Some of these oscillatory states
will be rendered massless
particles due to them being
in the zero energy state.
Another state with spin two is observed
and is also known as the graviton.
The masses of the massive string
states are of the order m >= 1/ls.
String interactions gets introduced
by letting the strings touch
each other and then get attached
into one single string -
these are basically the joining and
splitting interactions of strings.
The simplest of string theories
are the ones that live
in ten dimensions and are
observed to be supersymmetric.
The sum over string theory which
are emphasized with Feynman
diagrams can be performed
and yields finite results.
At considerable low
energies to the likes of
energies lower than mass
of the massive string
states E « 1/ls the only
excitation we will have
are gravitons and other
massless particles.
The interactions of these
particles are those of some
massless fields and also of
Einstein gravity fields.
This is exactly how string
theory quantize the gravity.
The description above is nothing except the
perturbative quantization of the theory.
Field theories also comprise
of extended solitons like
cosmic strings and domain
walls or cosmic string.
String theory also comprise of solitons and
solitons like these are named as D-branes.
Primarily, these D-branes have different
dimensions than that of the solitons.
They may have a pointlike
shape (D-0-brane), one
dimensional (D-1-brane),
two-dimensional (D-2-brane) etc.
Solitons have a specific
description in string theory.
Their excitations are described
by open strings that end on them.
When we put many branes together
theopen strings have two indices: i,
j labeling the brane where they
start and the brane where they end.
For both the cases concerned, the
parameters of the Standard Model would
heavily be depended on the brane
configuration or the internal manifold.
The compactifications that are done
to preserve 2,4 or 8 supersymmetries
at very low energies are accounted
for, to a great extent.
In the particular situation where a
single supersymmetry is preserved
is not that well accounted for
and hard for us to understand
how the supersymmetry can
even be broken like it
happens in the real
world, without generating
a very big cosmological constant as big as
crossing the supersymmetry breaking scale.
This the greatest hurdle
while explaining how the
Standard Model is embedded
in the string theory.
Idea of duality had been the source
of progress in string theory lately.
It is familiar that classical
electromagnetism is invariant
under the interchange of
electric and magnetic fields
This exchanges electric charges
with magnetic charges.
In field theories electric
charges are carried by
fundamental particles and
magnetic charges by solitons.
When the coupling becomes strong in terms
of some variables the theory has an
equivalent description in terms of some
dual variables that can be weakly coupled.
That is primarily how different string
theories are connected to each other.
This is the reason why in
supersymmetric theories
dualities are checked
more often than now.
Quantities protected by supersymmetry
as calculated are the followings:-
1) Masses and numbers of different
"protected" states that are special, a few
charged particles each corresponding
to the nature they typically exhibit,
2) Effective action of low energy
These are solitons when in dual theory
but elementary when under one theory.
Black hole entropy
Black holes are one of the most intriguing
objects that general relativity predicts.
In classical general relativity black
holes have a horizon, which is a surface
in spacetime such that if somebody
crosses it he/she cannot come back out.
For a black hole in four
dimensions the temperature
is inversely proportional
to its radius.
The fact that they are
thermal objects raises
very interesting and very
important theoretical
puzzles, solving these puzzles is one of the
challenges of a theory of quantum gravity.
We are used to the fact that when we
encounter a thermal object we can explain
its temperature as arising from the
motion of the internal constituents.
So, now the question that stays
is, what are the internal
constituents of the black hole
that explain its temperature?
This question is often
phrased in terms of
explaining the microscopic
origin of the entropy.
The entropy can be defined through the
first law of thermodynamics as dM = T dS.
The entropy comes off to be S = AH/(4GN).
Conversely, it can be stated that
the entropy is proportion is fixed
and depends on the area of the
horizon, taken in Planck units.
Quantum gravity can very well explain
all these entropy effectively.
In string theory it is
hard to calculate this
entropy directly since
strings describe small
fluctuations around flat
space while a black hole
represents a large deviation
from Minkowski space.
Recently, when the dynamics of
D-branes was understood, it became
possible to calculate this
entropy for some special cases.
Consider a compactification
of string theory down to
four dimensions that preserves
two supersymmetries.
In such a theory we could
consider charged black holes.
Charged black holes are expected to obey the
mass constraint which appear to be like
M>= Q just to avoid the
singularities, something
which not accounted
for by the horizon.
Moving further, the constraint
also states that M=Q falls along a
very limited representation of the
algebra defined by supersymmetry.
Not only that, the number of states
under that limited representation
is independent of any continuous
parameters of even coupling.
Black holes with M = Q are also special from
the point of view of the gravity theory,
they are called extremal black holes and
for them the Hawking temperature vanishes.
In these supersymmetric theories it is
possible to change parameters so that the
black hole configuration becomes a weakly
coupled system of D-branes and strings
whose entropy one can calculate
fairly easily,see figure 4.
The answer, of course, comes
out to be the same as
the area of the corresponding
black hole solution.
Since the number of BPS
states does not change
when we do this transformation
this provides a
derivation of black hole
entropy for these special
black holes in these
supergravity theories.
The entropy of general black holes
in completely general string
backgrounds cannot be calculated
with the present techniques.
Conformal field theories
and Anti-de-Sitter
space-times Although string
theory was described
above as a theory of quantum gravity, it
originated as an attempt to describe hadrons.
The string description
explained some features of the
hadron spectrum such as
Regge trajectories, etc.
We now know that hadrons are described
by QCD, but it is still quite
hard to do computations at low energies
due to strong coupling problems.
In fact we expect confinement.
Confinement is thought to arise from
the fact that the color electric
field lines form narrow bundles in
going from a quark to an anti-quark.
These fluxes look at low energies
like strings and one might expect
that at low energies a description
in terms of string might be valid.
It was shown by 't Hooft
that the proper way to
most precisely the number
of states that cannot
be combined into larger
representations, such
as the ones with M>Q,
remains invariant.
In supersymmetric theories these are
BPS states and their number does
not depend on the coupling, so we can
calculate the black hole entropy
by counting the number of states in
the gas of D-branes and strings.
Fluxes of the color
electric field forms a
narrow bundle leading to
a linear potential and
confinement of Yang
Mills theory with N = 4 supersymmetries
and a large number of colors.
Nit has been conjectured that these gauge
strings are the same as the fundamental
strings described above but moving
in a particular curved spacetime:
the product of five-dimensional
Anti-de-Sitter space and a five-sphere.
Five dimensional AdS a boundary
which is four dimensional.
The field theory is defined on
this four dimensional boundary.
There have been a large number of
checks for this correspondence.
Many checks are possible due to the
large number of supersymmetries.
The simplest check is the
observation that both
theories have the same
symmetries N=4 supersymmetric.
All these form the group
mathematically known as SO(2, 4).
This group is the group
of isometries of AdS.
Similarly the Yang Mills theory
has an SO(6) global symmetry
group, which is the same as
the group of rotations of S5.
In fact when we consider string
theory on AdS - 5 × S5 we
also have the same supersymmetries
as the gauge theory.
Something that has enough material to
puzzle is that the field theory doesn’t
take gravity into consideration unlike
bulk theory which typically does.
Going by the bulk theory, gravity
resemble the stress tensor
as given in the boundary and
it is explained as follows.
In agreement, Einstein argued against
the existence of black holes and
singularities, but they have become
accepted among established physics.
The black hole has been modified
for it to emit Hawking radiation,
but the singularity aspect of it
remains part of accepted theory
whereby interpretation of
the limiting aspect of
light speed with regard
to gravity allows for
conditions of infinite
mass-energy density within
an infinitesimal space
of no definable volume.
Infinity is generally a
mathematical problem in
relating laws of physics
to the observable world.
Each operator corresponds
to a particle, or more
precisely a string mode,
propagating in AdS.
In the same way, antiquark quark potential
can easily be determined just by a simple
string consideration which passes through two
separate points situated at the boundary.
This can be illustrated with
a diagram whereby movements
of strings are traced on
a ten dimensional space.
These moving strings are
true representations
of the fluxes of colour fields.
We can thus say that strings
made of gluons look
very much like ordinary
fundamental strings.
It was a problem relating the
thermal light energy (ultra
violet catastrophe) until
Planck introduced the quantum.
It continued to be a problem
with quantum physics
until the principle of
renormalization was applied.
In relation to the quantum, there is also
another problem with the aspect of special
relativity stipulating no information of
events transmit faster than light speed.
A mathematical singularity is
defined as two terms of an
equation, one indicating zero
magnitude and the other infinity.
This potential is not
confining and it should
not be, since the field
theory is conformal.
It is possible to deform the field
theory in such a way that one
destroys conformal invariance and
supersymmetry at low energies.
The theory which is
brought over as a result
is much expected to
be the confining one.
Even though the theory is
confining it is not pure
Yang-Mills, it is a strongly
coupled version of it.
In order to find the largeN limit of pure
Yang-Mills one needs to consider strings
propagating in a curved spacetime whose
curvature is of the order of the string scale.
In this situation the gravity
approximation would not be good enough.
Treating strings is
these small spaces is a
challenging problem,
which is being explored.
It is harder to use it in this
direction since the field
theory is strongly coupled
and therefore hard to solve.
There are, however, some general
statements that one could make.
One ofthe most mysterious objects in
a gravity theory is a black hole.
One can consider a black hole in AdS.
This black hole is, in
principle, described
by some thermal state
in the boundary theory.
The increase in mass-energy
is further shown to be
conserved by an exchange
of energy between systems.
For an analogy, a relative increase
in mass of the gravitational field in
addition of it entering into the field
should constitute work energy spent
with regard to an increase
in gravitational force
from an increase in
relative mass density.
As the field increases in mass,
it should radiate energy.
In the case of AdS3, it
is possible to precisely
determine the entropy
as per the techniques
given in field theory and
and the result hence
achieved conforms with
the idea of gravity.
Holography says that
in a quantum theory of
gravity we should be able
to describe physics in
some region of space by
a theory with at most
one degree of freedom per
unit of Planck area.
It is worth noting that the degree of
freedom with their numbers shows rising
with the area instead of the volume, which
is something we are used to normally.
Of course, for all physical systems that we
normally encounter the number of degrees
of freedom is much smaller than the area,
since the Planck length is so small.
It is called "holography" because
it would be analogous to a hologram
which can store a three dimensional
image in a two dimensional surface.
In this case we represent the
physics of the five dimensional
Anti-de-Sitter spacetime with a
theory that lives on its boundary.
It is a concrete example of holography.
Understanding it better might lead to
more insights about quantum gravity.
Causes of Gravitation
Newton formulated gravitational force according
to his inverse square law, but he was
unable to explain the cause of gravity other
than by an action at a distance principle.
Einstein explained gravity
as mass-energy following the
path of spacetime curvature
due to the presence of mass,
but more entailed explanation
of how the presence of
mass causes space time
curvature is still lacking.
Here, gravity has been
associated with the Hubble
Constant insofar as a minute
decrease in radiant energy
with regard to its propagation in
the medium of space allows for a
long range effect of a relatively
weak force of gravity per mass
in comparison to such other forces of
nature as atomic and electromagnetic.
However, although a vacuum effect is
possible in the wake of emitted radiation,
there is yet adequate explanation as
to how a restoring force maintains the
equilibrium state of local mass in manner
of conserving momentum in the process.
Explanation is here given
in view of a virtual vacuum
condition that is now an integral
part of quantum physics.
It assumes gravitational radiation
is consistent with the tired light
mechanism of space, whose main
objection is a lack of explanation
as to how space can decrease
the energy of light
and allow the visibility
of the distant stars.
How this visibility is
possible is thus given
explanation along with
conservation of momentum.
Electromagnetism is part of the
visibility explanation with regard
to a right hand rule and a more
causal explanation of interaction
between virtual particles
than as originally
proposed by Feynman with
limited explanation.
For instance, no causal explanation
of how virtual particles
cause attraction was deemed
necessary according to Feynman.
An explanation is here
given as more causal with
the inclusion of a concept
of zero point energy
(ZPA), which Plank later
proposed as a modification
of his original formulation
of the quantum.
The ZPA was further expanded on to
include a Casimir effect as a method of
attraction, which includes interaction of
virtual particles for further explanation.
Gravitational radiation
(gravitons) emitted for
gravitational effect also
are virtual particles,
but the explanation includes
more in depth analysis
of the method of radiation
superimposing to
form observable mass as
consistent with how mass
relates to both relative
motion and gravity.
Vacuum Effects
It has been argued primary substance
would dissipate into empty space without
any internal mechanism to form into
particles if space were partially empty.
Whether space is only
partially filled or is a
plenum, quantum theory now
describes vacuum space
as containing virtual
energy particles according
to the Heisenberg
uncertainty principle.
Such virtual particles as gluons
are to explain observable
effects that do not otherwise
comply with predictions of theory.
The gluon is confined as part of a
proton or neutron such that it cannot be
observed directly as an individual
particle apart from a proton or neutron.
It is verifiable only as an indirect
effect according to mathematical analysis.
It thus seemingly exists
as a virtual particle.
In general, the vacuum
of space is now assumed
to contain an assortment
of virtual particles.
This quantum vacuum condition is not
here contested; it is expanded to
include non-quantum conditions of
continuous change in motion as well.
Matter at rest absorbs and emits discrete
units of electromagnetic radiation
as quanta, but quanta also vary
according to the Doppler principle.
Relative motion, gravity and
electric charge all comply
with the Doppler principle of
continuous change in effect.
Electrostatic and gravitational
effects are explained as
vacuum effects occurring in the
wake of emitted radiation.
Even though effects are visible,
gravitons are virtual particles.
Although ordinary light
is a visible part of the
electromagnetic spectrum,
as x-rays and radio
waves are directly detectable,
virtual particles
can explain electromagnetic
effects as well.
Both gravity and electromagnetism
thus associate with a
‘virtual-vacuum-cause-and-effect of electromagnetic
radiation, whether virtual or not.
The virtual explaining of electromagnetic
effects is in view of Feynman diagrams.
The continuous change in force is
explained in accordance with a concept
of zero point energy Planck proposed
to modify his own quantum theory
for it to comply with the classical
theories of continuous change.
His effort was continued
with proposed causal
explanations of the particle-wave
paradox by De-Broglie,
a hidden variable approach by David
Bohm (1917-1992) and a stochastic
interpretation of quantum probability
conditions by Jean-Pierre Vigier (1920-2004).
It includes the concept of ZPE.
The absorption of energy by the field
implies spacetime itself contain energy.
(There is a virtual field of vacuum
energy in space free of matter
in accordance with a probability
condition of quantum physics).
If matter is an anomaly of spacetime, as a
finite universe, then its gravitational work
energy could be in a state
of equilibrium whereby
the laws of thermodynamics
are maintained.
There is neither increase
nor decrease of total
energy and total entropy
of the universe.
However, systems within it still need
to conform to conservation laws.
Energy is conserved by mutual
exchange between systems, but a local
change in a system changes the
view of the universe at large.
If an observer relatively at rest with
the universe at large accelerates
whereby the universe is then perceived
to have greater internal motion
relative to the new state
of the observer, then
mass-energy of the universe
relatively increases,
unless a relative decrease
in relative motion
occurs to the relative
increase in relative motion.
Such a condition referred to as a
Cosmological Principle is in effect with
regard to assuming the content of the
universe is finite and expanding.
Moreover, if the gravitational field
contracts to be a singularity of infinite
mass density, and the mass-energy of observers
in it contract relatively the same,
then the mass-energy of the universe
at large remains relatively the same.
However, the same principle of
maintaining relative mass-energy
density should apply to an
expanding universe as well.
Consistency of theory is at stake.
Universe’s expansion, if it starts from
the point of singularity, then it should
be increasing in mass-energy, which is now
evident of an increased expansion rate.
Zero Point Energy
Plank revolutionized physics
in the year 1900 with
the introduction of the
quantum as a solution
to an infinity paradox
of blackbody radiation,
but he did not accept
some of its implications.
He continued to pursue a more consistent
solution with classical electromagnetism.
He contrived a possible solution
in 1911 that assumed quantum
effects are the particular
oscillation mode of the atom.
However, his assumption contrasted with
Bohr’s atomic theory whereby quantum jumps
of discrete energy occur with absorption
of radiation as well as its emission.
In effect, the continuous manner of
change in the relative motion of mass
only occurs by reflecting radiation
instead of by its absorption or emission.
However, a particular aspect of Planck’s
new theory did receive recognition.
Plank added the term (½)hν
to his original equation relating energy
of radiation to absolute temperature.
He referred to this term as the zero
point energy of an oscillator, such
that the average energy at absolute
temperature zero is not itself zero.
Walther Nerst (1864-1941),
who had formulated the
third law of thermodynamics,
reinterpreted the term
in consideration of the
possible heat death due to
the loss of radiation emitted
out of the universe.
He compared the half
quantum frequency (½)hν
to temperature kBT, where kB is
the Boltzmann constant also used
for statistical analyses of the
classical theory of kinetics.
Further consideration of
Plank’s additional term became
evident in view of Heisenberg’s
uncertainty principle
in that otherwise zero energy at absolute
zero temperature contradicts the principle
in referring to possible determination
of exact energy for any particular time.
Any possible frequency
of radiation suggests
there is a possible
infinite magnitude of ZPE.
However, the uncertainty principle further
suggests an infinite magnitude of energy
is undetectable with regard to a particular
time and location being uncertain.
A possibility of this
uncertainty is explainable as
invisible effects of interaction
between virtual energies,
as similar to how thermodynamic
entropy is explainable as no
change occurring between two
systems of the same temperature.
For instance, gravity is
essentially invisible
except for its gravitational
effect because it is
able along with light waves
in general to occupy
the same space, whereas
matter supposedly cannot.
Such invisibility is
typical of wave action.
Waves superimpose to produce
visible effect only if the
medium of wave action changes
in a way it can be seen.
If action within a medium of interaction
is counterbalanced, the direct
change occurring within the interaction
need not be seen beyond it.
A connection between ZPE
and continuous change
is with regard to a
particle-wave paradox.
The photoelectric effect revealed
that electrons freed by radiation
are according to frequency instead
of the intensity of radiation.
Einstein explained this result as particle
effects of electromagnetic radiation.
The particles were referred to as photons,
as distinguished from particles of matter.
However, further experimental
evidence of interference
supported a wave
interpretation of light, and
the photoelectric effect can
be explained as according
to light frequency instead
of light intensity.
Frequency is also a wave property.
A higher frequency of light
instead of less frequent but
more intense light of the same
energy can free electrons
because higher frequency does not
allow enough time for the interaction
to respond, being inelastic in emitting
electrons of particular energies.
A higher frequency light of less intensity
thus requires a quicker response
for elastic consequence even though
is occurs less often per interaction.
Einstein later offered an explanation
of photons guided by waves.
The waves would be directly invisible to
us, but a particle guided by a packet
of waves interfering within themselves
could explain the particle-wave duality.
With regard to the existence of the particle,
De Broglie considered particle effects as
resulting from overlapping
waves in analogy to
the beats of sound occurring
from sound waves.
Schrodinger then developed De Broglie’s
idea in a consistent manner of Plank’s
attempt to relate the quantum to classical
electrodynamics and relativity theory.
Moreover, in 1954, Bohm
and Vigier mathematically
developed a casual wave-particle
duality explanation,
but the stricter indeterminism
interpretation of the
Heisenberg uncertainty principle
prevailed instead in only
explaining effects in
accordance with conditions of
probability with no further
need of causal explanation.
More support for zero point energy
is according to a Casimir Effect.
It was proposed in 1947 by Hendrik B.
G. Casimir (1909-2000).
He and Dirk Potter (1919-2001) experimented
with metallic plates for the measure
of the van der Waals force between the
plates and their polarized molecules.
They discovered an attractive force between
the plates if they were close enough.
Niels Bohr had suggested to Casimir that
the experiments could relate to ZPE.
Casimir complied with Bohr’s suggestion
by formulating a theory in 1948.
Experimental evidence as accurate
to within fifteen percent of the
predicted value of theory came much
later in 1997 by Steve K. Lamoreaux.
More accurate results followed.
However, exact results require
experimental conditions to the extreme,
such as an exact vacuum condition
and perfectly smooth walls.
The Casimir effect in relation
to ZPE is interpreted
in accordance with the
Heisenberg uncertainty
principle, which applies
to the quantum vacuum
in further reference to
quantum wave mechanics.
Assuming the vacuum is comprised of waves
of any possible frequency, equilibrium
conditions vary according
to arrangements from
which waves fluctuate
in and out of phase.
Two superposing waves in opposite
phase can momentarily cancel effect.
If the volume of space between walls
is relatively small, such that
momentary loss of energy allows the
walls to momentarily contract,
then wave energy as a virtual particle
reappears outside the volume between
the walls in allowing for the existence
of a new state of equilibrium.
Interpretation with regard to virtual
particles is that they are emitted due to
their relative confinements in space for
an immediate response to outside pressure
in preventing another virtual
particle to replace the emitted one.
The conditions of inelasticity and
frequency are thus again applicable.
The greater frequency is again in
play, but with different results.
Even though the direct interaction
of frequency is still inelastic,
contraction of the system occurs
instead of it simply losing electrons.
Virtual Spin and the Right Hand Rule
In relation to the Feynman
diagrams, there are
particles responsible for
attraction and repulsion.
Virtual particles repel electrons
from electrons and protons from
protons, and they attract electrons
to protons and protons to electrons.
Various effects arise.
For example, discovery of
Ampere could be cited here,
where two parallel wires
are observed to contract
as long as both have electric current
flowing in the same direction and
they also repel if the flow of currents
in them is in opposite direction.
The Feynman diagrams
suggest an explanation
according to virtual
particles, which is here to
be included, but it is
itself an underlying
explanation for a right
hand rule explanation.
The right hand rule explanation
of electrical attraction and
repulsion is in connection with
the polar property of magnetism.
A magnet is polarized
whereby like poles repel
each other and opposite
poles attract each other.
If the magnet is divided, each
part obtains opposite poles.
The right hand rule, which is a result
of experiment, describes a right hand
palm facing a current with the thumb
pointing in the direction of the current,
directed perpendicularly towards the
direction in which the fingers point.
The opposite poles of two
currents flowing in the same
direction thus align closer
to each other to attract
whereas like poles tend to align
closer to each other to repel if
the current flow is exactly in
opposite in direction of the other.
Why, beyond experiment, is
there a right hand rule?
Likely explanation is with regard
to chiral symmetry by which
the electron spins in a direction
opposite to the proton spin.
The electron being less massive
than a proton requires electrons to
maintain relative motion after interacting
with protons of opposite spin.
(The opposite spins move in the
same direction when they touch
each other, which results in
vibrant motion through the wire
for their induction of a
magnetic field in the
direction of each spin
according to the forward
motion of the electron
through the wire because
of it being of less mass
than the proton mass.
Physicists have cautioned that atomic spin
is not the same as that of a spinning ball.
Nonetheless, circular
directions of magnetic fields
from a bar magnet is verified
by the use of a compass.
A bar magnet is the polarization of
positive and negative charges from which
electrons are propelled from one pole
and attracted to the other pole.
They thus tend to circle around from the
positive pole to the negative pole.
How polarization of two opposite
charges exists is not yet explained.
They are to be explained as the
emission of virtual particles
in view of the electric
currents flowing through wires.
Explanation of this contraction
and repulsion is according to
the law of momentum and the
emission of virtual particles.
The electrons flowing
in the same direction
tend to emit virtual
particles with more total
momenta in the same
direction and less total
momenta perpendicular to
the stationary wires.
The virtual particles in turn
collide to emit secondary virtual
particles in the perpendicular
direction to those of the wires.
Secondary collisions are
of less energetic virtual
particles if they are
moving more partly in
the same direction of
motion than if they move
more partly in opposite
directions of motion.
Regard this explanation as fundamental
on a primary level from which
attraction and repulsion become functional
on subatomic and atomic levels.
There could also be an opposite
alignment according to
a left hand rule, which would
constitute antimatter.
The worlds often interact whereby
one is an anomaly of the other.
It’s been widely observed that physics,
without considering the laws of
gravitation using the quantum rules,
is not as consistent as it should be.
Hence, the necessity
for proper application
of quantum mechanics and
the its theories in
particular are very much
in need to understand
concepts such as big
bang theory and so on.
With that said, I must bring
it up here that all the
principles, formulas that was
discussed in this script so far,
must be combined together, which
is a method known as unification.
Combining them even more actually
includes the Clausius Principle of
mean free path for explaining why
internal motion of the molecules
does not explode in every
way, the Dirac matrix along
with Wave Mechanic, the
Stefan-Boltzmann fourth power law
as well as Einstein’s momentum-energy
tensor matrix - all together
gives us the complete picture
of the field we are studying.
The Stefan-Boltzmann fourth power
law, which is most dealing
with an increase in temperature
of electromagnetic radiation,
but then again heat and temperature relate
to the kinetic energy of gases as well.
A fourth power ratio of
nuclear mass to that
of its electron mass of
the hydrogen element
atom is perhaps a consistent interpretation
of the Stefan-Boltzmann fourth power law.
The deeper and detailed
interpretation of this
applies to Einstein’s
momentum-energy tensor matrix.
A relativistic increase in the ratio of
potential energy to internal energy is
in ratio to c4 if there is no relativistic
increase in the internal energy.
It simply signifies a
comparison of mass in relative
motion and/or a
gravitational field to that
relatively at rest in
gravitational free space
as an underlying principle
of the virtual field.
But, it does not appear to unify theory
in the manner that the Dirac matrix does.
The connection between general
relativity and the Dirac
matrix is with regard to
invariance and the fraction ½.
The fraction as spin of
particles of mass on
the atomic scale is of
their angular momentum.
The fraction relates to gravity as escape
speed squared in relation to gravitational
potential that that
also relates as angular
momentum squared, or as
orbital speed squared.
However, on the large
cosmic scale whereby the
gravitational field becomes
relatively homogeneous,
the gravitational potential converts to
gravitational escape speed c as a limiting
condition whereby both infinities of gravity
and quantum effects both renormalize.
It thus appears to be one more step of
equating Einstein’s and Dirac’s matrices.
Their interpretation
would be similar to the
combining of positive
and negative charge,
but it entails a more inner understanding
of the chiral symmetry of matter and
antimatter combining to result in virtual
radiation as gravitational radiation.
Hence we can safely say that with
the help of strong set of theories
combined together a whole class of
phenomena is studied and understood,
as was expected in any
theory of quantum gravity.
Many connections were found
between different string
theories and between string
theory and field theory.
It has been shown that string theory
reduces, in certain circumstances,
to ordinary four dimensional
field theories and vice-versa.
We hope that in the near
future we will understand the
theory better so as to make
contact with experiment.
