the technicalities, mathematics and complexities of quantum mechanics.

But while one needs no technical knowledge, one does need to know something of what quantum mechanics is all about and how it was developed. I gained such information (which in highly abbreviated form is passed on in the next chapter) from reading several of the many books written by people who are quantum mechanics experts, books written specially for those of us with little or no physics knowledge. Many, but not all of these works (I kept no records, and can't remember all the titles and authors) are listed in the **References**. My study began in the last couple decades of the last century as recreational reading. It was simply a hobby, having no goal beyond the satisfaction of idle curiosity. This is the full explanation why, as explained in **A Note on Notes** at the beginning, the references in this book are not as complete as I would like. During my decades of recreational reading I kept no record of the books read nor did I make notes about the material read, something a scientist always must do when reading in one's professional literature. Therefore, when I determined to write this essay I could rely for references only on the books in my personal library and those I could find at the Denver Public Library.

Not long after these studies began, the germ of an idea for a possible picturable mechanical explanation of the quantum mystery occurred to me. But because I am not a physicist, at the time I did not try to do anything with it. Recently, in bored retirement, I turned back to it to see if it could be developed. To my surprise and delight, while the initial notion required considerable amplifications and corrections, it turned out to be promising.

You may wonder why an explanation of the wave-particle paradox would occur to someone who knows neither physics nor quantum mechanics when the extraordinary geniuses who developed the theory could not come up with one.

There are three reasons, but none of them, I assure you, are because the experts are less smart. Indeed, one reason why the experts have found no realistic solution may well be that they are too smart. Specifically, physicists, as a group, are the most quantitatively intelligent of all scientists. Indeed, sometimes, physicists are as much mathematician as scientist. For Example, Enrico Fermi, often called "Father of the Nuclear Age", received his doctorate in physics, but his first two professional jobs were as an instructor of mathematics (Fermi, 1954). But the power of math and physicists' competence in using it can be dysfunctional if the solution is not in the data. For then, no matter how much nor how sophisticated the mathematical analysis of the data, no answer exists therein to be found, and in that case math is as irrelevant as horseshoes. That is precisely the case if Einstein is correct and quantum mechanics' inability to identify any quantum cause is because the cause is hidden from the data. Let me dwell a bit on this, for the point appears to have been missed by some very intelligent, very well informed persons. Indeed, by Einstein himself.

Mathematics has an almost magical power to uncover the implications of propositions. But if a conclusion is not buried therein, the math cannot discover it. There is an old story so apropos and amusing I cannot resist repeating it though in all likelihood many readers already know it.

One dark night a policeman found a drunk crawling around on the sidewalk under a streetlight. He asked what the man was doing, and the drunk replied that he was looking for his house key which he had dropped. Though he didn't also get down on hands and knees, the cop started helping look for the key. But he could see nothing. So he asked, "Exactly where did you drop it?" And the drunk answered, "Back there in the middle of the block." In exasperation the cop demanded, "Then why the devil are you looking for it here?!" To which the drunk replied, "Because the light is better."

If Einstein is right and the quantum mystery is caused by something hidden from the data, then there is no answer in quantum mechanics, and attempting to find an answer by mathematical manipulation of it, no matter how sophisticated or brilliant, will necessarily fail. And so far, while there are many sophisticated mathematical attempts to explain the quantum mystery, none has garnered general acceptance, nor indeed, much of any acceptance at all. An example is Healey (1989) which is presented solely to show there are such works, but most definitely not to imply your author comprehends it. This doesn't prove that no answer can be obtained with math, but it certainly suggests such possibility. I think the reason why someone ignorant of quantum mechanics has found a possible answer is because Einstein was right in his claim that something is hidden. My approach so assumes. It supposes that what is going on with quantum phenomena is hidden from the quantum data and therefore from quantum mechanics. Under this assumption math is as irrelevant to finding a solution as looking for a key where it ain't. And the explanation offered in **Part II** is totally nonmathematical. It doesn't involve even as much math as is used in baking a cake.

The second reason why physicists haven't come up with the realistic quantum explanation offered below is that, in their opinion, it is not a solution. It's not the scientific answer they sought. And indeed, it is not. As already noted, it is a metaphysical speculation. Nothing about quantum mechanics is changed in any way by it. It certainly does not improve quantum mechanics. So as far as the engineering use of quantum mechanics is concerned it is totally irrelevant. So it isn't the least bit remarkable that physicists haven't found it. They weren't looking for it.

But finally and most importantly, the quantum interpretation presented in **Part II** is based on outside-the-box thinking. And as noted in the **Introduction** chapter, the surest way to think outside-the-box is never to have been inside it. But anyone trained in physics perforce is inside the box, indeed, virtually locked inside. Quantum mechanics didn't arrive on the scene as an entirely new science. Rather, it came as the culmination of what is now called classical physics, science which at the time quantum phenomena were first discovered had centuries of unambiguous, spectacular success. It would be preposterous to throw out hundreds of years of solid achievements and start anew. But the quantum phenomena do not fit either the classical physics variables nor the classical physics processes. About this there is no question. Everyone agrees. It is inconceivable that physical reality is controlled in two different ways. Thus, physicists almost unanimously agreed: Somehow the quantum data had to be reconciled with the classical model. And in formulating their quantum interpretations that's exactly what physicists have tried to do. They have persistently struggled to hammer, force, squeeze and shoehorn inconsistent data into preconceptions which simply do not fit. Little wonder they haven't succeeded.

Frequently in the following discussion I will charge that physicists' thinking about the wave-particle paradox has been governed by, and therefore driven to failure by, prejudice and preconceptions. Because it underlies bigotry, prejudiced thinking is usually considered reprehensible. That is not my meaning. Physicists' thinking regarding the quantum mystery is not blameworthy. But, I maintain, it is demonstrably dysfunctional. Everyone agrees: Quantum phenomena are fundamentally different from those in classical physics. Therefore, I conclude, the only possible quantum solution must involve variables and processes which are fundamentally different from those in classical physics. And that's the kind of solution offered in **Part II**.

There's another way of looking at this, a more focused way which, although some physicists would concur ( _e.g._ , Gregory, 1988), others, I'm sure, would firmly disagree. So be aware: Some very well informed persons might very strongly condemn what I'm about to say.

When Newton published his great _Philosophiæ Naturalis Principia Mathematica_ , the foundation of classical physics, he thought he had discovered the very laws which God had created, and with which God governs the universe. For many years many physicists tended to agree. Although usually only an unexpressed predilection, like Einstein (as quoted above), they thought physics was discovering the way God created the universe. Now if one has this notion, if one presumes, consciously or not, that the laws of physics have divine provenance (or for nontheists, that they are transcendently true natural laws), one isn't going to feel free to arbitrarily modify them in order to try to make them make better sense to mere humans. Whereas, to my way of thinking, all scientific laws are, and can only be human inventions. And while we may aspire to make them isomorphic with God's laws (or for nontheists, natural laws), we have no way of ever knowing if we have succeeded, or even if we are on the right track, or even if such laws exist. All we can ever know is that those scientific conclusions we call natural laws seem to work. I have described and defended this contention elsewhere (Miklich, 2014), and refer you thereto for details. Believing that contention is true, believing physics' laws are only human inventions, _i.e._ , people-made devices which seek to make reality understandable to and controllable by people, I have no compunctions about modifying the variables and procedures the "laws" specify in order to make them more sensible to people. And I offer to you the objective quantum explanation in **Part II** in the hope you will find it makes more sense than the different unrealistic and often mystical and subjective interpretations which different experts claim to be truth.

As noted earlier, science is a social activity. So as a scientist, my first inclination was to publish my quantum interpretation idea. And as a scientist it seemed necessary to publish an idea concerning a scientific theory in a science journal. But after a little thought I decided against so doing for three reasons.

First: Such journals require at least a minimal scholarly discussion of how previous scientists have dealt with the problem addressed by the material in the publication. This is not simply a matter of fashion, but necessary to put the work in context. Since my knowledge of the quantum mystery was, and is, wholly based on popular, nontechnical sources, I clearly was, and am incapable of writing a scholarly review of physics literature.

Second: I chose not to publish the idea in a science journal because it is metaphysics, not science. Evidence is the essence of science. But the quantum mystery explanation I have to offer, the objective model described in **Part II** , specifically says no evidence of its essential feature is possible. Thus, the idea is, and can only be, metaphysical speculation.

Third: The metaphysical explanation I have to offer, even if it could be shown to be absolute truth, is totally inconsequential operationally. Because the explanatory variables and processes it proposes are by definition not observable, they can add nothing to quantum mechanics. They can't possibly improve it. They can only explain it, and then only to persons who believe the interpretation.

But in the past few years I have become more and more concerned with, indeed, distressed by the mystical non-scientific nature of existing quantum interpretations. Ignoring the fact that their speculations suffer from the same non scientific, nonempirical, metaphysical limitations as mine, some physicists are advocating their absolutely preposterous notions as scientific facts. Consider these, each a conclusion of one of the three leading quantum interpretations. 1: The universe does not exist until someone in the universe, and therefore someone who also doesn't exist, measures it and makes it real. 2: Every tiny fraction of a second millions upon billions upon trillions of new universes are created. Each is complete in every respect, each is absolutely and eternally isolated from the virtually infinite number of other universes, and every second each creates millions upon billions upon trillions of new universes. 3: Everything everywhere in the universe is in instantaneous nonlocal communication with every other thing in the universe.

Because these notions are totally devoid of any supporting evidence they are pure metaphysics. What is worse, they are flagrantly mystical, unrealistic metaphysics. Equally as much as my notion, these ideas are incapable of empirical confirmation and incapable of in any way improving quantum mechanics. Yet, because they are offered by physicists they have the implicit imprimatur of science. This is socially dysfunctional and potentially destructive. Here's why.

Civilization rests on technology. And technology more and more rests on science. Yet there are many people who reject scientific conclusions they do not wish to believe. Consider this example. There is an overwhelming body of evidence showing childhood vaccinations are safe and effective, yet some parents who know this nevertheless reject this science and deny their children the benefits of such protection. The more this is done, the more does it compromise what epidemiologists call herd immunity, thereby raising the danger to everyone. Indeed, there is some evidence such denial is more frequent among the college educated, persons who presumably have some awareness of science, rather than among persons lacking such knowledge. For example, the average education level in Colorado, my home state, is higher than the national average, but the childhood immunization rate here is lower. While I very much doubt if any vaccination rejecting parents ever cited the mysticism of quantum interpretations as justification for their science denying action, I cannot doubt that scientists' advocating empirically unsupported notions such as the three listed above can only serve to weaken the public's trust in science, and by weakening it contribute to such tragic science rejecting acts.

This line of thought led me to decided to publish this explanation of the quantum mystery and its wave-particle paradox. Certainly it is a metaphysical notion beyond empirical, scientific verification. But in this respect it differs not a bit from any other quantum interpretation. However, my reservations about publishing in a science journal still hold. All quantum interpretations are metaphysics. None is science. After all, that's why no knowledge of quantum mechanics is needed to intelligently consider them. So instead I offer my interpretation in this forum addressed to non-physicists. It is offered in hopes of showing that the quantum mystery, the wave-particle paradox, does not obligate one to believe in a mystical, or subjectively created reality.
The Quantum Mechanics Story

Probably the best place to start the quantum story is by explaining the term quantum. And probably the best way to do this is with a brief history. Near the end of the nineteenth century the German government agency analogous to the US Bureau of Standards was, for practical industrial reasons, studying radiation given off by an idealized object, the so-called blackbody. Radiation was then believed to be a wave. (With caveats, it still is. That's the fundamental part of the quantum mystery, the wave-particle paradox. We'll get to it shortly.) Radiant energy was known to vary by frequency, the rates at which the presumed waves oscillate, and the data being gathered showed for blackbodies of different temperatures the amount of radiation at each frequency. At the time there were two different theoretical predictions of what this research would find. One was found to fit the lower frequencies part of the empirical distributions but not the upper, while the other fit the upper frequencies but not the lower. Max Planck devised a purely mathematical way of combining these into a single equation which, for any given temperature blackbody, fit both the high and low parts of its empirical frequency distribution.

This was a significant achievement. But Planck's equation was nakedly empirical, a theoretical hodgepodge which explained nothing. So Planck tried to develop this equation from physical theory. He assumed a plausible physical thermodynamics model of how a blackbody radiates, and then tried to derive his equation from this model. Because his empirical equation fit the data exactly, he knew exactly where he was going. His problem was to get there, to show how the thermodynamic functioning of blackbodies caused their radiant energy to be distributed in the way the data and his formula showed it to be.

In December 1900, after a couple months of intense effort, Planck succeeded, but only by violating a presumption which then was considered established truth. This presumption said energy is continuous, but Planck could derive his equation from his theoretical model only by assuming the energy was given off discontinuously. What continuous means is that for any two different energy levels there is always an intermediate level. A children's slide is a good illustration of continuity. No matter how close together the heights of two different points on the slide, there is an intermediate height between them. Every point of a slide merges seamlessly into the points immediately above and below. On the other hand, the ladder children climb to get to the top of the slide illustrates discontinuity. It has a discrete number of separate steps, and there are no in-betweens. And Planck could derive his empirically proven formula from his thermodynamic model only if the blackbodies radiated energy stepwise, in separate discrete amounts with no radiation between steps. The step size is tiny, indeed, infinitesimal. But the correct formula couldn't be derived without it. And that's what quantum in quantum theory or quantum mechanics means, that energy exists in separate, stepwise, discrete amounts or quanta.

Thus Planck's theoretical equation said blackbody radiation is quantized, _i.e._ , separated into discrete different sizes. There can be a lot at any one level and a lot at the next higher and next lower levels, but there can be nothing in between. That was a problem. The distributions Planck's theoretical formula described were of frequencies, a wave attribute. Also, there was a century of compelling evidence as well as James Clerk Maxwell's superb and validated theory saying radiant energy is a wave. But the energy in a wave is continuous. It is not separated into discrete steps, _i.e._ , it isn't quantized. For this reason Planck was not convinced by his theoretical equation. He was certain radiant energy is a wave and therefore continuous. He suspected some unknown characteristic of blackbodies broke it up into steps, and quanta were a peculiar result of the particular apparatus and not a general feature of radiant energy. For some time most physicists also continued to believed energy was naturally continuous and Planck's quanta were some kind of aberration. To anticipate the story's outcome, Planck's attempt to preserve the continuous radiant energy idea failed. (Though some sources say he never fully surrendered it.) Quantum mechanics, allegedly the greatest of all physical theories, is founded on abundant evidence showing energy is quantized. At the human level the continuous assumption is an acceptable approximation. But it is only an approximation, and it only works because the quantum step size is so tiny, which is also why the quantum phenomenon was not noticed earlier.

For five years neither Planck no anyone else did anything with his empirically verified but theoretically inconsistent quantized energy idea. Then in 1905 Einstein used it to explain the photoelectric effect, the way light shined onto particular metals can cause an electric current in them. This effect was an incidental finding of Wilhelm Wien's earlier research demonstrating the reality of Maxwell's theoretically predicted electromagnetic radiation, _e.g._ , radio waves, and the effect had been subsequently carefully studied but with theoretically puzzling results. This research showed low frequency light, no matter how intense or bright, could not produce the effect, while even very dim light of higher frequency could. In other words, a tiny amount of high frequency light was stronger than a huge amount of low frequency. This made no theoretical sense whatsoever, for if light were a wave, then its strength would be proportional to its amount, its brightness. Ergo these results were completely inconsistent with the wave theory of light, the very Maxwell theory which had led to Wien's discovery of the photoelectric effect! Using Planck's quantized energy step size, and proposing that the energy in a quantum of light depended not on its intensity but on its frequency, the higher the frequency the higher the energy, Einstein explained this theretofore inexplicable effect. (He didn't use it, but some time later another scientist invented the term photon to refer to a quantum of light, _i.e._ , a unit of radiant energy.) Einstein well knew the photon idea was physics heresy. He knew abundant evidence and established theory said light is a wave. So at first he offered the notion only heuristically. That is to say, when he first presented it he did so as a possibly wrong but useful idea which might lead to a better understanding. But he soon became convinced that the photon idea was correct, and that energy paradoxically has both wave and particle aspects. Again to anticipate the outcome, within two decades this proposition was empirically proved correct.

For six years after publishing his photoelectric analysis paper Einstein worked diligently to advance the photon idea, trying to incorporate the quantum idea into Maxwell's wave equations. He never succeeded. But with his photon idea he was able to explain the specific heat for cold substances. Nevertheless, with few exceptions the greater physics community treated his work with skepticism. Since the evidence for light's wave nature was solid and abundant, they could not doubt it. Nor could Einstein. He became firmly convinced in the concurrent validity of both the photon and wave ideas. He confidently predicted physics eventually would have to conclude light has both characteristics. And indeed quantum mechanics now does so conclude, even though it can not explain the paradox. Such explanation is the goal of this essay.

In about 1911 Einstein temporarily abandoned his work on quantum theory, turning instead to the development of his general relativity theory, usually considered his _magnum opus_ , but a theory of no concern to the topic of this book. Shortly, however, another took up the quantum idea. In 1913 Niels Bohr used it in a preliminary effort to explain the functioning of atoms. Earnest Rutherford, with whom Bohr then worked, had shown atoms not to be globs of substance embedded with electrons, as had earlier been supposed. His research showed atoms to have a tiny nucleus, and he suggested this nucleus is surrounded by a halo of orbiting electrons. But the same well established (and still completely valid) electromagnetic theory which held radiant energy to be continuously distributed waves, _i.e._ , Maxwell's theory, said this is impossible. It says orbiting electrons would be pulled, virtually instantaneously, into the nucleus and a Rutherford atom would collapse. Using Planck's quantized energy idea and some arbitrary rules forbidding such collapse, Bohr proposed a Rutherford model atom which explained well known but completely mysterious spectroscopic phenomena. Different chemical elements were known to give off or absorb different specific wavelengths of radiant energy. But nobody had any notion how this worked. Working with hydrogen, the simplest atom, Bohr developed a model which precisely explained its spectroscopic data.

Bohr said electrons orbit the atomic nucleus of any particular atom in a set of discrete orbits characteristic of that particular kind of atom. The greater the electron's energy the further from the atom's nucleus is its orbit. But an electron in a higher orbit can jump to a lower energy orbit. When it does it surrenders an amount of energy equal to the difference of the energy levels of the two orbits, and this energy radiates away. This, Bohr said, is the energy spectroscopic studies detected radiating away from atoms. Alternatively, when the electron is in the lower energy orbit and the differential amount of energy is shined upon the atom, the electron can absorb this energy and jump to the higher energy orbit. Two things about this process were arbitrary and contrary to then established physics. Bohr simply said by fiat that for each kind of atom there is a lowest energy electron orbit, and Maxwell's theory notwithstanding, the electron cannot radiate away this minimal amount of energy and descend any closer to the atom's nucleus. He also said the electron literally jumps between orbits without passing through any of the intervening energy levels. To those trained in classical Newtonian physics this sounded like magic, not science.

Theoretically, Bohr's atom was an arbitrary hodgepodge, the kind of thing computer programmers call a kludge. But it provided the beginnings of an explanation not only for spectroscopic phenomenon but for chemistry also. Though it raised more questions than it answered, they were the right questions. And as every scientist knows, asking the right questions is the way to find the right answers.

The Bohr model was a magnificent achievement which led in a little more than a decade to the development of quantum mechanics, the theory which, as physicists proudly boast, completely explains chemistry, the physical properties of all atoms and the physical principles of how they function and interact. However, the Bohr atom model has had a detrimental effect on general knowledge. Electrons, the model implies, orbit the atomic nucleus the way planets orbit the sun. But this notion is explicitly inconsistent with well known facts and well established theory. Nobody knows how electrons surround an atom's nucleus, but it is well known not to be possible for them to orbit like micro planets. This fact is obliquely acknowledged by the term used to describe electrons' paths around atomic nuclei. The term orbits is not used. Rather these paths are called orbitals, a name which simultaneously both implies and rejects the erroneous solar system model. The realistic quantum interpretation in **Part II** can solve this problem. It leads directly to a theoretically consistent image of how electrons surround atomic nuclei.

In 1916 Einstein returned his attention to quantum theory in a series of papers. He derived Planck's formula for blackbody radiation in a theoretically more elegant way. He also introduced probabilities into quantum theory. Quantum events, such as an atom's high energy electron jumping to a lower energy, could not be predicted. Einstein showed a way to determine at least the probability of such quantum events occurring. He explicitly proposed this as only a temporary make-do, something to help lead physics to eventually figuring out exactly what is going on at the quantum level. But in one of science's greatest ironies, no one, neither Einstein nor any other genius has ever solved this puzzle, and his expedient became essence. About a decade later when quantum mechanics was developed probabilism was an integral feature of it. Quantum mechanics can calculate the probabilities of quantum events quite precisely and accurately, but it cannot predict if the events will in fact occur nor, if they happen to happen, when or how. The realistic interpretation presented in **Part II** also can not predict when. However, it suggests explanations of precisely how the phenomenon occurs and why no prediction of when it will occur is possible.

As the intended tentativeness of Einstein's introduction of probability into quantum theory shows, during the 1910's the theory was conspicuously incomplete. Some things it could explain; others it could not. And even the things it could explain depended often on arbitrary rules. But in the 1920's the situation underwent an almost miraculous metamorphosis. Like a beautiful butterfly emerging from an ugly cocoon, comprehensive quantum mechanics emerged from the jury-rigged hodgepodge of the decade before. Since many of these developments were concurrent, no temporally linear description can be given.

Early in this decade two different men who had made no previous contributions to quantum theory each made spectacular additions. The idea each man proposed was so extraordinary and original it provoked serious doubts in most physicists. In both cases Einstein recognized the idea's brilliance and endorsed it, thereby saving it at least from being much delayed in acceptance or, perhaps, from ever being recognized at all.

Satyendra Nath Bose developed yet another way to derive Planck's quantum equation, a completely quantum way involving no classical physics constructs. But his initial manuscript describing his idea was rejected for publication. He then sent it to Einstein who recognized its brilliance and got the work published. Einstein went on to significantly advanced Bose's idea, leading to a separation of all elementary quantum entities into two fundamental classes, bosons and fermions. But these developments, although of the greatest importance to quantum physics, do not specifically involve the quantum mystery, so they are of no particular concern in this book. However, the other idea Einstein recognized and, perhaps, saved, lies at the very heart of the quantum mystery. It is the idea in the 1924 doctoral dissertation of Louis de Broglie.

From the time of its discovery by J. J. Thompson in the late nineteenth century until de Broglie's proposal, the electron was considered self-evidently to be a particle, a tiny chunk of material. An infinitesimal billiard ball is the image often suggested. At this time it would have been considered lunacy to think of the electron as anything else. However, de Broglie not only showed how the electron particle has a wave aspect, he also showed how this could be empirically verified. The head of de Broglie's doctoral committee was unsure what to make of the radical electron wave proposal, so he requested Einstein's opinion. The master responded enthusiastically and passed around the idea. And when word got around it was discovered that, by remarkable coincidence, the empirical test de Broglie proposed had already been done for other reasons, and the results corroborated the electron wave idea.

(My sources are contradictory on this point. Some say the kind of data de Broglie suggested wasn't gathered for a couple years, although the intention was not to test de Broglie's theory. The coincidence version, however, is too romantic to ignore. Also: The proper pronunciation of Broglie is ambiguous. The name is originally Italian, and as such it would be pronounced something like "bro-lyea". A French lady whom I knew said she'd pronounce it "brog lee", whereas a couple of my sources say it is pronounced something like "broi" or "broy". Obviously, this confusion is sufficient reason for you and your significant other to take an extended trip to France to resolve. _Bon voyage_! And let me know what you learn.)

To again anticipate the outcome, eventually the de Broglie idea was shown to apply to all matter. Although it is logically impossible for any one thing to be both a wave and a particle, a fundamental conclusion of quantum mechanics now holds everything in the universe, every single bit of material has both wave and particle characteristics. This so-called wave-particle duality is the fundamental part of the quantum mystery, the mystery which the metaphysical interpretation in **Part II** attempts to pictureably explain.

When word of de Broglie's electron wave idea reached Erwin Schrödinger he immediately went to work, and in a short period of intense effort he invented an equation which provides a comprehensive quantum mechanics. Theretofore it had been appropriate to call the quantum issue a theory. Colloquially the word theory implies speculation, something only hypothetical. That is not how the word is used in science where theory refers to a more or less coherent explanation of empirical data. This meaning was quite appropriate for quantum theory in the first years of the 1920's, for a great deal was then securely known about quantum phenomena, but there were a lot of so-called loose ends. But development of what is called quantum mechanics was a major advance, for the Schrödinger equation pulled what was known together into a comprehensive, consistent package. It provided a method of calculating how the electrons in an atom do the things they do, a tool quantum engineers could use about as routinely and reliably as an auto mechanic uses a wrench. Schrödinger intended his equation as a description of an actual wave, and its mathematical form is a wave equation. Therefore, his variety of quantum mechanics is now called wave mechanics.

But as the last sentence implies, Schrödinger's wave mechanics was neither the only nor the first quantum mechanics. Somewhat earlier and completely independently Werner Heisenberg developed a quantum mechanics from a totally different premise. Heisenberg's version is model independent. Though he favored the particle model, his quantum mechanics is completely abstract. Rather than proposing any physical model for quantum entities, he made tables of data which could, at least in principle, be measured. And he showed how by mathematically manipulating such tabled data in a peculiar way one could probabilistically predict quantum phenomena. When he showed his work to Max Born, his mentor at the time, Born recognized Heisenberg's peculiar math as a well developed mathematics not then used by, and therefore not generally known to physicists: matrix algebra. With the help of Pascual Jordan, Born put Heisenberg's brilliant idea into the form it is now generally known, matrix mechanics.

As if two quantum mechanics were not enough, Heisenberg's work inspired Paul Dirac to invented a third, based on yet another mathematics. Dirac was more an applied mathematician than physicist, and he invented his own quantum mechanics math based on what is reported to be an uniquely suitable form, Hamiltonian equations. His method is usually considered mathematically the most elegant. Thus, none of the three quantum mechanics versions have the same mathematical form, but all produce the same results. This similarity led Schrödinger to compare his wave mechanics and matrix mechanics and he found them to be mathematically equivalent. Then Dirac showed all three to be mathematically equivalent.

This equivalence is a significant fact, something I believe is not given the importance due it. So let me digress a bit in an attempt to so do.

Because its math form is more familiar to physicists, Schrödinger's wave equation is the version physicists usually use and it is the usual referent when they speak of quantum mechanics. Of the three versions, only it was intended as a description of a physical entity. It was intended to mathematically model an actual energy wave. But Max Born showed this in fact not to be the case. He showed Schrödinger's equation rather to be an abstract method of calculating the probabilities of quantum events. A characteristic of the equation making unequivocally clear its status as a calculation algorithm, and not the math description of a physical wave as Schrödinger intended, is its definition in configuration space, an abstract multidimensional mathematical construct. Whereas real space has only three dimensions, Schrödinger's equation requires three separate dimensions for every electron in it. Thus, it requires six separate dimensions to describe the two electrons in a helium atom and 276 separate dimensions to describe the ninety-two electrons in a uranium atom. Computationally this can be a severe task, though conceptually it's no problem. Either way, however, it's obviously unrealistic.

(Readers who have heard of the modern theory of everything called string theory know it claims reality has more than three spatial dimensions. Nine is the number usually suggested. Even if string theory should be correct, and considerable opinion holds it to be impossible ever to empirically confirm or refute it (Hossenfelder, 2018; Lindley, 1993; Woit, 2006), its extra dimensions do not and can not resolve the spatial dimensions unreality of Schrödinger's equation. For while string theory proposes more than three space dimensions, this number is supposed to be the same for everything in the universe, whereas the number of dimensions required by Schrödinger's equation is different for every different number of electrons it considers.)

The other two quantum mechanics, Dirac's and Heisenberg's, were never intended to be anything but computational algorithms, physical-model-independent predictors of quantum results. This is conspicuously the case with the latter, for when he invented matrix mechanics Heisenberg deliberately avoided any physical model. Earlier attempts to develop a reality model based quantum theory had consistently run into problems. For example, the theoretical impossibility of Bohr's micro solar system atom model. So to avoid such problems Heisenberg made his quantum mechanics entirely empirical. His matrices contained real data, but no reality model.

To me, the mathematical equivalence of all three forms of quantum mechanics shows each to be only a calculation algorithm and not a math description of a supposedly real entity such as a wave or a particle. If so, then all are only computational tools, no more models of reality than is a slide rule. Yet sometimes they are considered models. Some accounts and some quantum interpretations say there exists a physically real but immaterial, energy empty probability wave which diffuses in space like a spectral essence or ghost. This is particularly true of the Pilot-Wave quantum interpretation (see below). Presumably this is said because the mathematical form most physicists use when doing quantum mechanics is Schrödinger's wave equation. But as Born showed, the wave equation is actually a probability function, and the wave math use is only a convenience. Heisenberg's matrices are mathematically equivalent, and they could be used instead. Would use of them mean there are immaterial, energy empty matrices existing in space?! Even if, despite Einstein's objections (see the next paragraphs), reality itself is probabilistic there is no reason to suppose anything like this immaterial probability wave exists. The unreal, mystical nature of this notion is as manifest as it is disquieting. This kind of supernatural thinking seems to me to be more appropriate for those whose metaphysics include the regular use of hallucinogens rather than in the musings of sober scientists. It is precisely this kind of occult metaphysics which the present book's realistic quantum model hopes to supplant. Regardless of the specific form used, the three forms of quantum mechanics are all merely algorithms, abstract prediction tools, not descriptors of any real but immaterial probability entity. At least, that's how it seems to me.

Having said my piece, let me climb down from the soapbox and return to the quantum mechanics story.

With three equivalent versions, quantum mechanics seemed to the great majority of physicists to have been completed. It seemed to have reached the same fundamental level as ordinary mechanics did after Newton. But there was a strenuous exception to this conclusion, an exception coming from a physicist whose views can not be ignored, Einstein. The three quantum mechanics produce identical results. But, except in a few trivial incidental circumstances, these results do not say what would happen. Rather they enumerated the probabilities of the various events which might happen in the particular quantum situation being considered. As noted above, this feature which Einstein himself had introduced into quantum theory as a temporary make-do, had become an essential feature of the complete quantum mechanics. But Einstein refused to accept it.

The probabilism of quantum mechanics contrasts starkly with the determinism of ordinary mechanics. Newton's laws are deterministic. From them one can make precise predictions. For example, from them engineers can predict exactly how much force is needed to move something of a given mass, and astronomers can predict exactly when and where a solar eclipse will occur. Indeed, running the analyses backwards astronomers can determine when and where past solar eclipses and/or other celestial phenomena did occur. But because quantum mechanics only provides the probabilities of events which might happen, nothing similar is possible with it.

Einstein did not object to probability _per se_. It exists in other areas of physics, the statistical mechanics most physicists believe to underlie thermodynamics, for example. And in fact, Einstein was an absolute master in the use of such methods. For example, his 1905 Brownian motion paper used precisely these means to demonstrate the reality of molecules and atoms, as did his doctoral dissertation's estimation of Avogadro's number, the number of atoms or molecules in a mole of any substance. But in this use probability is not considered fundamental. It is used in these cases because it is impossible to know the exact actions of billions upon billions upon billions of atoms and/or molecules. The probabilistic statistical approach is only a practical expedient for dealing with this inescapable ignorance. Fundamentally, however, these phenomena are believed to be, and indeed the statistical analysis is based on the premise that they are totally determinate.

Nor did Einstein object to quantum mechanics. He never said it is wrong. He accepted it as valid but incomplete. There is an obvious implication of this position which usually isn't explicitly spelled out in the popular literature. Since it is important, let me so do. Probabilism is not a necessary assumption of quantum mechanics. That is to say: None of the three quantum mechanics versions is based on an axiom holding quantum phenomena necessarily to be spontaneous and uncaused. Therefore, neither the math nor the logic of quantum mechanics requires probabilism. Indeed, the math is determinate (Woit, 2006, pg. 32). But the results are probabilistic, and the results, which Einstein conceded are valid, he also insisted are only partial, results which do not tell the whole story.

The usual Copenhagen interpretation says quantum mechanics is complete, and does tell the whole story. If this is so, then probabilism is fundamental, and quantum events are spontaneous and uncaused. And if that is so, then fundamental reality itself is random. It is this conclusion, and not quantum mechanics _per se_ , to which Einstein objected. He had absolutely no doubt whatsoever that reality is not and can not itself be random and uncaused. In a letter to Max Born he once expressed his conviction in a way which has come to be taken as his shibboleth on the issue. God, he said, does not play dice with the universe. To which Born wittily answered that Einstein should not presume to tell God what to do.

This disagreement will be considered more below where quantum interpretations are discussed. At this point it suffices to point out that the probabilism issue has had a major role in the quantum story and has never been resolved.

Returning to the quantum history synopsis: Invention of matrix mechanics, one would suppose, would have sufficed anyone for a lifetime achievement. For Heisenberg, however, it was only a beginning. Soon thereafter he developed the idea for which, perhaps, he is best known, Heisenberg uncertainty. This principle says some paired quantum entity attributes, called conjugate attributes, can never be both simultaneously measured to infinite precision. There always must exist a tiny amount of imprecision which may be divided between the pair in any way, but is inescapable. Since the imprecision amount is tiny, infinitesimal, for practical purposes it is immaterial. But for theoretical purposes, where absolute values may be necessary to show exactly what's going on, the more accurately one attribute is measured, the less accurately can the other be. Only dynamic attributes are conjugate. Position and momentum is one such pair, energy and time is the second. Other, static attributes, in principle can always be measured as accurately as may be possible. For example, there is no theoretical limit to the precision with which a quantum entity's electrical charge or size can be measured.

The implication of Heisenberg's principle is to put limits on science as a method of studying reality. Despite the flamboyant uninhibited reason-based projections of some theoreticians, the essence of science is its evidence foundation. Therefore, when the principle says it is physically impossible to obtain some kinds of evidence it is saying reality itself sets limits upon what science can discover about reality. At the human level, Heisenberg's limit is immaterial. But at the quantum level it can prevent science from discovering exactly what's going on.

The **Introduction** chapter of this book pointed out the goal Einstein had for science, a quasi religious desire to know reality, or, as he phrased it, knowledge of how God created the world. In view of this goal, you can expect Einstein to have been most unwilling to accept Heisenberg's principle. And indeed he wouldn't buy it. But though he struggled diligently to find a way around it, he never could. It stands as an inescapable scientific fact.

The cause of Heisenberg uncertainty is unknown. Different quantum interpretations give different reasons. Schrödinger, for example, argued that his allegedly real electron wave must cover an amount of space at least as large as its wavelength. But, as will be considered below, measured electrons always appear to be dimensionless points. Schrödinger showed mathematically how when a wave coalesces into a single point there is a necessary imprecision which is exactly equal to Heisenberg uncertainty. However, Heisenberg, in his development of the principle, assumed the quantum entity, _e.g._ , an electron, was a particle which had to be struck by another particle, a photon, in order to be located. The rebound from this collision created the uncertainty. But Bohr, although on occasion he used it, usually rejected Heisenberg's explanation. Instead he insisted an electron or photon does not have a position or momentum except when it is measured. Those who endorse this interpretation sometimes call this principle indeterminacy rather than uncertainty. Measurement is necessary to make any quantum attribute real, Bohr maintained, and conjugate attributes, Bohr insisted, cannot be simultaneously measured. Therefore, when one attribute is measured the other is necessarily indeterminate.

The above is a very brief account. But it suffices for the purposes of this book. For those who may have had no earlier introduction to the quantum mystery it provides enough background to put the following material into a meaningful context. If it has stimulated an interest in such readers to know more about this issue, and I hope it has, for the issue is fascinating, I refer them to the **References**.

Before leaving this historical outline it must call your attention specifically to the role Einstein played in creating quantum mechanics. He was not an outsider. His thinking and work were fundamental and integral to the theory's development, as is shown by his Nobel Prize. It was awarded for his 1905 photoelectric effect paper, the paper which introduced the quantized photon to physics, not for either of his more famous relativity theories (as many people erroneously believe). Though Planck discovered the quantum, he never really accepted its revolutionary implications, nor did he ever make any theoretical use of his discovery. He is said to have had doubts about it all his life. Whereas Einstein, as Douglas Stone (2013) has documented, was the first, and for a few years the only physicist to accept the quantum as an empirical fact pertaining to all radiant energy. In a real sense, therefore, Einstein, not Planck, should be considered the father of quantum mechanics.

This is important here because the goal of this book is to present a realistic, objective and logically consistent interpretation of quantum mechanics, something Einstein insistently and persistently advocated, and to do so by means of something hidden, a proposition Einstein also advocated. But the bulk of other physicists appear to have decided both this goal and this means are impossible. Einstein was one of history's greatest physicists. After writing a highly critical account of his work, Ohanian (2008) nevertheless concluded Einstein was, after only Newton, the greatest physicist ever. Therefore, if the all time number two physicist thought a meaningful realistic understanding of quantum mechanics was a worthwhile goal and could be achieved by something hidden, the present essay, I submit, however inadequate it may be, at least is addressing a reasonable issue in a reasonable way.
Two Slit Data

Let us now consider, not just the conclusions quantum mechanics has derived from quantum data, but some of these actual incomprehensible data. As noted above, we'll examine data from the two slit demonstration because, as Feynman said, it reveals the entire quantum mystery. It does so by illustrating the fundamental aspect of the mystery, wave-particle duality. With light photons, a simple apparatus suffices to do this. Similar but much more elaborate devices are needed to show duality with other matter, but this has been done with electrons, neutrons and even a couple atoms (Aczel, 2001, pgs. 21-4). The technical difficulties of such demonstrations grow exponentially with the size of the matter, so it is exceedingly unlikely it will ever be done with any macro object, anything visible to the naked eye. Quantum mechanics says this is only a technical limitation. It claims wave-particle duality characterizes all matter, up to and including the entire universe, and if technical problems could be resolved, duality could be shown with matter big enough to see. So far this claim has been substantiated. But so far this has been done with nothing larger than a couple atoms, and it takes billions and billions of atoms to make an object big enough to be seen. Thus, so far ordinary experience is inconsistent with the quantum mechanics claim. It provides no evidence, not even the tiniest hint of wave-particle duality with macro objects.

To illustrate the quantum mystery Feynman first describes what would happen when macro objects, things we can see, pass through something like a two slit apparatus. He considers bullets to illustrate what particles do, and water to illustrate how waves act. Then he contrasts the comprehensible things these macro objects do with the incomprehensible results of passing quantum entities through a two slit apparatus. The two quantum entities he discusses are photons and electrons. As he notes, and as quantum mechanics specifies, these entities respond essentially the same way, both illustrating the same quantum mystery.

Two slit demonstrations with light do not require any especially complicated equipment. Indeed, a tinkerer can make suitable two slit devices to show some of these phenomena. But one of the most puzzling parts of the quantum mystery can only be shown with electrons. Feynman describes what quantum mechanics says electrons would do in a two slit apparatus. His description is a thought experiment detailing what quantum mechanics predicts, not an account of an actual demonstration. At the time Feynman wrote actually doing what he described was too technically demanding. However, Gribbin (1995, pg. 7) said that in 1987 the electron version was empirically shown with much more elaborate instruments, and the results are exactly what Feynman and quantum mechanics say. So there is no inaccuracy in Feynman's approach. His presentation is merely a way of illustrating the quantum mystery to those of us with little physics knowledge without confusing us with difficult but nonessential technical details.

Since wave-particle duality is the phenomenon to be shown, it is well before considering the data to consider the paradox it demonstrates. Wave-particle duality is not merely paradoxical. After all, a paradox may be merely counterintuitive. But wave-particle duality is logically impossible. The duality paradox says every elementary piece of matter, _e.g._ , an electron, is both a wave and a particle. But nothing can be both a wave and a particle. Logic prohibits it. Consider: A particle is an object, a piece of substantial matter, "a tiny billiard ball" is an analogy often used. But a wave is not an object. It is an action, the rhythmic oscillations of the vast multitude of particles composing a material body. To say matter is both a wave and a particle is like saying a trumpet, a physical object, is the sound it produces, a wave in air. In anything but poetry such a statement is utter nonsense.

This, of course, is well known to the physicists who came to the wave-particle duality conclusion. But they say they had no choice. The data, they say, clearly show fundamental quantum entities to have both wave and particle characteristics. And indeed, as will shortly be considered, the data most certainly do. However, if wave-particle duality is taken to mean matter is a particle with incompatible wave characteristics, physicists' usual interpretation, or the less frequently alleged wave with incompatible particle characteristics, then I strongly disagree. Logic, it seems to me, demands wave-particle duality to mean matter is fundamentally some unknown entity having one characteristic resembling waves and another resembling particles, but which, since each characteristic contradicts the other, can be neither wave nor particle _per se_. Herbert, (1985, pg. 64) agrees. He says a quantum entity "is in reality neither particle nor wave, but an entity entirely new to human experience which exhibits the properties of both." (This opinion is expanded and explained below. I mention it here to alert you to the illogic of claiming fundamental matter is either a wave or a particle.)

It is appropriate to note the existence of one exception to this logical conclusion. The usual, almost universal assumption is that a quantum entity, _e.g.,_ a photon or an electron, is a single entity. If it is, then the logical restriction just noted applies. No single thing can be both an object and an action. However, one quantum interpretation, the Pilot-Wave interpretation, presented below, considers each quantum entity to be a conjoint pair of separate entities, a particle guided by an immaterial wave. This interpretation does not appear to have many adherents. Einstein entertained then rejected it. But it escapes the logical restriction noted in the above paragraph.

Returning to the two slit demonstration, consider a two slit apparatus for showing the wave-particle paradox with photons. It consists of a light source and a screen onto which the light shines. Between the source and screen, and parallel to the plane of the screen, is an opaque partition which I call the slitted partition because it has two parallel vertical slits. (Feynman speaks of holes, but the data are equivalent whether the device has slits or holes.) Each slit is exactly the same distance from the source as the other one. Thus a triangle can be drawn connecting the three, with each side from the source to a slit being exactly the same length.

The slits must be exceedingly narrow, about the width of the wavelength of light used, and there is an optimum distance between them. Also, the demonstration works best with light of a single wavelength. The longer the wavelength, the easier it is to demonstrate the mystery. Ergo red works best. But such details need concern only tinkerers who wish to set up their own two slit demonstration in order to see some of these data for themselves. Such tinkerers are referred for guidance to Baierlein's (1996, Section 4.3) splendid physics text for non-physics majors. Baierline (under the heading "Additional resources", pg. 103) also gives a source which, at least at the time his book was published, could provide appropriate glass encased slits.

Because the partition is opaque, light from the source can only reach the screen by passing through the slits. A person unfamiliar with physics might quite reasonably expect the light to make two parallel vertical bands on the screen, one positioned on a line extending from the source through one slit, and the other on a line from the source through the other slit. But this is not what happens. Instead, the light forms a series of parallel vertical lit and unlit bands on the screen. Each lit band gradually shades into the unlit ones on either side of it. Such pattern might be described as zebra-like. The brightest band is in the middle of the projection screen. Intuitively this makes no sense for a line perpendicular to the screen drawn from this brightest band back to the light source passes through the solid part of the slitted partition exactly midway between the slits.

You may sometimes see someone claim this zebra stripe pattern can be explained only if light moves as a wave. Indeed, for persons trained in classical, pre quantum physics this may seem necessarily so. But it's not. There are an unknown number of ways this pattern might be explained. For example, Feynman (1985) does so by assuming each photon, upon leaving the source, becomes a multitude of particles, one for each possible path from the source through the slits and onto a point on the screen where they all come together again into a single particle. (Though, it may be argued, this is merely a complicated particulate equivalent to a wave explanation.) But the wave explanation, while not unique, is overwhelmingly most parsimonious. That is to say, it is the explanation requiring by far the fewest and by far the least unrealistic assumptions.

Thus the wave inference is overwhelmingly the most likely explanation, and wave-particle duality arises from it. So how do waves explain the zebra stripe light pattern? To show this we need an image of waves, a concrete example, something you likely have seen or can demonstrate for yourself if you have not. Consider an undisturbed body of water. A children's wading pool (sans kids) is excellent. By undisturbed I mean the surface of the water has no waves. It is perfectly smooth and level (ergo the need to keep the kids out). Now drop a rock into the water at some point and note how waves spread out from the point. Each wave crest, of course, is a place where the water is higher than the water on either side of it, the wave troughs. The particular point on a wave, _e.g._ , its crest or trough, is called its phase. A picture taken of the water surface right after the rock is dropped would show a phase pattern spread across the water, successive crests and troughs in concentric circles around the rock drop point.

Such picture would also show a progressive reduction in the crest heights and trough depths as one goes from the drop point outward. Indeed, if the water body is large enough the waves will eventually attenuate completely and the surface of the water at a distance will be smooth and level. This occurs in water because the energy imparted by the rock drop is expended in pushing the water molecules back and forth to make the waves. Attenuation does not occur with light. If light is a wave, such wave does not weaken no matter how far it may travel. This characteristic seems to say that, whatever a photon of light might be, since it does not attenuate it cannot be a wave _per se_ , but can only be something which has a wave-like characteristic.

Another thing illustrated by such picture is wavelength or frequency. If one measures the distance across the phases of a wave, _e.g._ , the distance between two successive crests, or between two successive troughs, the distance will be the same, at least in the ideal case. (Any actual demonstration is vulnerable to a host of extraneous factors which might cause these measurements to vary. But the ideal is assumed.) This distance is called wavelength. Now suppose the waves to be moving. If they move outward from the rock drop point at a constant speed, then there is a precise inverse relationship between wavelength and the frequency with which any particular wave phase, _e.g.,_ their crests, moves past a fixed point. Thus, whether one speaks of frequency or wavelength, one is saying the same thing: Short wavelength is equivalent to high frequency.

Next we need consider how a wave would move through a slit. Again, water waves provide a visualizable analog. If a water wave encounters a gap in a barrier, it will create an identical wave on the other side of the gap. Wave crests and troughs will move out from the gap in concentric semicircles which will be exactly the same as the wave coming into the gap. They will have the same frequency and the same amplitude, _i.e.,_ strength, as the wave which created it. And if one water wave encounters a barrier with two identical gaps, the effect will be to create two waves in the area beyond the barrier, one coming from each gap. To have a term of reference let's call them daughter waves.

Since these daughter waves are continuations of the same original, pre-gap wave, and since the distance from the origin of the wave to each gap in the barrier is identical, the daughter waves will match the original in three respects. First: The daughter waves will have the same frequency. Second: the daughter waves will be in phase. This means when a crest (or trough) is emerging from one gap a crest (or trough) will emerge from the other gap. Third: The daughter waves amplitude or strength, _i.e.,_ the height of each wave crest (or the depth of each wave trough) will be the same as the initiating wave.

As these daughter waves spread out from their respective gaps they will overlap. The result of this overlap is called interference. It does not change the frequency of the waves. Nor does it change the total amount of energy in the wave, but it redistributes it, completely destroying the wave at some points, but doubling its amplitude at others. This also can be illustrated at a wading pool, although the pattern formed by the intersecting waves is complicated and a bit difficult to see.

Drop two identical objects (two golf balls are excellent) from the same height and about a couple feet apart into the smooth water. Look at the pattern formed by the intersecting waves somewhere ahead of the drop points (not between them). If you look carefully you will see some points where the surface of the water does not seem to be moving up and down. These are places where the intersecting waves are completely out of phase. That is to say: When the crest of one wave is at one of these points the trough of the other wave is. At these points the precise rate at which the crest of one wave decreases the trough of the other increases. Thus the height of the water at these points never changes. Again I must note that in any actual demonstration there are likely to be extraneous factors which will blur this response. But if the demonstration is done carefully, keeping extraneous factors to a minimum, the result can usually be seen. In the ideal case, at these points two completely (180°) out of phase waves will completely cancel each other's amplitude and the water surface will not move. Nor do these points move. Wherever one occurs it will remain while the waves continue. This effect is called destructive wave interference.

There will be other points, however, where the two intersecting waves are completely in phase. That is: When the crest of one wave reaches such point the crest of the other wave will also reach it. Thus at these points the amplitude of the intersecting waves will be twice the amplitude of the separate waves and the water at these points will oscillate up and down twice as much as it does in the separate waves when they are not intersecting. The effect at these points is called constructive interference, and like the destructive interference points, these points remain in place as long as the waves continue.

The water wave analogy is useful for intuitively illustrating interference, but it's potentially misleading. In a water wave each wave crest is followed by a wave trough, the distance between them, of course, being one half wavelength. This kind of wave is called longitudinal, meaning the wave extends in the same direction as its movement. Such waves occur in water or air. But the wave characteristic of light (or any other radiant energy) has been determined to be exclusively transverse, meaning the wave extension is at a right angle to the direction in which the light moves (Pais, 1991, pg. 60). Transverse waves don't occur in water or air because these substances are insufficiently dense. But they do occur in more dense material. Seismic waves such as are produced by earthquakes have a transverse component. In general there is a relationship between transverse wave frequency and the density of the material carrying the wave: The higher the frequency the more dense must be the wave carrying matter.

Nevertheless, transverse waves produce interference just as longitudinal ones do. So once one understands interference, one can see how the zebra stripe pattern produced by light shining through a two slit partition can be explained as due to it. Light from the source is presumed to go as a wave to the partition where it passes through each slit and creates, on the other side, two daughter waves of the same frequency and amplitude, and in the same phase. These daughter waves spread out and overlap creating an interference pattern. In places on the screen where a constructive interference point occurs there will be lots of light. At points on the screen when a destructive interference point occurs there will be none.

If one covers one of the slits, the light pattern on the screen is remarkably different. In this case the pattern is dominated by a single bright band centered on a point where a straight line from the source and through the slit strikes the projection screen. And though the one slit pattern has bands at its edges, the zebra stripe characteristic is much less pronounced than with both slits open. Because the one slit and two slit patterns are so different it is easy to assume that light must move differently in the different circumstances. But this inference is untenable. In fact, the one slit pattern also is an interference pattern, and as such it also is most parsimoniously explained by assuming light moves through a single slit as a wave (Baierlein, 1996, Section 4.7). And of course, since the quantum mystery pertains to all matter, exactly as with photons, electrons passed through a tiny single opening also produce an interference pattern, a pattern most parsimoniously explained by assuming electrons also move as a wave (Herbert, 1985, pg. 62).

In general, the most parsimonious, reasonable and realistic inference one can draw from these data, whether from one or two slits, is that light moves as a wave (Baierlein, 1996, pg. 170). As far as is known, only something like Feynman's conspicuously unrealistic photon with its alleged mysterious ability to separate into a multitude of particles when it leaves its source then magically recombine into a single particle when it reaches its destination can explain light as moving like a particle.

But while the data powerfully suggest light moves like a wave, they also powerfully suggest it interacts like a particle. Through either two or one slit, light forms bands. But each band in fact is composed of a vast multitude of individual light quanta, photons, flooding the screen there. Such flood completely obscures the separateness of each photon. However, their discrete nature can be shown by modifying the two slit apparatus in order to reduce the flood of photons to a trickle, _i.e._ , make the light source exceedingly dim. Also, the screen onto which the light shines must be replaced with something able to record each separate photon hit. A photographic plate works. The modified device is then set up in a dark room and allowed to operate for a brief period. When the photographic plate is developed, because the light was so very dim very few photons have struck it. And instead of bands of light one sees individual dots. Each dot is apparently the result of a single discrete photon, a single quantum of light, striking the plate at a single location.

Classic physics knows no other way to explain these discrete photon dots than to assume each photon is a tiny particle. And certainly this inference is reasonable. The reasonableness of the particle inference is enhanced by data which can be gathered from a two slit apparatus capable of registering such data as the exact time when a photon hits the screen and the duration of each hit.

(From here on, the two slit devices needed are too technically demanding for do-it-yourselfers. But experimental physicists have constructed such instruments and with them have obtained the data described next, data just as unambiguously ambiguous as that from simpler devices.)

Data from these more sophisticated two slit devices clearly suggest each photon is a separate, particle-like entity. They do so in two ways. First, when photons pass one-at-a-time to the screen, never is there more than a single dot per photon. Second, the duration of the interaction when a photon makes a dot on the screen is instantaneous, exactly what would occur if the photon is a particle.

But don't run off thinking the photon has been shown to be a particle, for even the very data suggesting this also suggests the photon is a wave. While each photon makes a single dot on the recording apparatus (whether a photographic plate or some other suitable device), these dots only occur where a wave would put them. That is to say: There are lots of these separate, particle-like dots in places where the pattern suggests constructive interference. But there are none where the pattern suggests destructive interference. And what seems particularly strange, an interference pattern is created even if the photons pass the apparatuses one at a time. Thus, in some unknown way, each separate and individual photon interferes with itself.

Yet another part of the quantum mystery is shown by these individual photon dots. While quantum mechanics can predict that the dots will be grouped into an interference pattern, nothing can predict where any particular individual photon dot will occur. Quantum mechanics can predict the _probability_ of a photon hitting at each place on the screen. And over a very large number of trials these probabilities are found to be precise and accurate. But absolutely nothing can predict where any individual photon will hit within the interference pattern. This illustrates the probabilism of quantum mechanics. As far as science knows there is no reason why any photon hits the screen at the particular specific location it does. (Pascual Jordan, recall, said the electron decides the location for itself.) The location must be somewhere in the interference pattern, but exactly where is unpredictable. As far a quantum mechanics can say each hit location is completely random.

Finally, the data also can be seen to suggest another aspect of the quantum mystery: Nonlocality. The data show individual photon hits to be spread out across the entire recording screen. This is particularly true when both slits are open, but even the pattern with a single slit open is wider than would be the case with any ordinary kind of particle, _e.g._ , a bullet. This dispersion is consistent with the wave conclusion. But consider the situation where photons pass through the apparatus one-at-a-time. At the instant when a photon, moving through the slit as a wave, interacts with the screen to leave a dot on it, the wave may be, and usually also is in touch with another part of the screen. Yet never is there a second hit. Somehow the information that the photon has interacted at one point on the screen must be instantaneously, _i.e._ , faster than light, conveyed to the rest of the wave, turning it off, as it were. In other words: A hit at one location must nonlocally inform the rest of the photon wave not to interact with the screen. Though nonlocality is a significant aspect of the quantum mystery, I've never seen this implication considered in popular expositions of data from the two slit demonstration. Usually other kinds of apparatus and/or procedures are used when nonlocality is being illustrated. But the nonlocal implication of these data is inescapable. (Einstein was the first to point out that if light moves as a wave yet interacts as a particle the nonlocal implication necessarily follows. He did so at one of the Solvay conferences. These were a series of theoretical physics meetings financed by Ernest Solvay, a wealthy Belgian industrialist, and attended, invitation only, by the greatest physicists of the time.)

At this point the data are massively ambiguous. The suggestion of nonlocality is disturbing to our usual understanding, though our usual understanding may well be wrong. The data also appear to show photons moving as waves yet interacting as particles. And that, as far as anyone knows or has yet been able to figure out, is simply impossible even if this conclusion did not imply nonlocality.

Unlike the erroneous impression given by many textbooks, where the objective is to present the conclusions of research rather than to document the often tortuous path by which these conclusions were reached, ambiguous data are not at all uncommon in science. And scientists have well developed procedures for dealing with such data. The first of these is replication. Collect the data again making absolutely sure no mistakes or sloppy procedures have caused the puzzling results. This has been done many, many times with two slit data. Beyond doubt these results are not due to any procedural errors. The data are reliable and real. And really puzzling.

The second standard way scientists deal with ambiguous data is by gathering more focused data. They zero in on the part of the phenomenon which is causing the puzzle. Unfortunately, in this case the cliché, "Easier said than done", applies with full force. We would like to watch the photon as it passes through the two slit apparatus in order to see exactly how it moves and how it interacts at the screen. But we can't. It is impossible to see a photon. We can only see its interaction.

But physicists weren't completely stymied. They figured out a way to at least approach the goal of watching how a quantum entity moved through the apparatus. First they switched from photons to electrons. This is perfectly rational because quantum mechanics says electrons, like all quantum entities, perform the same way as photons. For example, Herbert (1985, pg. 62) presents data, the so-called Airy pattern, which shows electrons exhibiting the same wave phenomena shown by photons. But the ordinary two slit apparatus does not work with electrons. So Feynman explained what quantum mechanics says would happen if it did. In other words, he fashioned a pedagogic thought experiment to explain the essential facts without getting into those technicalities which would only confuse his target audience, persons like myself who know no technical quantum mechanics. There is absolutely no inaccuracy in this because as Gribbin (1995, pg. 7) explained, using electron devices analogous to the two slit apparatus, results exactly like those Feynman (and Gribbin) report are found. With that assurance, we can skip the fictitious thought experiment details and simply consider the factual results these electron analogue two slit devices yield.

The electron cannot be seen everywhere in its passage through the two slit analogue device. Indeed, it cannot be seen at all. But it is possible to detect its passage by causing it to interact with a photon. This photon detector is set up immediately after the locations analogous to the slits in a classical two slit apparatus. And this is what the data from such device show: Sometimes electrons pass through the analogue apparatus without being detected. In this case they form a two slit interference pattern on the projection screen. At other times an electron is detected immediately after passing one or the other slit analogue. Never, however, is one simultaneously detected at both. And the several electrons which are detected at a particular slit analogue create a one slit interference pattern on the projection screen.

Instead of clarifying the two slit data, this more focused look at how quantum entities go through the two slit apparatus compounds the ambiguity. Any attempt to explain these data can only be a guess. Several popular expositions say it's as if electrons were conscious, knew they were being watched, and wanted to confuse experimenters. According to this conspicuously absurd conspiracy notion, each electron has impeccable foresight, and when it sees it is going to be detected after it has passed the slitted partition or its analogue (remember, the detector is located immediately after the slit analogue, not before it), the electron turns itself off at the other slit and goes through only the one where it will be detected. However, when the electron knows it won't be detected, it chooses to go through both. I doubt that this conscious electron suggestion is serious. Much more likely it is intended to say only that the weird results only resemble what would occur were electrons conscious and contentious. But even with a disclaiming "as if", this Jordan-like attribution of conscious decision making to the electron is disquietingly mystical. Nevertheless, such a preposterous explanation seems to be the only possible way to explain these data.
Ambiguous Data

Having introduced you to quantum data, it is now possible to point out the fundamental difficulty plaguing quantum research: Inadequate data. Indeed, to call quantum data inadequate is itself inadequate, for such data are not merely inadequate, they are grossly and, in some ways, grotesquely so. Consider the just presented two slit demonstration. We would like to know what photons and electrons are and how they go through the apparatus. But the most physicists have been able to do in this direction is to try to detect which slit(s) an electron passes through. Unfortunately, the data so obtained not only do not clarify matters, they introduce further ambiguity. They seem to show electrons going through only one slit when they are going to be detected, but both slits when not. The only explanation of this weird result seems to be the even more weird attribution of conscious deception to the electron!

In other areas of science a result like this would lead scientists to try to get more detailed data. That is science's standard response to ambiguous data. But with quantum entities it can't be done. Consider: We want to see how the electron passes the two slit apparatus, so we might consider flooding the device with light in order to watch every bit of the electron's passage. But it won't work. Remember Heisenberg's thinking when he developed the uncertainty principle. He reasoned that to locate an electron one would have to bounce a photon off it. But the impact would knock the electron off the course it was following in an unpredictable way. So, if one were to try in this way to expand the two slit electron watching procedure, even if it worked, all it would do is knock the electron around. One would learn nothing about how it normally moves.

The blunt, unwelcome truth of the matter is that data from the two slit experiment are inadequate and so too are those from every other kind of quantum experiment. All quantum data, no matter how they are obtained, give only the same vague, contradictory hints about what the quantum entities are or how they do whatever it is they do.

That's just the way it is, and not due any lack in the persons doing the research. Quite the contrary. That the inventors of quantum mechanics have accomplished so much despite the inherently muddled nature of all quantum data is a testimony to their very considerable genius. Unfortunately, popular quantum expositions do not emphasize loud and clear just how massively inadequate all quantum data are. Emphasis is necessary because the consequence of this inadequacy is that all quantum conclusions beyond those of the mathematics of quantum mechanics itself are and can only be guesses.

And that's precisely what physicists do. They guess. Not wild guesses. Indeed, it might be better if they did guess wildly. This is so because what they do instead is guess on the basis of their preconceptions. Waves and particles are fundamental entities in classical physics. But, of course, these two things are entirely different, so no single thing can be both. Therefore, on the basis of their knowledge of pre quantum ( _i.e._ , classical) physics physicists presume wave-particle duality means fundamental quantum entities must be either one or the other. Having so presumed, they further and overwhelmingly conclude all quantum entities must be particles.

For example, Feynman (1985, pg. 15) says: "I want to emphasize that light comes in this form — particles." Pagels (1983, pg. 118) is even more emphatic. He says: "There is no question that an electron is a true particle, because we can measure the charge, mass, and spin of an electron, and it leaves tracks in a Wilson cloud chamber." Of course, these are only two physicists. But the fact that the particle presumption is ubiquitous in physics is shown by the usual name of the sub discipline which studies fundamental quantum entities. Though sometimes referred to as high energy physics, the usual name is particle physics.

In order to show that the particle decision is a prejudice I am going to criticize Pagels' reasons. Not because I'm picking on him, but because he presented his reasons in a clear, straightforward way so there is no uncertainty about his thinking. Other popular writers whom I've read are more indirect or they simply write as if the particulate nature of quantum entities were self-evident.

Pagels says we know electrons are particles because we can measure electron attributes which he implicitly presumes to be particle attributes; charge, mass and spin. Though not necessarily so, that implication may be appropriate for charge and mass, but not for spin. Spin is a well established quantum entity attribute, but nobody knows what it is. However, it is well known not to be what spin is ordinarily conceived to be, _i.e._ , like a spinning top or billiard ball (Gribbin, 1984, pg. 94). Therefore, that the electron's spin can be measured means only that the electron is a quantum entity. Since quantum spin is nothing like the spin of particles, the electron's spin does not and can not show it to be a particle.

Moreover, if it is logically correct to conclude electrons are particles because they have some particulate attributes, then equally so the electron must be a wave, for equally obviously electrons have measurable wavelengths, something no particle has or could have. Clearly, in emphasizing the particulate attributes of electrons while ignoring their wave attributes Pagels provides _prima fascia_ evidence that preconception has governed his thinking.

Pagels' strongest argument for the particulate nature of electrons is that they leave a track in a cloud chamber. At first glance this clearly seems to prove his contention. It does because we implicitly presume what applies to phenomena at our level must also apply at the quantum level. Consider, for example, the following classical physics situation analogous to a cloud chamber. Suppose one were plinking empty cans from a fencepost with a BB gun. Obviously the BB is a particle, and the fact that the gun can be aimed implies that the particulate BB follows a predetermined path from the gun to the target. Indeed, if there were any question about this it would be possible to observe the BB's path, perhaps using high speed photography, to confirm this assumption. Flooding the path with light to enable the photography would have a completely inconsequential effect on the BB's flight. Even before the advent of such photography such measurement was possible at least in principle. But as was just considered, at the quantum level such a procedure is impossible in principle because a quantum entity such as an electron will in fact be significantly impacted by the illuminating photons.

At one time Heisenberg also thought the bubble chamber path proved the electron to be a particle. But he decided this inference is not tenable. He did because he became convinced the impossibility of measuring the electron's complete passage through the chamber made this scientifically unjustified. Heisenberg, like Bohr and others of the Copenhagen persuasion, firmly believed that presumptions like the one we unthinkingly apply to the BB can not be trusted at the quantum level. An experimenter can only be sure of where a quantum entity is when measuring it. Between measurements, one can only guess (Heisenberg, 1999, Chpt. III). Each bubble in the chamber may be taken as a measurement of the electron's location. But between bubbles we simply do not know where the electron is. To our eye, the distance between bubbles is small, a distance we are accustomed to overlook. But in fact, relative to the size of the electron, there is a vast, enormous space between successive bubbles, a space in which, Heisenberg concluded, the electron might be anywhere or anything. The data simply are insufficient to show where the electron is, what it is or what it's doing.

I find Heisenberg's argument completely persuasive. To presume the BB is a particle between the time it leaves the gun and strikes the can (if one's marksmanship suffices) if not actually, is at least potentially data verifiable. Moreover, one can see the BB is a particle when it goes in the gun and one can see it is a particle when we dig it out of the target. But we not only do not have such data for the electron, we can never get it. Moreover, the data we do have are not only ambiguous, they are contradictory. The cloud chamber may not do so, but the two slit demonstration shows the electron unequivocally to have both particle and wave characteristics. Therefore, to simply apply our BB analogy is to court error.

However, if fundamental quantum entities must be either waves or particles, as most physicists presume, then the latter is certainly the better choice. After all, the very fact that quantum entities are separate is consistent with a particle guess but inconsistent with a wave one. But beyond this, solid evidence shows light, _i.e._ , photons, and therefore presumably electrons and all other quantum entities as well, cannot be a wave.

For light to be a wave there must be a medium, a body composed of vast multitudes of particles which bounce back and forth against each other to create the light wave. For almost the whole of the nineteenth century physicists, believing that the evidence proved light to be a wave, were confident such a medium must exist. They called it the luminiferous aether. (This spelling is sometimes but not always used. The usual spelling is "ether". But it is best to avoid the usual spelling because it might imply the aether is the same as the chemical ether. Ether definitely exists. Aether does not.) The light carrying aether was assumed to permeate the universe. But repeated attempts to detect it all failed.

Also, the aether idea is logically untenable. As noted in the previous chapter, light's wave aspect is known to be transverse. But to convey transverse waves of light's high frequency the aether would have to be denser than any known substance. Yet solid bodies, _e.g.,_ planets and asteroids, pass effortlessly through space even though the aether idea says space is brimful of matter denser than lead.

So, if physicists believe quantum entities such as photons must be either wave or particle, and if photons cannot be waves, then persons who are trained in physics are disposed by their very educations to consider the photon, electron and all other quantum entities to be particles. Emilio Segrè reportedly often said the eye can only see what the mind is prepared to see, a psychological insight as profound and accurate as any of his physics discoveries. However, there is a downside to prepared minds, for frequently and normally the eye sees what the mind is prepared to see, whether it's there or not. In my opinion a major cause of the quantum mystery is physicists' education. It predisposes, indeed it effectively compels them to suffer from this dysfunctional, though normal psychological tendency. They see particles which may not in fact be there.

And in point of fact, as noted in the **Two Slit Data** chapter above, logic says quantum entities cannot be particles. To save you the bother of turning back to review this contention, let me repeat it. (And inasmuch as it appears generally to be ignored, it is well worth repeating.) Given the definitions of waves and particles, if a quantum entity is single, by far the usual assumption, it can be neither a wave nor a particle. For insofar as a quantum entity is a wave it cannot be a particle, and insofar as it is a particle it cannot be a wave. If they are single entities, logic demands quantum entities to be something else, some unknown thing which has some wave aspects and some particle ones, but which must be neither a wave nor a particle _per se_. Unfortunately the inadequate quantum data do not show what this unknown thing is. They give only vague hints.

Inadequate quantum data also causes what may well be the most famous scientific dispute in history, the Einstein _vs._ Bohr disagreement about the completeness of quantum mechanics.

From the time it was created until his death Einstein insisted quantum mechanics is incomplete. It is, he said, because except in limited unusual circumstances it doesn't say what will happen. It only lists possibilities, each with its probability of occurring. Classical, Newtonian physics is not like this. With it one can precisely predict future events, solar eclipses for example. So by the classical standard, the standard which implicitly Einstein considered _de rigueur,_ quantum mechanics unquestionably is deficient.

Einstein believed quantum probabilism occurs only because quantum data are inadequate. In a situation where quantum mechanics predicts more than one possibility, he claimed there is in reality only one predetermined outcome, but he insisted this condition is hidden and therefore lacking in the quantum data.

Bohr undertook to be quantum mechanic's champion. He insisted it is complete, even though the quantum data do not show what will happen. The quantum data do not contain information concerning the particular one event which will happen, he said, because till the event does happen it in reality is not determined. In effect he said it is reality which is incomplete, and the data merely demonstrate this incompleteness. Quantum mechanics extracts all the information in the data, Bohr implied, so it is as complete as it can be.

These two geniuses engaged in a couple intellectual jousts over this question at the famous Solvay theoretical physics conferences. With only one exception Bohr always won.

The exception was Einstein's first nonlocality charge against quantum mechanics. He drew a semicircular line to represent a screen onto which, from a point before the screen, a photon was projected. (This is not a version of the two slit demonstration. There is no partition between the light source and the projection screen is semicircular.) In this situation the data show the single photon strikes only a single point on the screen. But the data also seem to show photons move as a wave. Thus at the instant when the single photon hit is recorded on the screen the photon wave must be in contact with the entire semicircular screen. If therefore a quantum event is undetermined until it happens, as Bohr insisted, then when it happens something must instantaneously turn off the possibility of the photon hit occurring at any other spot on the screen. Thus Bohr's position necessarily implies nonlocality, the "spooky action at a distance" which Einstein considered self-evidently impossible. Although my sources do not say whether Einstein made the point, the implication of his argument is conspicuous: If, like the projectile in the above BB gun illustration, the hit point is predetermined when the photon leaves the projector, then no such impossible (to Einstein) nonlocality need be assumed.

My sources do not say whether Bohr responded to this. But about a decade later, when the famous EPR paper (for Einstein, Podolsky and Rosen) refined and strengthened the charge that quantum mechanics implies nonlocality, Bohr certainly did respond. His reasoning was the same as it had long been. _Viz._ , He brushed aside the nonlocality issue, implicitly conceding that quantum mechanics does indeed predict some nonlocal phenomena. But he continued to insist quantum mechanics is complete even though it does not predict exactly what will happen. It extracts all the information in the quantum data, but the data are inadequate to predict precisely what will happen because reality so functions that till a quantum event happens the event is undetermined. Bohr didn't convince Einstein, but we need consider the EPR argument more closely in order to decide if it can convince us.

To my mind most popular expositions of EPR get so involved with quantum details they obscure the essence of the paper's argument. The essence is quite simple. It involves a remarkable quantum attribute called entanglement. In effect entangled quantum entities become unified in such manner that what happens to one also affects the other. Sort of a quantum marriage, one might say. EPR considered a situation with two entangled quantum entities each possessed of the same kind of quantum attribute, an attribute having only two possible states. According to quantum mechanics, in this particular situation when the attribute is in one state for one of the entangled entities it must be in the other state for the other entity. Quantum mechanics does not specify what the attribute state is for either entity. It only says if the attribute is in one state for one entity then it must be in the other state for the other.

EPR considered a pair of entangled quantum entities which move apart. If after they are apart one of the entity's attribute state is determined, then according to quantum mechanics the other's attribute state will, without in any way disturbing or measuring it, be known with certainty. Now, EPR argued, if Bohr is correct, neither entities' attribute state exists until one or the other is determined. At which time both entities' attribute states are instantly fixed. But the entities are separated. There is a distance between them, a distance that could be as wide as the universe. Quantum mechanics, EPR implicitly conceded, is correct when it says when one entity's state is determined the other's is also known. Therefore, if Bohr is correct and in reality the attribute state is not fixed ( _i.e._ , it doesn't exist until a measurement is made) then upon becoming fixed for one entity it must immediately be fixed for the distant other. But since they are apart, some signal or effect must _instantaneously_ go across space from the entity where the determination is made to its unmeasured entangled mate. Such instantaneous effect, EPR (especially E) insisted, is something no reasonable person could believe.

As explained above in the **Introduction** chapter, there now is considerable evidence convincingly showing that in situations like the one EPR considered nonlocal effects do in fact occur. From this some persons conclude Einstein's idea that the attribute states are predetermined but hidden is wrong ( _e.g._ , Aczel, 2001). In fact, what is wrong is this conclusion. EPR does not address hidden variables. Rather, it attacks Bohr's quantum-events-are-undetermined-till-they-happen contention. The basis of the attack is that Bohr's quantum interpretation necessarily implies the occurrence of nonlocal phenomena, phenomena which, EPR claims, every reasonable person knows to be impossible. But subsequent research showed EPR's "reasonable person" to be wrong. Nonlocal phenomena definitely do occur. This invalidates EPR's argument. But disproof of EPR's anti-Bohr argument says nothing about the hidden variable alternative Einstein implicitly advocated. EPR did not address the hidden variable issue, so, as far as EPR is concerned, it remains undecided. And in fact, the Pilot-Wave quantum interpretation (considered below) is a mathematically consistent quantum mechanics interpretation, and according to it every event in the history of the universe is completely predetermined but this condition is hidden. So mathematically, at least, Einstein's implicit hidden variable hypothesis is tenable.

Quantum data are inadequate. They do not show what quantum entities are nor how they function. This ambiguity allows the data to be understood in many different ways. And though different people may be absolutely convinced their particular view is uniquely correct, as indeed both Einstein and Bohr were, scientifically the issue is unanswerable because the ambiguity of the quantum data allows a variety of different, even contradictory conclusions.

Science is based on evidence. But no research methodology ever produces evidence. They all yield only data. Scientists must analyze the data, must study and ponder it to figure out what it means in order to turn it into evidence. This fact is usually obscured by the way science it taught. Science education usually focuses on results, sidelining or even completely ignoring the scientific process. (As a one time university professor, I'm as guilty of this as anyone.) The truth of the matter is that data are seldom self-explanatory. Ordinarily they must be evaluated in order to be turned into evidence. It is my belief that in doing this physicists have gone astray. The quantum data are massively confusing. Nevertheless, they clearly show quantum entities not to be like macro objects, and quantum processes not to be like those of classical physics. But because classical physics is so colossally successful physicists persist in trying to shoehorn inconsistent quantum data into classical physics constructs. The most egregious case being their insistence that quantum entities are particles notwithstanding the fact that the data refute this conclusion. Because classical physics is so enormously effective such shoehorning is understandable. Nevertheless, it is in error. And the result, I believe, is to turn an inherently ambiguous condition into impossible absurdities, wild notions like the three quantum interpretations described in the **Orientation** chapter. The next two chapters consider these absurdities in more detail.
Quantum Interpretations: Copenhagen

The first thing to explain about quantum interpretations is the fact of their existence. As far as I know, in no other science discipline are its conclusions in need of such delimitations and amplifications. Other science areas may uncover data inconsistent with prior theory, may have ambiguities, even contradictions. In fact, often they do. But these are seen as indications of the need for and the possibility of more fundamental knowledge. They are believed to show the basics of the particular discipline to be not yet completely understood. As such they are expected to be eliminated with further research, and often they are.

In quantum mechanics, however, its wave-particle paradox, its ambiguities and inconsistency with prior theory are all quite reasonably seen as fundamental. As far as science has been able to determine, they are basic and irresolvable characteristics rather than temporary ambiguities which further research could remove. And in fact they have not been resolved. Since quantum mechanics' development in the late 1920's and early 1930's its essentials have been settled. It is claimed to be fully developed, and so far this claim has been substantiated. For while there have been advances, _e.g._ , quantum electrodynamics, the fundamentals have not changed. Thus these incomprehensible characteristics are aspects of the theory's essence. Interpretations are attempts to make sense of this.

Unfortunately, all the current ones fail. This failure characterization isn't just my view, the opinion of one who admits to quantum mechanics ignorance. It is shared by at least one expert, a physicist who has garnered Nobel Prize recognition, Steven Weinberg. He has said: "My own opinion is that today there is no interpretation of quantum mechanics that does not have serious flaws. This view is not universally shared. Indeed, many physicists are satisfied with their own interpretation of quantum mechanics. But different physicists are satisfied with different interpretations." (Hossenfelder, 2018, pgs. 123-4) So let's examine some of the more popular different interpretations to learn the nature of their serious flaws.

The most famous (and infamous) interpretation is Copenhagen. Unfortunately, it doesn't exist. At least, not in the form the name implies, _i.e._ , as a formal statement of propositions concerning quantum mechanics. Rather, Copenhagen is a loose conglomeration of opinions of various persons associated with Niels Bohr's theoretical physics institute, which happens to be in Copenhagen. But even this characterization is inaccurate. Max Born, for example, sometimes complained that while his views are usually included as part of Copenhagen, he was never associated with Bohr's institute. Thus there is some imprecision as to exactly what the Copenhagen interpretation says.

There is, however, a general consensus, and it is accurate and useful to distinguish two different aspects of it. The most fundamental may be called the engineering aspect, an appropriate title since engineering is the referent of the word mechanics in the name quantum mechanics. David Mermin has wittily, and accurately called this aspect the "shut up and calculate" approach. For indeed, that is essentially what one does in this approach since it adheres to a strict agnosticism about underlying quantum reality. Niels Bohr specified what are in effect standard operating procedures for doing quantum mechanics. They are efficient and effective procedures which prescribe the operational uses of quantum mechanics but proscribe any concern with the real nature of quantum entities and phenomena. It is this aspect which Bohr had in mind when he famously said there is no quantum reality, only a quantum description.

Rudolf Peierls insisted this version of Copenhagen is the only quantum interpretation. Since there are many, many quantum interpretations (Herbert, 1985, discusses eight, and Wikipedia lists more than a dozen) this claim seems clearly in error. But a wider view shows the point Peierls was making. As noted, the engineering version of Copenhagen which he considered the only interpretation, is strictly operational. It not only makes no attempts to understand quantum reality, it eschews, indeed it forbids the making of any such attempt. In short, Peierls' meaning is that this is the only _scientific_ interpretation. All other interpretations attempt to explain quantum entities and phenomena. To do so they must go beyond the evidence, and therefore are necessarily metaphysics. Peierls said such interpretations concern only philosophers, not physicists. The later, he claims, do not do metaphysics.

But this engineering approach leaves many profound questions hanging, most conspicuously, wave-particle duality. It's all very well to simply ignore this paradox, to work with quantum entities as waves when that approach is serviceable or as particles when that is. But it's hard not to wonder what these quantum entities really are and what the devil is really going on. Especially is it hard for scientists, the essence of whose professional purpose is to try to discover what the devil is going on. Peierls' insistence that only philosophers but no physicists concern themselves with such questions is simply wrong. Anyone who has ever seriously read in this area can name crackerjack good physicists who are very much concerned with what the devil is going on. The just mentioned David Mermin is one. He has suggested that the Copenhagen interpretation of quantum mechanics means the moon is only potentially real and doesn't exist as a body of substantial material until and unless someone looks at it. And that certainly isn't just shutting up and calculating.

This second aspect of Copenhagen leads to some profoundly subjective views of quantum mechanics, notions which say reality isn't really real till it is measured, the kind of mystical view which I hope to supplant with the objective interpretation offered in **Part II**. So in this and the next chapter let me lay the groundwork for my objective and, hopefully, realistic interpretation by considering a few unrealistic quantum mechanics interpretations. The rest of this chapter does so for Copenhagen.

Because it was so eagerly advocated by Bohr himself, complementarity might be considered the prime part of Copenhagen. However, the extent to which any of the other usual Copenhagen suspects subscribed to this proposition isn't clear. Certainly no one did so with the devotion, if not to say passion of Bohr. He persistently advocated complementarity as not only the definitive resolution of the quantum mystery, but as a fundamental philosophic principle of universal applicability and unlimited importance.

Complementarity concerns wave-particle duality. It says both the wave and the particle aspects of a quantum entity are true. However, they are not contradictory. Rather, they are alternative. When one measures the wave characteristic of a quantum entity, then that entity is a wave. And when one measures the entity's particle characteristic the entity is a particle. Never can the two attributes be simultaneously measured, Bohr insisted, hence a quantum entity can never simultaneously be both things. It is either a wave or a particle depending entirely on how you look at it, _i.e._ , on how the attribute is measured. (Bohr included the dynamic variable pairs included in uncertainty relationships, _i.e._ , non-commutative conjugate pairs, as having complementarity relationships. But these relationships are better understood by the precise scientific Heisenberg principle rather than by Bohr's vague metaphysical complementarity notion.)

Basic to complementarity is the assertion that it is impossible to measure both aspects of a quantum entity simultaneously. This assertion, I maintain, is conspicuously false. The **Two Slit Data** chapter considered data in which the separate locations of the individual photon or electron hits are recorded. From these hits it is possible to deduce that the quantum entity is a particle, but from the interference pattern formed by these very hits the wavelength of the entity can be calculated (Baireline, 1996, Section 4.4). This fact, I submit, shows the quantum entity can indeed manifest both characteristics simultaneously, and therefore both must exist simultaneously. This is not to deny that there are circumstances in which it is impossible to demonstrate both attributes with one measurement. But we need not consider them because a single exception to Bohr's either-or complementarity contention suffices to disprove it.

This disproof of complementarity is not an incidental point. Rather, it is fundamental to the objective quantum interpretation offered in **Part II**. The usual understanding of wave-particle duality holds it to be a paradoxical contradiction, and this view is abundantly supported by abundant quantum data. Complementarity is an attempt (desperate, mystical and unsuccessful, in my view) to escape from the duality paradox. In contrast, the objective quantum interpretation presented in **Part II** is an attempt to solve it.

The role complementarity assigns to measurement in determining a quantum entity's alternate essences illustrates the central role of measurement in the Copenhagen interpretation. Indeed, measurement is probably Copenhagen's major problem. This issue has many aspects and can be approached in many different ways. But I think the best way starts with the BB gun analogy considered in the previous chapter. As noted above, physicists generally (and illogically, I contend) believe quantum entities such as photons and electrons necessarily are particles, just as a BB is a particle. Since a BB gun can be aimed, by implication the BB's hit location on the target is determined (given no wind) when it leaves the gun. One BB takes one predetermined path to the target and strikes it at only one predetermined, the aimed at, place. But such isn't the case with a quantum entity. Consider a supposedly particulate electron passing a two slit apparatus. This electron takes nobody knows how many nor what paths to the screen and strikes it at a particular one of a set of many different locations quantum mechanics specifies as possibilities, but which, until it happens, is completely unpredictable.

Science is conservative. It eschews attempts to provide a new and different explanation for every slightly different phenomenon. Therefore, Copenhagen attempted to describe the supposedly particulate electron's movement in as similar a way as possible to the way it would describe the BB particle's movement. The notion Copenhagen came up with is this: In some unknowable way the electron, while it is passing through the two slit apparatus, is simultaneously going to every separate different location where it might, according to quantum mechanics, end up. This interpretation is called _superposition_. In everyday language one might say a quantum entity in such state is simultaneously going to every different place where it might eventually be found.

Well then, where might the electron eventually go? Quantum mechanics specifies quite accurate probabilities of every place where the electron might end up. But it does not say which specific location in this set will be the one where the electron will hit. What is much more problematic, it does not say the electron will ever hit anywhere. It simply says: "If it does hit, these are the probabilities it will hit at each of the places where it might hit." As far as quantum mechanics can say the world usually simply accumulates a vast conglomerate superposition of possibilities, none of which does it say will necessarily occur!

Quantum mechanics is extremely well developed. Some say it is the best developed theory in all of science. To reiterate a quote from Rothman and Sudarshan (1998, pg. 116), "Quantum mechanics ... is as close to true as science gets." It is based on abundant data, all supportive. Nevertheless, the sum total of its supporting data pales to infinitesimal insignificance against the body of data showing things happen. Indeed, the most unambiguous, absolutely true scientific conclusion is the simple statement, "Things happen." But not so with quantum mechanics. It doesn't deny that things happen. It simply does not and can not say they do. Therefore, since things absolutely do happen, it seems to me, as it seemed to Einstein, quantum mechanics is self-evidently incomplete.

But many theoretical physicists are not willing to concede the incompleteness of quantum mechanics. This puts them in a dilemma, for the very data on which their theory is based are happenings. If quantum mechanics provides a complete description, and if it says nothing happens, then how do these data, _e.g._ , that provided by a two slit demonstration, occur? Copenhagen says the answer is measurement. It says measuring a quantum entity causes the superposition to dissolve and a single one of its possibilities to occur. The phrase usually used is "measurement collapses the wave function", the wave function being quantum mechanics' mathematical statement of the probabilities of the various possible happenings. Unfortunately, no precise definition of measurement has ever been provided. Collecting data in a two slit demonstration most certainly is a measurement. Just glancing at the moon, according to some Copenhagen advocates, also is a measurement which collapses the moon's wave function and makes it real. But, as Einstein asked, can a rodent's glance do the same? Copenhagen provides no answer.

In the **Orientation** chapter, above, an absurd quantum interpretation was mentioned, _viz._ , "The universe does not exist until someone in the universe, and therefore someone who also doesn't exist, looks at it and makes it real." This supreme absurdity is Copenhagen's. You can now see how they got it. As far as quantum mechanics can say, nothing happens. Therefore, assuming quantum mechanics to be complete, when the universe began nothing happened. Instead possibilities endlessly accumulated to a virtually infinite number creating a superposition of mind numbing proportions until some kind of creature (human or rodent) evolved and looked at, _i.e._ , measured, the world and made it real. Unfortunately no advocate of this interpretation has been able to explain how some creature, who or which is itself not real but only a superposition possibility, can make a measurement, even if this requires only a glance.

Copenhagen's claim that physical entities can be in a superposition state which only measurement can resolve led to what is probably the most widely known image of the quantum mystery, one created by Schrödinger: His cat. This is a hypothetical experimental situation, the kind of thought experiment Einstein so frequently used. With it Schrödinger sought to make the absurdity of the Copenhagen position unmistakable and conspicuous.

Suppose a cat were confined in a box, he said, a box which contained a sealed vial of poison so toxic the cat would be instantly killed were the vile broken. Further suppose the box also contained a hammer mechanism so engineered that it could break the vial and kill the cat. This hammer would be controlled by a radioactive atom the decay of which is random. If the atom undergoes decay, the hammer breaks the vile and the cat is killed. Finally, suppose the box is such that after it were closed no one could in any way determine whether the cat were alive or dead. Only by opening the box could this be known. Now, Schrödinger said, while this box is closed nobody knows, _i.e._ , nobody can measure whether the cat is alive or dead. Therefore, according to Copenhagen, kitty is in a live-dead superposition. It is simultaneously both alive and dead. Not until the box is opened and someone determines, _i.e._ , measures, the state of the cat does Copenhagen allow that the cat is one or the other.

What the cat thought experiment does, of course, is create a macro object superposition. Unlike electrons and photons, which no one can directly see, everyone has seen cats. And no one has ever seen anything like a dead-alive cat. I believe the point Schrödinger was trying to make is something both he and Einstein believed, _i.e._ , that the superposition state does not exist, that in a situation like the two slit demonstration, while no one knows where a photon or electron will strike the projection screen, this is a matter of human ignorance. The quantum entity, they believed, is going to a definite spot, but that spot is unknown, and perhaps unknowable. In this view, measurement does not play any causal role in reality. It simply discovers what happened when no one was looking. This contrasts with Copenhagen's beyond science, supernatural notion of reality being subjectively created by measurement. Nothing really exists, mystical Copenhagen insists, until the magic of a measurement makes it exist.

I must confess, I find Copenhagen's measurement claim absolutely ridiculous. To believe the act of measurement _per se_ is the cause of what happens in a measurement situation is, to me, simply silly. Consider: Hold a rock under your hand at arm's length then release it. Obviously it will fall. But what caused the rock's fall? You, or gravity? Obviously it was gravity. If the rock were sitting on a table and you grabbed it the same way but did not lift it, then released it the same way, it would not fall. But your action would be identical to that when the rock did fall. Therefore, it isn't your action, but the lack of support which causes the rock to fall. All you did in the first case was remove the support your grip was providing. All you did was allow gravity to do its thing. You most certainly did not cause the rock's falling. And if you think you did, then I think you have rocks in your head!

When conducting any kind of quantum measurement, as in sending photons or electrons through a two slit apparatus, the same thing applies. All the measurement does is allow whatever natural process controls such quantum entities to control them as it presumably would control them whether or not a measurement were being made. To deny this presumption leads only to mystical metaphysics, to the absurd proposition that humans (or rodents) create the reality which contains them, but which logically they can't create because they themselves are part of uncreated reality and therefore can't exist until it does. Indeed, to deny the presumption saying measurement is a test of what happens whether or not a measurement is being made is to deny the whole meaning of making a measurement, for its very purpose is to measure how these natural processes function whether or not anyone is looking.

But the most important thing about Copenhagen's measurement problem is not its patent illogic. Rather, the notion that measurement causes events, _i.e._ , collapses the wave function, is an implicit confession of quantum mechanics' incompleteness. Don't let Copenhagen's confusion confuse you. Measurement is not a part of quantum mechanics. It is a nonscientific metaphysical add on, something Copenhagen had to append to the scientific theory in order to account for two facts: (1) Things happen but (2) quantum mechanics cannot say they will. When Einstein said quantum mechanics is incomplete he spoke the conspicuous and inescapable truth. The proof of his claim is the fact that Copenhagen, the great defender of the completeness of quantum mechanics, had to invent the "measurement makes things happen" myth in order to explain how things happen, something quantum mechanics, for all its wondrous capability, cannot do.

Quantum mechanics knows of no event cause. As far as it can say, events just spontaneously happen without cause. Either that's the whole story, and everything that happens is an inexplicable miracle, or quantum mechanics is incomplete. To allege that measurement or anything else causes things to happen necessarily is to allege that events are not spontaneous, but are caused. And if events are caused, then quantum mechanics is necessarily incomplete because it contains no causal mechanism, neither measurement nor anything else.
Two Other Quantum Interpretations

Copenhagen is certainly the best known quantum interpretation, but equally certainly it is far from the only one. As already noted, Wikipedia lists more than a dozen. We oldsters rely more on books than the internet, and most popular books consider a few interpretations, but scatter these discussions throughout their work. Eight are presented contiguously by Herbert (1985), so they can be readily compared. Gribbin (1995, Chpt. 4) reports that eight prominent physicists were interviewed on a TV show concerning quantum theory, and each supported a different interpretation (not necessarily the same as Herbert's eight). Since each physicist insisted all the other seven interpretations were wrong, we may conclude the eight interpretations were all different.

Beyond noting the existence of the many different interpretations (which shows that no one, especially no expert, knows what's going on with quantum mechanics) there is no need to consider all of them. However, it is worth considering two more. These two produce the second and third absurdities listed in the **Orientation** chapter above. They are generally well known, second only to Copenhagen. While each is based on sophisticated adjustments to the quantum mechanics math, there is no need for us to know any of this. No one questions their math, only their nonmathematical conclusions. So it is worth considering them briefly in order to further demonstrate the extreme mystical lengths to which physicists have gone in their efforts to make sense of quantum mechanics.

**Many-Worlds** is an interpretation which evades the problem of quantum mechanics' lack of a cause with an outrageously unrealistic assumption. It claims every single possible event specified by quantum mechanics always occurs. In other words, everything that can happen does happen. We simpleminded empirical scientists then ask why the data never show this. Consider the two slit apparatus passing a single photon through both slits. Quantum mechanics says the photon may hit anywhere in any one of the several constructive interference bands. But only one hit is ever recorded. It's difficult to imagine a more unambiguous outcome or a more unequivocal empirical refutation of the everything happens hypothesis.

But Many-Worlds believers refuse to accept the fact that the facts contradict their claim. The data never show more than one hit, they say, because every different hit creates a new world in which it and only it occurs. At the instant of creation each of these several new worlds is, except for its particular hit, completely identical to the one from which it evolved and identical to all the others so created. Every world is completely and forever isolated from all the others, and every world will continue evolving as if it were the only universe. Therefore, according to Many-Worlds, the data can only show what happens in one world. It can never show that every possible hit specified by quantum mechanics did in fact happen.

The Many-Worlds claim would be preposterously unrealistic if it only predicted one new universe. But a new world supposedly is created for every possible quantum event, and though nobody knows how many there are, the amount must be stupendous. Consider: As Gribbin (1984, pgs. 67-8) points out, just a spoonful of sugar contains almost a billion multiplied by a billion multiplied by yet another billion atoms. So the number of atoms in the whole universe is incomprehensibly immense. And every time any electron of each of these atoms changes in any way the Many-Worlds interpretation says a new world is created for every possible outcome. But that isn't the end of it. For every instant in every one of these breathtakingly many new worlds another breathtaking number of new worlds would be created, and for every instant in every one of these ... Well, you get the picture. The largest number with a name is a googol. It's a 1 followed by 100 zeros. The number of eternally separated new universes Many-Worlds claims to be created each instant makes a googol seem small by comparison.

A slightly different version of Many-Worlds says each quantum outcome does not create a new world. Rather, this version claims, infinite other universes already exist, and everything that can happen does happen in a different one of them (Gribbin, 2009). Since the other universes are not created but already exist, its adherents claim this version is more believable. Some devotees of this preexistent Many-Worlds version also claim superposition proves their proposition. A quantum entity in a superposition, they claim, is in every state, condition and/or place wherein it might eventually be found, and each is in a different universe. This proof claim is unequivocally false. The only thing it proves is the dogmatic conviction of those who make it. It is false because it is an attempt to prove one nonscientific metaphysical proposition, Many-Worlds, with another, an unconventional superposition interpretation.

Superposition is an attempt to characterize the unique inconsistency of quantum phenomena. In precisely identical circumstances the same outcome does not always occur. For example, consider a two slit device with light so dim only one photon at a time passes through it. Although never altered an any way whatsoever, successive single photons passed through his apparatus almost never strike the same point on the projection screen. In general, that is the case with all quantum phenomena. Identical conditions do not usually produce identical results. That is the fact. Superposition is an attempt to explain this fact. As usually defined it says the quantum entity, the photon in this example, is simultaneously potentially in every state, condition and/or location wherein it might eventually be found, but not actually in any.

Those who claim superposition proves the existence of Many-Worlds modify this definition. They say the quantum entity in a superposition state is in fact in every condition or location where it might eventually be found. That is demonstrably a nonfactual, metaphysical assertion. Many-Worlds advocates may believe it if they wish, but their belief doesn't change the facts. There simply are no data to show what state quantum entities are in when they are in a superposition. Indeed, as far as science can say, there never can be such data. One of the most fundamental facts of quantum mechanics is that every attempt to measure the state of a superposition entity destroys the superposition condition. Never have multiple outcomes been seen. Regardless of how many outcomes quantum mechanics may specify for a particular situation, only one outcome is ever found. Therefore to claim a quantum entity is in fact in every state, condition, location, etc. wherein it might eventually be found is not a fact. It is a metaphysical claim. And it's logically impossible to prove Many-Worlds, a nonscientific metaphysical speculation, with another nonscientific metaphysical speculation.

The most unbelievable thing about any of these unbelievable Many-Worlds interpretations is that any scientist believes any of them. But some do. The reason they give is because its mathematics is consistent. True, if an interpretation's math is not consistent it would be well to reject it, but the converse does not hold. Consider: The math used to describe the nineteenth century's continuous energy assumption was consistent, but notwithstanding this the wave theory has been empirically disproved.

Nevertheless, at one time Many-Worlds was widely believed. One reason is because the same conclusion can be derived from string theory. But string theory itself is, and according to its critics ( _e.g.,_ Hossenfelder, 2018, Lindley, 1993: Woit, 2006), can only be a metaphysical conjecture. But there appears to be growing dissatisfaction with Many-Worlds. Some say the infinity of universes, newly created or preexistent, simply stretches credulity too far. But the main reason for rejecting the interpretation is its flagrant contradiction of science's fundamental premise. Science is based on evidence. Without it there neither is nor can there be any science. Therefore, when the Many-Worlds interpretation says it is impossible in principle for any evidence of more than one outcome to be known it is expressly saying it is also impossible in principle for the interpretation to be science. And this is the case whether or not each quantum outcome occurs in a different universe. If someone can invent a quantum interpretation involving only one world, a world where every possible quantum outcome occurs but only one can ever be known, then in principle such interpretation still can not be science because the data necessary to determine what happens is explicitly prohibited by the very interpretation itself.

Finally, there is another, non-scientific reason for categorically rejecting Many-Worlds. Because this reason does not concern science, in this book's initial draft I omitted it. However, in response to the enthusiastic selling of the multiverse idea by some ( _e.g._ , Gribbin, 2009), I feel obligated to bring this point to your attention. The Many-Worlds quantum interpretation is profoundly dysfunctional and totally immoral. If everything that can happen does happen, then there is no reason whatsoever to exercise any control over one's behavior. Why avoid any harmful or evil impulse if you are necessarily going to do it in some universe? If Many-Worlds, profoundly improbable and unrealistic though it conspicuously is, nevertheless is true, then no matter however harmful an act of yours may be, either to yourself or to others, it is going to happen somewhere, so you might as well indulge yourself and go ahead and do it. Though it violates the decorum of an essay addressing a scientific issue, it is relevant to note that the man who invented the Many-Worlds interpretation was both self indulgently self destructive and immoral in the treatment of his family (Crease & Goldhaber, 2014, pg. 237). It is fair to wonder whether a Many-Worlds belief was responsible for his irresponsible behavior.

**Pilot-Wave** is the last interpretation considered here. It is a hidden variable interpretation based on David Bohm's reformulation of the quantum mechanics math. This did not change quantum mechanics' probabilistic predictions. Rather it shows how these predictions may, with complete mathematical consistency, be understood entirely differently from the conventional Copenhagen interpretation.

The Pilot-Wave interpretation says each quantum entity, _e.g._ , an electron or photon, is a particle which has an associated not material guiding wave. This immaterial wave is in immediate contact with everything in the universe, and it instantaneously adjusts itself accordingly, steering the particle in a completely deterministic manner (Herbert, 1985, pgs. 48-50). But while this wave guides the particle in this way, since the wave is immaterial, both it and its guiding actions are invisible, _i.e._ , hidden. So never can they be measured nor their effects predicted. Thus, although the interpretation is completely deterministic, it does not alter quantum mechanics probabilism. In fact, the Pilot-Wave predictions are precisely the same probabilistic ones as those of every other form of quantum mechanics. However, Pilot-Wave differs from standard quantum mechanics in attributing this probabilism to human ignorance. In other words the Pilot-Wave interpretation says quantum entities always exist in a completely determined single form, but this is inescapably hidden. In particular, the entity is believed never to be in a superposition. According to this interpretation the superposition notion is wrong, if not utter nonsense. This contrasts with the conventional, _e.g._ , Copenhagen, interpretation which says every quantum does not have a fixed single state until a measurement is made, and therefore quantum probabilism is complete knowledge, a valid representation of a probabilistic reality.

The Pilot-Wave interpretation disproves a claim some have made, the claim that the evidence of quantum mechanics nonlocality disproves Einstein's hidden variable idea. As noted in the **Ambiguous Data** chapter above, the error subsequent research demonstrated in the EPR paper is its claim that nonlocality is impossible, not its implied hidden variable alternative. Nonlocality in fact supports Bohm, for the Pilot-Wave interpretation assumes every quantum wave anywhere is immediately ( _i.e._ , nonlocally) aware of every quantum event everywhere.

The Pilot-Wave interpretation was first suggested by de Broglie not long after he revealed the wave aspect of the electron. But he ran into mathematical difficulties developing the idea, and abandoned it. Einstein took up the notion for a while, and reasonably so. For the assumption that each quantum entity is a conjoint particle and wave quite neatly solves the wave-particle paradox. Einstein even invented a German name for the immaterial, invisible wave, the _Gespensterfeld_ or ghost field. But he too abandoned the interpretation, leaving only this name. David Bohm took up the idea in the 1950's, and he succeeded in creating a consistent mathematics. As a result de Broglie came back aboard, and the interpretation now frequently is designated by both men's names. Einstein, however, did not renew his interest. He knew Bohm and was still alive when the younger man first published his Pilot-Wave idea. So he knew the interpretation, but he dismissed it. He said it was "too easy".

Nonlocality seems likely to have been the reason for Einstein's dismissal. As just noted, Bohm's interpretation is absolutely and totally nonlocal. It claims every event everywhere is instantaneously known to everything everywhere. Unlike Many-Worlds, this interpretation posits only one world. But it holds this one world to be completely and instantly interconnected. Einstein considered nonlocality to be an impossibility. In the EPR paper he said no reasonable person could accept it. He didn't explain why. Apparently he thought his belief self-evident, so no explanation was necessary. And indeed, there is an implausible magical character to nonlocality. Not only is there no apparent physical connection between a nonlocal cause and effect, but even if there were, everything we know takes some time to move, even light, the fastest known thing. Perhaps our determination of light's speed is deficient and it moves faster than we have measured it, but that's simply unsupported speculation. As far as the evidence says, nothing is instantaneous. So, given his belief that nonlocality is impossible, the total nonlocality of Bohm's Pilot-Wave interpretation would be sufficient reason for Einstein to dismiss it.

In comparison with the other two interpretations considered in this chapter, Pilot-Wave may seem more reasonable. As noted above, by supposing there to be two entirely different entities, a particle and a separate guiding wave, this interpretation avoids the wave-particle paradox. But the immaterial wave introduces an incomprehensible mystery of its own. What could it possibly be? Indeed, as Einstein's term suggests, it is like a ghost, a supernatural entity covertly and irresistibly controlling reality.

But the interpretation's major problem is its total nonlocality. Bohm's theory offers no suggestion of how it might work, the theory simply says it does. Moreover, the totality of Pilot-Wave nonlocality defies belief. One need not share Einstein's abhorrence of nonlocality in order to see Pilot-Wave nonlocality as excessive. To be sure, the evidence for nonlocal phenomena is compelling. But there is a vast difference between the kind of nonlocality demonstrated by this evidence (something which might humorously but not meaninglessly be called local nonlocality) and Pilot-Wave's universe pervading total nonlocality in which every quantum of energy everywhere in the universe is in immediate and intimate contact with every other quantum of the world's energy. Local nonlocality can be explained, as I will do in **Part II**. But the absolutely total nonlocality of Bohm's interpretation defies comprehension ... and credulity.

Finally, it is relevant and fair to note that however true it might seem to anyone else, Bohm did not hold his interpretation to be the final answer. Rather, he specifically held it to be a demonstration that, unlike the claims of Copenhagen, the science does not necessitate a probabilistic indeterminate reality. This demonstration, he felt, was only a first step toward an ultimate fundamental deterministic theory (Bohm, 1957).

**A mathematics note:** Before going on it is worth pointing out that if either one of the interpretations considered in this chapter is true then the other is not. Multi-Worlds says every possibility which quantum mechanics enumerates happens, whereas Pilot-Wave says only one does. Yet both are mathematically based, and in both cases the math is consistent. This shows that while inconsistent math is certainly good and sufficient reason for rejecting a theory (or interpretation), consistent math is insufficient reason for affirming one. One wonders why this obvious fact has been ignored by those theoreticians who advocated either of these or any other interpretation because of its math consistency.

### Part II: A Possible Solution

Fundamental Assumptions

The quantum picture, it is abundantly and inescapably clear, is abundantly and inescapably unclear. Rather, it is contradictory and profoundly bizarre. The questions then is: "What sense can be made of quantum mechanics?" This essay considers three options. The first is scientific agnosticism: No sense can now be made of it. The nature of quantum entities and the manner in which they interact is a mystery, one which science has not yet solved, and which it may never solve. In the **Quantum Interpretations: Copenhagen** chapter this approach was called the engineering interpretation. The second and third options go beyond science to metaphysics in search of understanding.

The other Copenhagen interpretation, the metaphysical one claiming the moon is not real unless it is being measured, is a second approach. It assumes the quantum data are complete and quantum mechanics extracts all the information in them, achieving a complete description of quantum phenomena. It acknowledges that this description is weird, for example in considering quantum entities to be both wave and particle, but this weirdness simply reflects the fact that quantum reality itself, if it really exists, is weird. This approach has been insightfully criticized by Rachel Wallace Garden, apparently a mathematician. In concluding her thorough study of the logic of quantum mechanics, she said: "It is surely sensible to see the quantum peculiarities as products of weak description rather than incomprehensible features of the world. It is surely more reasonable to suppose that our theory is inadequate than to argue that reality itself is bizarre." (Squires, 1994, pg. 122).

The third approach is the one presented below. It accepts Garden's view. That is: It assumes the weird aspects of quantum mechanics indicate an imperfect, incomplete theory, not a bizarre reality. It specifically assumes reality is not inconsistent with itself and that wave-particle duality is an inadequate conclusion arising from quantum mechanics' incompleteness. However, it does share one view with Copenhagen. It assumes quantum mechanics extracts all the information in the quantum data. But it also assumes something happens at the quantum level which does not show up in the data. This is similar to Einstein's hidden variable claim. However, the following interpretation does not agree with his hope that a more fundamental theory could uncover it. Einstein thought the hidden thing could be explained by a more fundamental theory, one explaining the reality underlying quantum phenomena. He spent the latter part of his life attempting to devise a unified field theory, something he hoped would explain and clarify the quantum reality arising from it. Unfortunately, contemporary physicists unanimously feel he failed completely.

Unlike Einstein's hope, the interpretation presented below does not presume to resolve or improve quantum mechanics. Its position is much closer to Bohr's contention that quantum mechanics is complete. Indeed, the present book considers Bohr's claim to be all but certain. At this time, almost a century after it was developed during which the intense efforts of many brilliant physicists have found no scientific answers to the questions quantum mechanics does not answer, it seems exceedingly unlikely quantum mechanics will ever be superceded. Indeed, that's why the interpretation below is offered. Quantum mechanics most likely is the last word scientifically. But equally likely Einstein and Garden are right when they say it is not the whole story. In short, the following quantum interpretation assumes the quantum mystery arises because, while quantum mechanics extracts all the information in the quantum data, the data themselves are incomplete. Therefore, quantum mechanics, being based solely on a rational, mathematical extrapolation of the quantum data, perforce leaves many questions unanswered. But the incomplete data do provide hints about what a full description might be. On the basis of these hints it is possible to imagine an entity and a process which, though forever invisible and therefore scientifically inaccessible, nevertheless can make realistic, objective and logical sense of the quantum mystery. This can not be a science conclusion, but at least it will make intuitive sense of quantum mechanics. That is what the interpretation suggested in the next chapter attempts to do.

Before describing this interpretation it will be helpful to explicitly spell out its fundamental assumptions. Many can be inferred from what has been said. Still it helps to state all explicitly and in one place.

First and foremost, a preexistent objective reality is presumed. We do not create reality. It creates us. It is a bottom-up reality, quantum phenomena being near the bottom, and the macro phenomena which comprise human experience being built up from them. Thus, psychological events are built from biological ones which in turn are made from chemical ones which arise from quantum phenomena. This seems to me to be a necessary assumption of science. Certainly it is the usual one, so there should be no ambiguity about it.

Some might call this approach reductionist naive realism. But be wary of that term for, at least to some people, it implies ideas which the following interpretation explicitly rejects. Reductionism as used here means that if a lower level did not exist, the levels above it could not. But some hold reductionism to mean nothing at a higher level, _e.g._ , biology, can be fully understood until and unless there is full and complete knowledge of all lower levels. That notion is categorically rejected. Rather, here it is assumed that although higher levels are created by the functioning of lower levels, such lower level functioning creates emergent phenomena, properties which enable a higher phenomena to be fruitfully addressed at its level as if it were fundamental. Newtonian physics is a good example. Even though quantum phenomena ultimately underlie the classical phenomena, _e.g._ , planetary orbits, described by Newton's laws, his laws are more than adequate to deal with these phenomena as if they were fundamental. As many astronauts and others in the space program have repeatedly pointed out, putting satellites into space or orbit is basically pure Newtonian physics. Thus classical physics is a compelling example of the principle assumed by the present quantum interpretation: Higher level phenomena can be sufficiently completely understood at their own level.

The assumption of phenomena being built up from below, quantum phenomena underlay chemical ones _etc._ , implies causality. And causality is a basic premise of this interpretation. The notion that quantum phenomena are spontaneous and uncaused, or Jordan's notion that quantum entities decide for themselves, are explicitly and categorically rejected.

But while the present interpretation rejects these claims, it doesn't reject every part of the Copenhagen interpretation. In particular, the idea of superposition is accepted. Indeed, superposition is presumed to be the usual state of quantum entities. To avoid possible confusion it's necessary to amplify this point a bit. As noted in the Many-Worlds discussion, above, some theorists consider a quantum entity in a superposed state to actually be in all the states in which it might potentially be found. That is not the meaning here. Rather, here an entity in a superposed state is claimed to be able eventually to be in any of those states or locations where quantum mechanics says it might eventually be found, but until it emerges into one of them it is not in any of them. In short, in the present interpretation superposition is a condition of multiple potentialities, not multiple actualities.

The essential idea of the present interpretation is that there exists a hidden but natural and frequent superposition dissolving process, a quantum cause. This may seem to be a novel and unsupported idea, but it is not. Roland Omnès (1999, Pgs. 199-211) has long advanced essentially the position outlined in the next paragraphs.

In fact there is considerable evidence for such superposition dissolving process. This evidence has been accumulated by those attempting to develop quantum computers. (Gribbin, 2014, provides an extensive introduction to this technology; Peacock, 2008, pgs. 149-59, a much more succinct one.) Quantum computers are, or will be if ever completely developed, instruments which employ the superposition state to accomplish calculations which even the fastest present supercomputers cannot solve. The idea is to allow a superposition to accumulate in such a manner that one of the possibilities it enumerates is the answer to an excessively complicated computation and then to collapse this superposition to this particular state, thereby revealing the answer.

If this sounds difficult, it most definitely is. Exceedingly, extraordinarily difficult! The major problem is maintaining the superposition state. Winfried Hensinger (Professor of Quantum Technologies at University of Sussex and Director of Sussex Center for Quantum Technologies) is one of the experts working to develop a quantum computer. In a recent essay he said (Hensinger, 2018, pg. 140): "While physicists have great experience observing the strange phenomena predicted by quantum mechanics, controlling them is extremely hard. Part of the reason is that any unwanted interaction will immediately destroy these effects."

The "strange phenomena" Hensinger mentions is the superposition state, and their immediate destruction is superposition dissolution. In the quantum computing literature this is called decoherence, and as Hensinger states, preventing it is "extremely hard". Indeed, as Gribbin (2014, pg. 228) notes, to make a quantum computer work: "there has to be a way of solving the old problem of decoherence." He further states that decoherence usually occurs within milliseconds, thousandths of a second. So you can see, the problem is indeed difficult.

The quantum interpretation offered below considers decoherence to result from the occurrence of the natural but hidden quantum cause. It categorically rejects the Copenhagen notion that measurement is the only quantum cause. That measurement can cause superposition collapse is conceded. But it can only do so by involving the hidden natural quantum cause, the source of decoherence. Measurement merely uses circumstances where this process regularly and naturally occurs to explore quantum phenomena. Thus the present interpretation holds quantum event measurements to be precisely like all scientific measurements, _i.e._ , attempts to empirically discover what naturally happens whether or not a measurement were being made.
A Realistic Quantum Interpretation: Basic Idea

You need be aware of some potential difficulties in the following.

First: Some of the entities and processes discussed below are suppositions, things not known to exist. But it is verbally cumbersome to continually qualify every relevant statement to this effect. So often when the discussion clearly concerns such things and no ambiguity should result, such qualifications will be omitted. This is only to facilitate the reading (and writing), and not an attempt to imply these ideas are scientifically established.

Second: The topic here is a metaphysical speculation. Of necessity, therefore, in places it will be lacking in detail. As noted above in the **Orientation** chapter, I am not a physicist and know no quantum mechanics. Were I a physicist, at places doubtlessly more details could be provided. However, such places are few and such details are incidental and would add nothing essential to the basic idea. The fundamental premise of the idea being presented is that the quantum cause and the quantum entities involved are inherently hidden. To suggest precise details about things which by definition can never be observed is at best useless and at worst specious inasmuch as it implies greater knowledge than is possible.

Third: Explaining this objective quantum interpretation presents something of the egg-and-chicken problem. Several ideas are simultaneously involved, but one cannot be fully understood until the other is. I have attempted to present these ideas in as nearly a linear sequence as possible, but, of course, the nature of the situation prevents that from being completely lucid. Therefore, I suggest you read this and the next chapter at least twice. Hopefully on the second reading everything will fit together.

With these caveats, let's proceed.

Our world, the reality we can experience, is composed of matter, and the essentially universal common presumption says the essential characteristic of matter is substance. In this essay substance means only that pieces of matter fully occupy and permeate an amount of space, excluding all other matter. This meaning is the common colloquial one, and is fully expressed by the old saying, "It is impossible for two different things to be in the same place at the same time." From this it follows that two pieces of substantial matter which converge on the same spot will hit and rebound. And this in turn leads to a corollary of the substance assumption: Things interact by touching. Though it seems self-evident to most of us and is integral to classical, pre-quantum physics, this touching corollary has invalidating logical difficulties (Lange, 2002, pgs. 7-13). Despite its intuitive obviousness, at the micro level there appears to be no possible logical way to explain how touching could happen. At the fundamental level touching seems to be impossible. This difficulty is avoided by the present quantum interpretation, for it rejects the substance presumption and its interaction-by-touching corollary.

This is not to say that substance does not exist. One only need stub one's toe to know it does. But substance is not basic or fundamental. Quantum entities, _e.g._ , photons and electrons, do not have substance. They are permeable, not substantial. But by their interactions they cause macro objects, things like you and me and most of the things we experience, to be substantial in effect. Substance, therefore, is an emergent, an "in effect" approximation, not a fundamental property of matter.

So, if quantum matter does not touch, how then can it interact in order to give rise to effective substance at the macro level? To answer it's necessary first to describe how this interpretation conceives of quantum entities.

Let's take the electron as our prototype. Under the traditional assumption it is a particle, a tiny bit of substance. An "infinitesimal billiard ball" is how it is often described. Infinitesimal is extremely small. Even so, to say the electron is infinitesimal is to say it is much bigger than the evidence indicates, for repeated efforts to measure the size of the electron have never found it to have any size at all (Herbert, 1985, pg. 61). As far as experimental physics can say, the electron seems to be a mathematical point, a dimensionless dot. This is a major logical problem for the conventional electron-is-a-particle notion. It is because the essence of a piece of substance is its occupation of an amount of space. But a mathematical point does not occupy any space.

The present interpretation does not suffer from this logical problem, not only because it claims the electron is not substantial, but also because it claims the electron usually has spatial extension. (I'll explain shortly how this can be and why this does not show up when the electron is measured.) If the electron has extension, our substance preconception immediately leads us to suppose it totally occupies the space where it exists, excluding all other matter. But the present interpretation says the electron can and does pass right through other pieces of elementary quantum matter, and they can and do pass right through it. In short, it says multiple quantum entities can and often do occupy the same space at the same time.

The idea that matter can pass right through other matter may seem obviously false. But it is a well established fact. Consider window panes. Light ( _i.e._ , photons) passes right through them, and right through many other transparent and translucent materials also. We usually suppose this is some peculiar characteristic of glass and these other materials. However, consider X rays. They also are photons, but of a different frequency. And they pass right through most anything. But the most striking example, however, is the neutrino (Pagels, 1983, pgs. 216-9). Billions of these elementary quantum entities are produced by and radiated from the sun every second, and the overwhelming majority of those which strike Earth pass right through it, right through almost eight thousand miles of solid Earth. So the notion that fundamental matter is transparent is neither novel to the present interpretation nor without solid scientific support.

It is impossible to see an electron, of course, but we can form a mental image of how it extends in space. If we could see it, the electron would appear to be made from ethereal gossamer material such as is popularly imagined to compose a ghost's diaphanous shroud. The electron consists of only the shroud, for the shroud contains nothing at all. The electron shroud grows as it exists. To picture this, suppose we had a two slit apparatus through which a single electron were being shot from some kind of electron gun. At the instant the electron leaves the gun it is a mathematical point. But it billows out, forming a growing membrane. Because the electron is heading in a particular direction the best image of this membrane is something like the finger of a glove, a glove with no hand in it. For like such a glove finger, the membrane is empty. The membrane continually grows, mainly in the forward direction, extending the finger, but also widening as it grows.

The slitted partition in the middle of a two slit apparatus seems to us to be solid except at its slits. According to the present interpretation it is not. Rather, it is a place where billions upon billions of elementary quantum entities are continuously interacting, an ongoing quantum dance, if you will. This dance makes the partition effectively substantial at our level, but not at the electron's. When the ballooning electron membrane reaches the partition, because neither it nor the myriad quantum entities composing the partition are substantial, the electron membrane will grow right through it. But it will do so more slowly through those parts of the partition which we perceive to be solid.

This reduced speed of passage idea also is neither unsupported nor original. Rather, it is based on the scientifically well established fact that light (which of course is wholly composed of elementary quantum entities, photons) moves more slowly through more dense material. This slowed passage is what causes refraction, the process which, for example, enables a lens to focus an image. The present interpretation simply extends this property to all elementary quantum entities.

But the electron membrane is not slowed at the two slits. Therefore, it grows ahead of itself as it passes through the slits, billowing out into the area past the partition. If we could see it, these two protuberances (one emanating from each slit) would resemble a single wave crest passing through the two slits. Just as with such wave crest, the two parts of the same electron membrane will expand into the post-partition side of the two slit apparatus and in places will meet. At these places the electron membrane will, as is the nature of elementary quantum entities, overlap and pass right through itself.

As explained above in the **Two Slit Data** chapter, when two different parts of a water wave overlap they cause interference. Where the interference is constructive it increases the amplitude of the wave; where destructive, wave amplitude is reduced. When the electron membrane overlaps itself it also causes an interference phenomenon. But unlike the water wave, this interference does not change the strength of the electron. Rather, it changes the strength of information scrolling across the electron's membrane.

This brings us to a fundamental premise of the present quantum interpretation: Each quantum entity's membrane is presumed to carry information identifying the kind of entity it is and the various superposed states it is in. Just how this information is physically embedded in the membrane is beyond knowing and therefore not worth speculation. But that it is, that the membrane carries self identifying information, is a basic assumption of this interpretation, for it is this feature which explains the wave half of wave-particle duality. This is how it is envisioned to function.

The self identifying information scrolls across the surface of the electron. The word "scrolls" is key, for the information sweeps across the membrane like the text on a scrolling billboard. To explain this, assume you were looking at the leading edge of the electron and you were magically able to see the information on it. You would see it change. The rate-of-change would be much too fast for human perception, but we are supposing magical vision. At the instant when the electron emerges the self identifying information on it would be complete. Then the information would begin to weaken. It would weaken till it contained no information. This would immediately be followed by a gradual increase in the strength of information to a maximum and a second decrease again to no information. The second phase, however, though it would present the same information as the first, would present it in a complimentary manner. By this I mean that although the information is the same in each phase, when two complimentary phases of the membrane overlap they interfere destructively, _i.e._ , they cancel their information content. But when the electron membrane's self identification wave overlaps itself in the same phase, constructive interference results and the information the wave conveys is made stronger. Again, just how this physically happens is unknowable and not worth speculation.

What I have just described, of course, is a wave of information scrolling across the electron membrane. And because it is a wave this information has the typical wave characteristics of frequency, wavelength and phase. This self identification wave immediately explains one of the most puzzling characteristic of quantum waves. As noted in the **Two Slit Data** chapter, each single quantum entity can interfere with itself. The present interpretation explains this perfectly. A single quantum entity can interfere with itself because the identification wave is on it. It may seem, therefore, that a membrane can interfere only with itself. Unfortunately, because it is impossible to know the physical nature of the self identification wave it is not logically possible to so conclude.

Another aspect of this identification wave deserves emphasizing: The wave involves no to-and-fro, longitudinal movement of the electron membrane. The membrane itself does not wave. Rather, the wave scrolls across the membrane's surface. In the **Two Slit Data** chapter it was mentioned that the wave aspect of light has been empirically proven not to involve longitudinal, to-and-fro movements. If, therefore, light were a wave, the wave would have to be transverse, _i.e._ , the direction of the waving would have to be at right angles to the wave's direction of movement. But as also noted in the **Two Slit Data** chapter, despite light's well established wave aspect, for other reasons ( _i.e.,_ the impossibility of any luminiferous aether dense enough to convey transverse waves of light's high frequencies) the hypothesis that light is any kind of wave is untenable. The present interpretation's identification wave, however, is completely consistent with the evidence showing no longitudinal movement for light's wave effect.

Again consider the single electron going through a two slit apparatus. As noted, the slitted partition is not solid and substantial. Rather it is a locale where billions of quantum entities are engaged in a continually interacting quantum dance. The same is true of the projection screen. It also is not substantial, though the interacting quantum entities comprising the screen make it effectively solid to us. As also noted, when the electron passes the slitted partition its membrane billows out in front of the slits creating two expanding membrane protuberances, each of which will pass through every point along the screen. Thus, at every point along the screen the passing two protuberances of the electron membrane will overlap and their identification information will interfere. The result will be an alternating pattern of bands across the screen. Each band will either display the electron's identity or conceal it. These bands, of course, correspond to places where the self overlapping electron membrane's identification wave is constructively or destructively interfering.

So far we have only considered a single electron passing the two slit apparatus. However the same pattern would occur with multiple electrons. Because each electron fired from the gun is in the same state and has the same frequency and because each starts from the electron gun in the same identification wave phase, every electron will map the same interference pattern onto the screen. Thus, when a large number of electrons have passed through the screen (whether one-at-a-time, as we have been considering, or _en masse_ ) each electron will interfere with its self identifying information in exactly the same way. Thus, collectively they will create the same interference pattern on the projection screen, the traditional two slit interference pattern.

At this point it's necessary to consider an idea which may seem outlandish, but which has good scientific credentials. Quantum entities such as the electron we have been considering are always real. They are because they carry energy. But only at the instant when they are a dimensionless point are they actual, and only when they are actual are they part of that branch of reality including humans and all those things humans can directly experience. During those times when a quantum entity is in its membrane form, it is in a superposition state. And although real, at these times it is potential but not actual. It is only actual at the precise instant when its superposition state collapses (described below). This potential condition is something Heisenberg emphasized. He said quantum entities, when in a superposition state, are in a condition very much like Aristotle's _potentia_ , not actual but able to become so (Heisenberg, 1999, Chpt. IV; Herbert, 1985, pgs. 26 7).

Heisenberg's opinion, it seems to me, is irrefutable. The very fact that we can not in any way experience quantum entities when they are in the superposition state, _e.g._ , we can't see a photon or electron passing through a two slit apparatus, is persuasive supporting evidence. Yet the reality so conceived is so totally different from our common idea it takes some intellectual effort to envision it. A couple examples which can help in this effort are the Neo-Impressionist painting style pointillism and modern video screens. In pointillism paint is not applied in continuous strokes but rather as multiple discrete dots, thousands of them. Yet when viewed from a distance these dots merge into a picture. Video screens also form their images with separate dots called pixels. For example, my (old) computer is set to present about three-quarter million pixels per screen. But more modern, high resolution screens compose their images with many more pixels. One can still distinguish the dots in a pointillism painting, and, if one looks carefully, one can sometimes also make them out on my old computer screen. But one can not do so with a high resolution TV screen. Yet the number of pixels in even the highest resolution screen is trivial compared to the billions of billions of billions of billions of quantum interactions which every nanosecond compose an apparently substantive thing in actual reality. (Another similar technology is digital audio. What one hears from devices such as compact disks is composed of a succession of multitudes of discrete bits blended together to create what we perceive as continuous sound.)

According to the present quantum interpretation, actual reality, the reality comprising and surrounding us is not an object. It is a process, an ongoing dance of googolplexes of googolplexes of quantum interactions. As will be shortly explained, a quantum entity will be a mathematical point only at the instant when it undergoes a quantum interaction, and only when it is such a point is it part of actual reality. When a quantum entity is in its membrane-superposition state, it is also real but it is only potential, not actual. A superposition-destroying quantum interaction makes it actual, but only for the instant of the interaction. When it is in membrane form it is real but not actual. At such times it is only potential, exactly as Heisenberg maintained.

This two-part, potential _vs_. actual reality idea is profoundly different from, if not alien to our usual thinking. But it is fundamental to the present realistic quantum interpretation. Therefore, it is well to risk being excessive in its description rather than insufficient. So let's consider it from a different perspective.

Suppose time were to stop. According to our usual reality assumption every object would remain the same. They would simply stop changing. They would be frozen, as it were, in whatever conditions they were in at the instant time stopped, and a creature from another universe could see and appraise them the same as we could if we hadn't also been frozen in time. However, the potential _vs_. actual reality idea says the time stopped situation would be quite different. Only those quantum entities which were undergoing a quantum interaction at the precise instant of time's stoppage would actually exist. The visiting creature from another universe could not see and appraise objects as we do. Rather it would see and appraise everything as collections of scattered dimensionless mathematical points, perhaps enough to vaguely suggest the object, but perhaps not.

In short, the potential _vs_. actual reality idea holds the essential nature of ourselves and the things in our actual part of reality not to be substance, but action. According to it, neither we nor any other apparently substantial thing in the universe is an object. Rather, each is a continuing sequence of vast numbers of quantum interactions. You may find this idea counterintuitive, but being based on the insight of such a profound thinker as Heisenberg you would be foolish to dismiss it out of hand.

Having described this interpretation's conception of the nature of reality, let's go on with the discussion and consider this interpretation's view of the nature and process of these quantum interactions which constitute actual reality.

Since the electron we have been considering is actual only at the instant of an interaction, the instant when its superposition state collapses, we need consider how the present quantum interpretation envisions such membrane collapse. In the two slit apparatus, collapse only occurs at those points along the screen where the interfering information wave displays the electron's identity. (Why it only occurs there is explained below.) To explain how this interpretation considers this to happen we must digress from metaphysics for a moment and introduce a bit of well established science.

According to modern physics there exists a kind of matter which isn't real because it carries no energy. It is called virtual matter. It emerges spontaneously from nothingness and endures for an instant during which it can become real if it is invested with energy. But if it isn't, and usually it isn't, it rapidly dissolves back into nothingness. This idea may sound preposterous, but it is established science with solid supporting evidence. Let me briefly explain.

Shortly after inventing his version of quantum mechanics, Dirac made a theoretical discovery, antimatter, matter which is fundamentally opposite to ordinary matter. At first neither he nor anyone else had any idea what it might be. But soon it became clear not only what antimatter is, but that it in fact exists, for Carl Anderson found antimatter electrons in cosmic radiation, _i.e._ , quantum entities falling to earth from space. It was soon well established that for every kind of quantum entity there exists what might be called a complementary opposite identical twin. The electron's twin is called the positron. (Not to be confused with the proton, which is the quantum entity at the heart of an atom. Its antimatter twin is simply called the antiproton.) As the name positron suggests, the electron's antimatter twin has a positive electric charge, exactly the opposite of the electron's negative charge. If a real electron and real positron come together they annihilate each other in a burst of gamma radiation. In general, if any pair of real antimatter twins come together they annihilate each other, releasing a burst of energy.

Virtual matter consists in quantum entity matter-antimatter pairs which are not real because they have no energy, _e.g._ , a virtual electron paired with a virtual positron. They randomly and unpredictably emerge from nothingness for a brief period then recombine and dissolve back into nothingness. The duration of their existence is exceedingly brief, and is governed by the Heisenberg uncertainty relationship. While the product of conjugate attributes of real matter must always be greater than uncertainty's limit, that of virtual matter must always be smaller (Pagels, 1983, Chpt 8). Virtual matter may sound like science fiction, but it is solid science.

A virtual entity, if it encounters suitable energy, can appropriate the energy and become real (Gribbin, 1995, pgs. 123-5. For those who may enjoy science when presented comic book style, see Gornick & Huffman, 1990, Chpt. 25. For those who want a more technical exposition, see Peacock, 2008, pgs. 97-9.). The present metaphysical interpretation takes this conclusion as the paradigm for all matter interactions. It says matter never interacts by contact. Rather, according to the present quantum interpretation, all matter interactions occur only at the quantum level, and all are instances of real quantum entities surrendering their energy to virtual entities then ceasing to exist. Human level interactions, _e.g._ , a bat striking a ball, are cascades of vast numbers of such energy exchanging quantum interactions. Because in our frame of reference this multitude of exchanges is virtually instantaneous, we perceive it as due to the bat contacting the ball. But the present interpretation says no contact can occur because only quantum entities exist, and they are not substantial. If they don't interact, they pass right through each other.

Let's return to the single electron passing through a two slit apparatus to see how this interpretation presumes an energy exchanging quantum interaction to function.

As described above, when an electron membrane passes the slitted partition it will grow more rapidly through the slits, forming two balloon-like protrusions of the same electron's membrane in the area between the slitted partition and the projection screen. These protrusions will also pass through the projection screen, overlapping as they do. And when they overlap they will, as described above, create along the screen an alternating series of self identification bands. The pattern of this mapping will be the ordinary interference pattern produced in a two slit apparatus when both slits are open. In this case the constructive bands will identify the electron as the entity it is, while in the adjacent destructive interference bands no such information will be available. If at the instant when one of the constructive bands is at the screen a matching virtual electron-positron pair should happen to emerge in one of these bands, then there is a probability the real electron's energy will transfer to the virtual electron, making it real.

If the transfer occurs it will be instantaneous. The new electron will then grow from the point of the energy transfer exactly as above was described an electron emerging from an electron gun. When the energy exchange occurs the residual, theretofore real electron will become, by virtue of having surrendered its energy, a virtual electron. It will combine with the virtual positron, the virtual entity abandoned when its partner assumed energy and became real. And this new virtual pair will dissolve back into nothingness. At the instant of the energy exchange, the whole of the theretofore real electron's membrane, _no matter how extensive it may be_ , will instantaneously dissolve into nothingness.

As the subtitle of this book says, its quantum interpretation is mentally picturable. The process is not actually picturable because quantum interactions occur only when quantum entities overlap each other, occupying the same space, and there doesn't seem to be any way to draw actual pictures of such overlapping. But it is possible to mentally imagine the process. And what this mental picture shows is the membrane of a quantum entity, in the case of the above example an electron, growing in a particular direction like a tube-shaped balloon being inflated. Scrolling across this membrane from its leading point back across it is a wave of self identifying information. All through the area through which the membrane is growing virtual pairs are emerging from nothingness, tarrying for the extremely brief moment allowed by Heisenberg uncertainty, then dissolving back into nothingness. These pairs emerge not only around the membrane, but many do so in the membrane itself. Suddenly the membrane disappears and from some point where it just was an exactly matching electron emerges and its membrane grows from this point. What has happened is that a virtual electron-positron pair, the electron of which is an exact match to the original electron, has emerged at a point where the original electron's wave was identifying itself, and the energy it carried immediately transferred to the matching virtual electron. This energy made the theretofore virtual electron real, and the loss of it made the theretofore real electron virtual.

The probability of an energy exchange happening varies with the strength of the incoming real electron's self identification. Just as the interference bands in an ordinary two slit demonstration with light do not abruptly change from bright to dark, but rather merge gradually and continuously into each other, the self identifying bands created by the electron membrane's information wave overlapping and interfering with itself do not abruptly change from no information to full information. The information will be much stronger in the middle of a constructive band than toward its edges. The emergence of the virtual electron-positron pair is random, and may occur anywhere. The stronger the matching real electron's self identification at the point of a pair's emergence, the more likely is an energy transfer.

The newly real electron will evolve from the mathematical point where, as a virtual electron, it emanated from nothingness. And just as the original electron grew from a point into an expanding membrane, the newly realized (or perhaps one should say "newly energized") electron will also grow as an evolving electron membrane. But while the new real electron will immediately grow as a membrane, only at the instant when the energy transfer occurs is the electron part of actual reality, the part of reality comprising we humans and all the objects we can experience. Therefore, only when it is actual can it be measured. This explains why the electron is always measured as only a mathematical point, a fact from which physicists have concluded (erroneously I maintain) that the electron is a particle. Another reason for the conventional particle conclusion is that the reaction is instantaneous, a speed which would be the case if the measurement recorded only a particle hit.

Before continuing it is well to clarify a few points which could reasonably be sources of confusion.

First: For obvious reasons I call the model being presented in this chapter the Membrane model. There is, I have recently learned, a variety of string theory also-called a membrane model. Beyond the name, I know nothing about this other model except that, being part of string theory, its membranes are said to exist in ten or more dimensions. Thus, despite the name similarity, the string theory membrane idea is totally different from the present interpretation, the membranes of which are presumed to exist in the ordinary four physical dimensions, three of space and one of time. The Membrane model presented in this chapter has no relationship with the similarly named string theory.

Second: According to the Membrane model, an energy exchanging quantum interaction causes the incoming quantum entity membrane, the membrane which brings energy into the interaction, to instantly vanish into nothingness. This sounds similar to the Copenhagen claim that a measurement causes the quantum entity's wave function to collapse. But though both explanations are metaphysical interpretations of the same phenomenon, their understandings are quite different. The present interpretation's membrane is considered to be physically real. It comes originally from nothingness, the well from which all virtual entities come, where it is not real. However, when it assumes energy it becomes real. And when a subsequent quantum interaction causes it to surrender this energy, it returns to nothingness and ceases to be real. Exactly what constitutes nothingness is a complex issue, but it is considered a scientifically well established part of reality (Genz, 1999).

Wave function collapse is entirely different. As the word "function" implies, it is a mathematical expression, one defined by Schrödinger's wave equation. But unlike his original intention, the equation does not describe any physical thing. Rather, as Born received the Noble Prize for showing, like Heisenberg's matrices or Dirac's Hamiltonians the wave function merely enumerates the probabilities of the possible outcomes of the particular quantum circumstance being considered. Although some quantum interpretations apparently hold this function to really exist as an immaterial ghost wave, or _Gespensterfeld_ as Einstein called it, in my opinion this is pure mysticism, a result of physicists' naive practice of reifying their theories. There is no evidence to show, or even to suggest, the wave function describes any real entity. Rather, it is simply an algorithm, a calculation tool, an idea in scientists' minds. And the most realistic view sees its collapse as simply these scientists' conclusion that the event has occurred, and the expression is no longer relevant.

To my mind wave collapse is precisely equivalent to horserace betting. At the instant when betting closes there exists a large number of potential outcomes which could be expressed by some mathematical function. When the third horse crosses the finish line this function could be said to collapse. Three of the possibilities have become realities, and all the remaining ones simply didn't happen. The math function enumerating all the horserace possibilities is never real and never exists anywhere except in the minds of the persons, mostly bettors, involved. When the race ends it isn't that the function collapses. It simply becomes irrelevant, and can be discarded along with the loosing betting tickets which litter the race stands. Precisely the same, I strongly believe, applies to the so-called collapse of the wave function. It never exists anywhere except in physicists' minds. It doesn't collapse. It simply becomes irrelevant.

Third: A quantum entity membrane's instantaneous dissolution upon the surrender of its energy violates the widely held opinion that nothing can be faster than light. This violation, however, is neither peculiar to nor invalidating of the Membrane model. Opinion notwithstanding, faster than light phenomena are experimental fact. As pointed out in the **Introduction** chapter, nonlocal phenomena are proven to exist, and nonlocal phenomena are faster than light. While experimental data can not show nonlocal effects to be instantaneous, they unequivocally show them to be faster than light speed. This model's instantaneous disappearance of a membrane which has surrendered its energy is, therefore, not only completely consistent with evidence, as is shown in the next chapter, it can also provide an explanation of this experimental fact.

Forth: It is now possible to explain an apparently (but not truly) paradoxical characteristic of the present realistic quantum interpretation, a feature noted above in the **Introduction** chapter. While the interaction process envisioned by the Membrane model is completely causal (energy exchange is caused by the emergence of a matching virtual quantum entity at a point on the membrane where its identity is displayed), the emergence of a virtual pair is completely indeterminate. Thus the Membrane model is causal but indeterminate.

These two attributes are usually considered to be contradictory. They are because causes themselves are usually presumed to exist for a discernable amount of time before they produce their effect. But the Membrane model makes a different assumption. In it the cause itself does not exist until the instant when it produces its effect. That is why the quantum data are incomplete. At the very instant when the virtual matter pair emerges from nothingness, the cause, it produces its effect. Thus, no information can exist in the quantum data from which the effect could be predicted. All the data can ever show is the effect, not the cause. In sum therefore, the Membrane model is completely causal, but since the cause itself is spontaneous, random and unpredictable the outcome is indeterminate.

Cynics might say this only adds a scientifically immeasurable step, a step which in no way changes the inherent indeterminacy of the process. And such cynicism would certainly be correct in pointing out that this interpretation leaves quantum probabilism completely unaltered. But such cynicism misses the vital point.

Probabilism is not the problem. Rather, the problem is that some persons reify quantum mechanics. They do not consider it a human construct, something necessarily restricted by human limitations, _e.g.,_ our inability to see things like electrons and photons. Rather they believe quantum mechanics is the absolutely perfect and complete law (God's or nature's) which governs quantum phenomena. Therefore, they presume that since quantum mechanics specifies no quantum cause, there can be none. Unfortunately, as explained in the **Copenhagen** chapter above, this conclusion puts them in a logical bind. They have quantum data in hand. Lots of it. If there is no quantum cause, from whence did it come?! To answer this question they invent a cause, measurement. Not only does this lead to the mystical notion of observer created reality, it is also a flagrant contradiction of the claim that quantum mechanics is complete. Quantum mechanics specifies no cause. Therefore, if it's complete, there is no cause, neither measurement nor anything else.

The goal of the present objective quantum interpretation is to avoid this subjective, observer created reality notion and this quantum cause contradiction. It is not to assert that reality is deterministic. There are those who seek, as Einstein did, a quantum interpretation which preserves the idea that everything is caused and reality is deterministic ( _e.g._ , Bohm, 1957; Smolin, 2019). The present interpretation is not one of these. It makes no assertion whatsoever whether a specific virtual pair's emergence is or is not caused, _i.e._ , whether ultimate reality is deterministic. It considers that an open question. The present interpretation merely insists that humans (and other critters such as rodents) are not necessary to create reality. Quantum reality, it insists, is objective and preexistent, not subjectively created.

Finally, the question arises why the electron membrane does not exchange its energy when it is passing through the two slit apparatus. Why does the interaction and membrane collapse occur only at the screen rather than when the electron is between the electron gun and the slitted partition, or between the partition and the screen? The answer proposed by the present interpretation is this: Real matter is assumed to determine the kind of virtual matter pairs which emerge in its vicinity. Thus, matter in the spaces between the electron gun and the slitted partition and between the partition and the screen, _i.e._ , air, does not occasion electron-positron virtual matter pairs to occur around it, so interactions with the passing electron membrane can not occur there. But the billions of interacting quantum entities comprising the screen causes the virtual electron-positron pairs which occur in their vicinity, whether such emergence itself is or is not spontaneous and uncaused, to be ones which can interact with an electron of photon.
Some Paradoxes and Puzzles Explained

The wave-particle paradox is the original and fundamental part of the quantum mystery. Therefore, explaining it should be the essential primary goal of any quantum interpretation. The Membrane model achieves this goal. Unlike usual interpretations, which struggle to shoehorn massively inconsistent quantum data into logically incompatible particle or wave preconceptions, the present interpretation shows how these two contradictory attributes can both arise, completely without contradiction, from a different kind of quantum entity, a membrane which is discrete, as is a particle, but which carries a wave of self identifying information. By rejecting the preconception of other quantum interpretations, the prejudice insisting quantum entities must be either particles or waves, or both (Pilot-Wave), it eliminates the wave-particle paradox which plagues them.

The wave-particle paradox is not the only part of the quantum mystery the Membrane model solves. As detailed in the above chapter, it also fully explains the fact that the wave aspect of quantum data involves no longitudinal movement of the quantum entity and that single quantum entities interfere with themselves. Furthermore, it does this without any _ad hoc_ assumptions. Rather, these explanations inhere in the model. Indeed, there are many other ancillary mysteries the model can explain. The present chapter sketches some, most of which have no other suggested explanations.

**Schrödinger's Cat:** This feline thought experiment is the quantum mystery mascot. Most people believe its purpose is to disprove the idea of superposition, for after all, no one ever has seen a live-dead cat. Presumably, therefore, no such thing exists. But Copenhagen believers maintain a simultaneously live-dead cat superposition could exist if nobody were looking. Looking, they claim, measures the cat's wave function and makes it collapse, thereby destroying the superposition and making the animal either dead or alive.

The Membrane model, of course, analyzes the matter differently. While it accepts the reality of quantum level superpositions, it considers looking to be irrelevant. According to it no one has ever seen a live-dead cat because such a thing cannot exist. In the first place, such a superposition would involve billions multiplied by billions multiplied by billions of quantum entities all in a stable superposition state. As the decoherence phenomenon discussion in the **Fundamental Assumptions** chapter shows, when experimenters are doing their best to maintain even a single superposition it usually dissolves within milliseconds. Therefore, it is impossibly unlikely that a whole cat could ever be in a superposition.

But the fundamental reason Schrödinger's Cat can't exist is the Membrane model's (and Heisenberg's) potential _vs_. actual matter distinction. According to the present quantum interpretation, actual reality is comprised wholly and only of quantum interactions. Thus this model says if a cat were a colossal live-dead superposition, it would be only potential and not exist in actual reality. Superpositions, the Membrane model insists, are real but only potential, never actual. Therefore, if a cat were in a total superposition there could be no actual cat to put in the box.

**Diffraction** : The wave _vs._ particle issue did not originate with quantum physics. It first arose as a debate concerning the nature of light, and goes back at least to the time of Newton. For while the great English scientist inclined to a particulate (he called it "corpuscular") theory of light, the Dutch theorist Christian Huygens held light to be a wave, an opinion he supported in part by the phenomenon of diffraction.

Diffraction is something easily demonstrated with nothing more than a flashlight, a paperback book and a dark room. Shine the light along the edge of the book and onto a flat wall. Note the shadow. While the book edge is sharp and distinct, the shadow edge is a bit diffuse. The further from the wall the book is, the more diffuse the shadow edge. If light were composed of particles the edge of the book's shadow should be as sharp and definite as the edge of the book itself. This follows from the fact that a particle's path is a straight line from its origin to its point of impact. Particles would not bend around in back of the book in order to produce a fuzzy shadow line. But a wave which passes a straight edge always wraps around a bit in back of it, _i.e.,_ it diffuses. Therefore, Huygens concluded light must be a wave.

Though the diffraction phenomenon first became an issue for light, it does not occur only with light. Diffraction occurs with all quantum entities. This isn't a bit surprising, for light itself is composed only of quantum entities, photons. The Membrane model explains how diffraction occurs even though quantum entities are not waves. According to this model the membrane itself tends to balloon out into open areas such as those beyond a book's edge. In so doing the membrane carries its self identifying information wave into these areas where, should a matching virtual entity emerge at a point where the real photon is identifying itself, an energy exchanging quantum interaction can occur. Thus the data will be ambiguous. They will show wave characteristics, but like all quantum interactions this reflects the wave-like nature of quantum entities' self identification. It does not show a wave-like nature of the entities themselves.

It may be noted that the speed of the light photons which are involved in such diffuse interactions will be changed. These photons move slower than light speed. Consider: The leading edge of the photon membrane is defined as moving through a vacuum at light speed. If an interaction occurs at the leading edge of such photon, then in its lifetime that particular photon will have moved at light speed. But if such photon undergoes an interaction anywhere behind its leading edge, then the photon will have moved a shorter distance than it would have moved at light speed. Which is to say: It will have moved more slowly. A slower speed, of course, is consistent with both theory and evidence.

**Mini-solar-system atom:** This widely, almost universally employed model holds the atom to be a nucleus around which electron particles orbit the way planets orbit the sun. But while this model may be universally employed, universal scientific agreement insists it is impossible. If electrons were orbiting particles, atoms would self destruct almost instantaneously. About this there is complete scientific agreement. According to Maxwell's laws, laws upon which much of our modern electronic technology is based, a negatively charged particle moving in the positive field of the atom's nucleus would virtually instantly radiate away all its energy and spiral into the nucleus, collapsing and destroying the atom (Gribbin, 1984, pg. 53; Pagels, 1983, pg. 52). As is shown by the practice of calling electron particles' supposed paths around atomic nuclei orbitals rather than orbits, the scientific impossibility of the mini solar system model is universally conceded.

The Membrane model resolves this impossibility in a simple, objective and obvious way. The electron is not a particle. It's a membrane. Therefore Maxwell's laws don't apply. The more fundamental laws of quantum mechanics do. As a membrane, the electron doesn't orbit the atom's nucleus. Rather, it surrounds the nucleus, wrapping around it like a shroud. Indeed, although it is considered a nonmaterial probability wave, quantum mechanics math (Schrödinger's wave equation, I presume) describes precisely such nucleus enveloping electrons (Herbert, 1985, pgs. 122 26).

For some cases, _e.g._ , explaining why quantum waves involve no longitudinal movement, no additional assumptions need be added to the Membrane model to achieve a complete explanation. In this case, however, an additional assumption must be made. As the previous chapter explained, membranes are described as growing. But an electron around an atom is not presumed to grow. Rather, the Membrane model assumes that when approaching an atomic nucleus an electron membrane surrounds the nucleus and meets itself on the opposite side where it stabilizes into a nucleus enclosing envelope. The sweep of self identifying information across the electron membrane is assumed to control this process by creating a standing wave on the membrane envelope. This resonance phenomenon is analogous to Schrödinger's quantum wave assumption. But whereas he assumed the electron itself to be a wave, here the electron is assumed to be a membrane on which a wave of self identifying information locks into a standing wave.

Just as the wave explanation of diffraction can be understood by the Membrane model without assuming that the photon is a wave, the atom model with membranous electrons can explain the wave characteristics of atoms' electrons without assuming them to be waves. To understand how this can be we must consider atoms.

There are about one hundred different atoms. The fundamental difference between them is the number of protons in their nucleus. The simplest atom, hydrogen, has one proton, and each subsequent atom has one more. As explained in **The Quantum Mechanics Story** chapter, an atom can hold as many electrons as it has protons. But it does not hold them in only one place, be they orbitals or envelopes. Rather, for each atom there is a particular set of different places. The more energy an electron has the further from its atom's nucleus is it held.

Consider a hydrogen atom. When the single electron it can hold has the lowest energy amount for a hydrogen electron it is called a ground state electron. There is a unique set of higher energy levels for the hydrogen electron with each increased level having a location further from the atom's nucleus. Each location can be precisely described with a wave equation. The wave description for an electron three levels higher than the ground state has a characteristic Herbert (1985, pg. 125) calls an "obvious difficulty." To wit: The description has a bulge on top and a matching one of the bottom, and the probability is 50-50 that the electron might be found in either bulge. But the two bulges are not connected and the probability of finding the electron on the separating line is zero. If the electron were a particle it would require improbable special assumptions to explain this. But if the electron were a wave destructive interference could explain it precisely. However, we know the electron can not be a wave. But if the electron is a membrane across which a wave of self identification information scrolls, the destructive interference explanation fits perfectly.

Atoms having more than one proton are capable of holding more than one electron. Often these multiple electrons are in the same orbital. If electrons were substantial particles, there would seem to be a great risk of collisions. Nothing like that has been reported. However, membranes are defined as being permeable, so several electron envelopes in the same place around an atomic nucleus is perfectly consistent with the Membrane model.

It is impossible to overstate the significance of the Membrane model's alternative atom image. Even if the only puzzle this interpretation could address were the atom model it would have to be considered much more likely than the particle prejudice. True, the Membrane model is only a metaphysical supposition which can never be scientifically proved. However, it is conceivable while the mini solar system model unequivocally is not. Therefore, to continue to use an impossible explanation, and especially to continue teaching it to school children is virtually deliberate deception. It would be far better to teach how atoms might be, candidly admitting science's uncertainty, than to continue teaching a model we know to be wrong.

**Quantum jumps:** This is the quantum feature which most upset Schrödinger, literally driving him to a sickbed at one time when he argued the point with Bohr. As just considered, an atom can hold an electron membrane in several different energy level envelopes or orbitals. Each different kind of atom has its own particular pattern of such alternative energy levels. These levels are quantized, _i.e._ , they are discrete with stepwise differences between them. Quantum mechanics says an electron can jump across these steps, it can instantly go from one energy level to another without transitioning through any of the intervening energy amounts. Schrödinger considered this impossible and absurd.

This jump phenomenon is perfectly explained by the Membrane model. To do so we must first expand the description of energy exchanging quantum interactions. The interactions so far considered are simple, meaning one real quantum entity surrenders its energy to one matching virtual entity. But the Membrane model also posits compound interactions, ones involving multiple different real and virtual quantum entities. Quantum jumps are considered to involve such compound interactions.

Consider the simplest atom, hydrogen. It, of course, can carry only one electron. Assume this electron is at the lowest energy level for a hydrogen atom, the ground state. According to the current quantum interpretation this electron is an energy carrying membrane which envelops the hydrogen nucleus, and waves of self identifying information continually sweep across the membrane surface. Now consider a photon which is passing the atom, a photon the energy of which is exactly the difference between a hydrogen atoms' electron's ground state energy level and its next higher electron energy level. Since elementary quantum entity membranes are permeable, they pass through and overlap other elementary quantum entity membranes. Thus, the passing photon membrane will pass right through the electron's membrane. Sometimes at the place where the two overlap the identities of both may be displayed. When this occurs, if at this point and instant a virtual electron-positron pair should emerge from the void, and if their potential energy level is that of a second level hydrogen electron, then the real electron and real photon may both surrender their energy to the virtual electron. If this occurs the theretofore real electron and real photon membranes, because they no longer carry energy, will have become virtual. As such they will combine and become a virtual electron capable of carrying the amount of energy in a second level hydrogen electron. Then they will combine with the virtual proton which was abandoned when its paired electron was made real, a virtual proton which, of course, also has the potential to carry the amount of energy of a second level hydrogen electron. This new virtual pair will then dissolve into nothingness. The net effect is that the electron will appear to have instantaneously jumped from the ground state energy level to the next higher level.

(A day or so after writing the first draft of the above paragraph I reread it checking for typos and mistakes. As usual, there were several. But most distressing, I found it difficult to follow the process described. To be certain everything balances, I drew little diagrams. These visual aids confirmed that indeed, everything does come out even. So you need have no doubts on that score. However, if the author's own writing confused him, there's a good chance it will confuse readers too. Therefore, I have refined the diagrams and the final version is presented as this book's cover. I have also written a detailed, item by item description of the process. Unfortunately, because it is so detailed, it is rather tedious. Therefore it has been removed to the **Appendix**. If the above paragraph's description of this interpretation's explanation of the quantum jump phenomenon is not clear, you may wish to study the cover diagram while reading the **Appendix**.)

An electron in the second energy level envelope of a hydrogen atom can jump to the ground state by a reversal of this process. To wit: If at a point and instant where this second energy level electron's identity is displayed a virtual electron-positron pair with potential energy of an electron in the ground state should emerge from nothingness, and if at the same point and instant there also should emerge from nothingness a virtual photon pair (photons are their own antiparticles) with potential energy of the difference between the second level and the ground state, then the following can happen. The real electron can surrender the ground state amount of its energy to the virtual electron, making it real, and the residual amount of its energy to one of the virtual photons, making it real. The newly energized electron will wrap its membrane around the hydrogen nucleus as a ground state electron, and the newly energized photon will radiate away. This leaves two virtual entities (the virtual base energy level positron and the other virtual photon with potential energy of the second level minus the base) without partners. They combine into a virtual positron with potential energy of a second level hydrogen electron and pair with the now energy empty original second level electron membrane. This pair then dissolves into nothingness.

With about one hundred atoms, each with many different membrane envelope possibilities, there are multitudes of different ways quantum jumps can occur, but the procedures just described provide a paradigm for all. The Membrane model holds there to be no limit to the number of real and virtual membranes which may be involved in compound quantum interactions which produce electron jumps. The only requirements are that the sum of the energy levels of the receiving virtual membranes be equal to the sum of the energy levels of the surrendering real membranes, and that the residual membranes, like the residual electron and photon in the above paragraph, can combine to make appropriate virtual pairs.

**Radioactive decay:** Electron jumps between different envelopes are not the only kind of random, spontaneous atomic changes. Changes can also occur to an atom's nucleus. These happen only to particular kinds of atoms, radioactive atoms, and these changes are called radioactive decay. When such an atom decays, quantum entities radiate away from it, hence the name. The same energy exchanging quantum interactions able to explain quantum jumps can explain radioactive decay. However different quantum entities are involved. To see what they are let us consider an example of such decay.

Perhaps the most widely known instance of radioactive decay is that of carbon 14. The number of protons in an atom's nucleus, of course, determines what kind of atom it is. Carbon 14, like all other carbon atoms, has six protons. The number fourteen means the nucleus of this particular carbon variety or isotope contains fourteen nuclear entities. The other eight are neutrons, the only other constituent of atomic nuclei. The kind of radioactive change in carbon 14 atoms is beta radiation, in which the radiated entities are an electron and an antineutrino. Neutrons are slightly more massive than protons, and the electron and antineutrino which are lost in a carbon 14 atom decay come from one of its neutrons changing into a smaller proton. This changes the atom from six proton carbon to seven proton nitrogen.

There is no way to determine or predict when any particular radioactive atom will decay. But as in all quantum interactions, each kind of radioactive decay has a characteristic probability. This is expressed as its half-life, the amount of time required for half of a collection of such atoms to decay. Precisely which particular ones will do so, however, is indeterminate. The half life of carbon 14, for example, is 5,730±40 years, after which half of the collection will have decayed. Before the fact, however, when and which atoms specific will do so cannot be predicted.

Physics theory holds neutrons and protons to be particles. With the caveat that their particulate character is an emergent and not a fundamental property, the Membrane model agrees. It does because physics theory also holds neutrons and protons to be composed of more fundamental entities, quarks. Thus, if quarks are the fundamental constituents, then the present model holds them to be membranes. And effective particulate entities such as protons and neutrons are not particles _per se_ , but ongoing quantum dances whereby real, energy carrying quarks continually exchange their energy with virtual quarks.

The Membrane model claims the kind of real matter in a area controls the kind of virtual matter which may appear there. Therefore, according to this model, radioactive atoms differ from stable ones which do not decay in that radioactive atoms cause the sometimes occurrence of virtual quarks in their vicinity other than those which only reproduce the atom. These unusual quarks, if they happen to undergo a quantum interaction, will yield a decayed atom.

**Chamber paths:** One of the strongest arguments supporting the conventional particle interpretation is provided by the paths quantum entities make when passing through a cloud or bubble chamber. Indeed, as noted above, some physicists consider such paths to be incontrovertible evidence that quantum entities are particles. They're wrong. Here's why.

All such paths are sequences of bubbles, not continuous lines. Each bubble is a measurement of a location of the passing quantum entity, and such entity may possibly be a particle. But as Heisenberg (1999, Chpt. III, pg. 47) pointed out, between bubbles the particle assumption is empirically unjustifiable. In these interstices, he argued, the quantum entity could be anything. Since there are no data there this conclusion is irrefutable. Therefore, the claim that the entities must be particles between bubbles is untenable. They could be particles, but only prejudice says they must be.

Implicit in the particle claim is the necessary assumption that there is no other possible way to explain these data. But the Membrane model provides a plausible alternative. To explain it we must first consider a couple more aspects of ordinary physics, and one more attribute of the Membrane model.

The paths quantum entities make in bubble chambers are curved. Indeed, it is from the specific nature of its curve that the quantum entity is identified. For example, in a particular field electrons curve in one direction, but positrons in the same field curve in the opposite direction. Ordinary physics defines curved movement in a precise, particular way. It is said to be accelerated. Acceleration's meaning in physics incorporates the colloquial meaning but includes other meanings as well. Specifically, physics defines any movement which changes direction and/or speed (either increasing or decreasing) as accelerated. This contrasts with movement involving no change of either speed or direction, which physics calls inertial. According to the Membrane model any quantum interaction which preserves a membrane's inertial movement will be a simple transfer of energy from one real membrane to one matching virtual membrane.

Inertial movement inheres in the moving object or entity. According to Newton's laws, it is fundamental, and anything moving inertially will continue to so move until and unless it is acted upon by some force. Such force will accelerate its movement by changing its direction and/or increasing or decreasing its speed. Physics has a usual model of how a force accelerates an object. Specifically, force bearing particles are said to be exchanged between the source of the force and the object. Except for claiming that these force carrying particles are really membranes, the Membrane model assumes this usual physics model. According to the Membrane model such accelerating interactions are not simple one-for-one exchanges such as occur with inertially moving membranes, but compound exchanges such as those which underlie quantum jumps.

Since there are no data between bubbles, it is no more speculative to suppose that in these interstices the quantum entity is a membrane than to assume it is a particle. Thus, the Membrane model can explain the paths of quantum entities in cloud or bubble chambers equally as well as the conventional particle model. To be sure, this membrane assumption is only a speculation. But so too is the particle contention. It only seems more reasonable because it is based on a deep seated preconception, _i.e.,_ prejudice, holding quantum entities to necessarily be particles. Both opinions are only metaphysical speculations, for as Heisenberg correctly insisted, in the absence of between-bubble data there can be no scientific conclusion.

As noted in the previous chapter, the Membrane model assumes the nature of the real matter in an area controls the kind of virtual matter which emerges there. Consistent with this provision, these chambers function only because of the particular material in them. Without these particular materials, no bubbles form.

**Inertia and acceleration:** The Membrane model can also explain a phenomenon associated with acceleration, the tendency for objects to continue their inertial trajectories for a short period of time after an accelerating force is applied. For example: An object in a moving automobile which turns to one side will seem to be thrown to the opposite side. If the car breaks objects will seem to fly forward. If the car increases its speed objects will be thrust backwards. All of these responses, of course, are illusions. Actually the object is tending to continue its constant unchanging inertial movement while the car's movement is changing.

The Membrane model's explanation of this phenomenon arises from its definition of such objects. The model denies that they are substance. Rather, they are defined as actions, ongoing energy exchanging quantum interactions of enormous numbers of quantum entities. And the fact that all these interactions are not simultaneous explains this phenomenon.

When an accelerating force is applied, it will introduce force carrying membranes into the process by which real membranes exchange their energy. Assume that the accelerating force is changing the direction of an car's movement. These force-carrying membranes will then begin to be involved in compound energy exchanges, each one of which will produce a new real membrane superposed with the new direction. Now recall: The nature of virtual membrane pairs emerging from nothingness in any given area is controlled by the nature of the real, energy carrying matter in the area. Thus, while compound interactions are creating new real membranes carrying the new direction, real membranes superposed with the old direction will continue to emerge in the area. And this real matter will continue to cause virtual entities superposed with the old direction to emerge in the area. Thus for a period of time while the accelerating compound quantum interactions are increasing the actual interactions with the new direction, there will continue to be quantum interactions which will be simple one-for-one exchanges interactions having the old direction. Thus the energy exchanges which the Membrane model defines as the actual object will, for a short time, be a mixture of those with the new and old directions.

**Tunneling:** This is one of the most puzzling quantum phenomena. It is possible for a quantum interaction to occur where, according to classical physics, it never could. Pagels (1983, pgs. 122 24) uses the illustrative example of a marble in a cup. It never happens that such a marble suddenly appears outside the cup. The common (but erroneous, I maintain) substance assumption is used to explain this. To emerge from the cup the substantial marble would have to pass through the substantial wall of the cup, something which substantial things are defined as incapable of doing. But at the quantum level such things occur. A quantum entity can emerge outside a barrier which it does not have sufficient energy to cross. The present realistic quantum interpretation can explain this.

According to the Membrane model, quantum entities are not substantive particles. They are permeable membranes. These membranes can pass through everything in the universe because everything is composed only of other quantum entities, every one of which has this property. Only one thing can therefore stop them from going anywhere in the universe, a quantum interaction.

The factor which normally prevents a quantum entity from crossing a barrier is not the barrier's substance nor the amount of energy in the entity. Rather it is the fact that the barrier causes particular kinds of virtual entities to occur around it. If an approaching quantum entity encounters and identifies itself to an emerging matching virtual particle it will surrender its energy and dissolve. And if the interaction is a compound one which creates a change of direction, or one in which the entering entity's energy is absorbed into the matter at the point of the interaction, the entity will not cross the barrier. Quantum mechanics assures us all quantum interactions are probabilistic. Even though the probability of an interaction happening may be exceedingly high, it is not certain, and infrequently one does not occur. And if it does not, then the quantum entity crosses the usually insurmountable barrier.

But if quantum entities can occasionally tunnel, and marbles are composed only of quantum entities, why then don't marbles tunnel? Quantum mechanics explains why. According to it, while there is a possibility of a single quantum entity passing through a barrier, this possibility is small. But a marble is composed of not one, but billions of billions of quantum entities, all of which must simultaneously tunnel through the side of the cup for the marble itself to so move. For illustration, assume the probability of a single quantum entity so tunneling were 0.1, or one-in-ten. Given this probability, elementary statistics says the probability of two independent tunneling events simultaneously occurring is 0.01 (one-in-a-hundred), and the probability of three is 0.001 (one-in-a-thousand ). For every additional quantum entity which must simultaneously tunnel in order for the marble to move through the side of the cup another zero is added between the decimal and the numeral 1, making the probability smaller and smaller. Quite obviously, therefore, the probability of billions of quantum entities simultaneously tunneling is less than infinitesimal. It's vanishing tiny, a conceivable but essentially impossibly improbable event. In fact, however, the probability is even smaller than this example suggests, for the single entity probability of 0.1 was chosen to make this example easy to calculate. It is unreasonably high. Thus, a more accurate single entity tunneling probability would make the probability of the entire marble tunneling through the side of the cup vastly more unlikely even than this example.

**Nonlocality:** This is the phenomenon whereby an event which happens at one place in space has an instantaneous effect elsewhere. Einstein called it "spooky action at a distance." He insisted it is impossible. Even so, as explained in the **Introduction** chapter, subsequent research has clearly demonstrated nonlocal phenomena. If one assumes reality to be a solipsistic illusion or some other such nonrealistic notion, then nonlocality can be explained as part of the illusion. But if one assumes a preexistent, objective reality, as Einstein, your writer and lots of other people do, then reality unequivocally contains real nonlocal phenomena. The Membrane model can explain them.

Though the EPR paper brought the nonlocality issue to the fore, it wasn't the first time Einstein questioned quantum mechanics' nonlocal implications. As noted above in the **Two Slit Data** chapter, during the discussion at one of the Solvay conferences Einstein drew a semicircle to represent the screen onto which a photon was projected. (Einstein's schematic did not depict a two slit apparatus. It had no partition, just a point of origin for the photon and a semicircular projection screen.) Then he noted the accepted consensus that photons move to the screen in the manner of a wave. Therefore, every part of the wave front will encounter every point on the semicircular screen at the same instant. Yet, a hit occurs at only one precise point on the screen, and only one hit is ever recorded. Thus, he concluded, if Copenhagen were right in claiming the moving photon is in a superposition state such that it is potentially at every point on the screen until the exact instant when the hit occurs, some instantaneous message must transition from the point of the hit to every other part of the wave front, turning off the possibility of any second hit anywhere else. Einstein's point, of course, was that he believed such instantaneous messages to be impossible. Therefore, he maintained, Copenhagen must be wrong. He believed the moving photon is not in a superposition state such that it potentially may hit anywhere on the screen, but rather it is on a predetermined path to only one particular but hidden and therefore unknown spot.

With the advantage of abundant more recent research we now know that nonlocality definitely occurs, confounding Einstein's argument. The Membrane model easily explains Einstein's thought experiment. According to it, the photon moves as a ballooning membrane, not a wave. But just like a wave, the membrane's leading edge will be semicircular and every part of it may be assumed to simultaneously encounter Einstein's semicircular projection screen. Only one hit can occur, however, because at the instant when the photon surrenders its energy to a virtual entity, the entire membrane instantly vanishes.

The nonlocality issue was brought to general attention, however, not by Einstein's Solvay conference thought experiment, but by the famous EPR paper. The situation it considers is of a pair of entangled quantum entities. Entanglement, recall, occurs when two quantum entities commingle forming essentially a single one. As explained in the **Ambiguous Data** chapter, the EPR argument can be stated as a circumstance in which each of two entangled quantum entities has the same attribute, one which can assume only one of two alternative states. Quantum mechanics says when this attribute is in one state for one entity, the other entangled entity's matching attribute must be in the other state. And Copenhagen says until a measurement of this attribute is made for one or the other entity the attribute state does not actually exist for either but is a superposition, both entities being potentially in both states. EPR then assumed the two entangled entities (presumably particles) moved apart, and when apart the attribute was measured on one of them. If the attribute state is set for both entities only at the instant this measurement is made, as Bohr and Copenhagen insist, then this is a prime example of nonlocality, a causal event at one place (in this case a measurement) having an immediate effect elsewhere.

Einstein insisted such a nonlocal effect is impossible. But as abundant research has subsequently proved, it occurs. The relevant issue now is to explain how. As far as I know, the Membrane model is the only quantum interpretation able to so do. First, this phenomenon involves entangled quantum entities, and entanglement is common quantum mechanics, not something particular to the Membrane model. When two quantum entities are entangled this model says their membranes merge into a single one. Exactly how this occurs is another of those empirically unknowable details which it is profitless to attempt to describe. (However, it seems to me, any such description would be much more probable than imagining two solid, impermeable, substantial particles so merging.) The entangled membrane is a superposition in which, just as Copenhagen maintains, the attribute is potentially in both states for both entities. And this superposition continues until one or the other entity undergoes a quantum interaction transferring its energy to a virtual entity.

Such an interaction will cause the entangled membrane immediately to surrender the part of its energy belonging to the measured entity to the emerging virtual entity. Only the energy of the measured entity is surrendered, and only the part of the entangled membrane pertaining to this entity unites with the virtual anti entity and dissolves into nothingness. This leaves the rest of the membrane, the part pertaining to the unmeasured quantum entity, extended in space. But now its attribute state will no longer be undetermined. Now because the other part of the entangled membrane is dissolved, the surviving membrane will have its attribute set.

This process is rather involved, and my description may very well not be clear. So let me reiterate in different words. We have two quantum entities, A and B. Both have the same attribute, and this attribute can be in only one of two different states, call them 1 and 2. The A and B entities are entangled. Thus they have a single, conjoint membrane which we may symbolize as AB12. What this AB12 represents is the single membrane of an entangled pair of quantum entities with the superposed possibilities of being disentangled into either A1 and B2, or A2 and B1. After the AB12 membrane expands in space a measurement is made to determine the attribute state of one of the entangled entities. Measurement, of course, involves a quantum interaction in which the energy of either the A or the B entity is surrendered to a virtual entity. Assume this interaction happens to involve the A entity. There are only two ways for such an interaction to occur. The A part of the AB12 entity can surrender its energy to either an A1 or an A2 virtual entity, depending entirely on the chance occurrence of one of these at a point where the AB12 entangled membrane is identified. Suppose the virtual entity which accepts the entangled membrane's A energy is an A1 virtual entity. In that case, at the instant of the interaction the A1 part of the entangled real AB12 membrane will vanish into nothingness. In effect A1 will be subtracted from AB12, leaving a residual real ( _i.e._ , energy carrying) B2 membrane spread out in space. And since it is already spread out in space, no faster than light message, nor indeed no message of any speed or kind must go from the place where the A entity was measured to wherever the residual B2 membrane may be. If before the measurement the AB12 membrane were spread across the entire universe, the instant after the A entity is measured and set to A1, an immediately subsequent measurement of the residual B2 entity, wherever it may be, can only find it to be B2.

Before considering the next puzzle it is worthwhile to compare the Membrane model's nonlocality explanation with the Pilot-Wave interpretation. In the latter, every quantum in the universe is presumed to be instantaneously aware of everything which happens to every other quantum entity everywhere. How such universal nonlocality can occur, however, is not explained. It is a mysterious, magical process assumed by the Pilot-Wave interpretation. The Membrane model, however, precisely explains how nonlocality occurs. But its nonlocality is not universal. Rather, the nonlocality it explains is limited to the particular entities involved. I like to call it local nonlocality. The surrender of a single real photon's energy to a single virtual photon, as in Einstein's Solvay conference thought experiment, only concerns those two. And the collapse of entangled entities only involves the entangled entities. Thus, according to the present explanation, for the most part reality is local. And it is important to note: Only local nonlocality has been experimentally demonstrated. Nothing remotely resembling Pilot-Wave's universal nonlocality has been empirically shown. Thus the Membrane model is precisely consistent with the nonlocal evidence while the Pilot-Wave interpretation goes incredibly far beyond it.

**Particle detection:** The **Two Slit Data** chapter ends with a description of the baffling results of trying to observe how electrons pass through an electron analogue of a two slit apparatus. To reiterate: An appropriate device is built to detect an electron immediately after it has passed through something analogous to a slit in a slitted partition, call it a window. Though both windows are open, the device never detects an electron at both. Rather, if the device detects a passing electron at one window, it never detects this electron at the other. A large number of electrons which trigger a response at a particular window form a one-slit interference pattern on the projection screen across from it, the same pattern created if the electrons had passed through the apparatus with only that window open. But those electrons whose passage is not detected form a two slit interference pattern on the projection screen.

The general consensus is that electrons which are detected have passed through only the window where they were detected, while electrons which are not detected have passed through both windows. But though this conclusion is widespread, it is an inference not a fact. The fact is that the data do not show either what the electron is, nor what it has done. The general consensus is a general guess.

No previous quantum interpretation known to me can explain these results. Some popular sources suggest the only possibility is to assume the electron consciously decides to go through only one window when it is going to be detected, but through both windows when not. With the possible exception of Pascual Jordan, however, no one believes an electron can be conscious. Moreover, even if anyone so believes, no one has suggested any reason why the electron would do this, nor how it knows before going through the window whether it is going to be detected after so doing, knowledge it must have in order to know whether to go through both windows or through only one. Therefore for previous quantum interpretations these results remain a profound mystery.

But the Membrane model explains these data in a simple, straight forward, conspicuously objective manner. According to it, the electron membrane always goes through both windows. If after so doing its passage is not detected, nothing happens to the electron, and the membrane's two protuberances, one through each window, continue on to the projection screen where, as described in the previous chapter, they strike in a two slit interference pattern. However, if after passing the slitted partition analogue an electron's passage is detected it means a quantum interaction has occurred in the detection location immediately after one of the windows, _i.e._ , a virtual electron-positron pair has emerged at this location at the precise instant when the passing electron membrane was displaying its identity. Upon this detecting interaction the original electron surrendered its energy to this virtual electron and the entire membrane of the theretofore real electron (at the other window and everywhere else it may be) instantly dissolved into nothingness. The membrane of the newly energized electron grows from the point of this interaction, which, of course, is immediately in front of the window. Therefore, this newly energized electron will precisely resemble the membrane of an electron which passed this window when only it was open. And a number of such newly energized electrons will create on the projection screen exactly the same pattern which would be created by a number of electrons which passed through this window when only it were open. In this way the Membrane model explains these profoundly puzzling results in a completely objective way, and no mythical, mystical, conscious electron need be assumed.

The Membrane explains most of these quantum puzzles without the need of other assumptions. However, in this case an additional assumption must be made. According to Feynman (1965, Chpt. 6), from whom this particle detection mystery was taken, the electron's passage is detected by bouncing a photon off it. The Membrane model must therefore explain how this can happen. The most parsimonious assumption appears to be that the stream of photons used for this purpose cause virtual electrons to emerge around them.

The study just considered is a prototype for a large number of similar ones. I call them detection studies because their goal is to detect how quantum entities such as photons or electrons pass through devices designed to elucidate various aspects of what these entities might be and how they may function. A large variety of devices and procedures have been used, and a large number of different guesses have been employed to explain the results obtained. These differences notwithstanding, the basic similarity of the studies implies that the Membrane model can explain all their results in the same objective manner as it does this prototype. It can because the membrane is considered to be as malleable as it is permeable. Just as it is contorted into different shape when passing a two slit partition it can be reshaped in any way, even divided into separate parts. And every part of it will instantly dissolve back into nothingness upon surrendering its energy in a quantum interaction.

Though it may quite reasonably be expected that the Membrane model will be able to fully explain all these various detection studies, demonstrating this is a considerable undertaking. Moreover, the task of showing this appears to be technical formidable. Thus, it is best to leave this to those whose professional knowledge is appropriate to the task. But there is one kind of detection study with conclusions so offensive to reasonable ideas of realism they must be considered, studies which purport to demonstrate how something done today can change what happened in the past.

**Time backward causality:** The preceding, **Particle Detection** , subchapter concerned efforts to find which window(s) an electron goes through in traversing an electron analogue of a two slit apparatus. As noted, there are two standard assumptions of what the data obtained from such studies mean. When an electron's passage is not detected it is assumed to have gone through both windows, and to have done so as a wave. But when an electron is detected it is assumed to have passed through only the window where detected, and to have done so as a particle.

Although usually implicitly presented as self-evident facts, these assumptions are anything but. At best they are empirically uncorroborated inferences. At worst they are dogmatic prejudices. The assumption concerning undetected electrons is the most tenable. The interference pattern these electrons produce, while not proof, is consistent with the idea that the electron moved as a wave. Also, the fact that the particular interference pattern is of the two slit variety compellingly argues that the electron went through both windows. But to assume the electrons which are detected are particles is conspicuously counterfactual. These electrons form a one slit interference pattern on the detection screen, and there is no plausible way a particle could form an interference pattern.

It is informative to consider how physicists came to the opinion that detected electrons must be particles. As explained in the **Orientation** chapter, one reason why the geniuses who invented quantum mechanics have not come up with a plausible explanation of the wave-particle paradox is that they suffer from a prejudice that quantum entities must be either particles or waves. The evidence strongly suggests electrons move as waves (Herbert, 1985, pg. 66), and physicists generally accept this is the case. Now, if a wave were detected after passing one window it would almost certainly also be detected after passing the other. Therefore, it is reasonable to assume an electron detected at only one window cannot be a wave. In which case physicists' wave-or-particle prejudice says the electron must be a particle. This logic is not wrong. However, the prejudice it's based on is. Quantum entities do not have to be either waves or particles. They could be something entirely different, membranes, for example.

For this reason the reservations which always should be attached to these two assumptions are always ignored, and the general (but erroneous) assumption is that they are factual conclusions. Given this prejudice based opinion it is possible to construct a situation in which it can be argued that something done now has an effect in the past. Such situations involve variants of detection studies in which the detection is delayed till a time well after the quantum entity has passed the slitted partition or its analogue. In that time interval the experimenter chooses the manner of measuring the entity. This choice can be either to measure it in a way which will cause it to appear, according to the assumptions just discussed, either to be a wave or a particle (Gribbin, 1984, pgs. 210-11; Gribbin, 1995, pgs. 138-44). There even is a form of such studies involving astronomy and astronomical years (billions) of alleged time backward causes (Herbert, 1985, pgs. 164-6).

The procedures and devices involved in this time backward inference are a bit complicated, but the essentials can be simply stated. To wit: When a quantum entity, _e.g._ , a photon, passes the slitted partition or its analogue it is presumed not to take any of the three possibilities open to it, _i.e._ , passing through either one or the other window or both. Rather, not until sometime thereafter when the experimenter causes the entity to be detected either as a wave or as a particle (according to the assumptions discussed above) is the path it takes through the slitted partition determined. Supposedly. Thus, this notion claims, the cause (the experimenter's delayed measurement) performed after the event (the passage of the entity through the slitted partition analogue) propagates backward in time to produce the effect (the quantum entity takes one particular path).

The Membrane model explains such studies without any time backward mysticism. First, it discards the two assumptions discussed above as empirically unsupported prejudice. Rather, the quantum entity's membrane is said always to pass through both windows. This distorts its shape, and this distortion makes it possible to overlap different parts of the membrane. If the subsequent detection (measurement) of the entity one way the two slit interference pattern will be found. If the detection (measurement) is done differently, the one slit interference pattern will be observed. But these events pertain _only_ to the detection process itself, and neither reveal how, nor have they any effect whatsoever on how the quantum entity moved in the past.

**Polarization:** Polarization refers to a characteristic of photons which the eye cannot detect. If one could, each oncoming photon would appear like a bar which would either be perfectly vertical or at some angle thereto. For example, if a photon's polarization angle were 90°, the bar would appear horizontal. Most light sources are unpolarized, meaning all the photons from them do not have the same polarization angle. Rather, the angle of successive photons varies randomly between 0° and almost 180°. This 'almost' limit follows because the imagined bars are not pointing in any direction, so a polarization angle of exactly 180° is the same as an angle of 0°.

There exist devices called polarizers. If unpolarized light is shined through one, all the angles of the emerging photons will be the same. Such light is said to be polarized. One kind of polarizer is quite common, ordinary polarized sunglasses. According to Gribbin (1995, pg. 109), such glasses "only allow photons with one particular orientation to pass through." This statement says polarizers are semitransparent lenses which pass some photons and block others, depending upon the photons' polarization characteristic. This statement also seems to imply that each photon has a fixed polarization, but as Gribbin quickly explains, that implication is not intended.

Rather than having a single polarization angle, the quantum data seem to show that each photon's polarization is a superposition of all angles but one. One angle is predominant. That is the angle referenced in the above paragraph's imagined sighting of polarization bars. The polarization at right angles to the predominant one is missing from this superposition, but all the other angels between these limits occur in the superposition with diminishing probability as the angle diverges further from the predominant one (Gribbin, 1995, pgs. 112-3. There's a typo on the first line of pg. 113. Exchange the numerals 30 and 60 to correct it.).

Polarized light has been frequently used to study the quantum mystery. And indeed, it does display it in many ways. For example, the mystery of how a polarizer can change a photon's polarization angle. Every photon which emerges from any particular polarizer is the same. This means it has the same predominant angle. But recall: Every photon is a superposition of all angles except the one at right angles, _i.e._ , 90°, to its predominant angle. So while a photon whose predominant angle exactly matches the polarizer's angle can pass through intact, many other photons whose predominant angle differs from the polarizer's angle, but which include in their superposition of angles one which matches the polarizer angle, might also get through. But in so doing, their polarization will change.

Consider this example. Suppose we have a polarizer the angle of which is 0°, vertical. Now suppose a photon with a predominant angle of 89° impinges on the polarizer. Because each photon is a superposition of all but one angle, there is a possibility this photon will "get through" the polarizer. Because its predominant angle is so different from the angle of the polarizer, the possibility for this particular photon is very small. But if it does get through the polarizer it will be massively changed, for the predominant angle of the emerging photon will now be that of the polarizer, 0°, almost a complete right angle difference from the impinging photon's predominant polarization when it entered the polarizer! None of the current quantum interpretations known to me can explain how this happens. But the Membrane model readily explains it, and it does so without the need of any special assumptions.

According to the Membrane model, polarizers are not lenses. They may block photons, _i.e.,_ they may cause a quantum interaction in which the light's energy is transferred to a quantum entity composing the polarizer. But polarizers do not pass photons. Rather, if they do not block an incoming photon they provoke a quantum interaction in which the photon membrane surrenders its energy to a virtual photon. The Membrane model says a polarizer produces virtual photons with only one polarized angle. Thus, if one of these virtual photons emerges in the polarizer at a point and time where an impinging real, energy carrying, photon's self identification wave is displaying its predominant and superposed angles, and if one of these angles happens to align with the particular angle of the polarizer's virtual photons, then the impinging photon will surrender its energy to such virtual photon and vanish into nothingness. The newly energized photon will emerge from the polarizer as if it has simply "got through", but that is an illusion. In fact, the Membrane model claims, the photons which emerge from the polarizer are all newly energized ones.
Believability

As explained at the start of this book, when the writing began I had a serious disagreement with the various quantum interpretations physicists have offered. None is realistic, and some are egregiously subjective. A host of other inadequacies plague them. They don't all have the same ones, but all have serious defects. Some are logically inconsistent, vague, mystical, or even magical. However, I had only an undeveloped idea for an objective and realistic alternative. In fact, at the start, the purpose of writing was to force development of the idea. Writing does this. Notions which seem solid when only in mind often fall apart when one tries to spell them out. This is so common the department where I received my professional education required every doctoral candidate to write a full formal proposal before allowing dissertation research to begin. The kind of careful evaluation needed to write such a proposal often revealed unanticipated problems, sometimes insurmountable ones.

So though I started with high hopes, my notion was not certain to hold up. And indeed, I encountered several unanticipated problems and ambiguities. Writing forced me to recognize and address them. At times I had to draw pictures and diagrams to find solutions. My rough initial notion changed and improved in the process. The result, of course, is conveyed in the three preceding chapters. I cannot say I am completely satisfied with the Membrane model. It isn't perfect. But it's far more believable than any other quantum interpretation of which I know. So I believe it. But the question is: Do you? And what might convince you if you do not?

One thing seems obvious. There is no need to continue explaining ancillary aspects of the quantum mystery, the kind of explanations in the immediately preceding chapter. What is presented convinces me, and I'm confident it will convince many others. But probably not everyone. The particle prejudice documented in the **Ambiguous Data** chapter runs deep in physics, and prejudices are hard to overcome. So it isn't unlikely that some will feel the data they have always accepted as particle evidence cannot be anything else.

But if the explanations in the above three chapters haven't convinced such persons, more of the same will not. Therefore, I have not attempted to figure out how the Membrane model might explain every single different demonstration of the quantum mystery known to me. And since I'm not a physicist, probably there are others unknown to me. So while the model convinces me, I can not and do not claim to know it can solve every aspect of the quantum mystery. Still, Feynman said an explanation of the two slit data would provide a complete answer, and the Membrane model not only provides such explanation, it seems to be the only quantum interpretation which can, at least without making bizarre proposals such as Pilot-Wave. Feynman may have been mistaken. Perhaps there's more to the quantum mystery than he thought. But if he was right, the Membrane model would seem a promising solution.

However, it isn't only the particle prejudice which must be surrendered to accept the Membrane model. Nor are physicists the only ones who must surrender prejudices. The goal of the Membrane model is an explanation which not only is objective but also intuitively plausible. And while I'm confident the first part has been achieved, the second part, I must confess, may not obtain.

One reason is the Membrane model's claim that elemental or quantum entities are not substantial. (Recall, this essay defines substance to mean only that matter fully occupies the space where it exists, excluding all other matter therefrom.) The belief that substance is the essence of matter is not simply a prejudice. Our deepest human intuitions insist on it. Our every instinct says it is impossible for two different things to be in the same place at the same time.

The first thing to say in defense of the model's rejection of the substance assumption, as noted when the issue was introduced, is that substance is not denied. Indeed, the Membrane model considers substance to be just as certain as our intuitions insist. But it is not held to be fundamental. Rather, it is an emergent property, something which results from the interactions of myriads of non-substantial quantum entities. But how does this happen? Simply put, I don't know.

It may seem, therefore, that all this book has accomplished is to substitute one mystery, the emergence of substance, for another, the wave-particle paradox. However, compared to the wave-particle paradox, the emergence of substance seems minor. After all, this is only a puzzle, not an impossible paradox. And physics has well developed theory explaining how its presumed fundamental particles are held together and/or apart. Four forces are said to do this; gravity, electromagnetic, weak and strong. (Modern theory specifies conditions under which the electromagnetic and weak forces merge, yielding only three.) All that is needed, then, is to figure out some way to apply this well developed theory to membranes instead of particles, and the Membrane model itself suggests an approach, energy exchanging quantum interactions.

Superposition is another postulate made by the Membrane model in violation of common intuition. To accept this model one must first accept that fundamental quantum entities can be in this multiple potential state. The usual intuitive assumption holds every iota of matter to be in a particular definite state at every instant. Indeed, violation of this presumption apparently was a significant part of Einstein's reasons for rejecting Copenhagen.

The superposition assumption is included in the Membrane model basically because, unconventional though it is, there's an overwhelming amount of evidence supporting it. Consider: When a photon is passed through a two slit apparatus there is absolutely no way to predict where it will hit the projection screen. During its passage it truly seems simultaneously to be heading to every place where it might end up. True, one could suppose the photon is heading to a single but hidden spot, as Einstein did. But the fact that he, one of the greatest geniuses in the history of physics, was unable to find any explanation based upon this particular hidden variable assumption, suggests it isn't fruitful. A final reason for accepting superposition is that it is generally conceded. Science is not a "majority rules" arrangement. And repeatedly in science's history a minority opinion has eventually been established. Bearing that caveat in mind, it nevertheless is relevant that the superposition thesis is accepted by the overwhelming majority of physicists (as far as I know, by every single one). Counterintuitive and impossible of empirical validation though it may be, superposition is accepted science.

But perhaps the most intuitively unacceptable assumption of the Membrane model is its division of reality into two parts, potential and actual. To reiterate, this model maintains that though energy containing matter is always real, only those instants when energy is passed from real quantum entities to virtual ones is it actual, and only when it is actual is it part of the reality we experience, the reality that envelopes and creates us. Thus neither the reality we live in nor we ourselves are always completely existent. Rather we are ongoing action sequences. According to the Membrane model, we and the world around us are not objects. All are processes, continuing dances of quantum energy exchanges. Intuitively this is absurd. But the idea isn't spun from whole cloth. Originally suggested by Heisenberg, this potential _vs_. actual matter idea has abundant supporting evidence. Indeed, once one accepts superposition this assumption becomes virtually inescapable because while superposition says quantum entities are potentially in multiple states or places, things in the macro world around us are always in only one state or place. There must, therefore, be a reason for this difference. The potential-actual matter distinction provides it. If the idea seems absurd to you, I refer you to Miguel de Unamuno's profound observation quoted at the start of this book, "Only he who attempts the absurd is capable of achieving the impossible." By accepting the absurd potential _vs_. actual matter division can one achieve the impossible, an explanation of the wave-particle paradox.

In summary, the Membrane model provides a plausible explanation of the wave-particle paradox. It also can explain many, and potentially all the ancillary puzzles associated with the paradox. But one must buy the model at a price. That price is acceptance of these intuitively unconventional assumptions.

### Part III: Foundational Premise and Extension

Hidden Variables

The word "hidden" is often used in the quantum mystery literature, usually to refer to Einstein's explanation of what he thought causes the quantum mechanics incompleteness of which he was convinced. He maintained there is a hidden variable. What this means can be understood by considering a single photon passing through a two slit apparatus. According to Copenhagen, and indeed, the Membrane model also, such photon is simultaneously going to every place where it might end up. Einstein refused to accept this. He insisted the photon is going to one and only one predetermined spot, the place on the projection screen where it eventually hits. But he held this targeted characteristic, or the circumstance(s) responsible for it, to be hidden from quantum mechanics.

As explained in the **Introduction** chapter, physicists long considered hidden variable explanations of quantum mechanics to be mathematically disproved. But while this disproof has itself been disproved, the physics community generally still continues to reject Einstein's hidden variable explanation of quantum mechanics, probably, as suggested in the **Introduction** chapter, because anything hidden necessarily can yield no evidence, and evidence is the _sine qua non_ of science.

The Membrane model also rejects Einstein's hidden variable idea, but not the hiddenness idea _per se_. In place of it, to explain why the photon ends up where it does the present interpretation proposes a hidden causal process occurring at the spot where, and time when the photon eventually hits. But though the two hypotheses are different, both Einstein and the Membrane model claim something is hidden. To have a common term, let's call any explanation based on something which does not appear in the data a hidden variable explanation.

The energy exchanging quantum interaction at the heart of the Membrane model is a hidden variable. No virtual entity can be empirically detected. But even if it could, since this model's energy exchanging quantum interaction is defined as occurring when a virtual entity emerges from nothingness at a place where a membrane's identity is displayed, nothing but the event itself can ever appear in data. Excepting the event which it is intended to explain, there never can be data showing that the quantum interaction envisioned by the Membrane model has in fact occurred. It's hidden.

The rejection of Einstein's hidden variable idea is said to be due a philosophical conviction that any hypothesis for which direct data can not be obtained is nonscientific and meaningless. This conviction is usually attributed to a philosophy of science called Logical Positivism. Though it had precursors in the nineteenth century, Ernst Mach is a leading example, this empiricist philosophy was formally developed at about the same time as quantum mechanics. Copenhagen presumably was developed in strict conformity to this Positivist doctrine. Because science is universally agreed to require an evidential basis, this science methods philosophy says science can not be based on anything that can't provide empirical evidence, that can't be directly detected. But by its very nature there can be no direct evidence of anything hidden, things which can only be inferred rather than directly detected. Therefore, this philosophy holds hidden variables to be meaningless.

The scientific problem produced by hidden entities is apparent, for indeed, inferences not based on palpable data are inherently uncertain. For example, the fact that quantum entities passing a two slit apparatus strike in only one place can be taken as indirect data supporting Einstein's belief that the entity involved was going to only one place. However, the fact that subsequent replications don't strike the same place, even though all conditions are identical, can also be taken to show that the quantum entities are simultaneously going to several different places, as Copenhagen claims. The interpretations are contradictory but both involve empirically unverifiable presumptions about what the entity is and what it is doing when it cannot be seen. Positivism attempts to avoid this ambiguity by proscribing hidden variables.

If the Positivist view is accepted, the Membrane model will likely be summarily dismissed as meaningless metaphysics. A reader may quite reasonably wonder why this is of concern. After all, this book openly concedes the metaphysical nature of the Membrane model. But this model is competing for your acceptance against quantum interpretations which maintain, at least implicitly, that they are scientific conclusions, not metaphysical speculations. In particular, Copenhagen specifically claims it not only is a scientific interpretation, it claims to be the only one. If any such claim were conceded the Membrane model could be rejected out of hand regardless of its comprehensibility or its ability to explain the wave-particle paradox which, save the unbelievable infinitely nonlocal Pilot-Wave interpretation, no other interpretation can. So in order to defend the believability of the Membrane model, let's consider this issue.

Is it true that science is meaningless if it includes anything hidden? Usually this question starts an intense philosophical debate. For example, although highly critical of her profession for substituting math for evidence, Sabine Hossenfelder (2018, pg. 102) nevertheless has said: "There isn't a priori anything unscientific about a theory that contains unobservable elements." Obviously, opinions are highly contradictory. So to avoid being stuck in a quagmire of conflicting opinions, let's approach the issue differently. Let's do it scientifically. After all, the topic here is science, so let's look at the evidence. What in fact is done in science? Does any accepted science include hidden variables? Since the concern here is physics, let's restrict our investigation to this science. And there's no better place to start than with Copenhagen itself.

Superposition is a proposition central to Copenhagen, indeed, it may reasonably be considered the interpretation's principal principle. But in fact every superposition is a hidden variable. There is not an iota of direct data showing any superposition. Nor can there ever be any, for every attempt to measure a superposition destroys it. The only data of any kind are before and after it. Specifically, in research with quantum entities, identical circumstances usually do not lead to identical results. Superposition is Copenhagen's hidden variable explanation.

At first glance I may seem to be accusing Copenhagen followers of hypocrisy. I'm not. And I am not because I'm quite sure they see a fundamental difference. I just think they are mistaken. Superposition, they maintain, simply accepts the data as they are, whereas Einstein's hidden variable hypothesis invites data fabrication. In fact, however, the superposition idea does not simply accept the data. In fact superposition fabricates facts, the superposition state. The fact is, between a photon's launch and its hit upon the projection screen, there are no facts. As Heisenberg (1999, pg. 48) has said: "Quite generally there is no way of describing what happens between two consecutive observations." To claim the quantum entity between two consecutive observations is in a superposition state is, therefore, to fabricate facts.

We are left with a great irony. Copenhagen rejects Einstein's hidden variable simply because it is hidden, while advocating an idea of its own idea, superposition, which in reality is also a hidden variable. But Einstein's hidden variable hasn't led anywhere whereas Copenhagen's has. To wit: Quantum computing may never achieve its fabulous potential, but it works. What might be called proof-of-concept research has been accomplished. A quantum computer has factored 15 (Gribbin, 2014). But if the superposition hidden variable claim that quantum entities can be potentially in several different conditions were false, then this factorization would be impossible.

So superposition is one scientifically accepted hidden variable, but are there others? Yes. Atoms. At least when first introduced to science they were.

The idea of atoms originated, of course, with the ancient Greeks. Philosophers such as Democritus considered atoms to be the indivisible building blocks comprising all matter. This was mere philosophizing. But by the nineteenth century the idea was being applied in science. By then chemists had accumulated a considerable body of empirical facts, and they explained and related these data in terms of hidden variables, atoms. Despite the fact that the atom idea was proving quite useful in explaining chemical phenomena, some prominent scientists of the time, forerunners of Logical Positivism, objected because atoms were hidden variables. No atom could be seen. Today, of course, these objections seem silly. Today atoms are established science. But they still can't be seen. At least they can't be seen well enough to learn anything about their functioning by watching them. There are micrographs showing atoms as tiny dots. This shows that the entities, atoms, which we know about from theory and an enormous amount of indirect evidence, really are there. So in that sense atoms are no longer hidden variables. But for decades they were hidden in every sense. And while they were, scientists built a considerable amount of solid science upon them.

The fact that the atom idea is now established science despite having long been only a hidden variable does not, of course, show that any other hidden variable is valid or will also eventually become established science. However, it does show that hidden variables are not _per se_ necessarily scientifically meaningless, as Copenhagen's Positivist philosophy maintains.

The ancient idea held atoms to be fundamental and indivisible. That is to say, these philosophers thought atoms were the basic building blocks of matter which themselves had no constituent parts. But even before all scientists had accepted the atom idea, the discovery of electrons and also of the residue of radioactive decay showed that scientific atoms had constituent parts. Then when Rutherford discovered the separated atomic nucleus, it became unmistakably clear that the ancients' atoms-are-irreducible idea is scientifically wrong.

Driven by what can only be described as a quasi religious faith born of the ancient atom idea, a faith that there must be some single or at most few fundamental thing(s), physicists started emulating Rutherford in more and more elaborate (and more and more expensive) ways. With great technical competence they constructed devices to bounce atomic parts off one another or smash them together in an effort to break them apart and find their fundamental component(s), the more elementary thing(s) their faith assured them must exist. Unfortunately their faith failed them. For instead of finding fewer, they found an abundance (some physicists consider it a veritable zoo) of subatomic things called hadrons.

But eventually a theoretician, Murray Gell-Mann, found a way of organizing all these hadrons. He figured out how each could be constructed from a much smaller set of fundamental parts which he whimsically called quarks. For this he was awarded the Noble Prize, so its fair to consider the quark idea to be certified science.

But again ugly reality intervened, for intense efforts to see a quark all failed. No one has ever found the kind of palpable, direct quark data which Positivists and Copenhagen insists is required to make an idea scientifically meaningful. As Pagels (1983, pg. 203) says, "Most physicists today believe quarks will never be seen." Or in the words of another physicist, William Poundstone (Gribbin, 1995, pg. 191): "Quarks are counterfactual: Not only has an isolated quark never been observed, but (under most theories) an isolated quark is impossible." In other words, quarks, unequivocally established science though they are, are hidden variables.

Quarks are an aspect of arcane particle physics, an area of science not generally known by the ordinary educated person. It may better make my point to choose an example from more widely known science. The Big Bang cosmogenesis theory will do. For example, I recently saw a little ten question true-false test which was designed to measure basic literacy. One of its questions asks whether this theory is true, to which the literate allegedly would ascent. So by this test's standards the theory is a scientific truth which everyone should know.

Fundamental to this theory is the hypothesis that the universe is expanding. General relativity theory says it can, but there neither is nor can there be any direct evidence of such expansion. The direct data necessary would be repeated measurements of the distance to distant astronomical objects. If the universe is expanding these would show a consistent increase with time. But such measurements are all indirect. And there is no possibility that direct measurement will ever be possible. Consider: Radar and radar-like measurements of the distance to nearby astronomical objects are direct, valid and precise. But it takes time for the signal to reach the object and return. For measurements of the moon the delay is a matter of mere seconds. But the nearest full sized external galaxy is Andromeda. Indirect measurements estimate its distance as two million light years. That means to directly measure its distance would probably require millions of years. If the indirect distance measurements are at least ballpark correct, it would take about four million years: two million for the signal to go out and two million for it to get back. But even such measurement would be superfluous, for indirect measurements also say Andromeda and the Milky Way are pulling together, not apart. Theory explains this as due to local gravity, so theory says their separation is not relevant to the expanding universe hypothesis.

Astronomers have developed indirect distance measurements, _e.g._ , relative brightness. And with these they have developed something called Hubble's Law. It says the more distant a galaxy the more is light from it shifted to the red end of the visual spectrum. And if the distances between galaxies is increasing, such red shift is precisely what would happen. So Hubble's Law, although indirect, is some of the main evidence used to support the Big Bang cosmogenesis theory. But this usage raises the main deficiency of indirect measurements, alternative interpretations. Specifically, is expansion the only thing which can cause red shift? That is a matter of disagreement among astronomers.

A well known astronomer, Halton Arp (1987; 1999), consistently opposed the claim that the Hubble's Law red shift is due to expansion of the universe. He assembled considerable evidence which he claimed to show astronomical objects which are near to each other have different red shifts. If this is correct, then Hubble's Law is contaminated and unreliable. But Arp's interpretation suffers from the same problem as the expansion hypothesis. It is also based on indirect measurements, so it also is uncertain and may be wrong. Arp's view, it must be noted, is decidedly a minority one. Most astronomers buy the only-expansion-causes-red-shift hypothesis. But science is supposed to be based on evidence, not opinions. So the issue is scientifically uncertain, a fact which Positivists may, with eminent fairness, cite as support for their contention that only direct evidence should be scientifically admissible.

Red shift isn't the only indirect evidence cosmologist claim as support of Big Bang. Another is the so-called cosmic background radiation (CBR). According to the Big Bang hypothesis the universe has expanded from an initial essentially infinitely dense speck, which according to elementary physics theory would be extremely hot. As the universe expanded, it cooled. The CBR is the alleged residue. In 1965 a radio signal which approximated theoretical predictions of the hypothetical CBR was serendipitously discovered by Penzias and Wilson. Theoreticians immediately decided it is the CBR and the Nobel Prize was awarded its discoverers. Ergo this claim is certifiably scientific.

But these data are indirect. Hypothesis says the CBR exists in every corner of the universe. Therefore, a direct measure would require measurement to be made everywhere, or at least in a random sample of the universe's every corner. But that, of course, is impossible. Just one intergalactic measure would be vastly more reliable than what we have, but even that is impossible. We can't even get an intra-galactic ( _i.e._ , within the Milky Way but away from Earth) measure. The signal has been measured only in and around Earth. True, it comes in approximately equal strength from every direction. That's consistent with hypothesis. But it's also indirect. So CBR is also a hidden variable.

Let's consider just one more case, string theory. The majority of theoretical physicists consider it the ultimate description of physical reality. As one not included in this majority says (Hossenfelder, 2018, pg. 190), "within the physics community few doubt its use." Thus the average physicists will certainly classify it as science. Yet every physicist agrees direct evidence for string theory is impossible because such evidence would require an atom smashing device larger than Earth. Indeed, critics say there is not even indirect supporting evidence (Hossenfelder, 2018; Lindley, 1993; Woit, 2006). Nevertheless, to the consternation of these and other critics, the attitude amongst most physicists is that the beauty and symmetry of string theory, and its ability to incorporate gravity in its explanation, renders it believable even in the total absence of supporting data. So strings are by far the most hidden of all hidden variables, and most physicists claim them to be not only science, but the most advanced science.

As this brief review makes clear, science of all types and all degrees of establishment include hidden variables. Therefore, there is no scientific justification for rejecting the Membrane model simply because it also is based on a hidden variable. A reader may then fairly and appropriately wonder why I claim only metaphysical status for the model. If all levels of science include hidden variables, such reader may ask, the Membrane model is no different from and no more metaphysical than many established scientific conclusions.

The answer is that this restriction is simply a matter of personal preference. My ideal is something like Logical Positivism. And in my ideal world science would be based only on unambiguous patent direct data. But the world is far from ideal, and imposing this standard in the real world would shackle science. Therefore, indirect data are inevitable.

Nevertheless, I believe scientists should be much more candid and forthcoming about the limitations of indirect data. For example, to say, as abundantly many do, that the universe is known to be expanding, is to flirt with deliberate dishonesty. The truth is that there is a body of reliable data which may be reasonably interpreted as due to the expansion of the universe. But whether this interpretation is valid or not is presently, and for the foreseeable future, beyond empirical proof. I think scientists, science reporters, professors and popularizers should be upfront about this. Their job is to educate, not proselytize.

And the degree of data directness, when honestly appraised, forms a meaningful hierarchy of convincingness, a scale one may use to determine how much belief to invest in the Membrane model. Some may place issues on this scale differently, but I think most place the quark idea rather high on it, just below the level of direct proof. But because of the total absence of direct evidence the Big Bang hypothesis must be placed much lower on this scale. I think the Membrane model falls between these two, which would place its believability between the probably true quark model and the hypothetically possible Big Bang.
Hoist with His Own Petard

The ubiquity of hidden variables in scientific theories must lead one to wonder how the strictures against them ever became popular enough to govern the construction of Copenhagen. Wondering leads to wonderment when one learns that a substantial part of the hostility to Einstein's hidden variable explanation of quantum mechanics was based on his own work. Specifically, in developing his special relativity theory Einstein ridiculed the idea that science could be based on anything which can not be directly measured. Paul Ehrenfest, his friend and fellow amateur musician, pointed out this inconsistency to Einstein at one of the Solvay conferences, but the great theoretician's response was only a wisecrack that a good joke should not be repeated.

This wisecrack notwithstanding, one must suppose as profound a thinker as Einstein would have given considerable thought to his inconsistency. If so, however, he never was able to resolve the matter. This shouldn't surprise anyone, for the resolution requires one first to recognize that special relativity has serious problems. And that is something Einstein could never do. Relativity theory was the great love of his life. For example, although he received the Nobel Prize for his photoelectric paper, his acceptance speech was about relativity theory.

It is worthwhile to examine this issue here, for, as will be shown, the Membrane model not only explains the quantum mysteries, it can also equally simply explain the two completely separate but equally great mysteries posed by special relativity. This is of paramount and fundamental importance, so significant the circumstance must be considered lest the point be overlooked.

Both quantum phenomena and those of relativity have puzzling aspects. But they are completely, totally different and unrelated. Special relativity is part of pre-quantum, classical physics. Unlike quantum mechanics, it does not concern the functioning of atoms. Rather it concerns the effects of movement. And unlike quantum effects, relativity's effects are determinate, not probabilistic. They are, however, counterintuitive, so much so some nonscientists cannot believe them notwithstanding the fact that they are unequivocally empirically established. But completely unlike the quantum data, which are a logically impossible paradox, the relativity data are paradoxical only in a psychological sense. They are counterintuitive. In no way, however, are they illogical.

The Membrane model was invented only and exclusively to explain the quantum mystery, specifically, the logical paradox of wave-particle duality. That it seems able to do this whereas other quantum interpretations cannot is impressive, but not unexpected. After all, the Membrane model was invented precisely to explain what it explains. But it was not formulated to explain anything whatsoever about special relativity. Nevertheless, without any further assumptions nor modifications whatsoever the model can also completely explain the completely unrelated phenomena of special relativity. This outcome was not intended. Indeed, it could not have been expected. It is like a gift from heaven.

This result is not simply surprising. It's astounding. The unexpected and unsought ability of the Membrane model to also explain the phenomena of special relativity powerfully suggests that it is not simply a way of looking at quantum phenomena, but apparently provides a comprehensive and comprehensible picture of the whole of physical reality. Indeed, for some persons this ability to explain completely unrelated phenomena is compelling evidence of the Membrane model's validity. Nevertheless, without supporting direct empirical evidence the model can only be metaphysics. So its validity, while strongly suggested by this unintended and unexpected achievement, properly remains beyond scientific certification.

It is therefore well worthwhile to consider special relativity and how the Membrane model explains its counterintuitive predictions. However, be warned. This examination cannot be accomplished by a slight digression. Rather, we are going to have to get into the special relativity issue with some detail. But the topic of this essay hasn't changed. For this examination leads us right back to the Membrane model and its ability without additional assumptions or modifications to provide a picturable, mechanical explanation of special relativity's counterintuitive phenomena.

**Special relativity background:** The first thing one needs in order to understand this issue is an appreciation of the distinctive and unusual nature of Einstein's thinking. He did not approach science in the customary empirical manner. Instead, as at one time he said: "In a certain sense, therefore, I hold it to be true that pure thought is competent to comprehend the real, as the ancients dreamed." (Lenzen, 1949, pg. 361). By this Einstein did not mean he was abandoning empirical evidence, but that he was subordinating it to reason. What he apparently meant was that instead of the usual empirical way of doing science, _i.e._ , gathering data then trying to make sense of it, he believed science could proceed by first trying with reason to figure out reality and then looking for evidence to support one's pure thought conclusions.

To achieve anything by pure thought requires great intelligence. And it is commonly supposed that this was Einstein's most salient characteristic. Indeed, I have seen popular claims that his was the greatest intellect of any human who ever lived. He may have been, but intelligence was not the most distinguishing characteristic of his thinking. To be sure, Einstein was a genius. That's self-evident. But in comparison with his peers it wasn't his intellect which made him, as Ohanian (2008) concludes, history's second greatest physicist. It was his intellectual audacity. Einstein had no fear of looking stupid. He was the veritable embodiment of the person described by Miguel de Unamuno in the quote at the beginning of this book: "Only he who attempts the absurd is capable of achieving the impossible." Einstein eagerly sought to achieve the impossible by attempting the absurd. And he had sufficient ego strength to bear the charges that his audacity resulted from intellectual inadequacy, if not lunacy.

Case in point: As noted at the end of **The Quantum Mechanics Story** chapter, Einstein deserves to be considered the father of quantum mechanics. He was the first, and for a decade he was almost the only physicist to accept Planck's evidence that radiant energy is quantized. He was the first to make any use of this fact. During that time the overwhelming majority of other physicists, including Plank himself, thought quantized energy was an incidental quirk and Einstein's light quanta idea was, to put it colloquially, just plain nuts. In fact Robert Millikan, the American experimentalist who received the Nobel Prize for proving Einstein right, not only set out to prove him wrong, but even after he had proven him right still could not believe it (Gribbin, 1984, pgs. 65 & 82).

In 1905 when Einstein published his photoelectric paper arguing that light can be considered to come in discrete quanta (subsequently named photons by another physicist), the paper for which he was eventually awarded the Nobel Prize, the overwhelming majority of physicists overwhelmingly rejected the notion. They did because an overwhelming body of evidence says light is a wave. Einstein didn't say it wasn't. Rather, he said it had to be considered both wave and particle. It was, and still is, logically absurd to so claim, but that's what Einstein persistently did. And that's what quantum mechanics, physic's greatest theory, eventually concluded. It takes an enormous amount of courage to stand up against a phalanx of opinion holding one to be absurd. Especially does it for a young man just starting out on a career in science. But to again put it colloquially, Einstein had guts, the courage of his apparently absurd convictions. And in the end he won the day, at least with respect to photons.

In his special relativity theory Einstein showed similar intellectual audacity by suggesting another absurdity. Unfortunately, as will shortly be shown, in this case the data have not supported him. In order to show this we must consider some details.

Special relativity theory concerns the physical effects of movement. With this theory Einstein deduced by pure thought a set of what are called transformation equations. They state precisely the effects of motion. These effects are: 1) The size of a moving object is reduced in the dimension of the direction of its movement. Thus, an object moving either north or south will become shorter in its north-south dimension. 2) Time passes more slowly for a moving object. This effect is called time dilation.

Of all science's theories special relativity is the most misunderstood and most misconstrued. Much of this is due the word "relativity". Einstein didn't choose this term. He started with a more appropriate name. But after others, mostly Planck, insistently used it, Einstein was forced to go along. "Relativity" suggests to non scientists that the theory has something to do with relativistic ethics or esthetics or differing points of view. It has nothing to do with such things. The term refers exclusively to the "only directly measured data are scientific" approach Einstein used in developing his theory. Specifically, it refers to Einstein's claim that movement can be measured and meaningfully understood only relative to palpable objects, rather than to impalpable space.

Some of the confusion aroused by special relativity is due the counterintuitive effects predicted by the transformation equations. Many nonscientists insist such things are impossible. They are wrong. The predicted effects are unequivocally empirically established, weird though they may be.

Some popular works, to their discredit, imply that Einstein was the originator of the transformation equations. He was not. Better works avoid this error by following the customary scientific practice of naming them after their originator(s). These better works call them Lorentz or FitzGerald-Lorentz equations. This is to honor George FitzGerald, who first suggested the size contraction effect, and Hendrik Lorentz, who allegedly was the first to derive the equations. Unfortunately, Lorentz wasn't. I mention this not to nitpick, but to illustrate another aspect of the colossal confusion surrounding special relativity. Let me quote from Abraham Pais, an expert, and an avowed Einstein devotee who had no desire to minimize the accomplishments of his hero. According to Pais (1982, pg. 120), the persons involved before Einstein were: "Voigt, the first to write down Lorentz transformations; FitzGerald, the first to propose the contraction hypothesis; Lorentz himself; Larmor, the first to relate the contraction hypothesis to Lorentz transformations; and Poincaré." These researchers' earlier publications specifically related to the equations were: Woldimar Voigt, 1887; FitzGerald, 1882 and 1889; Joseph Larmor, 1900; Lorentz , 1904; Henri Poincaré and Einstein, 1905. So with respect to the equations at the heart of special relativity theory, Einstein was Johnny-come-lately.

These facts notwithstanding, when physicists refer to any transformation equation developments, _e.g._ , E=mc2 or spacetime physics, they only cite special relativity, implicitly (sometimes explicitly) crediting only Einstein's theory, ignoring all the original equation developers ( _e.g._ , Taylor & Wheeler, 1992). The problem is not one of assigning credit, but rather one of relating the theory to the questions it addresses. To dismiss prior work on this issue is a gross distortion, a confusion inducing error much of the blame for which must go to Einstein himself. It must because his 1905 special relativity paper cited not a single reference, not one of the important prior publications on the issue. Why he omitted such crucial information is unknown. Galison (2003) suggested it might be because at the time Einstein worked as a patent clerk, and patents quite deliberately refrain from any reference to prior works. Einstein's omission is often mentioned, even criticized in the popular science literature. But insofar as I am aware, no one has ever even implied that it might have been an attempt to plagiarize. And indeed, there isn't the slightest reason to suspect such dishonorable intentions. My own opinion is that Einstein was so into the issue, so wrapped up in his attempt to solve the problem that he simply lost track of the origins of many of his ideas. If you'll excuse a personal allusion, an incident from my own life illustrates how easily this can happen. Like Einstein I am an amateur musician, and once I thought I had composed a beautiful song. Not till sometime later when I happened to re-listen to a recording of a work I had at earlier times played until the groves in the vinyl disk were almost worn through did I realize that my "composition" was in fact merely a paraphrase of a song I had so often earlier heard.

But while there is no reason to suspect plagiarism in Einstein's omission, it nevertheless was an egregious error which set the stage for and has contributed to physicists' erroneous practice of attributing the science based on the transformation equations to only special relativity. John Stewart Bell pointed out the error of this (Bell, 1987, Chpt. 9). He recommended teaching this subject in a different manner, a manner which would enable students to see that the science is in the transformation equations themselves. For the fact of the matter is this: However differently the equations may have been developed and/or explained, they are identical, precisely identical. Whatever the equations from special relativity may predict, or whatever may be derived from them, is predicted or derived identically by the equations of Larmor, Lorentz or Poincaré. Mathematically the several equation sets can not be distinguished. Therefore, it is a gross error and a cause of enormous confusion and misunderstanding to credit special relativity and only it, the last work to develop the equations, with the science based on them.

Another extremely widespread special relativity confusion claims this theory proves nothing can move faster than light. It neither does this nor claims this. The simplest way to refute this error is to note the existence of the idea of the tachyon. It is described in the 1999 CD version of the _Encyclopædia Britannica_ as an "hypothetical subatomic particle whose velocity always exceeds that of light." While this particle has never been experimentally detected, and therefore may not exist, as this article notes, the tachyon "appears consistent with the theory of relativity." The fact that special relativity does not either claim nor prove that nothing can move faster than light is also shown by the fact that in the EPR paper Einstein says no reasonable person can believe in instantaneous, _i.e.,_ faster than light, nonlocality. However, had he believed special relativity proves such a thing impossible, he instead would have so said since it is a much stronger claim. And indeed, the abundant empirical proof of faster than light nonlocality (see the **Introduction** chapter), though consider weird, is not considered inconsistent with special relativity.

Yet another widespread misunderstanding of this theory concerns general relativity. This erroneous notion holds special relativity to be merely a particular limited case of the general theory ( _e.g._ , Coleman, 1969, pg. 50). Indeed, the two theories' names in effect say precisely this. But the names are misleading. Except for their confusing names, the theories are different. As noted, special relativity concerns movement. General relativity, however, is a theory of gravity. To be sure, it includes an effect similar to time dilation. But the causal variable is not movement. It is gravity. Specifically, general relativity predicts clocks to run slower in stronger gravitational fields, and the evidence shows they do. But this is an entirely different phenomenon from time dilation, something which, in this case, is clear from the effect's different name. General relativity's time effect is called gravitational red shift (Will, 1986, Chapter 3).

The special _vs._ general theory confusion is so widespread it justifies including the remarks of an expert to assure you it is wrong. Herbert Dingle was Professor of History and Philosophy of Science at The University of London, and a special relativity expert. His expertise, it is relevant to note, was acknowledged by Einstein who listed Dingle's book on special relativity in the bibliography of his own popular book on relativity (Einstein, 1961, pg. 158). At the beginning of his book Dingle corrects this common special _vs._ general relativity confusion. Dingle (1940, pg. 8) states: "It may be remarked at once, however, that it is only from a certain viewpoint –that of a particular mathematical formulation– that the special theory becomes a particular case of the general theory. In essence the two theories are independent, and the modification of pre-relativity physics which we will find to be required by the special theory cannot be deduced from the general theory." The modification Dingle mentions is the pair of counterintuitive effects predicted by the transformation equations, size contraction and time dilation.

A further illustration of the almost institutionalized special relativity confusion is the widespread belief that with this theory Einstein disproved the luminiferous aether hypothesis. Nineteenth century physics insisted the aether existed. It did because light and other electromagnetic phenomena were believed on the basis of solid evidence and theory to be waves, and a wave has to have a substance in which to wave. The aether supposedly was that substance. Einstein wanted to do away with the aether notion, and that was an explicit goal of special relativity. But he never claimed his theory disproved it. Indeed, he himself explicitly corrected the common error that it did (Einstein, 1983, Chapter 1). Using again the word from his original 1905 paper, in correcting this mistaken belief Einstein said special relativity renders the aether "superfluous", but does not disprove it. This is not to say the aether exists. It does not. There is not a shred of evidence for it, and considerable evidence against it. But as Einstein insisted, special relativity does not disprove it. His theory simply sidesteps it.

Well, what then did special relativity do? To answer this question we need consider how and why the transformation equations were first developed.

Empirical research in the Nineteenth century raised serious questions about the speed of light, and these in turn raised serious questions about the aether. In particular, though he was not the first to empirically address this issue, in 1881 Albert Michelson, an American studying in Germany, published such research, a study which, to high precision, failed to discover any difference in the speed of light whether it was moving in the same direction as Earth or at right angles thereto. This result diametrically contradicted what was then considered established science, something we might call the additive law. Here's how.

Suppose a moving train carries a large container of water, something like a children's wading pool. Also suppose the train's movement is such that the water in this pool is flat and still so the speed of waves made by dropping a rock into the pool can be easily measured, _i.e.,_ the train is moving inertially. It can be shown that the speed of these waves with respect to the ground depends upon their direction. Waves going in the same direction as the train itself will have a speed given by adding the wave's speed to the train's. Waves heading in the opposite direction will have a speed with respect to the ground of the train speed less the wave speed. And waves at right angles to the train's direction of movement will have a yet different speed, one requiring a bit of geometry to describe.

The fact that Michelson's data contradicted the additive law raised serious uncertainties about the existence of the hypothetical aether because, as described above, such an outcome is impossible with ordinary waves, or with any other moving thing of common experience. Why then, did Michelson not find light to be faster when moving in the same direction as Earth, and what did this mean about the hypothetical aether which supposedly was at rest in space?

Although a few eminent physicists were aware of Michelson's unexpected finding, to his understandable disappointment, his initial work did not elicit the widespread attention its revolutionary results warranted. One suspects this was because the result was so inconsistent with the then existing theory that other scientists dismissed the finding as an experimental error. So after returning to the US, and in association with chemist Edward Morley, Michelson repeated and refined the study. They found the same null result and published it in 1887. This study caught everyone's attention and has been repeated many times since. With one minor exception, eventually concluded to be a fluke, the results are the same: Light does not follow the additive law. (When Einstein first heard of the fluke research he rejected its now abundantly discredited results with the famous statement, "Subtle is the Lord, but malicious He is not.")

The Michelson-Morley study gained universal attention and aroused efforts to try to make sense of its results. That, of course, is what scientists like Larmor, Poincaré and Lorentz did. It is important to emphasize that, although Poincaré and Lorentz sometimes communicated, Larmor worked independently. The fact, therefore, that they all came up with exactly the same transformation equations is consistent with the fact that the equations are not theoretical speculations. They are empirical generalizations, _i.e._ , mathematical descriptions of the M&M data. This approach is called curve-fitting, a name often used derisively because this approach only describes data. It does not seek to theoretically explain them. To be sure, all three of these scientists offered theoretical explanations, but these were devised after the equations had been determined and arbitrarily tacked onto them. The FitzGerald hypothesis that the M&M results occurred because of size contraction is the only plausible realistic explanation of these data. Once one accepts it the equations are required. This is well shown by the work of Lorentz. He tried desperately to avoid time dilation, to find equations which would describe only the FitzGerald contraction response. But it can't be done. Once the contraction hypothesis is adopted the transformation equations with their time dilation effect are a given, an empirical generalization, _i.e.,_ something known to occur without knowing how or why.

Also, once the equations are known the apparent inconsistency between the M&M results and the additive law is reconciled. The transformation equations show their effects to depend on the speed of the moving object, becoming apparent only as it approaches light speed (about one hundred and eighty six thousand miles or three hundred thousand meters per second). For things like trains and water waves the effects are real but undetectably small.

With the transformation equations in hand each of these scientists invented a theory to try to explain them. My sources imply and/or state that all these theories, though not the same, sought to explain how the transformation equation effects happen in terms of the aether. Obviously, since this was a quarter century before development of quantum mechanics, and since the aether concept has been subsequently and appropriately discarded, these theories are now obsolete and of only historical interest. However, since the aether was considered to be stationary in space, it is accurate to say these theories held motion to occur with respect to space.

**Einstein's approach:** The idea of motion relative to space, a not measurable hidden variable, is the assumption Einstein ridiculed and which, with special relativity, he intended to remove from science. His work in this area was completely theoretical. In keeping with his Plato-like belief in the power of pure thought, he was trying to use it and only it to comprehend the effects of movement. This was completely unlike his predecessors, who, as just noted, derived the transformation equations empirically by fitting them to the Michelson-Morley data. Indeed, near the end of his life when Pais asked Einstein about this he replied that as well as he could remember he had not even been aware of the M&M study when he developed special relativity (Pais, 1982, Chapter 6). In this his memory failed him, for there is ample historical evidence he knew of it (Galison, 2003; Pais, 1982, Chapter 6; Rothman, 2003, Chapter 7).

That Einstein did not remember knowing of the Michelson-Morley study seemed incredible to Pais, but I think it is both consistent with and revealing of Einstein' nonempirical, pure thought, Plato-like manner of deriving the transformation equations. Historical evidence proves he had learned of the M&M study and of Poincaré's efforts to make sense of it. But all of this was buried in a preconscious back corner of his mind, for unlike his three predecessors he wasn't trying to incorporate discrepant data into prior theory, _i.e.,_ the aether. He was attempting by pure thought to create a new theory without an aether. As noted above, that also probably explains why in his special relativity paper he failed to cite even a single one of the important prior works in the area. He had preconsciously incorporated their findings into his own thinking. Though psychologically understandable, this is most unfortunate. In not relating his theory to prior work Einstein committed a gross scholarship omission the consequences of which still confound our understanding of these matters.

As also noted above, Einstein's scholarship failure was not driven by any plagiaristic motive, but rather by an _idée fixe_ , his almost obsessive desire to do away with hidden variables and thereby set physics on a new path. His obsession led him to reject some things, _i.e.,_ the aether, and preconsciously incorporate others into his own thinking. He wasn't working like a scholar, carefully finding, cataloguing and analyzing other's work and ideas, but rather like an innovator, someone struggling to weave all the various ideas he had picked up and lodged in his preconscious into a new understanding. He had been convinced by Logical Positivism precursors like Ernst Mach that hidden variables are not scientific. Physics, he had decided, must strictly eschew them, and that's what he sought to do with special relativity. By deriving the transformation equations without any reference to hidden space or the aether, the entity which theretofore had been considered to be the space marker, his pure thought derivation would make both concepts superfluous, thus killing two hidden variables with one stone.

The consequence of his approach, of course, would be that mechanical models of electromagnetic phenomena would be abandoned. The aether, after all, is the only possible way to explain how waves, as light was then believed to be, could move through space. With his pure thought based special relativity theory Einstein in effect said comprehensible models are scientifically unnecessary. If the math is consistent and accurately describes the phenomenon, he implied, that's all physics needs. Science, he implicitly maintained, doesn't need to understand how phenomena happen.

In his Einstein biography, Pais (1982) emphasizes that with special relativity Einstein changed the fundamental orientation of physics research. Before his theory the objective of physics was not only to mathematically describe phenomena, but to discover a way to make them mechanically understandable. Indeed, in those times the goal of the math was largely to show how precisely the data fitted the model. Kelvin, one of the great physicists of the Nineteenth century, was often quoted as saying that unless he could form such a mental picture he couldn't understand the phenomenon. And when Maxwell developed his great electromagnetic theory, although it was abandoned at the end, he originally based it on just such a mechanical model. So too did Plank when he developed his great quantum breakthrough. But with special relativity Einstein threw all this out. His pure thought, Plato-like derivation of the transformation equations involved neither data nor model. Instead it was entirely abstract math. In this way, Pais emphasizes, Einstein changed the nature of physics.

The difference between the then traditional goal of making physics theory mechanically comprehensible and Einstein's new notion is tellingly illustrated by an encounter between Poincaré and Einstein at the one Solvay conference both attended. When Einstein sought the internationally renowned elder scientist and mathematician's opinion of special relativity Poincaré asked how the then young theoretician explained the transformation equations' effects. When Einstein answered that he did not propose any explanation Poincaré dismissed the theory, to Einstein's considerable annoyance. The two geniuses simply had different ideas of what constitutes science.

A couple decades later a couple other geniuses, Heisenberg and Dirac, developed forms of quantum mechanics in much the same way Einstein developed special relativity, that is they offered only abstract, model free math able to predict the probabilities of quantum events quite accurately, but unable to provide any explanation of how the quantum phenomena occurred. Then Born showed Schrödinger's wave equation not to describe a wave-like electron, but rather to merely be another way to abstractly calculate the probabilities of quantum events. Thus all three quantum mechanics approaches provided only abstract math, probabilistic math which included no cause, a situation which offended Einstein's unshakable conviction that God does not play dice with the universe. Einstein's deterministic prejudices were severely offended, but he was snared in a trap of his own making.

So let's consider how Einstein heisted himself on his own petard.

In keeping with his Plato-like belief in pure thought Einstein developed special relativity by mathematically deriving the transformation equations with neither data nor model. His goal was to avoid any reference to space. By eliminating space he sought to circumvent and obviate (or as he said, to make superfluous) the aether idea, the hidden variable which the other equation developers all held necessarily to exist and to be at rest in space and thereby, if the aether could be detected, marking locations in space.

Einstein began by noting, quite correctly, that we can not identify any spot in space. Therefore, he asserted, again quite correctly, we can not measure movement relative to space. He considered space referenced movement to be a scientifically meaningless hidden variable. In his little book on relativity which he addressed to non scientists, he ridiculed space referenced movement and explicitly explained his space avoiding approach. He said:

"We entirely shun the vague word 'space,' of which, we must honestly acknowledge, we cannot form the slightest conception, and we replace it by 'motion relative to a practically rigid body of reference'." (Einstein, 1961, pg. 9)

The phrase "motion relative to a practically rigid body of reference" defines the scope of Einstein's theory. This definition means the theory does not concern every kind of motion. For example, at the moment I am seated at a computer. There are many practically rigid bodies in the room, but I am not moving with respect to any of them. Nor am I moving with respect to the house nor its geographic location. However, we all are moving because Earth is moving. It's rotating and orbiting. And while this movement could be referenced to other practically rigid bodies, _e.g._ , the sun, and the sun's movement could in turn be referenced to other celestial bodies, there is no ultimate practically rigid body. Ultimately all this movement can only be referenced to space. Einstein's definition explicitly excludes such motion from special relativity's purview. His theory only concerns the relative motion of practically rigid bodies. Their motion relative to space, if any, is explicitly excluded. Indeed, by implication Einstein's approach claims movement relative to space is not simply hidden, but in fact is a meaningless notion.

The practically rigid bodies Einstein used in his derivation were two inertial reference frames moving inertially with respect to each other. Both inertial qualifications are vital. The frames themselves must be inertial, and their relative motion also must be inertial. As noted above, physics defines two kinds of movement, inertial and accelerated. To reiterate: Inertial movement is constant in speed and direction, while accelerated refers to all other kinds of movement. The **Inertia and acceleration** section above considered empirically detectible consequences which can occur when something is accelerated. However this earlier discussion did not note the fact that, though in practice often difficult to detect, in principle acceleration always produces such consequences. But inertial movement never provides evidence of its movement. So if one is isolated within an inertial frame of reference there is no way to know whether it is moving with respect to space. Therefore space is not involved. That's why space shunning Einstein derived the equations with inertial reference frames.

Inertia plays several vital roles in Einstein's derivation. Most importantly, the fact that the two reference frames are each inertial leaves out any reference to space. Also it allows one to assume certain variables are equal in the two frames. And the fact that the two frames are moving inertially with respect to each other allows the mathematical derivation. If their relative motion were accelerated, variables describing this acceleration would have to be included in the beginning equations, and this would prevent the derivation because there then would be too many unknowns.

Einstein's nonempirical pure thought derivation is a model of mathematical elegance. It is based on only two assumptions: Light speed is a measurement limit which is the same everywhere, and what Einstein calls the principle of relativity. It has been argued that the first assumption may reasonably be considered to be implied by the second. In which case the derivation is even more elegant. The principle of relativity means many things, but it is vital to note: Insofar as Einstein's pure thought math derivation of the transformation equations are concerned it means _only_ that the laws of physics are identical and in their most elementary form in both reference frames.

The derivation says one frame is moving inertially with respect to the other, and the resultant equations say the size and time dilation effects occur to objects which are at rest in the moving frame, _i.e.,_ in the direction of their movement they become smaller than, and their clock runs slower than objects and clocks at rest in the stationary frame. To quote Shakespeare, "There's the rub!", for the sole purpose of using inertial frames is because it is impossible to tell if they are moving. So if one has two inertial reference frames moving inertially relative to each other, which is the moving one where the equations' effects apply and which is the stationary one where the equations do not apply?!

Just as with his eventually successful insistence that, absurdity notwithstanding, light is both a wave and particle, Einstein sought to solve his special relativity conundrum with another audacious absurdity. To wit: He asserted that everyone must assume one's self to be stationary. This claim has a central role in special relativity, so we need a term of reference. As far as I know there is no commonly used one, so let's call Einstein's claim the self stationary dogma. It is appropriately called dogma because, unlike his claim that light is both wave and particle, for which there is abundant, if paradoxical, evidence, there is not a shred of evidence for the dogma, not a single iota. Moreover, because of the inertial restrictions required by Einstein's space eschewing derivation and the enormous speed required to demonstrate the equations' effects, at the time Einstein made this claim it was virtually impossible that there could be any pertinent evidence. As will shortly be shown, the dogma is logically impossible. And as also will be shortly shown, insofar as any evidence may be considered to bear on it, the dogma is empirically refuted. There unequivocally is no evidence to support it. In ugly fact therefore, there is nothing to support the dogma but Einstein's claim. It is an empirically unfounded, logic defying attempt to do science not simply by pure thought, but by fiat.

It is important to emphasize that, just as with the separate theories of those who derived the transformation equations empirically, the self stationary dogma is a hypothetical add-on having no integral relationship to the equations themselves. What this means is that there is no requirement, neither mathematical, logical nor empirical, tying the equations to either the aether affirming theories nor to Einstein's dogma. The equations are empirically valid, but their validity implies nothing with respect to the validity of either the theories of scientists like Larmor, Lorentz or Poincaré nor Einstein's self stationary dogma. Logically, therefore, all these add-ons may be, and I assert that in fact they all are invalid.

The self stationary dogma is conspicuously absurd. It says the transformation equation effects always occur to the other guy. But one's self is the other guy's other guy, so Einstein's dictum says the effects occur to one's self too, which is impossible. Consider: Time dilation, the slowing of time for a moving object, is one effect specified by the transformation equations. According to Einstein's claim, of two clocks moving inertially with respect to each other, each will run slower than the other! That's not simply absurd. It's absolutely impossible! Impossible or not, this absurdity has become a dogma in physics. There are enough discussions of this dogma to fill many volumes, but let me verify that its absurdity is universally recognized with only a few short quotes.

First, a representative quote from the popular literature. In an excellent little popular book entitled simply _Physics_ , David Bryant (1971, pg. 168) writes: "Moving objects appear to shrink in the direction of their movement relative to stationary observers. Moving clocks appear to lose time compared to a stationary clock. ... These outlandish predictions become even more weird when you realize that 'moving' and 'stationary' can equally well apply to either observer."

Next, an authoritative source, the _Encyclopædia Britannica_. The 1999 Standard Edition CD version says if one accepts Einstein's dogma then it follows that: "Whenever two observers are associated with two distinct inertial frames of reference in relative motion to each other, their determinations of time intervals and of distances between events will disagree systematically, ... if they compare their respective clocks, each will find that his own clock will be faster than the other; if they compare their respective measuring rods (in the direction of mutual motion), each will find the other's rod foreshortened."

(I'm in a bit of a quandary about how to reference this quotation, or about who wrote it. It's from the 1999 Standard Edition CD version. You can access it by entering "Relativity: The Special Theory of Relativity" in the program's search engine and then choosing this title from the options listed. When this page presents, choose Next Section then scroll down five paragraphs to the one beginning "Once this theoretical deduction is accepted ..." The above quote is excerpted from this paragraph.)

Lastly, the remarks of a recognized special relativity expert, the already identified Herbert Dingle. The 1971 (print) edition of the _Encyclopædia Britannica_ contains an article by Dingle on the philosophical consequences of relativity (Vol. 19, pgs. 101 3) which concludes in amazement that the obvious logical impossibility of the self stationary dogma is universally ignored in the physics community. Unfortunately, although as a special relativity expert Dingle was invited to participate in the festschrift honoring the mature Einstein (Schlipp, 1949), he chose not to challenge the self stationary dogma. Perhaps, one might reasonably suppose, Dingle did not wish to be critical in a venue intended to honor Einstein. This is unfortunate, for had he challenged the dogma, Einstein might have responded, and his response would have been most informative, for, as some of my sources complain, Einstein never provided a full explanation nor defense of the dogma.

That the self stationary dogma is absurd is and has always been obvious to everyone. But that this absurdity has absolutely nothing to do with Einstein's derivation seems to be oblivious to everyone. So let me emphasize the point. Einstein's absurd claim, the self stationary dogma, has nothing to do with the logic or mathematics of his derivation of the transformation equations. Absolutely nothing! It is an arbitrary add-on. If you have any doubts about this I refer you to Einstein (1961, Appendix I) where the equations are derived with math anyone who has had elementary algebra can follow. Einstein's "everyone must consider one's self stationary" dogma is never mentioned. It simply has no role whatsoever in the derivation.

The transformation equations, counterintuitive though their effects may be, are unequivocally empirically valid. However, the self stationary dogma is not. Let's consider some evidence.

(Before proceeding there is a point with respect to the transformation equations' empirical validation which must be noted. Contraction of size in the direction of movement has never been demonstrated and never can be. To do so a moving measuring rod would have to be stopped and placed for comparison along a stationary rod. But then there is no relative movement, and any contraction caused when one rod was moving would not occur. However, a clock (or any time dependent process) which has run slower when moving will show less elapsed time when it stops moving, so it can be compared with a stationary clock. Thus, time dilation can be, and has repeatedly been empirically demonstrated. Lorentz expended considerable effort attempting to derive equations for the contraction effect without time dilation and found it couldn't be done. Therefore, the equations are considered a package, and demonstration of time dilation is universally accepted as proof of both effects. I know of no one who has ever questioned this conclusion.)

**The Hafele-Keating study:** In the first of the above quotes illustrating the universal awareness of the self stationary dogma's absurdity, the word appear is used. This illustrates an opinion that since the dogma is logically impossible, the transformation equation effects must be an illusion, something which only appears to occur. This is a widespread opinion, understandably so since it is the only logical way to avoid the dogma's logical impossibility. Unfortunately, it doesn't solve the problem, for it is inconsistent with the facts. There is compelling evidence showing the effects are real ( _e.g._ , Bohm, 1965, pgs. 76-7). Indeed, the fact that they were originally derived as an empirical generalization means that the effects must be real.

A physics professor, J. C. Hafele, wanted to demonstrate this reality to his students. Specifically, he sought to demonstrate the so-called clock paradox. Einstein predicted that if a pair of identical clocks were set to the same time then one were placed on a rocket ship and sent on a circular voyage into space and back to Earth, upon its return the rocket-borne moving clock would show less time than the clock which remained stationary on Earth. Others, attempting to emphasize the counterintuitive nature of the predicted outcome replace the identical clocks with identical twin persons. But, of course, the principle is the same.

Exactly executing Einstein's rocket-borne experiment was not feasible. But Hafele did some calculations and determined that the speed of ordinary passenger jets suffices to produce a very small time dilation effect, one of nanoseconds or billionths of seconds. Nanoseconds are much too small to register on any ordinary clock, but Hafele knew they could be measured with atomic clocks. Therefore an equivalent clock paradox demonstration could be done by putting an atomic clock on a passenger jet. That's exactly what he and astronomer Richard E. Keating did.

They sent a set of four portable atomic clocks around the world on regularly scheduled passenger jet flights. (Hafele & Keating, 1972A and Hafele & Keating, 1972B. The A article presents the authors' view of the theory involved. The B presents their data.) They did the study twice, once circumnavigating Earth to the west and once to the east. After the flights they compared the time shown on each of the plane-borne atomic clocks against the precisely accurate time kept at the US Naval Observatory in Washington, DC.

The first thing to note about their results is the competent way these scientists handled their data. As was pointed out above where the erroneous notion that special relativity is a particular case of general relativity was discussed, general relativity specifies a time effect due to gravitational red shift. Specifically, clocks run slower the stronger the gravitational field they are in. A plane at altitude is in a slightly weaker gravitational field than one on the ground, so its clocks will run faster. For airline operations this nanosecond effect is much too small to be of concern. But since the time dilation effect Hafele and Keating sought to demonstrate also is in the nanosecond range, this gravitational red shift effect was a contaminating factor which these scientists quite knowledgably took into account and removed from their data. The fact that this required a completely separate and independent analysis than the time dilation analysis reflects the essential independence of the two relativity theories. If the common erroneous notion that the special theory is merely a limited case of the general theory were true, if it were possible to deduce time dilation from general relativity (And as Dingle explicitly emphasized, it is not.), then the time dilation analysis would have been a part of the general relativity analysis.

With respect to time dilation there are two questions at issue in this study. The first concerns the self stationary dogma, and the data unequivocally contradict it. The dogma says each clock must be considered to be stationary, and must therefore run faster than the other. Since this is impossible it's impossible to say what the data would be were the dogma true. Presumably on each replication, the eastward and the westward, there would be two different sets of data, one from the Naval Observatory perspective and one from the perspective of the portable atomic clocks. According to the dogma each of these data sets would show its own clock to have run faster. In fact, however, for each study replication there was only one data set. And this one data set was the same from both perspectives.

The second issue concerned whether movement associated time dilation would occur. Indeed it did; on both replications. On the eastbound trip the moving clocks' were slower than the stationary Naval Observatory clock, exactly as Einstein predicted and within reasonable experimental error of the amount specified by the transformation equations. But on the westbound trip the data dramatically contradicted Einstein's prediction. In diametric contradiction of his claim that the moving clocks would run slower, the westward moving clocks ran faster!

At first glance these results seem inexplicable. Einstein's clock paradox takes Earth as the stationary reference frame, the frame whose clock, the self stationary dogma says, always runs faster. Obviously the Naval Observatory is the equivalent in Hafele and Keating's modified design. So for Einstein's presumably stationary observatory clock to run slower when the planes flew to the west diametrically contradicts his prediction. But even if it were argued that the plane-borne clocks were stationary, then the eastward replication of the study contradicts the prediction. The study design can be construed in only two ways. Special relativity says one of two reference frames must be considered stationary. In this study that means either the observatory or the aircraft. But no matter which one is assigned this role, one of the study replications contradicts Einstein's special relativity prediction. Nor can the self stationary dogma save the case, for as just noted, the data clearly refute it. There is no out. The Hafele-Keating empirical evidence is unequivocally inconsistent with special relativity.

Nevertheless, these scientists explain their baffling results so rationally, realistically and reasonably their analysis must be correct. That isn't just my opinion. Their analysis has been in the scientific literature for almost half a century, and never questioned.

In order to understand Hafele and Keating' explanation of their seemingly inexplicable results they ask readers to (in their exact words): "Consider a view of the (rotating) earth as it would be perceived by an inertial observer looking down on the North Pole from a great distance." (Hafele & Keating, 1972A, pg. 166) Then they go on to describe mathematically their study clocks' movements with respect to this place in space. The math need not concern us. Its point can be made more simply by noting that from this spatial perspective the Naval Observatory on the eastwardly rotating surface of Earth is moving through space to the east. So when the plane-borne clocks are also moving east they are moving through space ahead of and more than the observatory. Since the portable clocks' movement with respect to space-a-great-distance-above-the-North-Pole is greater than the observatory's, the eastbound portable clocks experience the time dilation specified by the transformation equations. But when the plane-borne clocks are heading west they are actually reducing the amount of their movement with respect to space-a-great-distance-above-the-North-Pole. Therefore, the observatory's movement with respect to space is greater than the portable clocks', and the observatory clock shows the transformation equations' effect.

Hafele and Keating's explanation of their data is the only plausible way to explain their results, so it is unquestionably correct. However, it is the explanation which theorists like Larmor, Lorentz and Poincaré would give, an explanation which relates movement not to Einstein's "practically rigid body of reference", but to space! As has just been explained in detail, and as you can confirm for yourself in Einstein's little book, movement with respect to space, whether a great distance above the North Pole or any other space, is precisely what special relativity was designed to circumvent. That Hafele and Keating were well aware their analysis used space as their motion referent is shown by their theory paper (1972A) which refers more than once to movement with respect to space but never to anything which in any way refers to Einstein's "motion relative to a practically rigid body of reference". The two researchers attempt to make their analysis conform to Einstein's derivation by always calling their referent space inertial. But that is irrelevant and obfuscating. Space is space. Einstein derived the transformation equations with all their inertial restrictions precisely in order to avoid space, any kind of space, as the referent of movement. So you won't have to turn back to find it, let me repeat what he said: "We entirely shun the vague word 'space,' of which, we must honestly acknowledge, we cannot form the slightest conception." (Einstein, 1961, pg. 9)

So was Einstein wrong to say we cannot measure anything's movement with respect to space? Absolutely not! Exactly as he said, "we cannot form the slightest conception" of space. Or as other physicists more colloquially say, "There are no signposts in space." Therefore, since nothing marks any spot in space, it is impossible to measure anything's movement with respect to it. But as shown here and in many other scientific conclusions, _e.g._ , quarks, it is not necessary to measure something in order to use it meaningfully and fruitfully in one's scientific analysis. Indeed, Hafele and Keating did not measure movement referenced to space. They measured only the relative movement of the observatory and the aircraft. But, as they so accurately and compelling explain, the movement of the objects in their demonstration can only be understood when ultimately referenced to space.

Clearly there are two different movement referents involved in the Hafele-Keating demonstration. One, the movement with respect to space above the North Pole, was identified and provided the basis of the analysis. But it was not measured. The other, the only one measured, is the movement Einstein specified in special relativity, the relative movement of practically rigid bodies of reference, the aircraft and the observatory. There is, therefore, a source of confusion as to exactly the kind of motion involved in the Hafele-Keating demonstration, confusion which no doubt is responsible for the fact that neither these researchers nor the science community generally have recognized the fact that these results flagrantly contradict special relativity.

To clarify this confusion it helps to first specify a couple definitions. Let's call movement referenced to space "absolute movement" and movement referenced to a practically rigid body "relative movement". Though not universal, these definitions are widely used, and with them we can precisely state what Hafele and Keating did. To wit: They demonstrated time dilation arising from _relative absolute movement_.

Consider: In each of their replications, the eastward and the westward, Hafele and Keating measured only the portable clocks' relative movement, specifically their movement relative to the observatory. This does not mean the observatory did not move. As these researchers correctly pointed out, because it's on the surface of the moving (rotating) Earth, obviously it did. So as they went on to explain, the observatory underwent movement relative to space (a great distance above the North Pole). And space referent movement is absolute movement. The portable clocks shared this absolute movement. After all they flew above the rotating Earth. So since the moving Earth part of the absolute movement was the same for both the observatory and the portable clocks, it was unnecessary to measure it. All that was needed was to measure the difference, the relative absolute movement.

It is worth noting that the particular spot in space these researchers chose as their movement referent (a great distance above the North Pole) is completely immaterial. Because it is the same for both the observatory and the aircraft and therefore does not show up in the analysis, it could have been anywhere.

There is enormous and widespread confusion about the Hafele-Keating study. It is remarkable that two obviously competent scientists would provide an analysis in terms of absolute movement when they presumed they were studying relative movement. But the confusion is not confined to them. The editor and the one or two expert reviewers who oversaw publication of their report were similarly oblivious to this contradiction. Moreover, as already noted, Hafele and Keating's absolute movement analysis has been in the scientific literature for decades without being questioned. The erroneous conclusion that this study demonstrated the effects of einsteinian relative movement, therefore, is widespread. Obviously there exists a prejudice leading physicists to believe they see relative movement even while they endorse an analysis showing and explicitly stating that the movement at issue was absolute. Therefore, it is worthwhile to dwell a bit on this issue in hopes that by considering the facts from a slightly different perspective more people will be enabled to see that the data do not support this prejudice.

One of the meanings the **Merriam Webster** dictionary gives for "relative" is for two things to have a necessary dependence or connection. That is exactly the sense of the word when applied to special relativity. According to Einstein's theory, the two inertial reference frames have a necessary dependence. As Einstein developed them the transformation equations' effects are asserted to be caused to occur to objects at rest in the reference frame deemed to be moving. Further, the theory says these effects are caused to occur in an amount determined by the speed of the affected frame's relative movement, _i.e._ , its movement relative to the presumably stationary reference frame. According to special relativity, if this relative movement had been faster or slower such different speed would necessarily have caused a different amount of time dilation.

However, relative also can connote mere comparison without any connection whatsoever. For example, a comparison could be made of the relative amounts of hair you and I have. You almost certainly have more. But obviously your more abundant hair didn't make me bald. Equally obviously, if you get a haircut it is not going to have any effect on the amount of hair I have. Precisely the same is true of the Hafele-Keating data. As their analysis correctly concluded, the time dilation they observed in either of their platforms, _i.e._ , the observatory or the airplanes, occurred because of the platform's absolute or space related movement. Anything's absolute movement depends only on it and space. Any other thing's movement, whether it is relative or absolute, is irrelevant. If one platform had moved more or less this would have caused it to experience more or less time dilation, which would have altered the relative, _i.e._ , comparison, data. But its different movement would have had no causal effect on the amount of time dilation which occurred in the other platform.

Perhaps the best way to see the difference between einsteinian relative movement and Hafele and Keating's relative absolute movement is a thought experiment extrapolation of their westward replication. Diametrically contradicting Einstein's prediction, the time dilation it found was on the observatory clock. As Hafele and Keating conclude, this was because the observatory's relative absolute movement was greater than the plane-borne clocks'. To obtain the observatory's relative movement these researchers subtracted the plane-borne clocks' movement from the observatory's. Now consider what the data would have been if the aircraft carrying the portable clocks had been faster than they were. Specifically, if the planes had had a speed _through space_ exactly equal to the observatory's speed through space, their relative absolute difference would have been zero. This is so because the distance which Earth's rotation carried the observatory _through space_ to the east would be precisely equal to the distance the planes carried the portable clocks _through space_ to the west. And since the relative absolute movement would have been zero, no time dilation would have been observed. But the clocks' einsteinian relative movement would have been far from zero, for the clocks would have moved in opposite directions. Thus, had the westward clocks traveled at this higher speed, special relativity would have predicted measurable, if not appreciable, time dilation. But none would have been observed, an outcome which no amount of pro special relativity prejudice could have ignored.

This is not a speculation. It is only a slight extension of the Hafele-Keating demonstration. Indeed, a replication with these parameters probably is technically possible. A spot at the equator moves east through space at approximately 1,000 mph. A plane would have to fly west at approximately two thousand mph ground speed to move through space at the same rate. (Since the ground under the plane is moving east at 1,000 mph, if the plane's ground speed were only 1,000 mph it would only be maintaining its spot in space. It would have to double this speed to move west through space at the same speed as the spot on the equator is moving east.) I believe some military planes can achieve this speed. But if the study were done at higher latitudes where the Earth's circumference is smaller, such a study could be done with much slower planes. Such a study is well worth doing. To date the physics community has dogmatically refused to recognize that Hafele-Keating totally contradicts special relativity. By demonstrating zero time dilation in circumstances where special relativity must predict a perceptible amount physicists should be enabled to see their dogma for what it is.

Hopefully, this clarifies the confusion of relative and absolute movement in the Hafele-Keating study. But it also raises a question. Somehow all the study clocks responded to their own absolute movement, their movement with respect to space. But how? If there are no signposts on space, and there certainly are not, how can a clock's location in space be imparted to it? Or to phrase the question anthropomorphically, "How does a clock know where it is in space?" The Membrane model provides an answer. But before returning the discussion to the model and its ability to explain this and the two transformation equation effects it's appropriate to provide some closure on the special relativity issue.

**Special relativity wrap-up:** Nothing about the Hafele-Keating study is consistent with special relativity. Not surprisingly, since it is impossible, their data do not show time in each platform (both the observatory and the aircraft) to be faster than in the other. So the self stationary dogma unequivocally is contradicted. And as the authors' analysis compellingly shows, the amount of time dilation observed was explainable not as a result of the clocks' einsteinian relative movement, but rather as due to the clocks' relative absolute movement.

Nevertheless, though by their own analysis and explicit statement their data are inconsistent with special relativity, Hafele and Keating present their study as validation of it! To do so they distorted the meaning of the transformation equations as developed by Einstein. Instead of two "practically rigid" inertial bodies moving inertially with respect to each other, they changed the theory to say it concerns two things moving within the same inertial space. That is wrong! Anyone can prove this to one's self by consulting Einstein's derivation in the little popular book mentioned above (Einstein, 1961, Appendix I). Even if one cannot follow the algebra, one need only follow the derivation's accompanying verbal description to see that the Hafele and Keating claim is a gross error. Einstein mentions nothing referring to movement _within_ any space, inertial or other. In fact the derivation never mentions space at all. To use Einstein's own word, his derivation "shuns" space. It refers exclusively to inertial reference frames moving inertially with respect to each other. Beyond any possible doubt, the Hafele-Keating "two things moving within one inertial space" claim is a gross error. The most amazing thing about this, however, is not that it is so manifestly wrong, but that the physics community endorses it. ( _e.g._ , Baierline, 1996, pgs. 277-81.) As pointed out in the **Introduction** chapter, despite what its proper practice requires, irrational dogma is not absent from science.

Though Hafele and Keating are completely wrong in claiming their study supports special relativity, this erroneous claim is also completely consistent with physicists' common dogmatic practice. Every study demonstrating the validity of the transformation equations has been claimed to support special relativity and only special relativity ( _e.g._ , Taylor & Wheeler, 1992). But in blunt fact none does. Studies done on or in the air above Earth can not appropriately test Einstein's theory, and every such study has been so done. The problem is inertia. Special relativity demands the inertial restrictions Einstein used in deriving his version of the transformation equations. They are not simply desirable but unnecessary supplements. Inertial movement is the absolute requirement, the _sine qua non_ , the very essence of Einstein's space avoiding approach. Without these inertia restrictions, his elegant derivation of the transformation equations is impossible. Therefore, though his equations are mathematically identical to the equations as earlier empirically developed by others, his have the implicit but nevertheless inescapable restriction of applying only to inertial things moving inertially with respect to each other, restrictions which do not pertain to the empirical derivations.

No test done on Earth can satisfy special relativity's inertia requirements because Earth is not an inertial platform. As Hafele and Keating correctly note, it rotates. This means that every instant anything on or flying above earth is changing direction, and that is an acceleration, precisely what Einstein had to explicitly exclude from his derivation in order to remove space as the referent of motion. The acceleration produced by Earth's rotation isn't conspicuous, but it unquestionably exists. The Coriolis force or effect whereby rivers of air or water are deflected to the right in the northern hemisphere but to the left in the southern proves Earth's acceleration. Also, some of the most compelling time dilation demonstrations involve quantum entities falling to Earth from space ( _e.g._ , Bohm, 1965, pgs. 76-7). But as Galileo showed, any falling thing, no matter how tiny, is accelerated the same amount by earth's gravity. So these studies too are irrelevant to the inertia handicapped equations of special relativity.

Every test of the transformation equations yet done has been done on Earth, and no such test is appropriate for special relativity. To use a test done on Earth to test special relativity is equivalent to use of Prostate Specific Antigen (a test for prostate cancer which, of course, occurs only in men) to test for cervical cancer in women, or to use the Pap smear (a test for cervical cancer which only occurs in women) to test for prostate cancer in men. Both instruments are valid cancer diagnostic tests, but such uses are utterly and conspicuously inappropriate. So too are special relativity tests done on Earth.

Indeed, many physicists claim it is impossible ever to test special relativity appropriately anywhere in the universe. For example: Suppose there could be two identical clocks moving inertially with respect to each other somewhere far out in intergalactic space. To test whether this movement has caused time dilation the clocks or their data must be somehow brought together for comparison. Many ingenious notions for doing this have been suggested. Unfortunately, all are technically impossible now and for the foreseeable future. But many experts insist none of these, even if doable, could be done without changing the direction of ( _i.e._ , accelerating) at least one of the clocks or without encountering invalidating problems in simultaneously setting and/or measuring the clocks' times. Thus, a considerable body of expert opinion holds it to be impossible ever to appropriately test special relativity. To nevertheless hold it to be valid science is to abandon evidence, the very essence of science. Because the Membrane model can never provide empirical evidence it is rightly considered to be only a metaphysical speculation. If it is the case that special relativity also can never provide empirical evidence, as these many experts insist, then it too can be only a metaphysical conjecture.

It is doubly paradoxical that Hafele and Keating thought their study supported special relativity because not only did their data refute special relativity's predictions, their demonstration was flagrantly inconsistent with the inertial requirements of Einstein's theory. Neither clock platform (observatory nor planes) was inertial and the aircrafts' starts, stops and turns definitely accelerated the platforms' relative movement. Thus these author's thinking must have been governed by dogmatic pro special relativity prejudice. They are not alone in this. The fact that neither the editor and reviewers of their articles nor their readers have objected to these researchers' manifestly false claim that their study confirms special relativity compelling shows this dogma is widespread. In short, there incontrovertibly exists a widespread prejudice insisting special relativity can not be wrong, a dogma sustainable only by the most egregious distortions.

It is not surprising that this dogma began with Einstein. After all, one would be expected to have a supportive opinion of one's own theory. But it is surprising that Einstein should have never realized that special relativity violates a premise which, as in the EPR paper, he always insisted no reasonable person could accept, nonlocality. For in fact, special relativity is as nonlocal as quantum mechanics.

Consider: The transformation equations as derived by Einstein say of two things moving relative to each other, the movement causes one to experience size and time effects. But the theory involves no physical connection between them. None whatsoever. Indeed as far as the transformation equations are concerned the two moving reference frames not only have no connection, but they could be separated by the width of the universe. How then can whatever it is that controls time dilation control it? If there is no connection of any kind between the two practically rigid bodies, then how can any process on one of them be controlled by its undetectable movement relative to the disconnected other? Without implying Pascual-Jordan-like consciousness to things like clocks, this question can be stated more colloquially and perhaps more comprehensibly if phrased anthropomorphically. _Viz._ , How does the clock subject to time dilation, _i.e.,_ the one supposedly moving, know how much to slow its time if it doesn't have any way of knowing how much it has moved with respect to the other, supposedly stationary clock? Such disconnected, _i.e._ , nonlocal, effect is precisely the spooky action at a distance to which Einstein was so unalterably opposed.

Why, in the face of so many negative factors is special relativity treated by physicists with the kind of unquestioning deference with which devout religionists treat their respective sacred dogmas? Why, as Dingle pointed out in his _Encyclopædia Britannica_ article, do physicists persist in their refusal to acknowledge the logical impossibility of the self stationary dogma? I know of no data pertaining to these questions. But there are a few conspicuous facts which provide a basis for a presumptive answer.

First: As is shown by the usual name of the transformation equations, the Lorentz equations, when Einstein proposed his theory the equations he came up with were already known to be empirically valid. As such he seemed to be providing an explanation for already demonstrated but incomprehensible phenomena. If without this prior proof that the effects are real he had proposed equations specifying such counterintuitive effects as time dilation, he likely would have been ignored.

Second: By the mathematical nature of their discipline physicists are disposed to consider anything like Einstein's nonempirical, pure thought mathematical conclusion to be definitive. Or to state the matter more bluntly: Physicists tend to consider math to be absolute truth and therefore necessarily more reliable than evidence. Indeed, string theory critics (Hossenfelder, 2018; Woit, 2006) have said precisely this.

Third: Einstein's derivation is not simply math, it is beautiful, elegant math. Even though I have not had the benefits of physicists' extensive mathematical training, I find it requires an act of intellectual discipline to doubt the conclusion of so elegant a derivation.

Forth: Some very significant conclusions have been derived from the transformation equations. Most widely known, of course, is E=mc2, derived from the equations by Einstein himself. If one believes, as physics students are taught (indoctrinated?) that the equations' validity is not an empirical finding, but rather something proven with Einstein's pure thought, to suppose that such thought might be in error is to question these unquestionable conclusions.

Fifth: Special relativity was specifically designed to avoid the dubious aether concept. As Einstein said, his theory makes the aether superfluous. Therefore, since there is abundant solid reason for rejecting the aether concept advocated by the likes of Larmor, Lorentz or Poincaré, special relativity seems the only possible alternative.

Sixth: The phenomena predicted by the equations are profoundly counterintuitive. The validity of these predictions is unquestionable, but understanding how something like the passage of time could be affected by an object's movement taxes the imagination. Einstein's theory can not explain this, but it offers an out, an excuse. It says there is no human way to understand the equations' effects, so we should surrender this unachievable understanding goal and accept that the math alone suffices.

Some of these conjectures are simply facts. The first three are. Their destructive role in supporting a conspicuously invalid theory can be eliminated only by acknowledging their role in maintaining a dogma. But the other conjectures can be answered.

The answer to the forth conjecture, the claim that the unquestioned validity of things like E=mc2 proves that Einstein's pure thoughts must be true, is that these developments are based on the equations themselves, not on Einstein's empirically disproved pure thought derivation. We can trust that the empirically derived transformation equations are valid because they are merely a mathematical description of the abundantly replicated Michelson-Morley data. Once FitzGerald's suggestion of size contraction is accepted, the equations become the only way to mathematically describe these data. Since it is impossible, as Lorentz found, to have size contraction without time dilation, and since time dilation has been repeatedly empirically shown, the equations are demonstrably valid. In particular, since the empirical derivations of the equations involve no inertial restrictions, the fact that all the time dilation demonstrations have involved acceleration is simply immaterial. Thus, all those great developments attributed to special relativity, _e.g._ , Einstein's E=mc2, or Dirac's electron equation, or the Chandrasekhar limit, are based on the equations, not on Einstein's pure thought metaphysical theory. Therefore, if physics students were taught this, rather than the dogma that special relativity is pure thought revealed truth, we could retain all the scientific achievements based on them but escape all the problems and absurdities of special relativity.

As noted in the **Special relativity background** section, this approach has been suggested by none other than John Stewart Bell, one of the brightest of the Twentieth century's profusion of brilliant physicists, brilliance shown by his identification of the error in von Neumann's hidden variable disproof, an error to which the physics community unthinkingly submitted for decades. More importantly, Bell's brilliance is shown by his invention of the nonlocality inequality, something which has revolutionized physics. In 1976 he suggested (Bell, 1987, Chapter 9) that the teaching of special relativity focus on the equations as originally empirically derived. One must wonder why the physics community has ignored this wise suggestion of one of its greatest. One must wonder why physicists who have had different ideas concerning various phenomena addressed by special relativity, have not constructively criticized Einstein, but, as Ohanian (2008, pg. 99) says, "always treated him as a sacred cow".

The last two conjectures, five and six, are addressed in the next chapter where it is shown that the Membrane model not only avoids the nonexistent aether but also can plausibly, mechanically explain the transformation equations' counterintuitive effects, time dilation and size contraction.

With these Membrane model explanations the irrational, dogmatic support of special relativity should dissolve and allow us to honestly and candidly face up to special relativity's many, serious problems. Strictly speaking, because of its inertial requirements the theory can not be tested. Therefore, it can not be a scientific hypothesis. At best it can only be a metaphysical speculation. If however, one chooses to ignore the theory's inescapable inertial restrictions, and accepts the data from tests involving acceleration, as for more than a century the theory's dogmatic supporters have, then the Hafele-Keating study also is relevant. And while in that case this study validates the transformation equations themselves, it also unequivocally empirically disproves Einstein's pure thought theory.
Membrane Model Resolution

It's unlikely that anyone has ever done an opinion survey among physicists asking "Why do you continue to advocate special relativity despite its irresolvable problems?". But we don't require the data from such survey to know the probable main reason: The aether. For compelling reasons (some of which are considered in the **Ambiguous Data** chapter) physicists are convinced it does not and can not exist. But those scientists who empirically derived the transformation equations encumbered and contaminated them with theories including the aether. Not special relativity. Indeed, as noted in the **Special relativity background** chapter, some have erroneously concluded special relativity disproves the aether. And while this belief is in error, as Einstein himself pointed out, his theory conspicuously excludes the aether. Therefore, for those determined to avoid it special relativity seems the only choice.

That, however, was in the past. Now the Membrane model increases the options, for it also makes no use of the aether concept. But it is clearly superior to special relativity in this regard. For while the theory merely sidesteps the aether issue, the model offers a solution. To wit: Radiant energy is not a wave _per se_ , but rather a membrane across which a wave of identifying information sweeps. Thus, the model explains the abundant evidence for a wave aspect of things like light, something special relativity cannot do. But it does so without any need to postulate anything like an aether. Of course, the Membrane model is only a metaphysical speculation. But as the previous chapter demonstrated, at best so too is special relativity. However, special relativity contains the conspicuously illogical self stationary dogma and suffers from the Hafele-Keating empirical disproof, while the Membrane model is burdened by no such problems. So it is manifestly the superior metaphysical hypothesis.

Another reason why physicists adhere to problem plagued special relativity concerns the transformation equations' counterintuitive effects. The aether theories proposed by those who empirically derived the transformation equations sought to explain these effects. Even were one willing to accept the existence of an aether, however, these explanations are obsolete. Special relativity. however, makes no attempt to explain these phenomena. Rather, it holds the math alone to be fully sufficient and understanding therefore to be unnecessary, even unscientific. Thus, special relativity only dodges the issues of size contraction and time dilation. But the Membrane model offers more than excuses, it suggests mechanical explanations. To wit:

**Time dilation:** The first effect the Membrane model can explain is time dilation. Unfortunately, the first thing to say in order to explain its explanation sounds utterly preposterous. But bear with me for a moment and you will see it is not. It only seems so because we never look at the matter this way. The seemingly preposterous proposition is this: It is impossible to measure time.

This sounds inane because there are clocks and watches everywhere. In all probability you are wearing one on your wrist as you read this. But what is the fundamental thing which all these clocks and watches measure? It isn't time _per se_. It is change. Just as there are no signposts in space, there are no tattoos on time, nothing we can see or perceive in any manner whatsoever. We only know time passes because things happen. Therefore we can only measure the passage of time by counting happenings, by counting changes. Perhaps the most compelling proof of the fact that we can only measure time by counting changes is the universal image of stopped time: All changes are imagined to stop. Indeed, the frequently used image of stopped time pictures flying objects and/or jumping people (or other animals) suspended in space unmoving and unchanging.

Time is the metaphysical dimension which we suppose to underlie happenings, instances where change occurs. And like all other metaphysical entities, it cannot be measured, either because it doesn't really exist (Einstein once said time is a persistent illusion) or because, like space and the Membrane model's energy exchange process, time itself is imperceptible. Time bears no hallmark. Ergo, while changes can be and are measured, the time dimension we suppose to underlie changes can not be.

A consideration of the various ways by which we measure the passage of time shows that indeed, we measure time by measuring changes. Probably the most intuitive time measurement is by changes in the position of the sun. One of the earliest devices, the hourglass, measured time by the changes in the amount of material which flowed from the upper to the lower chamber. The earliest mechanical clocks counted the number of times a pendulum changed positions from one side to the other. And ordinary mechanical clocks and watches count the number of oscillations, _i.e.,_ changes of position, of analogous devices. Even the atomic clocks Hafele and Keating used in their study only count changes. Specifically they count quantum state changes in the cesium-133 atoms at their heart, changes which occur 9,192,631,770 times a second.

As these examples demonstrate, the duration of anything or any process is determined by the thing or process itself. Thus geologic changes, such as the erosion which created the Grand Canyon, are slow. Changes in the cesium-133 atom are fast. And sun positions change at a rate intermediate between these. In contrast with the various durations of various things or processes, our common conception says time itself passes at a steady, constant rate, a rate that is completely independent of everything else. According to this view the passage of time itself is unaffected by the rate at which things change in time. Thus time itself is no faster for cesium atoms than for geologic ages.

Though common, this is also how the great Newton defined time, and therefore how time is considered in classical physics. But with the discovery of time dilation Newton's definition became suspect, for time dilation seems to say the passage of time for any particular thing depends upon the speed with which that thing moves. Since the discovery of time dilation generations of physics teachers have ridiculed the common, Newtonian time notion. They say it implies the existence of a great grandfather clock in the heavens ticking off universal seconds, seconds which are simultaneous and identical everywhere in the universe. Such clock obviously doesn't exist.

Indeed, there is no universal grandfather clock, but there may well be universal time, time in which each second is simultaneous and of the same duration everywhere in the universe. For the conclusion that time is not universal is based on an unexamined assumption, a prejudice which, interestingly enough, is precisely the kind of assumption Einstein's special relativity paper questioned. Special relativity concerns not only the physical effects of motion. It also concerns the issue of how scientists measure things, and how one's method of measurement delimits and determines the meaning one can apply to one's conclusions ( _e.g._ , see Bridgman, 1983). And the conclusion that time dilation shows there is no universal time is based on the implicit assumption that clocks measure time itself. But as has just been noted, they do not. To restate the fact: We measure happenings or changes, not time _._ In fact, therefore, time dilation is a misnomer. The phenomenon to which it is applied is abundantly empirically established. But in order to make it clear that clocks do not measure time itself the phenomenon should have been called something like rate-of-changes dilation.

We commonly, unthinkingly assume time and our measured rate-of-change are identical. They may be. But this is an unexamined, naive presumption. Moreover, failing any means of directly measuring time, this naive assumption can never be empirically confirmed. Logically, therefore, it is possible for the passage of time and the rate-of-changes by which we measure time not to be the same. Logically it is possible for happenings to slow, or even to stop, while time continues passing at its constant, universal, self-sustaining rate just as Newton and our common prejudice presume. The Membrane model assumes this is in fact the case, and this separation explains time or rate-of-changes dilation. Specifically, the Membrane model asserts that it is happenings, not time itself, which movement slows.

An analogy may help clarify this idea. Consider music. Notes differ in the number of beats they are given. Whole notes each receive four beats, quarter notes each receive one beat, and four sixteenth notes fit in one beat. But the duration of a beat depends upon the tempo of the song being played. Presto is a very fast tempo. Largo a very slow one. Thus the duration of a whole note in a presto song will be much less than a whole note in a largo song. Time doesn't speed up or slow down for different compositions. Tempos do.

The rate-of-change of physical events may be likened to tempo. Thus geologic ages and whole notes are relatively long duration events in their respective domains. Cesium-133 atom changes and sixteenth notes have relatively short durations in their respective domains. Changes in the sun's position and quarter notes have moderate durations. But just as the actual duration of a note depends upon a song's tempo, the Membrane model claims physical things also have a tempo, a rate-of-change controlled by the speed with which the physical thing moves through space. And to make this idea clear the remaining parts of this essay will use the term "tempo dilation" for the phenomenon usually referred to as time dilation.

This is how tempo dilation occurs.

Just as did Newton, the Membrane model assumes reality occurs in three Euclidian dimensions of space and one dimension of time, a time that is constant, universal and independent of anything that happens. Recent decades have seen endless promotion of the Big Bang cosmogenesis hypothesis, which assumes the non-Euclidean four dimensional curved spacetime of general relativity theory. This widespread Big Bang acclaim has mislead many to believe Newtonian space and time have been disproved, but this most definitely is not the case. In fact quantum mechanics is based on Newtonian space and time (Rothman and Sudarshan, 1998, pg. 213), and quantum mechanics is universally considered to be science's most valid theory. In fact, one of the major problems facing modern physics is to try to reconcile general relativity's hypothetical four dimensional spacetime with quantum mechanics' abundantly confirmed Newtonian space and time. Therefore, it is neither unscientific, implausible nor unreasonable, but in fact highly appropriate for the Membrane model also to be based on Newtonian space and time.

Assume there is a reference frame moving in this Newtonian space and time. Unlike the reference frames in special relativity, neither this reference frame nor its movement need be assumed to be inertial. The Hafele-Keating study unequivocally empirically proved movement occurs with respect to space. So all the inertial requirements Einstein built into special relativity in his attempt to escape space-referenced movement are irrelevant, and the spinning, orbiting Earth may be taken as this moving reference frame.

As I hope was clearly conveyed in the **Fundamental Assumptions** chapter, according to the Membrane model, fundamentally the only thing that can happen, the only happenings or changes that occur in actual reality, are quantum interactions, _i.e._ , instances where energy is surrendered from real to virtual quantum entities. Of course there are macro happenings, but they are actually ongoing cascades of uncountable vast multitudes of quantum interactions.

Now consider how the membrane model describes a quantum interaction. A virtual matter pair emerge from nothingness at a particular spot in space. If a matching real, _i.e._ , energy carrying, membrane displays its identity in this spot there is a possibility of a quantum interaction whereby the real entity surrenders its energy to the virtual one then disappears into nothingness. Underlying this exchange is a recognition process by which the virtual matter's match to the passing real membrane is determined. Just how this process works is beyond human knowing, but if the Membrane model obtains, such a process must occur. Though this recognition process may seem instantaneous to us, it must take time for it to happen. From our human perspective the time required is infinitesimal. Nonetheless, and tiny though it is, a bit of time is required. Therefore, the faster the quantum membrane passes the point in space where the virtual matter has emerged, the lesser the chance of this process occurring, and the lesser the chance of a quantum interaction.

The moving reference frame is composed of enormous numbers of interacting quantum entities. But all are moving through space at the same average speed, the speed of the reference frame's movement. Therefore, the faster the reference frame moves through space, the lesser time there will be for the recognition process to occur. Thus change, _i.e._ , quantum interactions, will be less frequent the faster the reference frame. And at the limit, there will be some speed so fast that the recognition process can not occur. For any membrane moving through space at or above this speed no interaction can occur.

Thus the speed of a passing quantum entity membrane controls the probability of a quantum interaction. But this has no effect upon time. Indeed, the constancy of time is responsible for the effect. So according to the Membrane model, the phenomenon traditionally called time dilation in fact involves no dilation nor change in the rate of time's passage. Instead, the speed of a membrane's passage controls whether a quantum interaction occurs. And the fewer happenings resulting from faster passage is appropriately, indeed, properly called tempo dilation, not time dilation.

**Location in space:** It is possible now to redeem the promise made above, the promise to explain how a clock's position in space is marked upon it. As has been noted, according to the Membrane model a macro entity such as a clock is not a substantial object. Rather it is an ongoing action, the continuing dance, if you will, of billions of billions of billions of interacting energy exchanging quantum interactions. Each of these interactions takes place at a particular location in space, the place where a virtual quantum entity pair happen to emerge from nothingness. So according to the Membrane model the multitudinous quantum interaction dance which we humans perceive as an object is inherently occurring at a particular location in space. Thus the model needs no process nor method for determining anything's location in space. An interaction's location in space is an inherent, essential fact of its becoming a part of actual reality. Einstein unquestionably was correct when he said we humans cannot measure anything's location is space. But this is immaterial because we humans play no role in the effects predicted by the transformation equations. According to the Membrane model these effects are completely objective processes.

The Membrane model does not solve only the problem of how things locate themselves in space. It also avoids the location problem Einstein created when he invented special relativity. In the **Special relativity wrap-up** section, above, it was noted that the affected reference frame in Einstein's theory has no connection with the unaffected one. Yet the theory sys the amount of the transformation equations' effects depends upon the speed of the frames' relative movement. But with no connection between them, what could possibly control this?! Or to state it colloquially: How does anything in the affected frame know how much of the effect to cause if it has no way of knowing how fast it is moving relative to the other frame?! As it never does, special relativity offers no explanation. With einsteinian relative movement this problem is inherent and inescapable. But with the absolute, space referenced movement of the Membrane model this problem simply does not arise. And as the Hafele-Keating evidence shows, in fact movement is absolute.

**Size contraction** : Because it can not be measured, size contraction tends to get lost in discussions like the above, _i.e._ , considerations of the empirical evidence for the transformation equation effects. But we should remember that it was the size contraction effect, first suggested by FitzGerald then later independently conceived by Lorentz, which led to the empirical derivation of the transformation equations. So this effect is of fundamental importance to this discussion. As you now well know, special relativity can offer no explanation of the size contraction effect. But as will now be explained, the Membrane model can.

The first thing to do to describe the Membrane model explanation of size contraction is to reiterate the model's conception of an object. Though at the human level objects seem to be substantial, fundamentally they are not. Fundamentally objects are not objects but ongoing processes, temporal pointillism in which each point is an energy exchanging quantum interaction. So for this model an object doesn't exist as such. Rather, it is continually being created by an ongoing sequence of unimaginable billions upon billions of quantum interactions. To reiterate: Each of these interactions occurs when a matching virtual entity happens to emerge at a point in space where a passing real, energy carrying entity is displaying its self identifying information.

The kind of virtual matter to emerge at any location in space is controlled by the kind of real matter there. So the area where an object is being continually created, the area which at the human level we see as occupied by the substance of the object, demarcates an arena where virtual matter pairs appropriate to the kind of matter composing the object continually emerge and either are made real by an energy exchange, thereby contributing to the continuing re-creation of the actual object, or dissolve back into nothingness. At our level the edges of this area are precise and exact. But at the level of the virtual energy pairs this is not the case. Rather, there will be a gradient extending out at the edge of the arena in which the energy exchanging process is occurring such that the density of emerging virtual pairs will progressively diminish at progressively greater distances from this edge. These distances, of course, are miniscule when considered from the human level, probably even much smaller than nanometers.

It is the quantum interactions occurring at the edge which determine where the continuing object recreation process will continually remake the edge. All things considered, the probability of an interaction occurring to one of the edge located virtual pairs is no different from the probability of an interaction by a similar pair in the middle of the arena demarking the object. But the consequences of an interaction being missed at the edge will be much more significant than the consequence of a missed interaction in the middle, say, of this arena. Specifically, when a pair at the edge is not involved in an interaction, the edge, which is defined by fewer virtual pairs than in the middle of the object arena, will be reduced. In short, faster moving membranes will lead to fewer quantum interactions. In the middle of the arena demarking the object the resulting reduction in interactions will only reduce the density of interactions. But the reductions of interactions at the edge will tend to contract the edge, making the object smaller.

Thus the Membrane model offers a plausible mechanical mechanism for the size contraction resulting from more rapid movement of an object. There is a caveat, however.

The edge reducing process just described will occur at all edges of the object. But the transformation equations provide for constriction only at the edge of the object facing its movement. This may seem to invalidate this Membrane model size constriction process explanation, but it does not. Recall, the equations were developed in two entirely different ways. Larmor, Lorentz and Poincaré developed them empirically from the Michelson-Morley data, data which pertained only to one dimension of the object, the dimension at right angles to the direction of the light in the study. The other dimensions simply were not reflected in the data. So if the constriction were on all dimensions, as the Membrane model holds, the M&M data would never show it. Thus, although the empirically derived equations predict no constriction in the object's dimensions at right angles to the movement, this does not mean there was none. It means only that these dimensions were not measured so they could not enter into an empirical determination. On the other hand, special relativity developed the equations theoretically, so according to this theory size constriction must occur only in the dimension of the movement. Thus, this theory does contradict the Membrane model's size contraction explanation. But as the **Special relativity wrap-up** section concludes, this theory is empirically unverifiable, at best, or empirically refuted, at worst. Thus, while the Membrane model's prediction that size contraction occurs in all dimensions is inconsistent with special relativity, this does not invalidate the model because special relativity itself is either irrelevant or invalid.

### Conclusion

Final Thoughts

So there you have it, the Membrane model. Or at least, you have it if you are willing to believe it. To repeat what was said at the start of this book, whether or not you believe it is entirely up to you. It is because the model is a metaphysical speculation, something ultimately supported only by each individual's particular convictions, not a scientific hypothesis provable by evidence. Indeed, by the nature of the quantum interaction process at its heart the Membrane model can never have the supporting evidence required to make it a science conclusion.

Nevertheless, there are excellent reasons for believing it. Foremost, insofar as I am aware, (there are literally dozens of quantum interpretations, and I certainly don't know them all) Pilot-Wave is the only other interpretation able to explain the wave-particle paradox. But the Membrane model also explains many other mysteries, _e.g._ , nonlocality, quantum jumps and tempo ( _i.e._ , time) dilation, whereas Pilot-Wave explains nothing else. Moreover, as detailed above, Pilot-Wave is burdened with the inconceivable and empirically unsupported notion of universal instantaneous nonlocality. So the Membrane model seems clearly more believable.

Furthermore, surprisingly and impressively, although the Membrane model was invented only to explain the quantum mystery, it was found also able to explain the completely unrelated phenomena of special relativity. This unsought, gratuitous ability strongly suggests the model does indeed describe fundamental physics functioning.

However, the Membrane model also specifies a condition which is exceedingly counterintuitive, the actual _vs._ potential division of real matter. Notwithstanding the fact emphasized by Heisenberg, the fact that evidence indicates matter is often only potential, the notion of substance is integral to our intuitive conception of the nature of things. Thus many persons will be unwilling to surrender this intuitively compelling assumption. Accordingly, they will reject the Membrane model.

In all probability some readers will accept the Membrane model, others will reject it, and still others will be left without an opinion, or maybe even in a decision dilemma. For these latter persons it may help for me to detail my own convictions. You might expect them to be wholehearted belief in the Membrane model. They are not. As a quantum interpretation, I do unequivocally believe it. Not only does it explain the fundamental wave-particle paradox, it also explains many other quantum mysteries. It also explains the completely independent transformation equation effects usually attributed to, but not explained by, relativity. But most importantly, the Membrane model is objective. The subjectivity of the most widely accepted quantum interpretation, Copenhagen, the notion that someone who is not real must make a measurement in order to make reality real is logical nonsense. I do not, can not and will not believe it. Beyond any doubt the quantum data are baffling. However, Copenhagen's attempt to explain these puzzling data with an absurdity only compounds the confusion.

However, I do not think the Membrane model is true. By "true" I mean the kind of ultimate knowledge Einstein sought. That kind of knowledge, I firmly believe, is humanly unattainable. Indeed, I think it appropriate that Einstein was a child of twelve when he transferred his desire for knowledge of ultimate truth from religion to science, for I think the goal is childish. It is a desire to see reality as if it were an object separate from us. But a fundamental and inescapable truth is that we are locked inside reality, hence we can not possibly see it as an external God could see it.

Elsewhere (Miklich, 2014) I have detailed my reasons for considering science, although unequivocally humanity's greatest knowledge gaining tool, to be incapable of discovering Einstein's kind of truth. Though subsequent research has muted one of my examples, gravity waves, the essentials of my argument still hold, and interested readers may refer thereto for a more extensive presentation. But the following suffices to explain the argument's main points.

Despite the propaganda dished out in virtually every science class, no science conclusion is a natural law. Absolutely beyond any possible doubt every science conclusion is something some human(s) invented. These inventions are intended to precisely state or to be isomorphic with natural law, _i.e._ , to be truth. Unfortunately, there is no way to confirm this. For all we can ever know these so-called natural laws may be no more than mnemonic devices, elaborate stories we invent and tell ourselves in order to make our makeshift knowledge easier to remember and use. The successful technologies based upon these supposed natural laws are commonly believed to prove their truth. But they do not. A couple examples suffice to show this.

The amount of technology based on Newtonian physics is immense. One of its fundamental claims is that there exists a force, gravity, which among other things holds satellites in orbit. Repeatedly persons in space programs have noted that these programs are based on Newtonian physics. Yet many, apparently most, physicists believe there really is no gravity force. Rather, they accept general relativity theory which says that what Newton attributed to a gravity force is really objects following their inertial paths through curved four dimensional space-time. So according to these physicists, the vast body of technology based on Newtonian physics does not prove it to be true natural law.

What these physicists are saying is that something may work, not for the reasons supposed, but rather for unknown other reasons which have the same or similar effect. And what I'm saying is that we humans obviously don't know everything. Therefore, any and all so-called natural laws well may work for alternative reasons which we don't and may never know; indeed, for reasons which humans may simply not be smart enough to know.

Because general relativity theory is abstruse and mathematically demanding, its example is a bit obscure. A more readily comprehensible example is provided by the disease malaria. At one time it was thought to be due to bad air, the kind of foul air occurring in a swamp. Indeed, the very name malaria simply means "bad air." If when this bad air idea was current anyone had drained a swamp to reduce the bad air and thereby reduce the incidence of malaria in its locale this would have been successful, supposedly proving the truth of the bad air idea. But of course, we now know that swamp draining is effective not because it reduces bad air, but because it destroys the habitat for the mosquitoes which transmit the malaria causing pathogen.

In general, with malaria as with gravity, we can never be certain things which effectively work do so for precisely the reasons we suppose. Because we don't know everything, and never can, there always remains a possibility some unknown factor is really responsible for our technological successes. If one's only concern is with technological accomplishment, this doesn't matter. But if, like Einstein, one's concern is with ultimate truth, then such possible unknown factors are an insuperable obstacle.

In short, there is only one way to prove any scientific conclusion is in fact a natural law. The law and the conclusion must be compared. But this is impossible. We do science precisely because we do not know natural law, and failing such knowledge such a validating comparison can never be made. Even the conception of natural law itself is beyond any possible confirmation. Natural law might exist. But it might not. Reality may be controlled in an entirely different manner. Indeed, substantial numbers of people are convinced it is. These people hold religious convictions that supernatural beings are in control of everything either immediately or ultimately. I do not subscribe to any of these convictions, but most people do. They might be wrong, but there is no way to disprove their belief.

So the notion of natural law is itself metaphysics. As a practical matter, this is immaterial. Even if natural laws do not exist, the concept is of indispensable utility to technology. And therein lies the crux of the matter, utility.

There are two general and opposite purposes for doing science. One is to discover what works, _i.e._ , utility, and the other is to discover truth. While any particular scientist's motives may be a combination of both, a combination which may fluctuate from time to time, for some particular scientists one or the other goal is dominant. That was the case with quantum mechanics' two great antagonists, Einstein and Bohr. Einstein sought ultimate truth. He once said he wanted to know if God had any choice in creating the universe. As speculated in the **Introduction** chapter, this desire to find transcendental knowledge was his lifelong goal, a goal which as a boy he pursued in religion, but which he shifted to science when he decided the answers found in the Bible could not be true (Schlipp, 1949, Sec. I).

Niels Bohr, however, focused on the utilitarian goal of science. Since his thinking is much less widely known than Einstein's, it's helpful to document this contention with a couple quotes. Once Bohr said: "It is wrong to think that the task of physics is to find out how Nature _is_. Physics concerns what we can say about Nature." (Bell, 1987, pg. 142) Or again: "Our task is not to penetrate into the essence of things, the meaning of which we don't know anyway, but rather to develop concepts which allow us to talk in a productive way about phenomena in nature." (Pais, 1991, pg. 23)

On this point I agree with Bohr. Your opinion is entirely up to you. It is because there is no _a priori_ way to choose between these goals. Neither is guaranteed to avoid error. For example, both these geniuses (and both most certainly were geniuses) advocated logically preposterous conclusions. Einstein did with his self stationary dogma, and Bohr did with the notion that non-real entities must make measurement to make potential reality real. But in my view Bohr's utilitarian science is achievable, while Einstein's ultimate truth is not.

That is why I do not claim the Membrane model is true. Indeed, it is an attempt to answer the kind of questions Einstein asked. But by its very nature it is impossible ever to know whether it does, _i.e.,_ whether it is true. It is and always can be only a metaphysical speculation.

Nevertheless, until anyone can come up with a better guess, the Membrane model is what I'll believe.
Dear Reader:

You would have abandoned this book before here if you did not have an interest in the quantum mystery. But an interest does not imply what opinion you have of the Membrane model. It may range anywhere from enthusiastic endorsement to categorical rejection. Whatever your opinion, your response should be the same: _Viz._ , Share it.

If you believe the Membrane model explains the mystery, you will want to do what I will try to do, bring the model to the attention of as many potential believers as possible. However, if you think the model is in error you can not stop we believers from spreading the word, so you will want to publicize your objections which, much as I am loath to admit it, may be sound and worthy of consideration. My guess, however, is that most readers will be between these extremes. Most readers probably will want to consider the issue further, and they, more than anyone, will want to tell others about the Membrane model in order that these many others will consider it from many different perspectives, a diversity of views which then may help them form an opinion.

With conventionally published books there are well developed means for accomplishing such wide consideration. But regular publishing is not an option for this book. It usually takes a year, sometimes more. But I am 85, and while reasonably healthy for my age, obviously the probability of my not surviving for such a period is much less than that of the usual author. And since I have developed the Membrane model in isolation, there is no one to whom a publisher could turn should I not survive to accomplish what regular publishing may require, _e.g.,_ rewriting.

So to preclude the possibility of the promising Membrane model dying because I do, as soon as this book is finished I will self publish it at Smashwords.com. And because I am selling ideas not books, I will make it available free.

This creates a couple problems. First: Smashwords.com is a commercial endeavor. While they generously allow books published on their site to be free, nevertheless those of us who take advantage of this in fact are freeloaders. So I'd like to ask you to look over the extraordinarily large selection of books available at this website and buy anything which appeals to you.

The second problem is that persons with an interest in the quantum mystery are unlikely to spontaneously look for relevant works at a website which primarily provides works of fiction. So though this method of publishing gets the Membrane model idea out, it also puts it in a niche where it may seldom be found.

Therefore, I ask you to bring this book to the attention of any and everyone whom you think might find it of interest. A major publisher's web page says every author should do this. It recommends social media as the most fruitful method. However, I have spent my time reading books about, thinking about and writing about the quantum mystery. Thus I am ignorant of social media. I trust you are not as deficient in the respect as I and can and will make good use of this publisher's suggestion.

Many, many thanks,

DRM
Appendix

The **Quantum Jumps** subchapter's description of the jump of a hydrogen atom's electron from the base to the second envelope (orbital) may not be completely clear. If not, the book cover may help. It presents a schematic diagram of the quantum interaction which the Membrane model holds to underlie this jump. The cover is a diagram, not a picture. The four quantum entities involved are considered to occupy the same point in space, and there is no way to picture this.

The diagram is color coded. Virtual entities are in black; real, _i.e.,_ energy carrying, entities are in red; and orange indicates entities which are exchanging energy.

There are four lines in the diagram. Each line represents a successive stage in the interaction. The first line shows the four quantum entities entering the interaction. The second shows the energy exchange. The third represents how the entities which have surrendered their energy realign themselves. The fourth line shows how the quantum interaction is completed.

**Line one:** Four quantum entities enter the exchange, a virtual pair, a real electron and a real photon. The virtual pair is represented by two touching black circles, one labeled VP2 for a virtual positron and the other VE2 for a paired virtual electron. The 2 in each label indicates that these virtual entities have the potential to carry the amount of energy of an electron in the second envelope of a hydrogen atom.

The two real entities are each displaying their identity at the interaction point. The electron, E1, is represented by a circle which may be interpreted as showing the electron to envelop the hydrogen nucleus. The 1 indicates that the electron is in the lowest hydrogen energy envelop, the base state. The photon, F2 1, is represented by a torpedo-like figure open to the right. This opening and the wavy lines on the figure are to indicate that the photon has come to the spot of the interaction from some unspecified different location. The numerals 2 1 indicate that the amount of energy carried by this photon is exactly the amount of energy needed to add to a base state hydrogen electron to raise it to the second envelope energy level.

**Line two** : This line represents the energy exchange. The virtual positron, VP2, is unchanged. However it is detached from the virtual electron which is now shown in orange because it is receiving the energies from the theretofore real electron and real photon. This exchange is indicated by the arrows from the theretofore real entities. Because their characteristic is being modified, as shown by their orange color, none of the entities involved in the energy exchange are labeled.

**Line three:** This line represents how the entities are reconfigured after their energy exchange. Again, the virtual positron, VP2, having not been involved in the exchange is not changed. However, the theretofore virtual electron, VE2, has now become real. Its new character is shown by its red color and its new label, E2. The two theretofore real entities, the electron and photon which have surrendered their energy to E2, have now become virtual, VE1 and VF2 1. To show that they no longer carry energy they are drawn in black. And they are drawn as touching, which is intended to show that they are combining into a single virtual entity.

**Line four:** This line shows the result of the quantum interaction. The new electron, E2, is shown as a red circle which may be interpreted as showing the electron to be in the hydrogen atom's second energy envelope. The two theretofore real entities which have surrendered their energy have united to form a virtual electron capable of carrying sufficient energy for a second envelop of a hydrogen atom. This resultant virtual entity is labeled VE2. And the figure of the virtual positron, VP2, has been moved to the right beyond this new E2 and drawn as touching this new virtual electron. This is to indicate that the two have become a new virtual pair which will dissolve into nothingness.
References

Aczel, Amir D., _Entanglement._ NY: Plume, 2001.

Apr, Halton, _Quasars, Redshifts, and Controversies_. Berkeley, CA: Intersteller Media, 1987.

Arp, Halton, _Seeing Red: Redshifts._ Cosmology and Academic Science. Montreal: Aperion, 1999.

Baierline, Ralph, _Newton to Einstein: The Trail of Light_ 2nd. Ed. Cambridge, UK, Cambridge U Press, 1996.

Becker, Adam, _What is Real? The Unfinished Quest for the Meaning of Quantum Physics_. NY: Basic Books, 2018.

Bell, J. S., _Speakable and unspeakable in quantum mechanics_. NY: Cambridge U. Press, 1987.

Bohm, David, _Causality and Chance in Modern Physics_. Philadelphia: U. of Penn Press, 1957.

Bohm, David, _The Special Theory of Relativity_. NY: Routledge, 1965.

Bridgman, Percy Williams, _A Sophisticate's Primer of Relativity_ , 2nd Ed. Middleton, CT: Wesleyan U Press, 1983.

Bryant, David, _Physics_. Teach Yourself Books. Available in the USA at NY: Random House, 1971.

Capra, Fritjof, _The Tao of Physics: An Exploration of the Parallels between Modern Physics and Eastern Mysticism_ , 5th Ed. Boston: Shambhala, 2010.

Coleman, James A., _Relativity for the Layman,_ 2nd Ed. NY: Signet Books, 1969.

Crease, Robert P. & Goldhaber, Alfred Scharff, _The Quantum Moment: How Planck, Bohr, Einstein, and Heisenberg Taught Us to Love Uncertainty_. NY: Norton, 2014.

Dingle, Herbert, _The Special Theory of Relativity_. London: Metheun, 1940.

Dingle, Herbert, Relativity: Philosophical Consequences. _Encyclopædia Britannica_. London: 1971. Vol. 19, pgs. 101 3.

Einstein, Albert, _Relativity_ , _The Special and General Theory_. NY: Bonanza Books, 1961.

Einstein, Albert, _Sidelights on Relativity_. NY: Dover, 1983.

_Encyclopædia Britannica_ CD. 1999 standard edition.

Fermi, Laura, _Atoms in the Family: My Life with Enrico Fermi._ Chicago: U of Chicago Press, 1954.

Feynman, Richard, _The Character of Physical Law._ Cambridge, MA: MIT Press, 1965.

Feynman, Richard P., _QED: The Strange Theory of Light and Matter_. Princeton, NJ: Princeton U. Press, 1985.

Galison, Peter, _Einstein's Clocks, Poincaré's Maps: Empires of Time_. NY: Norton, 2003.

Genz, Henning, _Nothingness_. Cambridge, Mass: Persues, 1999.

Gilder, Louisa, _The Age of Entanglement: When Quantum Physics was Reborn_. NY: Konpf, 2008.

Gornick, Larry & Huffman, Art, _The Cartoon Guide to Physics_. NY: HarperCollins, 1990.

Gregory, Bruce, _Inventing Reality: Physics as Language_. NY: Wiley, 1988.

Gribbin, John, _In Search of Schrödinger's Cat: Quantum Physics and Reality_. NY: Bantam Books, 1984.

Gribbin, John, _Schrödinger's Kittens and the Search for Reality: Solving the Quantum Mysteries_. Boston: Little Brown, 1995.

Gribbin, John, _In Search of the Multiverse_. London: Allen Lane, 2009.

Gribbin, John, _Computing with Quantum Cats_. Amherst NY: Prometheus, 2014.

Hafele, J. C., & Keating, Richard E., Around-the-World Atomic Clocks: Predicted Relativistic Time Gains. _Science_ , Vol. 177, 1972A. Pp. 166 8.

Hafele, J. C., & Keating, Richard E., Around-the-World Atomic Clocks: Observed Relativistic Time Gains. _Science_ , Vol. 177, 1972B. Pp. 168 70.

Heisenberg, Werner, _Physics and Philosophy: The Revolution in Modern Science_. NY: Prometheus, 1999.

Hensinger, Winfried K. _Quantum computing_. Chpt. 11 in Al Khalili, Jim, Ed., _What the Future Looks Like_. NY: The Experiment, LLC, 2018.

Herbert, Nick, _Quantum Reality: Beyond the New Physics: An Excursion into Metaphysics_. New York: Doubleday, 1985.

Hossenfelder, Sabine, _Lost in Math: How Beauty Leads Physics Astray_. NY: Basic Books, 2018.

Kumar, Manjit, _Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality_. NY: Norton, 2008.

Lange, Marc, _An Introduction to the Philosophy of_ Physics. Oxford: Blackwell, 2002.

Lenzen, Victor F., _Einstein's Theory of Knowledge_. Chpt. 13 in Schlipp, P. A. (Ed.) _Albert Einstein: Philosopher-Scientist_. La Salle, IL: Open Court, 1949.

Lindley, David, _The End of Physics: The Myth of a Unified Theory_. NY: Basic Books, 1993.

Miklich, Donald R., _The Fallacy of Scientific Truth: Why Science Succeeds Despite Ultimate Ignorance_. Smashwords.com, 2014.

Nadeau, Robert & Kafatos, Menas, _The Non-Local Universe: The New Physics and Matters of the Mind._ NY: Oxford UJ. Press, 1999.

Ohanian, Hans C., _Einstein's Mistakes: The Human Failings of Genius_. NY: Norton, 2008.

Pagels, Heinz R., _The Cosmic Code: Quantum Physics as the Language of Nature_. NY: Bantam Books, 1983.

Pais, Abraham, _Subtle is the Lord: The Science and the Life of Albert Einstein_. Oxford: Oxford U. Press, 1982.

Pais, Abraham, _Niels Bohr's Times: In Physics, Philosophy, and Polity_. Oxford: Clarendon Press, 1991.

Peacock, Kent A., _The Quantum Mystery: A Historical Perspective_. Westport, Conn.: Greenwood Press, 2008.

Rothman, Tony, _Everything's Relative: And Other Fables from Science and Technology_. Hoboken, NJ: Wiley, 2003.

Rothman, Tony & Sudarshan, George, _Doubt and Certainty_. Reading MA: Persus Books, 1998.

Schlipp, P. A. (Ed.), _Albert Einstein: Philosopher-Scientist_. La Salle, IL: Open Court, 1949. Chpt I: Einstein's Autobiography.

Smolion, Lee, _Einstein's Unfinished Revolution: The Search for What Lies Beyond the quantum._ NY: Penguin, 2019.

Squires, Euan. _The Mystery of the Quantum World._ Bristol UK: Institute of Physics, 1994.

Stone, A. Douglas, _Einstein and the Quantum: The Quest of the Valiant Swabian._ Princeton, NJ: Princeton U Press, 2013.

Taylor, Edwin F. & Wheeler, John Archibald, _Spacetime Physics: Introduction to Special Relativit_ y, 2nd Ed.. NY: Freeman, 1992.

Will, Clifford M., _Was Einstein Right? Putting General Relativity to the Test,_ 2nd Ed. NY: Basic Books, 1986.

Woit, Peter, _Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law_. NY: Basic Books, 2006.

