1
The Relationship Between the Theory of Everything
and the Constants of Nature
Chian Fan
Abstract: In System of Units, time, length, and mass are the most fundamental units of measure, corresponding
to physical time, space, and energy, respectively, and they determine all other dimensions. The three natural constants,
the speed of light c determines the invariance of the relationship between space and time, the Planck constant h
determines the invariance of the relationship between energy and momentum, and the gravitational constant G
determines the invariance of the relationship between energy-momentum and space-time. Space-time and energy-
momentum are the basic elements of the universe, and that is all there is. The uniqueness and invariance of natural
constants are the foundation of everything, and they must be included in the Theory of Everything, which cannot be
reduced. This paper briefly discusses the basic features that the Theory of Everything should have, and the necessary
relationship between it and the natural constants, and points out what kind of equations in physics are the ultimate
unified equations. The unified equation produces two types of elementary particles with structural supersymmetry,
Light Strings (bosons) and Light Rings (fermions). Light Strings and Light Rings can lose or gain matter properties,
electric charge, magnetic charge, mass and , through conversion to each other, and give rise to the laws of
supersymmetry between Special Relativity and General Relativity, constrained by energy-momentum conservatism.
Keywords: Axiomatization, Supersymmetry, Maxwell’s Equations, Light string and Light ring, Physical Constants.
CONTENTS
Introduction ....................................................................................................................................................... 2
Basic Features of the Theory of Everything ............................................................................................. 4
Physical Constants and Dimensions ........................................................................................................ 10
Natural Constants and Light ...................................................................................................................... 12
Axiomatic Unified Equation ........................................................................................................................ 17
A. Constants and Equations ....................................................................................................................... 17
B. Supersymmetry: Light Strings and Light Rings ............................................................................... 20
C. Properties of Matter and Sources of Forces .................................................................................... 26
Conclusions ................................................................................................................................................. 37
Index .............................................................................................................................................................. 38
References ................................................................................................................................................... 40
2
Frank Wilczek wrote, in his “Unification of force and substance”, Gauge symmetry is perhaps the
supreme realization of Heinrich Hertz’s famous tribute to the Maxwell equations:
One cannot escape the feeling that these mathematical formulae have an
independent existence and an intelligence of their own, that they are wiser than we
are, wiser even than their discoverers, that we get more out of them than was
originally put into them.
Introduction
Einstein said, “I would like to state a theorem which at present can not be based upon anything
more than upon a faith in the simplicity, i.e., intelligibility, of nature: there are no arbitrary
constants ……. that is to say, nature is so constituted that it is possible logically to lay down such
strongly determined laws that within these laws only rationally completely determined constants occur
(not constants, therefore, whose numerical value could be changed without destroying the theory)”
[1, 2]
1
.
There is no standard definition or even standard terminology for the Theory of Everything (TOE).
It will generally be referred to as Grand Unified Theory (GUT), Unified field theories、Theory of Ultimate、
Final Theory [3, 4], The God Equation [5], etc.. The usual understanding of the theory of everything
can be expressed as follows:
“An ultimate theory of everything—one complete and consistent set of fundamental laws of
nature that explain every aspect of reality” [6]; “The Theory of Everything is a term for the ultimate
theory of the universe — a set of equations capable of describing all phenomena that have been
observed, or that will ever be observed” [7]; “Theory of Everything to represent the ambition of string
theory to describe all the elementary particles and their fundamental interactions”; “A theory to unify
all the fundamental interactions and explain the number and couplings of all the elementary
particles”[8]; “Theory unifying all fundamental forces into one” [9]; “a theory joining the gravitational
and the electromagnetic field into one single hyper field whose equations represent the conditions
imposed on the geometrical structure of the universe” [10]; etc..
It is a public perception that the theory of everything is a challenge [11]. Disbelief in the existence
of a theory of everything is also widespread [9, 12-14]; or the idea that a theory of everything should
be a family of interconnected theories, each describing its own version of reality [15]; or from the
practical point of view of the study of physics, that unification is not necessary
2
. The reasons for each
of these views cannot be considered sufficient. Whether from the perspective of philosophy of
physics
3
, or the observation and analysis of physical phenomena, the theory of “Big Bang” [16], cosmic
1
Wilczek said, “We must aspire to calculate all those numbers.” However, we believe they are not calculable, or
they do not have to be.
2
Freeman Dyson argued that the “division of physics into separate theories for large and small” is acceptable and
a unification not necessary in his review of Brian Greene’s bestseller “Fabric of the Cosmos”.
3
Including a theological viewpoint, but this article is from a physics position only.
3
microwave background radiation (CMB) [17], the uniqueness of space-time, the universality of
interactions, the conversion and conservation of energy-momentum, the certainty of physical
dimensions, and so on, all support the existence of a theory of everything.
From reductionism [18, 19]
1
, any theory that could support the infinite divisibility of things would
conflict with real physics, and thus the decomposition of things must terminate in some kind of
fundamental constituent unit. In turn, there is no reason to think that primitives cannot build a
complete universe. The fact that a complete universe can be constructed proves that there must be a
common ground for everything. Although every interaction stratifies matter and produces new and
different laws [13, 20], the notion that there is a unified theory will not be rejected. The problem is
that our knowledge of the lowest level primitives, and of the highest level of the universe, is not
sufficiently advanced to establish a reasonable prediction. The standard model of elementary particles
based on quantum field theory [21], and the model of the universe based on general relativity [22],
are still in practice only sufficient to satisfy our explanations of intermediate phenomena.
Hilbert, Weyl, and Einstein are all pioneers of unified theory [23]. Currently, mainstream physics
considers that three of the four forces of nature, electromagnetic, weak, strong, and gravitational,
have been unified in quantum field theory, and current efforts are directed towards the search for
gravitons to add gravity to the unified model [21]. Over the decades, numerous new ideas such as
string theory [24], loop quantum gravity theory [25], holographic theory and many others have arisen
[26], yet there is no sign of a breakthrough. The general direction of mainstream physicists is to "look
forward", hoping to solve the problem of gravity through new ideas. However, such a tendency has
put aside or even covered up many of the fundamental problems of physics that have not yet been
clarified, leading many young physicists to believe that there is no need to re-examine the
foundations of physics, and that there is no need to "look backward". Non-mainstream physicists or
non-professional physicists tend to take a questioning attitude towards the views of mainstream
physics, either rejecting those non-classical behavioral explanations in quantum mechanics and
quantum field theory, and choosing to start from a more realistic perspective, or going to the other
extreme, pursuing excessively bizarre and unprovable scenarios.
There are so many different kinds of physical constants that they could be compiled into a book
[15, 27]. According to the recommendation of the Task Group on Fundamental Constants (TGFC) of
the Committee on Data of the International Science Council (CODATA) [28], there are about 300+
constants in nature [27]. Particle physics and cosmology identify 31 dimensionless physical constants
[29]; The Stand Model has 19 adjustable parameters, One must go to experiment to fit these [30]. The
unequal status of physical constants was recognized early [31]
2
and is often called by various
additional names
3
to reflect the difference in importance: fundamental constants, fundamental
constants of nature [32], fundamental physical constants [28], general constants, universal constants
[32, 33], constants of nature [33], natural constants [34, 35], classical constants, absolute constants
1
Here we restrict the validity of reductionism to the physical level only, and do not address areas above biology,
such as the concept of consciousness.
2
Millikan: Among all physical constants there are two which will be universally admitted to be of predominant
importance; the one is the velocity of light, which now appears in many of the fundamental equations of theoretical
physics, and the other is the ultimate, or elementary, electrical charge…….
3
There may be differences in the meaning of these terms in different literatures. In the same literature, differences
may also be implied by different names. e.g. some of these play an essential and pervasive role in physics. They are
variously called “general”, “fundamental”, or “universal” physical constants. However, in general there is no standard
definition in physics.
4
[36], etc.. Sometimes, the word Parameters is also used [15, 29, 37]. The large number of physical
constants, the debate on whether they are "constants" or not [38-40], "the fine-tuning problem" [37],
the various bizarre interpretations
1
[29, 41], and the inconsistent name-calling all indicate that physics
has not yet developed a clear understanding of the physical constants.
The first way to find the theory of everything should be to try to identify those functions and
essential features that must belong to it, and then to construct a reasonable relationship between it
and current well-established physical theories and experimental discoveries. For example, energy is
universally existent, convertible, and transferable, and since the smallest unit of energy is h, are all
forms of energy entities capable of forming a unity on the Planck constant h.
Basic Features of the Theory of Everything
We believe that since the "theory of everything" is the grand unified theory that determines
everything in the universe, the meaning of unity must be broad. It should be a comprehensive and
consistent expression from space-time to energy-momentum, from material structure to interaction
force, from microcosm to macrocosm, and it is the "first principle" and fundamental law of nature.
However, in reality, the microphysical disobedience of causality, the seemingly independent
complexity of different physical levels [20, 42], the indescribable structure of elementary particles, and
the inaccessibility of cosmic singularities and the orientation of the evolution, have confused us, and
left the attempts of physics to unified theory without any reliable criterion and a clear direction.
At the turn of the 19th and 20th century, the earliest attempts at a unified theory came from
three different channels, "Electromagnetic Worldview" [3] and "Energism" [43-45] in the physics
community, and "Axiomatisation of Physics" [46] in the mathematics community.
Early physicists tried to construct an "Electromagnetic view of nature" based on their
understanding of the relationship between the electromagnetic field and the electron. O. Heaviside
[47], Wilhelm Wien, Walter Kaufmann [48], Max Abraham [49], Henri [50], H A Lorentz [51], and other
famous physicists put forward their own ideas or models. This was not a crazy idea at that time and
the basis of reasoning was not wrong. However, due to insurmountable difficulties in conceiving the
structure of the electron, its charge distribution, and its pure electromagnetic mass [52], this idea
slowly faded and ultimately disappeared [3].
Energism was born out of the fact that energy is the only thing that communicates between
physical phenomena. Ostwald argued that matter and energy had a “parallel” existence, he developed
a more radical position: matter is subordinate to energy, and identified five “Arten der Energie”: I.
Mechanical energy, II. Heat, III. Electrical and magnetic energy, IV. Chemical and internal energy, and
V. Radiant energy. Each form of energy is assigned an intensity. And formulated two fundamental
laws of energetics. The first expresses the conservation of energy during transfer and conversion; the
second explains in terms of intensity equilibrium what can start and stop the transfer and conversion
of energy. “Energy is always stored or contained in some physical system. Therefore, we will always
have to think of energy as a property of some identifiable physical system”. “Ostwald regarded his
Energism as the ultimate monism, a unitary "science of science” which would bridge not only physics
and chemistry, but the physical and biological sciences as well” [43]. This idea has already expressed
the thought of "pure energy" as a "unity" and has conceived the process of energy interactions.
1
e.g. merely accidental, a random variable, the anthropic principle.
5
However, due to the fact that it was not possible to determine exactly what energy is [53-55]
1
, he
suffered from the opposition of both scientific and philosophical communities
2
[43, 56, 57].
"The study of those physical sciences in which mathematics plays an important part by means of
axioms" was the sixth of the 23 "Mathematical Problems" proposed by Hilbert in 1900 [58]. He then
proposed his own Unified theory of electromagnetism and gravitation [23] based on Gustav Mie's
Electromagnetic Theory of Mattera and Einstein's General Relativity
3
.
More mysterious still was what Hilbert called his invariant energy equation, which he based on a
complicated construct that came to be known as Hilbert’s energy vector e. He derived this vector using
classical techniques for producing differential invariants, an approach that differed sharply from Einstein’s
much more physically motivated derivation of energy conservation in [Einstein 1916a]. Klein later showed
how Hilbert’s energy vector arose naturally from the variational framework used in his theory.
“They have believed in the existence of an underlying mathematical explanation of reality: an
explanation of great simplicity and beauty and sense of inevitability. Weinberg speaks of the beauty
of present theories as being an anticipation, a premonition, of the beauty of the final theory” [59].
Today, at a time when we have succeeded in establishing a standard model of quantum physics,
and further efforts have not been showing clear results, will going back and reviewing the opinions of
these three different channels, structure, energy, and axioms, trigger us to rethink whether our studies
have deviated from the right direction because we have forgotten or neglected the original
foundations of physics.
To think of the grand unity of physics as unifying the four fundamental forces into one coherent
framework [60] is not a sufficiently appropriate way. If we start from the concept of "force" alone, it is
impossible to reach the final goal. The force defined by classical physics is not an expression of the
nature of things, it is a representation based on the collection of interactions between objects
4
, which
can only be an abstract statement. The forces defined by quantum physics are based on virtual particle
exchange [61], which masks the specific way of interaction that is distributed at the microscopic level.
Although according to quantum field theory "symmetry dominates the interaction" [62], it seems to
have unified the three forces except gravity, we do not get the essence of the interaction if we defined
as interaction any relationship that occurs between all different things, properties. For example,
whether the effect of Higgs field that makes elementary particles gain mass is an interaction or not
[63], and whether the "coupling" of different strengths in quantum field theory is a special kind of
interaction or not [64]
5
. The definition of interactions in quantum field theory is still limited to high-
1
Richard Feynman, said in his Lectures in the sixties, ‘‘It is important to realize that in physics today we have no
knowledge of what energy is’’. In Bergmann and Schaefer’s Experimental Physics, 1998, one reads, ‘‘nobody knows
what energy really is’’ Dransfeld et al. (2001), Cengel and Boles (2002), Halliday et al. (2003), among others, pointed
out the difficulty in defining energy. Hence, Feynman introduced energy as an abstract quantity from the very
beginning of his university teaching.
2
The two major scientific critics of Energism, Max Planck and Mach, dismissed Energism as useless "metaphysics”.
VI Lenin is another critic.
3
Mie’s approach to field physics also exerted a strong influence on Hermann Weyl up until around 1920 [Weyl
1918a].
4
The essence of interactions is energy-momentum exchange, and they must likewise conform to the uncertainty
principle. Therefore, there should be no notion of forces at a certain point or moment in time; interactions must be
described as distributed dynamics.
5
“The first disaster is that the different gauge bosons, although they do similar things, do not do them with the
same vigor. In other words, they couple to their respective color charges with different strengths.”
6
level symmetry expressions rather than ultimate symmetries
1
. Ultimate symmetry is not the result of
symmetry breaking[65], but the source of breaking, which determines all interactions and the structure
of elementary particles.
If there were just isolated elementary particles with no (external) interactions, the theory of
everything would still need to describe it
2
. A description based on forces alone will obviously not serve
the purpose. What we need to focus on is the common foundation of physics, which is energy-
momentum. This is something that all elementary particles contain, whether bosons or fermions. If a
unified expression of energy-momentum can be found, then the expression of everything will be
realized. The conservation of energy-momentum would determine all structures and interactions, and
only its abstract expression could be the force. Such unity is true unity in accordance with the principle
that all interactions are equivalent.
Physics accepted a flawed interpretation in quantum theory. Such interpretations have misled
and even terminated the development of physics. The most important of them are: 1) the denial of
causality
3
, which stopped quantum mechanics at statistical interpretation [66-68]. 2) the
understanding of the "uncertainty principle" [69-71], which left the invariance of the analyzed object
aside and played with it inappropriately by assigning to it the characteristics of the action force, which
has become the basis of a number of new physics theories [72]. 3) The understanding of the "Dirac
sea" [73, 74], which postulates the vacuum energy and the vacuum excitation mechanisms
4
of
elementary particles [75, 76]. Each particle is considered as a counterpart of a field, and the natural
world as a superposition of dozens of different fields [21, 76]. Physics has also fully embraced general
relativity, treating gravity as a geometrical effect under the curvature of space-time [21, 77], although
no one has been able to imagine a four-dimensional space-time curvature
5
. The dynamics behind
the motion of an object in a gravitational field is thus erased, but the search for "gravitons" similar to
the action of photons continues [21, 78]. These ideas prevent physics from further investigating the
nature of space-time. If we give up this understanding and keep digging, the main body of quantum
field theory, the Standard Model, and relativity will not be rejected, but it is possible that we will be
on the right path from now on.
Physics pursues the unification of geometry-based gravity and statistics-based quantum physics.
If geometry is the spatial representation of interactions, the first thing we should geometrize is
energy-momentum. Although we have discretized the energy-momentum, if they cannot be
geometrized, they can never be matched to space-time.
Reductionism is the basic ground on which the unified theory is constructed. If reductionism does
1
Symmetry is hierarchical, and we believe that at the lowest level of nature, conservation, invariance, symmetry,
and causality are perfectly equivalent.
2
So any theory that avoids the structure of elementary particles must fail to reach its ultimate goal. ψ of quantum
field theory implicitly describes the structure of fields.
3
Causality and randomness are opposites; if there is an ultimate origin of causality, is there an ultimate origin of
randomness? It is impossible to satisfy both. Therefore, the foundation of the world must be causal. Randomness can
only be an illusion.
4
Vacuum excitation is one of the reasons to explain the "identity" of particles. But what we need to explain more
is what kind of vacuum electron field can be excited by what kind of process which contains the properties of charge,
mass, magnetic moment, gravitational field and so on.
5
Feynman constantly questioned the notion of "spacetime curvature", using the spacetime "metric" concept of
SR as a direct replacement for "curvature" in his general relativity lesson plans. Weinberg, on the other hand, thought
it might be more appropriate to consider geometry as an analogue of GR, euphemistically expressing his scepticism.
L. Susskind, teaching GR, said that no one knows what four-dimensional spacetime bending looks like.
7
not hold, then we will not be able to construct the current world. In reductionism, we are looking for
the ultimate "primitives", the things that we can see that are consistent from the bottom to the top,
even though they are unknown at the present time, and that will be our basic basis. Such things are
"energy-momentum" and fundamental constants. They also run through all of physics, and it is
reasonable to believe that the fundamental constants must be involved in the description of the
fundamental energy-momentum. At the same time, matter is reducible, and its corresponding laws
of physics must of course be reducible. The laws of physics corresponding to the ultimate irreducible
"matter" must also be irreducible. This ultimate irreducible law of physics would be the theory of
everything.
The conservation of energy and momentum is absolute, any conservation beyond that is not
absolute and can disappear. Mass can vanish, charge can vanish, and Lepton number can vanish. We
need to emphasize the essential difference between the concepts of conservation and disappearance,
such as mass and charge. Mass and charge are both fundamental properties of elementary particles,
but they behave differently. The fact that mass is not conserved and charge is conserved indicates
that there is a difference in what constitutes them, or how the elements behave. However, although
charge is conserved, it can vanish, which is substantially different from energy and momentum
conservation. Therefore, the conservation of charge is essentially a "pseudo-conservation". For
example, Lepton number and charge is conserved in , but for an electron, its Lepton
number and individual charge just vanished after the reaction is completed. Obviously, this is different
from the conservation of momentum which does not lose its component.
The theory of everything is the most fundamental physical theory of the universe. It must exhibit
some foundational features that determine the theory to be the ultimate theory of everything and
not any other intermediate theory. Even though we cannot yet prove what the theory of everything
is, we can infer from the relationship between physics and mathematics [79], the manifestation of
energy-momentum [80], and the way the real world effectively operates, the conditions it must fulfils
as well as the features it should has, to establish the basic basis of our search for the theory of
everything.
Axiomatization - The theory of everything must be the ultimate axiom
1
. It does not depend on any other
theories or assumptions, it is a natural existence; it has no roots, no beginning and no end; Time-Space,
Energy-Momentum are its closely related and unique elements. This ultimate axiom can be regarded as the
"first cause" and "first motivation" of nature. The ultimate axiom is obligatory
2
, and without it, there is no
basis for unity
3
. This is the most basic signature of the theory of everything
4
.
Uniqueness - The theory of everything must be unique, there are no axioms beyond the ultimate axioms,
1
In mathematics, Hilbert has summarized the three basic requirements for axioms: compatibility, independence
and completeness. We believe that it is equally applicable to physics.
2
That is, it must always be enforced without any condition, even if it is not visible at higher levels of physics, such
as in classical physics. The use of the term “mandatory” is just to change the way of thinking. Virtually all laws of physics
are mandatory under certain conditions.
3
Einstein said “the axiomatic basis of theoretical physics cannot be an inference from experience, but must be
free invention.”
4
However, there are also doubts in the physics community about the axiomatization of physics. C. N. Yang said
in 2004, the idea axiomatizing physics is a useless thing. It’s today such kind of effort in such a direction is not
considered to be a useful way to push physics forward. So we are trying to be physicists and not logicians in discussing
physics. This actually reflects the reality that our understanding of the big picture and roots of physics is not yet clear.
8
there are no alternative
1
. Physics and mathematics are absolutely identical. The physical process is the
mathematical process of deduction
2
. The fundamental quantities of mathematics
3
, scalars, vectors, spinors,
and the operational relationships between them, must be represented first, and this is the basic guarantee
for the operation of everything. The theory of everything should be expressed in mathematical equations that
operate uniformly in space-time.
Completeness - The Unified Equation is able to explain everything in nature and determine everything
in nature, from microscopic elementary particles, to all stages of evolution of the macroscopic universe. The
Unified Equation determines the structure, properties, and interaction processes of all elementary particles,
astronomical bodies, and provides the answers to all questions of physics. It is the root of all other laws of
physics. This principle reflects the fundamental, universal, and deterministic nature of the theory of
everything.
Conservation - Energy-momentum is the only content of the eternal operation of all things, and they
must be conserved. The definition of conserved quantities in the Theory of Everything, and the equations of
operation of the conserved quantities, must obey the requirement of "uniqueness", i.e., the unified equations
must be equations of energy-momentum. This is the simplest and most adequate expression of the content of
the axiom. The universe is a "perpetual motion machine", and the conserved quantities must have at least
two states that can be transformed into each other, whether they are the tiniest elementary particles or the
grandest of universes, in order to satisfy the requirement of "oscillation". Therefore, the unified equation
itself must be eternal, invariant, symmetrical, and conserved, and thus determine the causality of all things.
Infinity - The Theory of Everything does not need, cannot depend on any initial conditions, boundary
conditions. It determines all conditions in its own evolution by itself. If additional conditions are required,
the source of the conditions must be pursued, which becomes something beyond the Theory of Everything.
This principle determines that the unified equation must not only be expressed directly in mathematical
equations, but also that the space-time parameters in it must be of infinite nature and not subject to any other
constraints. This principle also determines the necessity of the existence of multiverses
4
.
Finiteness - The operation of everything is interaction, and any local interaction must be physically
finite and realistic, i.e., no mathematical expression of infinity is allowed
5
, and no abrupt changes or leaps
are allowed. This principle determines that the energy-momentum parameter in the unified equation must be
finite, i.e., the energy-momentum unit must be quantified.
1
Even with a TOE equation, there is still J. A. Wheeler's question: Why these particular equations, not others?
There is only one possible rational answer to it, and that is that the physical world is an analogue of the mathematical
world, and that there is absolutely no alternative to it, it is unique.
2
Pythagoras' idea, the world can be constructed from concepts, algorithms, and numbers [Wilczek, F. (2006)].
There are also objections to this view. In a letter to Pauli in 1921, Klein reproached Hilbert with his “fanatical belief in
the variational principles, the view that one can explain the reality of nature by means of purely mathematical
considerations.” [Kosmann-Schwarzbach, Y. (2011)]
3
Fundamental quantities are quantities that cannot be expressed by other types of quantities; they are
independent. A tensor is not a fundamental quantity; it is a combination of fundamental quantities. Spinors can also
essentially be broken down into combinations of vectors, but their combination is mandatory.
4
We define the universe as the sum of multiple universes, and universes within a multiple universe as "
subuniverses", e.g., the universe in which we currently live is a subuniverse. All subuniverses are of equal status. Physics
has proposed many different models of multiverses and cyclic universes, but they are all too complicated.
5
For example, the Fourier transform often appears as an infinite number of terms in mathematical representations,
but in physical reality, it must be constrained to be a finite number of terms. The Fourier transform is an indispensable
representation of the interaction, and the finite term transformation means that the interaction must be discrete. This
is the root cause of the necessity to quantizes.
9
Validity - The equations of unity do not enter any singularity
1
. Even if there is a singularity solution to
the equation
2
, the physical operation will not enter that state, whether it is a time singularity or a space
singularity. The reason is that entering a singularity will lead to a local infinity, which means that the Unified
Equation collapses, is no longer valid, and will lose all its physical properties and enter a random state.
Therefore, the Unified Equation must have the ability to self-coordinate between its own different states in
order to avoid the singularity. This principle guarantees the eternal validity of the ultimate equation. At the
same time, it also requires that it must include the interaction of energy and momentum with spacetime.
Independence - the unified equation should have the simplest expression; it should not be a combined
set of equations. It must contain independent physical constants that can be defined as true "constants of
nature"
3
which are not computable
4
and eternal and unchanging at any stage of evolution in any universe.
It must contain a minimum number of spacetime dimensions and operate all the laws of physics without
redundancy. Under this principle, it will embody all the information in natural relationships.
Stability - The universe that operates under the dictates of the theory of everything is absolutely stable,
its mode of operation does not change regardless of any disturbances. There are no the anthropic principles
5
.
Compatibility - the unified equations must be consistent with the fundamental theorems, confirmed
conclusions, all phenomena observed in current physics, all data obtained by experiments, and in particular,
with the interpretation of the phenomena of quantum mechanics
6
, relativity theory. The consistency of the
spacetime view of quantum theory, Special Relativity theory, General Relativity theory is guaranteed
7
. If all
interactions must be expressed geometrically in spacetime, then the energy-momentum must also be
geometrical.
Any theory of everything that does not fully satisfy these conditions is not the ultimate unifying
theory. It must be flawed, or it may be completely wrong.
1
We must note that all "singularities" are indistinguishable. For any mathematical equation, the conditions for
entering a singularity may be different, but the result is the same: a complete disruption of the course of the equation.
For physical equations, the interpretation of the result of the singularity depends on the object described by the
equation, but for any current physical equation, entering the singularity is a failure of the equation, and causality is
necessarily interrupted, and all current physical properties must be lost. Looking through Einstein's writings, one can
see that one of the concepts he was obsessed with at various times was the "singularity". For example, he conceived
of the quantum as a singularity surrounded by a huge field of vectors, and he asked what the solution to the
gravitational field equation would be if there were no singularities in all of space. Another concept that Einstein often
emphasized was the idea of finding the "simplest" equations.
2
We can divide singularities into two categories: real singularities, which are singularities that are accessible to
the physics equations, and imaginary singularities, which are singularities that are present in the physics equations but
will not be accessible. Real singularities exist in the higher-level physical equations, such as when Ferrimagnets, Crystals,
and Superconductors undergo phase transitions [Nambu 2009]. But the lowest level unification equations will never
enter a real singularity, which is the last line of defense after the failure of all levels of physics equations.
3
Planck said, “They are independent of special bodies or substances, which necessarily retain their significance
for all times and all environments, terrestrial, human or otherwise ……”. The true constants of nature are eternal and
unchanging at any stage of evolution in any universe. The various "natural constants" and "natural units" used in current
physics are not strictly defined.
4
Here "not computable" means not accessible by computation or derivation, unlike Turing's notion of
computability.
5
The simplest way to understand this is that the physical world without humans is still the current physical world.
6
Important aspects include, quantum, superposition, wave-particle duality, uncertainty, wave function
interpretation, Pauli exclusion principle, and so on.
7
It is important to ensure a rational interpretation of the absolute and relative, continuous and discrete,
homogeneous and non-homogeneous, infinite and finite, flat and curved, passive and active, spacetime energy
momentum and dimensional symmetry of the spacetime view.
10
A theory of everything, when it is called a "theory" of everything, already implies that it will
determine all causal relations in the physical world, and must exclude any randomness in the lowest
level of microphysical behavior [81], as well as any spontaneous transition or spontaneously broken
concepts. But this absolute causality does not leave enough room for "determinism" [82]
1
. This is
because, firstly, the global infinity (space-time, energy) is unpredictable, and no prediction can
accommodate an infinite number of interrelated states. Secondly, the physical world is hierarchical
and all higher level physical equations may have singularities and enter them under certain conditions.
A singularity causes the equations at that level to fail completely, i.e., causality at that level is
completely destroyed. However, this singularity is unpredictable from the bottom level because some
of the necessary conditions come from the top level, which constitutes a prediction conflict.
Physical Constants and Dimensions
There is no strict definition of what is a physical constant, the role and status of the fundamental
constants of physics have been widely debated [83]. In the most general terms, a constant is only
fundamental as a matter of convention [27, 84]. In terms of the role of presentation, there are various
descriptions: Some fundamental constants have profound geometric meaning [2]; Underlying every
universal constant of nature there is one of the fundamental laws of physics and chemistry; The
fundamental constants are like the DNA of our Universe; In our Universe, depending on the particular
physical phenomenon and its scale, we will need some fundamental constants to explain it; With this
handful of constants we can describe our physical world from atomic, mesoscopic, microscopic,
macroscopic, astronomical to cosmological scales [32]; We shall define these constants as the set of
physical parameters that are not determined by the theory we are considering [83].
We cannot measure a single constant, but obtain it by combining several experimental results
and solving equations [33]. Physical constants do not have equal status and lack precise positioning,
and are usually categorized in some way according to the field in which they occur or the range of
their effects. For example, the charge
e
, mass
m
and Planck's constant
h
are known as the three natural
constants of atomic constants [34], the speed of light
c
, the Newtonian constant of gravitation
G
, the
Hubble expansion rate , the CMB temperature , etc. are known as the Astrophysical constants
and parameters [16]. Another clearer basis for categorization is whether it can be used as a benchmark
for "the natural system of units" or "fundamental systems of units" [36].
Based on natural units and dimensional analysis, it is more natural and revealing to group the
fundamental constants into two categories, units-independent (A), and units-dependent (B). only
constants in the former category have values that are not determined by the human convention of
units, we argue that they are true fundamental constants in the sense that they are inherent properties
of our universe [85]. Such a conception has a history of development in physics, C. F. Gauss, J. C.
Maxwell, and G. J. Stoney all proposing different natural systems of units, but Planck's "units of
measurement", because it was considered to be the scale of quantum fluctuations in space-time,
evolved into the later Planck-scale physics [86] and thus has a special status.
Planck's natural units involve just three physical constants: c, h and G, which give rise to length,
time, mass and temperature, respectively [87]. George Johnstone Stoney called it "truly natural series
of physical units" and made it clear that it has an intrinsic natural meaning [88, 89]. From Planck units
1
“Laplacian Demon——Someone who knew the laws and the complete initial condition, would be in a position
to know everything”, its possibility is denied.
11
were developed Planck scales
1
:
（）
（）
（）
They represent Planck Length, Planck Time and Planck Mass. Planck has given it high marks,
“These quantities will retain their natural meaning for as long as the laws of gravity, the propagation
of light in vacuum and the two principles of the theory of heat hold, and, even if measured by different
intelligences and using different methods, must always remain the same” [33, 87]. The fact that the
metric series of units in physics can be established by relying only on three constants [90, 91]
2
implies
that they, and the physical theorems behind them, must have some kind of completeness. They should
be the most fundamental constants, and the corresponding theorems should be the most
fundamental theorems. However, Planck scales have an unsolvable problem, which is the conflict with
Special Relativity (SR) [40]. According to SR, Planck Length should not be rigid length.
The truly practical (international system of units) uses seven fundamental constants. They
include the speed of light , Planck constant , The elementary charge , The Boltzmann constant
, The Avogadro constant 、 and
3
, which were determined in 2019 [92]. We may refer
to them as Constants. Base units are defined in terms of these constants or properties which, for
all practical purposes, remain the same in common frames of reference. The base units give rise to
secondary units which are used to develop all the other derived units [93, 94]. The major difference
between them and Planck scales is that instead of using the gravitational constant G, other redundant
constants are used.
The "natural system of units" is used in many situations in physics
4
. “Natural units” is a system of
units in which the vacuum speed of light c and Planck’s constant are dimensionless with unit
magnitude. All physical quantities are then expressed in terms of a power of a single unit, usually mass
or energy [94]. Thus, c and are not so much fundamental constants as conversion factors [95],
revealing the basis for all conversions between energies. But this is only one of the natural unit systems,
and there are other different unit systems [36, 96]. For example, with the aid of the two constants
and k which appear in the universal law of radiation, we have the means of establishing units of length,
mass, time, and temperature, which are independent of special bodies or substances, which
necessarily retain their significance for all times and for all environments, terrestrial and human or
otherwise, and which may, therefore, be described as “natural units.” [87]
Another way to categories is: Divided (nonuniquely) into two groups, dimensionless ratios (which
1
Planck units and Planck scales are often used without distinction in various literature.
2
Other examples, Classical units based on G, c, e; Atomic units based on h, e, me; Strong units based on h, c, mp;
and many others. They show the close relationship between the various constants.
3
The luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, The unperturbed ground state
hyperfine transition frequency of the 133Cs atom.
4
First proposed by Planck, in German "natürliche Einheiten".
12
are the fundamental parameters and are pure numbers) and fundamental units, which have
dimensions. How many such fundamental units are needed is still debated[83]; By order of increasing
generality [97], grouped the fundamental physical constants into two categories
1
: 1) constants
characterizing whole classes of physical phenomena (such as the electric charge e and the universal
gravitational constant G); 2) universal constants (such as c and h) which act as concept or theory
synthesizers (for example, Planck’s constant h synthesizes the concepts of momentum and
wavelength through the relation
); Or based on whether or not the same values are
maintained in inertial and non-inertial systems, determining the truly fundamental and inherent
constants of nature [85].
Usually we use the terms "equally fundamental", "more fundamental", "truly fundamental ", "most
fundamental" to describe the status of physical constants, but there is no clear consistency among
the various natural unit systems, although the possibility of obtaining the most fundamental physical
constants can be seen [85, 96]. Whether there exists a most fundamental set of physical constants,
and that this most fundamental set of physical constants must be unique and must be the coefficients
of the ultimate unified equations, is something we need to explore.
Natural Constants and Light
The physical phenomena we observed are hierarchical and conditional, and different levels and
conditions correspond to different system structures. System structure is a broad concept; we can
regard elementary particle as a system structure [98], helium nuclei, hydrogen atoms, crystals, the
solar system as system structures at different levels, and ultimately the whole universe as a system
structure. These system structures combined matter and spacetime together and constitute the
objects of analysis in physics. Of course, space-time without any matter should also be regarded as a
system structure
2
.
Different system structures contain different modes of behaviour, i.e. modes of interaction. From
the point of view of forces, these can be broadly categorized as "maintain forces" and "interaction
forces". Maintenance forces are regarded as the forces that maintain the structural integrity of the
system, while interaction forces are regarded as the forces that occur when different structures interact
with each other. For example, when separated protons and electrons meet, they exhibit interaction
forces. And the internal action that maintains protons and electrons as mutually independent
structures belongs to the maintenance force. If protons and electrons are combined into atoms, the
interaction between them transforms into a maintain force. Different modes of behaviour are
determined or described by different theorems and laws. At different levels, the functions of physical
theorems and laws are different, and the constants contained in them have different meanings.
According to reductionism, the structure of matter at the highest level, from microscopic to
macroscopic, should be the superposition effect of the physical equations at multiple levels. For
1
The Lévy-Leblond division is cited here. Originally it was divided into three categories: A) Physical properties of
particular objects: for instance, the masses of fundamental particles, their magnetic moments, energy widths of
unstable ones, etc. B) Constants characterizing whole classes of physical phenomena: these are mainly the coupling
constants of the various fundamental interactions, such as Newton’s constant G associated with gravitation. C)
Universal constants, such as c or h, which enter the most general theoretical framework available, independently of
particular objects or specific interactions. It is clear that the division into three categories better highlights the functional
characteristics of the different physical constants.
2
But the concept of vacuum energy is not involved.
13
example, quarks build protons and neutrons, protons and neutrons build nuclei, nuclei and electrons
build atoms, and atoms depend on valence electrons to build lattice structures. As the mass grows
larger and gravitationally prominent, stars are formed. Each level of construction can be described by
a specific equation, regardless of the "maintain force" on which they depend. It is clear that when we
break down the structure of a system from the top down
1
, the system must evolve in such a way that
the equations at the higher level fail, and the equations at the lower level take over to maintain the
state at the lower level. Each level of the equation (set) must contain specific coefficients or constants.
Without considering the question of real possibilities, we must be able to obtain a state at the lowest
level, and the equation that maintains this state must be the ultimate equation, which cannot be
broken, and which embodies the very fundamental particles and fundamental interactions. The
coefficients and constants contained in this ultimate equation we define as natural constants. If we
can make the universe evolve inversely, then the ultimate state will necessarily be so. Analyzed in
terms of this procedure, there is a major problem with our current understanding of forces. The force
must be embodied by a unifying equation, and the mechanism of the force must always exist; it does
not come into being or go away. It is the force that causes the structure, not the structure that
produces the force. Electromagnetic and strong forces behave differently not because of the
mechanism of action of the force, but because of the difference in the structure of the system that is
formed as a result of the action of the force. Electromagnetic force is expressed between electrons
and nuclei within atoms, and strong force is expressed between quarks within baryons; weak force
and strong force are different in that one expresses the transformation of a sibling structural state,
and the other expresses the maintenance of the stability of the structural state; gravity is a spacetime
property, which is generated by the energy-momentum of matter particles.
How do we determine the final state and the constants in it? There are a couple of basic bases.
Firstly, what is the final stable product after a large enough energy breaks a state. If the product
formed is unstable, what is the stable product formed by its decay. Second, what is the most stable
particle in free space. Third, what is the most unique thing observed in physics. Fourth, what are the
constants that cannot be fundamentally eliminated from the fundamental laws in physics. Fifth, what
are the natural constants that must be involved in all interactions, explicitly or implicitly, directly or
indirectly, and which must be equally invariant when the interactions are translation invariant [99],
gauge invariant [100], Lorentz invariant, and diffeomorphism invariant. Thus, "a truly fundamental and
inherent constant of nature is that it must have the same value in both inertial and non-inertial frames.
"[85]. Sixthly, the most fundamental physical constant does not have an origin [101]
2
[102]
3
, it does not
arise and it does not annihilate, it must be the determinant of the other physical constants.
Upon comparison, we see that all of the above manifestations point to light. The photon is shown
to have very different properties compared to all the elementary particles in the Standard Model [103].
Light is a product of the annihilation of all elementary particles and most commonly a product of
particle decay [42]
4
, and particle collisions. This means that light may be the limit of structure and
1
For example, if conditions such as high pressure, high temperature and collision are applied and a certain
threshold is reached, it must be destroyed.
2
“Some of the constants appearing in the Standard Model could indeed be cosmic accidents, i.e. quantities which
were fluctuating wildly at the time of the creation of the universe, but were frozen immediately afterwards. These
constants could be called ‘‘frozen accidents”. This reveals that we do not yet have a clear picture of the process by
which physical constants emerge.
3
Wheeler also has an opinion on whether the physical constants generate and collapse with the universe.
4
“The smallest of all particle masses is likely to be special because the lightest particles can no longer decay -
14
symmetry reduction. When a photon is irreducible, it is the limit of entropy reduction, whereas the
same is true for the light-corresponding blackbody radiation, which is the limit of entropy increase.
Bounded by the energy-momentum of the photon, light as a boson and fermions as particles of
matter can be converted into each other by the process of "pair production", suggesting that there
may be two different states of the same thing, which is the true criterion for determining whether or
not a particle is an elementary particle. The speed of light is independent of the inertial system in
which the observer is located, and light determines the Lorentz transformation; when light is
transformed into fermions, the gravitational force corresponding to the mass is generated, which in
turn determines the generalized covariance; and light embodies supersymmetry from the structure
of spacetime to the principle of spacetime. The eternal dynamics that light has in itself, without cause,
necessarily indicates that it is based on what must be axioms.
Combination of constants can form a system of units. some combinations of constants are
directly related, such as or , etc. [104], where is the mass of the electron. among
the many Unit schemes [96], not all of them can be selected to be named as fundamental physical
constants, most of them have redundancy. Only the three constants that make up the Planck Scales
(Planck units), the speed of light c, the Planck constant h, and the gravitational constant G,
undoubtedly stand out as natural constants
1
. The idea of using them to relate all forces came to Planck
as early as 1899 [90]. A. Eddington (1918) in his "Report on Relativity Theory of Gravitation"
characterized the three physical constants as "fundamental constants of nature" [105]. Comparing
with other physical constants [101]
2
, we can summarize the following features.
1) "three fundamental constants of nature that depend on the elasticity of the vacuum: c, h and
G" [21], perfectly reflect the dynamical nature of space-time. If h characterizes light, the speed of light
c reflects the ability of light to propagate through space-time, The ordinary gravitational constant G
parameterizes the stiffness, or resistance to curvature, of space-time [2]. The spacetime field is the
fundamental being of the universe, and the electromagnetic field is the fundamental being of the
energy-momentum in the universe, both of which are real, and their interrelationships will reflect all
the relationships in the universe.
2) The three natural constants take up separate dimensions [22], are completely independent,
express all dimensions, are complete and have no redundancy. In most Unit schemes, c and h are
necessarily included, but not necessarily G. Instead, the choice is between G and either the electron
mass or the proton mass . This does not mean that G is not a fundamental constant, but that
there is a direct relationship between it and mass. However, the constant G is not included in the latest
SI, nor is any mass term included, "The main reason to exclude G from the new SI system of units is
the lack of precision enough to define a unit of mass" [32], and thus had to be replaced by other
physical constants.
3) The three natural constants are relativistically invariant and Planck's natural units are unique.
Other systems of units, are composed of combinations of universal constant and are systems
convenient to the physical system under study, rather than important in an absolute sense [90]. Not
they can no longer decay into lighter particles. They will inevitably dominate the universe”. We can think of the
photon as the limit of all decay, because it has zero mass and never decays.
1
There may be physical constants that have not yet been discovered, but there cannot be fundamental physical
constants that have not yet been discovered, because no laws of physics can be constructed without them.
2
For example, “The major drawback exhibited by the Standard Model is the fact that a large number of constants,
in particular many mass parameters, have to be adjusted according to the experimental measurements and cannot be
predicted within the theory.”
15
only are they invariant, but their most crucial characteristic is that they are indestructible
1
. Any other
"constant" can be annihilated at any time, as in the case of positive and negative electron annihilation,
where the charge e and the electron mass are annihilated, but and remain. In proton
accelerators, is also eventually annihilated, but and remain, and all masses are
relativistically variable.
The constant invariance of the speed of light
[106, 107] provides a mandatory
constraint on the time metric and the space metric, unifying time and space. "Special relativity
postulates symmetry operations (Lorentz transformations) that mix space and time. however, space
and time are measured in different units, so for this symmetry concepts to make sense, there must be
a conversion factor between them. That role is fulfilled by c" [104]. This unification is extremely
significant. In the Newtonian view of space-time, time and space are absolute and independent, i.e.,
the time metric and the space metric are fixed, but there can be no definite constraint
relationship between them. This means that we can define the values of and separately, and
this independence obviously leads to a lack of consistency in the description of the course of events,
so that we can only choose arbitrary "events" as the benchmark for physical clocks and scales
2
, and
describe ourselves in terms of ourselves, without any real basis. The invariance of the speed of light,
on the other hand, provides an absolute criterion for the relationship between space and time,
showing us that at any point in space and time, the speed of light,
, should be invariant as
long as it is present. Any change in the speed of light [83, 108-110]
3
, leads to a break in symmetry,
negating the global nature of the Lorentz transformation. Understanding the speed of light c in terms
of symmetry, either as a conversion factor [95]
4
or as an enforced constraint, requires that the metrics
, cannot be changed independently of each other under any conditions, even in "curved
spacetime".
The Planck constant h is an elementary quantity of action. “Quantum theory postulates an inverse
relation between wavelength and momentum and proportionality between frequency and energy, as
aspect of wave-particle duality; but the pairs of quantities are measured in different units, and h must
be brought in as a conversion factor” [104]. Light passes through the energy , the momentum
, and embodies their definite relationship. This means that the "wave function" of a photon
must contain the constant h and the frequency ν, or the wavelength λ. Any change in the speed of
light, , leads to an uncertainty in the frequency ν and the wavelength λ, and thus to an uncertainty
in the energy E, the momentum P, and the proportionality between them. Mass is related to the
frequency of light by . If we set , length and time are measured in
seconds and mass in hertz. This choice highlights the unifcation achieved by relativistic quantum
mechanics [35]. Considering the variability of the frequencies ν and λ, must be the true
1
Note that the absence of light is not the same as the absence of the speed of light c, the absence of light energy
E = hν is not the same as the absence of the Planck constant h, and the absence of mass is not the same as the absence
of the gravitational constant G.
2
Not only do mechanical clocks and rulers fall into this category, but even atomic clocks, which measure the
frequency of light emitted, have difficulty expressing real time, because we still need to measure frequencies by other
means.
3
The persistent questioning of the constancy of the speed of light is clearly a misestimation of the importance
and status of the speed of light, overlooking the important point that letting a constant vary implies replacing it by a
dynamical field consistently, and makes the exchange of the energy-momentum of light lose its unitary basis, and is
no longer measured by ν and λ alone; c has to be involved as well. The latest experiments reconfirm the invariance of
the speed of light.
4
A. Zee states that "c and h are not so much fundamental constants as conversion factors."
16
fundamental unit of action [25], which has dimension , and ν and λ are just quantities when energy
and momentum are measured. “the mathematical formalism of quantum theory possesses the
symmetry that the formalism is immune to possible change of the actual value of h”. As ,
quantum theory reduce to classical theory [111]. This means that Planck's constant dominates
quantum mechanics, rather than being dominated. Planck constant's conservation is the most
fundamental quantum guarantee, and by means of the Mass-Energy equation, it can be determined
that Planck constant's conservation must determine some invariance of all elementary particles. In this
way, the relationship between the conservation of the speed of light, , and the conservation of the
Planck constant, , extends from the photon to the other elementary particles.
“General relativity postulates that spacetime curvature is induced by energy-momentum density;
but curvature and energy are measured in different units, and must be brought in as a conversion
factor” [104]. is a constant conversion factor that must be present [112]
1
, to determine the
deterministic relationship between the energy-momentum and the space-time metric. Regardless of
whether the "space-time metric" is interpreted as "space-time curvature" or "space-time density", if
we consider the change of spacetime metric as a force, then represents the efficiency of the
conversion of energy-momentum into force through spacetime. It indicates the emergence of a
gravitational field, and should be defined as the fundamental quantity of the gravitational force of
the object, while the mass m of the object is its weighted value, which can be defined as the "mass
charge".
Direct methods to measure are not known. In fact, there are few physics equations where
and appear together [32]. This suggests that and are not directly related and that they
perform two different functions, determining the energy-momentum of the photon and
determining the gravitational field generated by the energy-momentum. The reason why various
measurements of , including methods based on quantum mechanics, show non-convergence in the
results is not because of the theoretical incompatibility between QM and GR, but we have not figured
out how the relationship between energy-momentum and space-time is constructed.
(4) They can constitute the "natural system of units". Their normalization to the value of a unit
does not affect the evolution of any physical equation. This is of great importance. Natural constants
must be a natural existence along with the ultimate axiomatic equations, and they cannot be
presented in isolation. When we ask "the origin of physical parameters and their specific values", other
physical constants must be expressions of higher-level physical phenomena, the result of derivation,
but the values of the natural constants are not the result of derivation, and there is no coincidence,
among the infinite possibilities, only the value one can reflect its existence, at the same time avoiding
the choice dilemma
2
. We can think of the natural constants as being embodied in the equations as
mere dimensions, which do not have to be seen at all, and yet retain their natural significance
permanently. They are not optional to be one, but must be one, i.e. [42]
3
. The
natural system of units is therefore the true unit dimension in physics from which the values of all
other physical constants are deduced. This is where G. J. Stoney's "nature as it really is" and Planck's
1
Dirac has a large number hypothesis, Varying G theory. He is as conjectural as those who think that natural
constants are created by the universe and do not exist eternally, or whatever "large number coincidences" are.
2
Only in this way can Leibniz's Principle of Sufficient Reason be demonstrated.
3
Barrow said, "Many people expect that a complete theory will be able to calculate some constants, such as c,
h, G, with arbitrary precision. this is an ideal scheme for testing the completeness of the theory. "We think this is a
false expectation.
17
"the quest for the absolute" [89][33, 113]
1
. Lévy-Leblond, J.-M. concludes: Universal constants thus
express synthetical transcending not of isolated pairs of In this sense, a universal constant is a "theory
synthesizer", more than a mere "concept synthesize" [97]. The unique behaviour of the physical
constants c, h and G presupposes that the laws of physics to which they are attached must be able to
determine all physical phenomena and become the unified equations of the theory of everything.
When the natural constants are determined in this way, the Planck Scales can all be normalized
to a combinatorial product that no longer embodies any scale specificity [86]
2
, including its
relationship to Compton wavelength and Schwarzschild radius. What we have thought of in the past
as the particularity of Planck scales is due to differences between baselines for defining time, length,
and mass. If such specificity is lost, we need to re-examine the relationship between new physics and
Planck scale [25].
The meaning of defining natural constants as "fundamental physical constants" and "absolute
physical constants" is clear in physics. The reductionism of physics consists of three elements, the
reduction of structures, the reduction of laws, and the reduction of constants. The natural constants
are the reduced values of numerous physical constants. Their true values, which do not have to be
calculated, cannot be deduced. What we have to do now is to find the reduced physical law with the
place where the natural constants should be and the structure of the physical primitives determined
by this law. Such a law should be the unified equation in the theory of everything.
Axiomatic Unified Equation
Pythagoras declared, “All things are number”. But a world of just numbers is a static world; it
doesn't run. It is important to have a relationship that operates automatically between numbers.
Therefore, there should also be a law that makes "Everything is in flux" [114]
3
. The relationship between
numbers and flux, as in Planck's concept of absolute units, that is, units constructed from fundamental
parameters that appear in universal and immutable laws of physics. But are there such laws [115]? If
everything flows, can “immutable" never exist? Is it necessary to demand that there should be
something which is itself a "flow" and yet possesses "immutable"? This would be the characteristic of
the theory of everything, which is able to unite all things and flows, always flowing, but never changing.
However, between abstract math and physical reality, we need to determine the primary and
secondary relationships. Abstract theorems cannot be presented without equations that operate on
physical reality. Thus, Einstein said that Maxwell's equations lead to the "Lorentz group", but the
"Lorentz group" does not lead to Maxwell's equations [62]. This is true of Special Relativity, General
Relativity, Gauge field theory, and also Noether's theorem.
A. Constants and Equations
We have established the essential and fundamental role of the constants h, c, G. Now we examine
what they specifically represent and how they are represented and conveyed in the equations of
physics. We believe that they must not only be able to generate all the other constants from the
1
Planck, “We must insist on this in our positivism-impregnated age. When in the study of any natural
phenomenon we move from that which is particular, conventional and causal to that which is general, objective and
necessary, all we do is look for the independent behind the dependent, the absolute behind the relative, the perennial
behind the transitory.”
2
New Physics relies too much on Planck Scales, but questions about their reliability remain.
3
Heraclitus is a material monist who believes that all things are modifications of fire. Everything is in flux.
18
dimension, but must also be able to generate all the laws of physics on the fundamental physical
equations. By analyzing several of the key laws and relationships that determine physical phenomena,
we will find that they are directly or indirectly related to h, c, G, and gain a clearer understanding of
the deterministic role of natural constants.
Mass-Energy Equation [116, 117]
（）
The correctness of the mass-energy equation is unquestionable [118, 119]
1
, and it reveals in
essence that the energy E and the mass m contained in matter must be related only to light, and to
nothing else, since c represents the conversion relation between m and E, and c can represent only
light. The annihilation of positive and negative matter particles into photons, , is a
reflection of this relationship.
Electromagnetic Mass [120, 121]
2
（）
is the static energy of an electron, is the static mass, and is the electromagnetic mass.
This is the earliest "mass-energy equation", proposed by Lorentz on the basis of the relationship
between electrical and mechanical properties of charged objects. It seems that one part of the mass
is related to electromagnetism and the other part is not. Thomson, Kaufmann, Abraham, Lorentz,
Feynman all agree that all masses are related to electromagnetism
3
, only one part is electromagnetic
explicit and the other part is electromagnetic implicit [122]. From the above equation, it can be seen
that the ratio of electromagnetic mass to energy is still only related to light, again showing that mass
can be formed by light alone.
Fine Structure Constants[123]
（）
This is the constant that physicists are most attached to[124-129]
4
, a measure of the strength
of electromagnetic interactions. The composition of the fine structure constant itself actually indicates
the construction of the electron. It requires that the electron must be composed of fundamental things
1
According to Einstein's method of proof, the result is approximate, but according to Planck's method of proof,
the equation is exact.
2
This is the “4/3 puzzle” of the energy-mass relation of the classical electron. Schwinger has also expressed
doubts about this, arguing that it shows no relationship to the real world.
3
There is more controversy over whether the electromagnetic mass of a charged particle represents its full mass.
The key issue here is that some composite particles, such as neutrons, do not display an electric charge, yet still have
mass. This can result in a judgement that electromagnetic mass can only be a part of mass. But we must note that all
matter particles are charged, and their composites are able to cancel out the charges as a whole, but the mass is more
of a summation.
4
There has been extensive discussion about whether the fine structure constant is constant. Using different
methods for different conditions, studies have shown that it may be variable. For example, the current assessment of
the time-varying measurements of the fine structure constant is
, or it is thought to increase at high
redshift.
19
that can embody the natural constants h, c and e, as determined by the invariance it possesses. What
we need is to find out exactly what kind of structure h, c and e express for light.
Gravitational Coefficient [120]
According to general relativity, this equation expresses the proportion of mass converted into
spacetime curvature. It makes it very clear that it is only light, and nothing else, that causes the
relationship between the energy-momentum tensor of matter and the spacetime tensor.
The Law of Black Body Radiation [87]
B
where is the Boltzmann constant, relates temperature to energy, . Equation (8)
relates the temperature of a blackbody to its radiation spectrum, and it is in the derivation of this
equation that the concept of quantization of energy arises. Since the temperature is not a real
physical quantity, cannot represent a fundamental physical constant. Blackbody radiation is
related to light alone, which means that the substantial constants h, c, contained therein should all be
represented in the expression for light.
Not only is the fundamental quantity of action of thermodynamics, but it is the fundamental
quantity of action of all physical phenomena, and for to be represented everywhere, there must
exist something that can convey the fundamental quantity of action . We already know that
is the fundamental energy of light, and there is nothing about it that can compresses its information.
The only way to make it also embody the fundamental energy of matter is to relate it through structure.
This will lead us to a reasonable definition of the structure of light and the structure of matter.
Temperature of the Black Hole [25]
Hawking emissions are a quantum effect [95, 130] as well as a thermodynamic one [131, 132].
is the conversion factor and corresponds to the weighting factor, which still do not represent
fundamental physical constants. "It must be emphasised that the expression for contains all
fundamental constants of nature." This actually predicts, in one way, that the extreme macroscopic
objects that determine These constants are the most fundamental constants of nature. From
another point of view, this means that if there is structure in a celestial body, it must still consist of the
same fundamental unit of action, h, regardless of its energy level.
In addition to the above relations, there are many other key physical relations that are determined
by the fundamental physical constants. For example, de Broglie wavelength
; Bohr
radius
; Compton wavelength
; Classical Electron radius
; Lamb shift scale
; Bohr magneton
; Magnetic flux
quantization unit
……; Of these physical constants, e, m are equally regarded as fundamental
physical constants on many occasions. However, since they are subject to annihilation, they should
obviously be excluded, and we need to find out the reason for their appearance and the true meaning
20
they represent.
B. Supersymmetry: Light Strings and Light Rings
The Unified Equation would not be deduced because it must be axiomatic and can only be
defined or discovered. The process of obtaining it can only be through analysis, searching and
judgement. It does not need new and higher energy means of verification, because physics has
evolved to the point where reliable theories and a large number of observations and experiments
have provided more than enough data, anything that can be matched to them is already verification.
The Standard Model of elementary particles is the most successful physics to date, and we follow
it to find the most fundamental physical equations, coefficients, and elementary quantities; “The
standard model is specified, in practice, by its Lagrangian. Given the Lagrangian, we can derive the
equations of our current best world-model, and their physical interpretation, following the methods
of relativistic quantum field theory” [2]. The Lagrangian contains all the physical information about
the system [133].
We must emphasize that the essence of the Lagrangian is energy, and that all theorems derived
from it are fundamentally energy-specific, whether it is the principle of least action, Noether's theorem,
general relativity, or gauge field theory [62, 134]. Energy quantization is a manifestation of universality,
rather than different forms of energy having different concepts of quantization. This dictates that
there must be a common energy primitive, which is the meaning expressed by the mass-energy
equation . This primitive must have the most basic symmetry, invariance and conservation.
Therefore, as long as we can find the basic energy unit, all the root questions can be answered.
Through the law of blackbody radiation [87] we have learned that the most fundamental energy
unit is the energy of light ; through Special Relativity we have determined that the most
fundamental momentum unit is the momentum of light
[135]. Through h and c, the laws of
conservation of energy and momentum have merged into a single law [1], i.e., energy and momentum
are always synchronized
1
; through SR and GR we know that space-time can be a variable of energy
and momentum, whether it is "Length Contraction and Time Dilation" or "Spacetime Curvature";
through the principle of uncertainty [136] we know that energy and time, and momentum and space,
are each a pair of non-commuting observables. Therefore, if we can determine the basic definition of
energy and momentum, it is possible to link all these phenomena together.
Light is the most special energy-momentum form and the clearest thing we can observe and
understand. Maxwell's equations, which has the strongest symmetry [137], is considered to express
all the phenomena of the electromagnetic field.
Faraday's Law [15]:
Ampere's Law:
Coulomb's Law:
1
The implication here is that there must be conservation of momentum if there is conservation of energy, and
that there is a fixed and unchanging relationship between energy and momentum at the primitive level. Therefore, a
stationary object must not only have intrinsic energy, but must also have intrinsic momentum.
21
Gauss' law:
where denotes the electric field, denotes the magnetic field, denotes the current
density, denotes the charge density, and we have
. The essential implication of
this equation is that the current is the product of a change in charge.
The independence and completeness of these four equations are controversial [138-141], and
although they do not have any impact on existing engineering applications, they may be deeply
problematic in terms of theoretical understanding. We have overlooked the phenomenon that all
equations contain E and H in common; that and are the "sources" of E and H
1
, respectively,
and that is the source of , and that there is no output other than this; and that all elementary
matter particles contain . If we regard an integral region as an encapsulated black box, everything
can be expressed as E and H in the outside world, or at a higher level, or vice versa.
Since their parameters are the same electric field E and magnetic field H, why are they
independent? If we consider that electromagnetic waves in free space-time correspond to bosons,
and charged matter particles correspond to fermions, can they form a supersymmetric (SUSY)
expression of the ultimate symmetry of boson-fermion [142-144], and thus achieve a breakthrough
in understanding?
Based on the observation of various physical phenomena and the examination of existing
physical theorems, together with the basic requirements of the theory of everything discussed in
Chapter II, we try to define the following axioms. These axioms are based on the known physical
foundations
2
, and they are likely to lead to reasonable answers to all physical phenomena in a natural
and rational way without any other unusual and compulsory assumptions [80]. They may dominate
the evolution of not only microscopic particles but also the entire universe under the invariance
constraints of such axioms [145].
First Axiom: The fundamental quantities of physics are time T, space S, magnetic field H, and electric
field E. They are both dependent and independent variables. Time T is characterized by one dimension, one-
way infinite extension and can be non-uniform, i.e. Δt is variable; space S is characterized by three
dimensions, two-way infinite extension and can be non-uniform, i.e. Δs is variable. Time and space exist
simultaneously inseparable and orthogonal; space-time has both coordinate and metric properties,
coordinate space-time is absolute and metric space-time is relative [145]. The magnetic field H and the
electric field E are unipolar vectors; the magnetic field and the electric field exist simultaneously inseparably
and orthogonally. The magnetic field H interacts with time and the electric field E interacts with space. The
eternal, fixed relationship between the fundamental quantities of physics is:
1
“Just as electric charge is the source of electromagnetism, or the electromagnetic force, so colour is the source
of the strong force.” [https://www.britannica.com/science/strong-force]. This is the common perception. It is natural
to think that charge is the source of electromagnetic fields, not only for electrostatic fields, but also for
electromagnetic radiation. It is never thought that it can be the other way round, never thought that charge can be
an abstract being, a product of E.
2
https://www.researchgate.net/publication/369527872_Supersymmetry-Light_String_and_Light_Ring
22
This is the Faraday equation in Maxwell's equations, where,
The initial and boundary conditions for the Faraday field equation (14) can only come from the same
equation. Since all four quantities in the equation can be variables, then under no conditions does it undergo
a sudden change and there is no singularity.
The speed of light
is eternally constant, and the following equation,
holds at all times, both in uniform spacetime and inhomogeneous spacetime. Free spacetime is homogeneous
spacetime, and spacetime with localized regions of matter is inhomogeneous spacetime. The velocity of light
is the basis of the spacetime metric , which is also the metric of energy-momentum. Due to
the inseparability of time and space, and the constraint of the speed of light c, the Faraday field equation
must have a product with its symmetry, a free-space expression for the Ampere equation (11):
Electromagnetic energy
1
: the electromagnetic energy of any region of space-time is defined and
measured by the rate of change of the magnetic field H therein with respect to time,
This differential form is always invariant. The definition applies to non-uniform time and has
global invariance
2
. Energy has no spatial directionality, only a single temporal directionality, so it can
take only positive values and its time density is finite. According to the symmetry of E and H, the same
exists for
.
Electromagnetic Momentum: the electromagnetic momentum of any region of space-time is defined and
measured by the rate of change of the electric field E therein with respect to space,
This differential form is always invariant. The definition applies to non-uniform spaces with global
1
The definitions of energy and momentum match the energy operator
and the momentum
operator in quantum field theory, and the definitions here are at the root of what makes them possible. Feynman
had devoted a large part of his "The Feynman Lectures on Physics (II)" to questions such as "Where is the energy-
momentum of electromagnetic waves and fields placed" and "Why is there an eternal flow of energy". The definition
here gives a definitive answer, and also identifies that the so-called static electromagnetic field must be a composite
result of the dynamic electromagnetic field, otherwise the energy-momentum could not be represented.
2
Hilbert had conceived an energy equation based on his definition of an energy vector. Klein called it Hilbert's
invariant energy theorem.
23
invariance. Momentum has directionality and vector superposition, and its spatial density is finite. By
the symmetry of E and H, there exists also
.
Electromagnetic energy and momentum are inseparable, i.e., electromagnetic energy and
electromagnetic momentum always occur simultaneously and together. Equation (14) can be
understood as energy drives momentum and momentum carries energy. The time occupation of
energy determines that it is impossible to measure the energy at a certain moment; the space
occupation of momentum determines that it is impossible to measure the momentum at a certain
spatial location. This is the source of their respective "uncertainties" [69].
In differential expressions (18) and (19), by default classical physics assumes that time t and space
s are uniform, i.e., the metric is always invariant; in GR it is assumed that time and space are
uniform but can be curved with the expression. We redefine the properties of spacetime as
always flat but can be non-uniform.
The inhomogeneous spacetime is the modulation of the homogeneous free
spacetime (empty space) by matter, which is usually a function of spacetime
coordinates [145].
Note the difference between the space-time coordinates and the spacetime metric
at a given spacetime coordinate point. We define that the Pythagorean theorem Eq.
(16) holds under any condition, which expresses a flat spacetime. If , then the space-
time there is a uniform flat space-time, otherwise it is a non-uniform flat spacetime. Unlike the
definition of Space-Time Curvature in General Relativity, when expressed in terms of , it is always
a diagonal matrix, . The non-uniform spacetime actually represents a
"space-time density" and the amount of energy and momentum contained in the space-time itself.
This is the result of the adjustment of the "density of matter" represented by the Faraday field
equations to its "space-time metric density". We define:
Spacetime Energy
1
: Spacetime energy is defined and measured by a metric attached to free time,
It is actually generated by electromagnetic energy in material form and is generally a function of
space-time coordinates.
Spacetime Momentum: Spacetime momentum is defined and measured by a metric attached to free space,
It is actually determined by the electromagnetic momentum of the material form, which is
generally a function of space-time coordinates.
1
The spacetime energy-momentum expression here matches the spacetime gauge expression in general
relativity. The difference is that the energy-momentum is directly assigned to it and is no longer spacetime curvature.
24
Free spacetime does not contain any energy-momentum and is set to zero energy-momentum
spacetime, the lowest reference point for spacetime energy-momentum. The existence of any
material particle gives rise to spacetime energy-momentum, i.e. the energy-momentum of the
gravitational field. There is no electromagnetic field energy-momentum in pure spacetime energy-
momentum, but there is spacetime energy-momentum in the electromagnetic energy-momentum
field, except for free electromagnetic waves. Special Relativity's "Length Contraction and Time
Dilation" and General Relativity's "Spacetime Curvature" are both manifestations of changes in
Spacetime Energy-Momentum.
Second Axiom: The Faraday field equation (14) is the fundamental equation, and any initial and
boundary conditions still come from the same equation and do not depend on any other conditions. Equation
(14) has two stable solutions, a "light string" in a free homogeneous spacetime and a " light ring" in a non-
homogeneous spacetime. Light strings are the smallest building blocks of all energy-momentum, and there
are an infinite number of them, all of which propagate in a stable quantum form in free space-time. The light
ring consists of light strings, of which there are an infinite number, but only a very small number of which
have observable stability, and is the smallest building block of material particles.
The wave function of a Light String is a single period sine wave
1
,
It consists of an orthogonal electric field E and a magnetic field H, where h is the Planck constant,
the minimum amount of action, in Js. According to the first axiom, the energy of a light string is the
photon energy , and the momentum of a light string is the photon momentum
,
matching the definitions obtained from blackbody radiation and Special Relativity. It is actually the
photon in free space. Light strings can be cascaded or combined without restriction according to the
Faraday field equation (14).
The wave function of a Light Ring is a closed Light String in the complex plane,
This is the physical entity formed by the spatial encirclement of the superposition of two light
strings of the same frequency with a phase difference of
. We call this the "Euler Light Ring",
which is the fundamental unit of the particles of matter and is the basis for why imaginary numbers
can exist in physics [146-150]. If we take just its real part, i.e., the light ring is composed of a single
row of light strings, we see that it would be another, more widespread particles of matter [151]
2
. The
direction of rotation of the light ring introduces a conjugate symmetry that determines its positive
and negative properties. The light ring can be combined arbitrarily according to the Faraday field
1
Quantization is an inevitable choice for the physical world. The real world does not allow for responses
at local interactions, i.e. all expressions must be physically achievable. According to the Fourier transform, it requires
that both the time and frequency domains must be discrete. For example, when an electron is impacted, the exchange
of energy-momentum can only be physically achievable if it is "discontinuous". The "discontinuity" must be free of
abrupt changes, which also requires that all energy-momentum exchanges can be expressed continuously. Note the
different roles of h and ν here.
2
If we just take its real or imaginary part, the particle from which it is made would not have a charge, but would
still have mass. That's exactly what we want for a dark matter particle.
25
equations.
This ring structure is divided into two parts of inner and outer symmetry by its radius and
left and right symmetry by the complex plane. This structure is very important in that it has no energy
level limitations and is capable of generating all the properties of fermions as well as black holes,
including charge and its potential field, spin, mass, gravitational field potentials, and rationally explains
the phenomena of gauge invariance, asymptotic freedom, confinement of quarks, and general
covariance [21]. The radius is similar to a "trapped surface", which provides a barrier to the virtual
"singularity" that must exist at the centre of the light ring [152-154]
1
, and can resolve the "infinity"
puzzle [120]
2
. This is also the reason why "Renormalization" [155] is effective.
The continuous interconversion between the light string and the light ring can be achieved, which
is equivalent to the conversion between Special Relativity and General Relativity, from Lorentz
invariance to diffeomorphism invariance. However, the intermediate states of the transition from the
light string to the light ring, the energy forms between the light string and the light ring, are all
unstable states, although they still obey the Faraday field equations. The parameter describing this
state can be defined as the "closure degree" of a string, i.e. the angle of the centre of the circle
corresponding to the length of the string, which varies in the range of 0~2π. The intermediate state
is unavoidable, and is a manifestation of the continuity of the supersymmetric transition.
The light string is the most elemental unit of electromagnetic energy-momentum, which
determines the light ring as the most elemental unit of energy-momentum of material particles, and
thus will also determine the elemental unit of spacetime energy-momentum of the gravitational field
generated by material particles.
Third Axiom: the sum of "electromagnetic energy-momentum" and "spacetime energy-momentum" is
invariant, i.e., the energy-momentum of any interaction is conserved. If there are I interacting
electromagnetic objects and J purely gravitational fields in a local region, the sum of the energy-momentum
of the local region can be expressed as a superposition of them:
where
denotes the electromagnetic energy-momentum of the interacting
object, and denote the spacetime energy-momentum of the interacting region,
respectively. There are two kinds of spacetime energy-momentum, the energy-momentum of a pure
gravitational field detached from the source, i.e., the gravitational wave form [156], and the gravitational
field that is not detached from the source but the source does not exhibit electromagnetism, i.e., the usual
macroscopic gravitational potential.
1
Coincides with Hawking's Singularity Theorem, but the light ring never can reach that singularity until
decomposition due to various factors occurs. This is presumably the singularity that Einstein imagined for elementary
particles, surrounded by huge vector fields.
2
Feynman said "We don't yet know how to form a consistent theory - including quantum mechanics - of how
electrons, or any point charge, don't give rise to an infinitely large self-energy. And at the same time, there is no
satisfactory theory that describes a non-point charge."
26
What is expressed here is that all interactions must be transmitted via either the electromagnetic
field or spacetime
1
. The result of their interaction is a linear superposition of the electromagnetic and
gravitational fields within the constraints of the Faraday field equations, both of the fields change. All
interactions force the conservation of energy-momentum, which forces the differential process of the
electromagnetic field to change, causing the object (the energy-momentum package) of action, which
is dominated by the electromagnetic field, to move in spacetime, and the effect of the "force" arises
as a result.
The Faraday field equations contain all the fundamental quantities of mathematics, scalars,
vectors and spinors, and the binding relationships between them. When they are converted into
physical fundamental quantities, space-time is fused into energy-momentum, which becomes
everything; the expression of everything is the field equations; and the universe is a field without
boundaries superimposed on the fields of everything. The evolution of the universe is the evolution
of the energy density expressed by the field equation
2
. From the differential equation perspective,
everything is motion. The motion of a finite density, infinite total amount of energy-momentum in
infinite time and space, from microscopic to macroscopic, in the interconversion of the two states of
the light string and the light ring, will deduce all the physical states and the basic mathematical
relations
3
.
Therefore, Faraday's field equations are the "axiomatic equation" and "unified equation" of the
theory of everything [157]
4
. Eq. (26) and (27) reflect the interactions between the fundamental
quantities during the interaction. In contrast to the "unification equation", which is also based on
axioms, Gustav Mie's world function that would lead to an electromagnetic theory
of matter[158], Hilbert's world function , which was invariant under general coordinate
transformations
5
, Weyl's world function
, and Einstein's Lagrangian
equations H=B+M [23], we have the same goals and ideas, the key difference lies in the definition
of the axioms and the specific energy-momentum.
The basic basis for judgement of the correctness of the axioms and unified equations presented
here should be whether or not it can satisfy the conditions required by the theory of everything
presented in Section II. Since all the parameters of the Faraday field equation are defined as complete
variables, it is clear that it cannot have singularities, and the key to uniqueness and completeness lies
in its ability to satisfy Maxwell's equations and express all the properties of the elementary particles
6
:
charge, spin, mass, and gravitational field.
C. Properties of Matter and Sources of Forces
According to the standard model of particle physics [21], bosons and fermions have different
1
Even light determined by this equation can be considered as a result of E and H interacting with spacetime.
2
Broadly speaking, the concept that microscopic elementary particles, macroscopic stars, and black holes all
belong to energy packets, which all have specific energy densities.
3
This even includes irrational numbers, such as the formulation of quasi-periodic structures in condensed matter
physics.
4
"So far as we can see today, the laws of physics cannot have existed from everlasting to everlasting. They must
have come into being at the big bang”. For this type of opinions, we need to ask whether the Big Bang is not
constrained by equations.
5
The Lagrangian , where K is the Riemannian curvature scalar and the electromagnetic Lagrangian L
depends on the metric tensor , but not on its derivatives.
6
Orthogonal composite structures of elementary particles would exclude the need for "color".
27
physical properties. The bosons include, the photon γ, which transmits electromagnetic interactions,
with no mass, no charge, and spin; the [159], which transmits weak interactions, with mass,
charge, and spin; and the gluon, which transmits strong interactions, with color charge, no mass, and
no charge. Fermions include three generations of matter particles, all with mass, charge, and spin
properties, with quarks also having the property of color charge.
The standard model is a successful theory, but it is not a completely correct one, with many flaws
and Unnaturalness [30, 143, 160-163]. Wilczek, discussing the problems of the standard model, said
that "A fundamental constant is a parameter whose value we must supply in order to specify the
Lagrangian of the standard model" [2]. This must have touched the root of all the problems. Modifying
these deficiencies requires answering several important, but easily ignored and even dismissed,
questions at the root: why do fermions have this property and not that, how are these properties
bound together, what should be their origin, and should they be the product of structural symmetry?
If these questions are avoided, the Standard Model will be confined to the current description of
symmetries and no further progress can be made.
Among the various properties mentioned above, if we do not know the structure, then we can
only distinguish the nature of bosons and fermions from the properties. However, when we set light
strings and light rings as the basic structure of elementary particles, this structure should embody and
match various properties. In our empirical perception, photons and electrons are the typical two
elementary particles, and the difference in their properties should represent the difference in the
essence of bosons and fermions. The following simple argument will give the conclusion: the essential
difference between bosons and fermions is the presence or absence of mass
1
, and mass is a product
of structure; all fermions possess two pairs of properties, electric and magnetic charge, mass and
gravitational field, .
The vector decomposition theorem of Helmholtz states that any three-vector field that vanishes
at spatial infinity can be expressed as the sum of two terms, the longitudinal and transverse
components, which have the properties [164]
，
Looking at the Maxwell‘s equations, the Helmholtz decomposition is the decomposition of the
orthogonal field in Euclidean spacetime, into another form of orthogonal field. Electromagnetic waves
in Euclidean spacetime are two orthogonal fields, sinusoidal E and H, which are dynamic. When they
curled, they became static orthogonal fields, still E and H. But one was a radial vector field and the
other was an axial spinor field. H was the spin corresponding to time and E was the vector
corresponding to space. This is the necessary and only form. The conversion of the light string field
to the light ring field satisfies this decomposition transformation.
According to the axioms, electric fields and space interact, and when a light string is bent into a
ring of light, the transversely vibrating electric field is converted into a radially vibrating electric field,
and the tangential direction of the ring of light presents a magnetic field perpendicular to it, which is
the only option in which the two fields can be expressed orthogonally. When the sinusoidal and
1
The difference between bosons and fermions in the Standard Model is whether the spin is integer or not. Here
the spin of a light ring and the spin of a light string are two different modes of operation; the spin of a light string is
polarization in the direction of propagation, and the spin of a light ring is propagation around. But the spin number
still holds.
28
cosinusoidal rings are superimposed, there is the Euler ring expression (25), which presents a constant
positive and negative electric field associated with [87]
1
. This is the same as that produced by
positive and negative "electric charge" [165-167]
2
and satisfies Coulomb's law in Maxwell's equations
(12). Therefore, it can be argued that the "charge" is not an entity or an independent property [85]
3
,
but rather an effect of the electric field presented by the synthesis of the light ring [168, 169]
4
. This
solves the problem of how to keep charges from splitting due to mutual repulsion if they are
distributed [50, 170, 171]
5
. The "charge" is a conserved quantity under the condition that the ring
structure is invariant, it not only has the same positive and negative charges, which remain invariant
under any rotational transformation , but it is also Lorentz invariant independently of the
magnitude of the energies (masses) that make up the ring, i.e., independently of the frequency of the
light strings. This is precisely the reason why the energy levels of the three generations of elementary
particles in the Standard Model can differ enormously [172], and yet the charges are all of the
fundamental magnitude
.
The magnetic field H, orthogonal to the electric field E, interacts with time, and the unipolar
magnetic field exhibits in the axial direction (perpendicular to the centre of the complex plane) a
constant positive and negative magnetic field associated with a constant amplitude . At + the
magnetic field passes through the centre of the light ring from left to right; at - the magnetic field
has the opposite polarity and passes through the centre of the light ring from right to left. Regardless
of the direction, the magnetic field at all times exhibits a "bipolarity" as defined by the ring surface,
exactly the same as the magnetic behaviour of a closed current ring
6
. That is, on one side the magnetic
field enters the ring and on the other side it leaves the ring, making it appear that the ring has both
an S-pole and an N-pole at the same time. This can actually be regarded as an indivisible and equal
bipolar "magnetic charge". It fulfils Gauss's law (13) and the divergence is always zero. In a ring
structure, the magnetic field lines must pass through the ring and it is impossible to form a unipolar
magnetic field, thus denying the possibility of a "magnetic monopole" [173]
7
. The intrinsic spin
1
Planck said, “Probably the most direct support for the fundamental idea of the hypothesis of quanta is supplied
by the values of the elementary quanta of matter and electricity derived from it”. This suggests a close relationship
between h and e.
2
Thomson: the cathode rays carry a charge of negative electricity, measurements of the ratio of the mass of
these particles to the charge carried by it; Millikan: the oil drop experiment to provide confirmation of the
elementary electrical charge.
3
In 1963, Dirac made an interesting conjecture regarding fundamental constants in physics, “The physics of the
future, of course, cannot have the three quantities h, e, and c all as fundamental quantities. Only two of them can be
fundamental, and the third must be derived from those two.
4
Based on measurements of the electric field of the electron, the early "charge" was actually something we
surmised. This concept was reinforced by the discovery of discrete and conserved e. We always thought that it was the
"charge" that produced the electric field, and we never thought about whether the electric field would produce the
"charge". The non-integral charges of late quarks were derived by M Gell-Mann and George Zweig based on the
eightfold way and the conservation of charges, "triplets with integral charges".
5
To solve this problem, Poincaré had supposed that there was a sustaining force of a non-electromagnetic nature
inside the electron. From a feasibility point of view, any description of charge would be mutually exclusive, or a
singularity. Therefore, the best answer is that there is no charge, only an electric field. A synthetic "charge" is the only
correct solution. From a modelling point of view, this can be thought of as a spherically distributed charge with radius
R0.
6
The consistency between the classical current ring model of magnetism and the light ring model looks like a
coincidence.
7
This is consistent with Dirac's charge-magnetism relationship, but there will be no magnetic monopoles. The
magnetic charge will be in the form of magnetic moments due to the presence of scales. This is exactly how the
29
magnetic moment of a fermion is generated by the "magnetic charge" [174, 175]. The spin quantum
number is determined by the number of light strings that make up the ring. A light string is one cycle,
so when the ring is made up of two light strings linked in a closed loop, it takes two cycles for the
light to travel around the ring, so its spin quantum number is 1/2. This is the minimum number
required to form the ring structure, and it can be kept constant during interactions, such as the
transformation of d quarks into u quarks in the weak interaction.
There are various analogues for spin, but there is no agreement. Schmitz gives the closest
description to the definition given here [21].
What spin really is, is not known. There are many physicists that will just say that spin is an internal
degree of freedom, thereby stating that it does not make sense to explain qualitatively what spin is because
we really do not know exactly. We just know its properties in a mathematical sense……. Spin can be viewed
as a wave going around on a circle. This spin wave is part of the waves that make up a “particle”. One could
see that wave as a helix. The spinning property of waves originates from the relativistic properties of space-
time. One could say that the vacuum imposes a “standard” type of circle on all particle waves.
It is clear that his starting point is based on the quantum field theory that elementary particles
originate from vacuum excitations. This paper does not support this view, but rather argues that all
elementary particles are modelled on a common light-ring structure, which can answer the question
of the origin of "identical particles" as well as the question of "zero-point energy".
C. N. Yang has given a talk on spin which, after a brief historical review, raises three questions
that remain unanswered [175]
1
:
“The concept of spin is both an intriguing and extremely difficult one. Fundamentally it is related to
three aspects of physics. The first is the classical concept of rotation; the second is the quantization of
angular momentum; the third is special relativity”.
The light ring gives reasonable answers to these questions: the spin is not mechanical spin but
light spin, so there is no question of superluminal velocities; the spin angular momentum must be
quantized because the ring is made of photon; all light is Lorentz-invariant, and the ring itself is light,
which must be in accordance with Special Relativity.
The stability of the ring structure of light is an important issue, as the light string momentum of
the closed coupling, if no other disturbances are taken into account, possesses on its own the power
to maintain that it will not break. We need to emphasize that when light has only two topological
states to choose autonomously, it can only be either/or. How it chooses depends on the state of
spacetime, which is never in a difficult situation, because the four fundamental quantities in the
Faraday field equations are all variable. And the state of spacetime may be the only thing that
determines the emergence of hierarchy of masses.
The light ring that has been formed changes the spacetime metric around it, in the ideal case
forming an equal metric distribution around the circumference of different radii. If we borrow the
expression from general relativity, this is the formation of . The reason here is that
the light ring, in order to satisfy the Faraday field equations in the curl case, its electromagnetic field
properties of electrons manifest.
1
In this speech, C. N. Yang also pointed out the problems in the physics community. He said, “When we do
something in physics, after a while, there is a tendency to forget the overall meaning of what we are working on. The
long range perspective fades into the background, and we may become blind to important a priori questions.”
30
must propagate along the circumference while also spreading in the radial direction. And in order to
maintain energy-momentum conservation at the same time, it must cause the sinusoidal wave
synchronized along the circumference to decay radially according to
, which forces a
simultaneous change in the spacetime metric wherever it goes, i.e.,
decays by changing the
spatial metric as r increases, resulting in the formation of a non-uniform spacetime. The
magnetic field, orthogonal to this axial direction, also obeys such a requirement, differing only in
direction. The change in the metric of the spacetime field produces a gravitational field, and this is
the source of the consistent expression of Coulomb's law and Newton's laws of universal gravitation.
This is also the reason that all potential fields are associated with energy and can be expressed in
Lagrangian and Hamiltonian quantities.
The interpretation of should not be "Space-Time Curvature", but should correspond to
the "Energy-Momentum Density" which leads to the change of Space-Time, and be interpreted as
"Space-Time Density", which is the most direct and complete expression of . The gravitational
constant G will bind the transformation of the light ring energy-momentum to the
space-time metric, namely
This direct expression is the same as Einstein's original expression of the field equations,
[176]. G is the supersymmetry transformation factor for light, which does not change anything
about the nature of light, but changes only the distribution of the energy-momentum density in
spacetime. The mass-energy equation, which relates mass to energy, only defines an
equivalent conversion and does not reflect the original meaning of mass. Only the gravitational
constant G embodies the inertial meaning of mass, which would require it to be consistent with Special
Relativity.
Abandoning the complicated Riemannian geometrical description of general relativity
1
and
changing the concept of "gravity = spacetime curvature" [177] to "gravity = spacetime density" does
not result in any practical loss of functionality. It maintains the flat and dynamical nature of space-
time, which makes Noether's theorem valid under all conditions [99], and explains how the
gravitational force is generated, which solves the energy-momentum formulation problem in general
relativity [178, 179]
2
.
To the light ring itself, it is still travelling along the "straight" path of its own made, exactly like a
light string in free spacetime. The difference is that the light string travels in a straight line through
infinite spacetime, whereas the light ring travels in a perpetual circle through a limited local spacetime.
This is also the reason why permanent magnetism exists and why magnetism is always indivisible into
unipolarity.
C. N. Yang has also repeatedly emphasized when talking about spin [175]
3
:
1
We need to remind that Einstein never made any argument or explanation for choosing the concept of
spacetime curvature in his study of GR. He emphasized the dynamical, dielectric nature of spacetime, but never
considered expressing the density concept in terms of a metric, even though it is more compatible with the Length
Contraction and Time Dilation effect in SR.
2
Strictly speaking, it is energy-momentum conservation that determines General Relativity, not General
Relativity that chooses energy-momentum conservation.
3
This question was first posed by Tomas.
31
And most important, we do not yet have a general relativistic theory of the spinning electron. I for one
suspect that the spin and general relativity are deeply entangled in a subtle way that we do not now
understand.
Although it is not clear what he based it on exactly
1
, our description matches his conjecture that
spin and gravitational fields are inseparably linked, and that without the spin-ring structure of light,
the gravitational field would not arise. Although they can be expressed separately, they are
not independent things unless the gravitational field propagates out of matter, as in the gravitational
wave scenario.
Another important property of material particles is "mass" [180]. Weyl observed the nature of
mass and charge when he said, "But mass is a gravitational effect: it is the flux of the gravitational field
through a surface enclosing the particle in the same sense that charge is the flux of the electric field"
[181]. Light strings do not have mass
2
, only light rings that can be relatively stationary have mass. The
"mass" of the light ring is the damping effect on the forced motion caused by the ring in order to
maintain the constancy of its speed of light and the conservation of energy and momentum. The
essence of the forced motion is to change the current energy-momentum and spacetime state of the
light ring. mass is the official "charge" of gravity [21], just as the "charge" is not externally given, "mass
charge" does not need to be provided by an external Higgs field
3
through "coupling", but it can be
fully explained by the Higgs mechanism [63].
The quantum field theory explanation of the Higgs mechanism is usually formulated as follows
(cf. Fig. 1):
The potential, V, as a function of the complex field,. The U(1) symmetry, , corresponds
to rotations about the vertical axis. The vacuum state is chosen to lie along the direction. The two
frequencies of oscillation about this vacuum are shown; the radial mode is the Higgs boson, the angular,
zero-frequency mode is the Goldstone boson [182].
We associate the light ring to this interpretation, where the electric and gravitational potential
fields of the light ring exhibit symmetry bounded by the radius of the light ring. The external
potential field decays as the distance r increases , and similarly the internal potential field
should show a trend of decay as r increases (radially inwards to the single point at the centre;
is not taken here, both for the purpose of symmetric expression and to match the trend of the
spacetime metric). This results in an extreme state at radius . This trend expression is the same as
for the Higgs potential and we can still explain the formation of mass following the symmetry breaking
of the Higgs field [183, 184]. When the light ring is not undergoing any motion in the stationary
inertial system, it is in a state of complete symmetry, with the intrinsic light running around without
resistance, as shown in Fig. 1 in the bottom dashed ring. This is actually the internal spin of the light
ring in the steady state. When there is no external action, it does not show mass effect, so the light
ring at this point can be considered as a product of the global symmetry breaking of light strings, in
1
What can be guessed is that the conversion of Dirac's electron theory to gravity makes sense.
2
Also gravitational waves don't have mass.
3
Physicists have also proposed many Higgsless models.
32
accordance with the Goldstone theorem
1
[185, 186], and its rest mass is shown to be zero [187]
2
, i.e.,
it belongs to the Goldstone Boson [188]. However, once it is forced to move by an external action, in
either direction, the original space-time state no longer satisfies the Faraday field equations, and the
stability of the speed of light faces disruption. At this point, the light ring will undergo "symmetry
breaking", forming a "damping" in the direction of motion, forcing the light ring to deform or move
as a whole in order to maintain the invariance of the Faraday field equations. The effect of this
damping is expressed as "mass". Since the Faraday field equations are linear equations, the mass must
be proportional to the energy of the light ring [189, 190]
3
Nambu argues that the mass hierarchy
problem is related to spontaneous symmetry breaking (SSB), "The BCS mechanism seems relevant to
the problem. It generates a mass gap for fermions, plus the Nambu-Goldstone and Higgs modes as
low-lying bosons" [183]. The most plausible explanation seems to be provided here.
Fig. 1 The Higgs potential is similar to the potential field of a light ring, with its extreme point at the radius. At rest, the light
ring is perfectly symmetrical, and the intrinsic light runs freely around it. However, when subjected to an external action, the
light ring has to move in one direction, and the principle of constancy of the speed of light, the conservation of energy and
momentum, dampens this change, which leads to a "symmetry breaking" of the light ring. This is the true expression of
"mass". Moreover, when two or more light rings are orthogonally nested, this potential field distribution also produces
"asymptotically free" strong interaction effects. For example, three orthogonal light rings (similar to the proton structure) are
stable structures, but an attempt to pull out a light ring will be met with increasing resistance as the potential difference
between them grows further away. The Higgs potential field may have multiple modes [191] such as Landau-Ginzburg Higgs,
Nambu-Goldstone Higgs, etc. Their corresponding physical reality may be a parallel nesting of multiple concentric light rings,
and hence multiple peak points. The figure is taken from the literature [182].
1
Goldstone’s theorem: “if there is continuous symmetry transformation under which the Lagrangian is invariant,
then either the vacuum state is also invariant under the transformation, or there must exist spinless particles of zero
mass.” According to this principle, this actually means that there must be a corresponding light ring for the light
strings, and that the concept of supersymmetry is equivalent to a symmetry breaking.
2
The relevance here to Penrose's notion of the zero-rest-mass field equations for each spin (s=0, 1/2, 1,
3/2 …….) remains to be investigated.
3
In this sense of light damping, the concept of negative mass would not exist in reality. This should have
consistency in relation to the positive mass theorem.
33
The principle of equivalence shows that the Inertial and Gravitational masses of an object are
indistinguishable [22, 192]. Here is provided the fundamental basis that they must be the same, that
they are not mutually independent phenomena, and it is shown that all interactions are equivalent,
independent of the cause of the motion of the object, and independent of the scale of the object. If
we think, in turn, of the phenomenon that the acceleration of different objects in a gravitational field
is independent of the nature of those objects, and that they are always the same [1], it can only be
shown that the objects must have exactly the same mechanism of interaction in order to be able to
provide such a guarantee. Thus once we have clarified the origin of mass, the equivalence principle
becomes a concept that has no need to exist.
This effect of mass can also be understood from another perspective. When an external force
compels the light ring to move, energy-momentum must be transferred to the light ring, and the
light ring must receive and store it. The only way to do this, according to the aforementioned
definition of energy-momentum, is to change the frequency and wavelength of the light ring, i.e., to
reduce the scale of the light ring (in the view of a third-party observer). This is a manifestation of the
"Length Contraction and Time Dilation" effect of Special Relativity. An increase in the energy-
momentum of the light ring must be accompanied by an increase in its mass. This is a change in the
state of the real physical structure, which is the same as the expression required by GR (29).
There exists another physical form of the Euler light ring. If one just takes its real or imaginary
part, i.e., the light ring consists of a single row of light strings, it would not be able to synthesis electric
and magnetic charges, yet it would still have mass. Matter particles in this case are exactly what we
require for the nature of dark matter particles, whether one considers neutrino dark matter or
Majorana dark matter [193, 194], or supersymmetric dark matter [195], Q-Ball dark matter or
Primordial black holes as dark matter [196, 197]. Moreover, it can be intuitively concluded that under
equal conditions in the formation of light rings from light strings, the more frequent stable states will
be such rings. There is an agreement between this ratio and current cosmological estimates of the
proportion of matter, such as 90% of the galaxy is dark matter (DM) [198], matching the greater
production and survival chances of dark matter particles.
Euler light ring can be composed of different types of stable particles through different
composites based on the constraints of Faraday's field equations, ultimately forming symmetries
specific to matter. SU(2) is defined in two orthogonal complex dimensions with four different
combinations of quadrants; SU(3) is defined in three SU(3) is defined in three orthogonal complex
dimensions, with eight different combinations of quadrants. There are an infinite number of
possibilities for these combinations, which hold at all energy levels, but very few of them can have
appreciable lifetimes, for reasons that we cannot yet speculate on, but the only factor is space-time
conditions. In any case, the basic composition of all particles is a light ring, and their composite form
does not destroy this structure, since everything must operate according to the Faraday field
equations. The three generations of particles in the Standard Model are among the survivors, with
quarks and leptons having natural unity. As for the single light ring, since it does not have a synthetic
charge, it cannot be composited into stable particles of matter, and exists more in an isolated form
that is difficult to interact with, which makes it "dark" in that it does not radiate or absorb photons.
Einstein once surmised that the elementary particles of matter are, by their very nature, nothing
more than the condensation of electromagnetic fields ……; if the gravitational field and the
electromagnetic field were merged into a single unified entity, that would, of course, be a huge step
34
forward [1]. The literature [199] argued, ”the Lorentz program of a ‘purely electromagnetic electron’
can be completed successfully, in the stationary setting at least”. “the properly renormalized purely
electromagnetic particle consists of an additional contribution which we call photonic, for it is the
mass of an object without rest mass which rotates with equatorial speed equal to the speed of light.”
The three aforementioned equations (24), (25) and (29), affirmed the electromagnetic properties
of the matter world, and the three natural constants found the most reasonable position and
relationship. They are implicit in the unique equation Faraday's field equation, and they are explicitly
taken as unit values, . Instead of changing any physical formulation, this reflects the
nature of physics even more.
Light strings and light rings provide clear answers to various difficult concepts in quantum
mechanics [122]. They are particles made of waves and therefore have "wave-particle duality"; they
have an intrinsic frequency that can be related to the wavelength of matter, as conjectured by De
Broglie [200, 201]; their energy has a specific duration, their momentum occupies a specific space,
they are not point particles, and therefore their measurements must have an "uncertainty" [69]; The
wave function is still essentially an electromagnetic field, so both photons and electrons interfere with
themselves in an interferometer [202], whether it is a single particle or multiple particles …….
Physics is committed to the unification of the "four forces", but there is no definitive definition of
a force. If force is the process of interaction, is "coupling" a force? What kind of force is at work in
"positive and negative electron annihilation"? Where does the motivation for "quantum fluctuation"
come from? The unification of forces should not be a search for more forces, but a search for
something common among the existing forces. If the four forces are independent, then there is no
question of unification; if the four forces are the same, then there is no hierarchical problem of
unification [172], and there should not be the question of unification at what energy level [203], they
should be united at all times and in all places.
“Force and substance. Supersymmetry bring those together”, ”Supersymmetry, by allowing
transformations that exchange bosons and fermions, re-establishes unity” [203]. If we look for the
unity of forces only, instead of the common unity of matter and forces, then it is impossible to reach
the final goal. Once we have defined the energy-momentum according to the Faraday field equations,
the conservation of the energy-momentum not only determines that the mechanism of all interacting
forces is the same, but also that the structures and interactions of the elementary particles are identical.
All interactions are transmitted and exchanged through the four fundamental quantities, the time and
the space measures, the electric and magnetic field strengths. This is actually the same understanding
of the concept of force as in quantum field theory, except that it goes one step deeper by specifying
the meaning of the energy-momentum field, which gives a visual and concrete expression.
The "gravitational redshift" is one of the most intuitive exhibition of interacting forces [204]. When
a photon of wavelength λ is generated from a star and moves away from it, the spatial and temporal
metric of the star, , changes with the distance, and the wavelength and frequency of the
photon are forced to change with the spatial metric of the gravitational field in order to keep the
speed of light constant. When the spatial metric of the gravitational field becomes longer and longer,
the wavelength of light becomes longer and longer, which is actually the interaction between photons
and space-time.
Explaining matter particles in terms of this scenario is the same because they are all light. The
four fundamental quantities of any particle have to respond to any change in external conditions that
occurs, most notably a change in the spatial metric causing motion. For example, when two electrons
35
appear, each of their four fundamental quantities has to affect the other, and both must respond
under the condition of conservation of energy and momentum. The Faraday field equations, each
operating independently of the other, become at this point a co-operating equation, requiring that
they must be satisfied at all points within the region of spacetime that they jointly occupy. As a result,
electrons of the identical charge must separate in order to compensate for the enhancement of the
electromagnetic field in the region of intersection, and electrons of the opposite charge must come
closer together in order to compensate for the weakening of the electromagnetic field in the region
of intersection. This is the nature of force [23]
1
, which is a process of adaptive regulation based on the
conservation of energy-momentum, changing the spacetime metric or being changed by the
spacetime metric.
We can think of gravity and electromagnetism as different manifestations of the same force, or
that gravity is just a by-product of electromagnetism [23]
2
. But in the microscopic case, the abstract
gravitational force no longer exists, and both the weak and strong forces are electromagnetic forces,
but the spacetime metric becomes a more influential variable in the field equations. The so-called
"the Hierarchy Problem" is only an illusion due to the different structural environments, distances and
functions. Electrons travelling in atomic orbitals are mainly electromagnetic, while the nucleus is not
split by the strong force, which is the difference in distance; the weak force is the conversion between
two different light rings in the same structure, while the strong force is trying to pull out a light ring
in the same structure, which is the difference in function. We only need to be clear that structure is
the result, not the cause, of acting forces, i.e., it should be known that the forces must have a common
source to make Baryogenesis, Big-Bang nucleosynthesis (BBN) possible at the beginning of the Big
Bang [205].
Light strings and light rings represent bosons and fermions, respectively, which are expressed by
unified equations, and this supersymmetry unites forces and matter [203], without emphasizing the
concept of virtual particle exchange. If we call mass "mass charge" or "gravitational charge". Then,
when a light string is converted into a light ring, the electric charge undergoes the transition
and the mass charge undergoes the transition . Between light strings and light rings, there is
no stable third state. Under dense spacetime conditions, they cannot both be completely destroyed;
they can only transform into each other. particle exhibits the intermediate result when a d-light-
ring transforms into a u-light-ring. We have not been able to determine the true cause of this
structural problem, which appears to have a statistical "lifetime". However, the light ring does have a
lifetime factor in that it has a "virtual singularity" at the centre of the ring that is constantly approaching
over time [1]
3
. The extension of the field of the light ring is symmetric inside and outside, with the
radius being a definite reference, and the energy density tends infinitely to zero outside, but not
1
One can compare Mie's thought, “In Mie’s theory, the forces that hold atoms and electrons together should
arise naturally from the formulation of Φ, whereas in the classical theory of electrons the forces have to be
specifically added.”
2
Note the difference here with Einstein's view that microphysics has nothing to do with gravity: Hilbert’s ambitions
for a unified field theory of “everything” passed over to a ready acceptance of Einstein’s position, namely that general
relativity had no immediate relevance for microphysics [Renn/Stachel 2007].
3
Einstein was at all times very concerned about singularities, and in discussing Lorentz's unified theory of
electromagnetism he commented that "……. corresponds to a solution having a singularity. Physicists have therefore
tried for a long time to achieve this by modifying Maxwell's equations, but these attempts have not been successful";
"the whole theory must be based only on partial differential equations and their solutions without singularities".
Uniform equations must have singularities, and avoiding them is the only way not to destroy causality.
36
inside. The internal spacetime is compressed by the curl
1
, and the internal and external time metrics
are reversed. As , , , , , i.e. the spacetime metric tends to the
free spacetime metric when the field extends outwards infinitely. As , , ,
, , i.e., when the field is constantly approaching the centre, the time metric becomes
infinitely long, and hence time is infinitely slow [152]
2
; the space metric becomes infinitely long, and
hence the scale becomes infinitely short. This is clearly consistent with the "Length Contraction and
Time Dilation" of SR, in which the speed of light
always remains the same, regardless of
whether the extended field is outward or inward. In this case, the inner field of the light ring can never
enter the singularity within the constraints of the Faraday field equations [154]
3
. It can only keep
approaching the singularity until the process reaches a certain limit or encounters some external
interference, and the light ring form is forced to transform either directly into a string of light of the
corresponding energy, or into some other light rings. Decay appears to be such a process, annihilation
appears to be such a process, and black hole explosions are likewise such a process.
The conditions for interconversion between light strings and light rings are determined by the
environment. Indeed, positive and negative particle annihilation is one of the situations in which a
light ring is converted into a light string [206]. Hadron colliders, on the other hand, may convert one
light ring into a light string and another light ring at the same time. "Pair production" is one of the
scenarios in which light strings are converted into light rings [207], which also includes the production
and radiation of particle pairs during Hawking's radiation process [130, 208]. Pair production actually
simulates the production of elementary particles during the early evolution of the Universe, where
high-energy light enters the interior of matter, which is equivalent to entering spacetime with
increasingly dense energy-momentum and increasing gradients. The large difference in the
spacetime metric gradient relative to the wavelength of the incident light is an important condition
for warping the strings of light, and an additional condition is the change in the distribution of
electrical properties deep inside the atom. But in any case, it ultimately all comes down to a
morphological adjustment of the Faraday field equations. Pair production is actually the process by
which supersymmetry breaking of light strings occurs, which has similarities to Gravity mediated SUSY
breaking proposed by the current research on supersymmetry breaking mechanisms [144], but does
not require the the supergravity couplings to matter. There should be only one kind of gravitational
force, and there will not be many kinds of them, just as there is only one spacetime, not many.
The Maxwell’s equations are direct descriptions of light strings and light rings: the Faraday field
equations describe the light strings, the Ampere equation describes the mixing of the two, and
Coulomb's law and Gauss's law describes the electric and magnetic fields, respectively, of a static light
ring field. Because all matter particles are themselves Maxwell field equations, it is a given that gauge
invariance and general covariance can hold; they are both products of the invariance requirements of
the Faraday field equation. In turn, any electromagnetic and gravitational potential fields that exist in
1
Imagine a spring being bent into a loop, with the outside of the loop becoming sparse and the inside of the
loop being squeezed. A sinusoidal field is similar when it is curled.
2
Penrose, in discussing gravitational collapse of black holes, believed that the body passes within its
Schwarzschild radius r = 2m, to an outside observer the contraction to r = 2m appears to take an infinite time.
Nevertheless, the existence of a singularity presents a serious problem for any complete discussion of the physics of
the interior region.” Note the relationship between time measure and time, space measure and length.
3
“Whether such "naked" singularities can occur or whether the singularities are always hidden behind the event
horizon is an unresolved question.” This is Penrose's idea of the singularity.
37
reality will satisfy gauge invariance and general covariance, which means that their objects must be
the result of Maxwell's equations [203]
1
.
The fact that all interactions, all changes in physics are mathematically describable processes is
the basis for ensuring causality. There are no things in physics that do not interact, which means that
they must all be the same thing. With the most realistic light being able to determine all relevant
properties of matter and explain all invariants through shape transformations, continuing to expect
other Strings or Rings imagined under Planck scales to bring a more realistic physical meaning [23]
2
requires more logical explanations.
Conclusions
If the theory of everything can be called “God equation”, then the natural constants in it can be
called “God number”, and the fundamental quantities operating in it can be called “God quantities”.
The supersymmetric GUT constructed in this paper states that the “God Equation” is the Faraday field
equation in Maxwell's equations; the “God Number” is the natural constants, the speed of light c, the
Planck constant h and the gravitational constant G. “God quantities” are the four fundamental
quantities, time, space [209], the electric field vector E, and the magnetic field vector H. The “God
particles” are “light strings” and “light rings” [80] with supersymmetry obeying the Faraday field
equation, which correspond to bosons and fermions in the Standard Model. The two pairs of
properties of fermions, the quantized electric charge and magnetic charge, as well as the mass and
gravitational field, are all generated by the spinning light ring.
Everything is light, and light determines the unity of time and space, of energy and momentum,
of energy-momentum and space-time, thus realizing the unity between interaction and matter
structure. Light is the ruler of space-time, it has global symmetry and invariance, from which all other
invariance originates. As soon as we are able to recognize the existence of an environment in which
an infinite number of light strings and light rings can be transformed into each other, we are able to
see the universe emerging in all its diversity [145]. The essence of all this lies in the reality of the
indistinguishability of mathematics and physics, which are completely unified in nature [81].
1
Wilczek, “Local gauge symmetry arises when one formulates the Maxwell equations using potentials. It states
that one can subject the potentials to an enormous group of transformations, parametrized by a function of space
and time, while leaving their physical consequences unchanged. On the surface this seems like a very odd principle.
It begs the question, why one uses the (largely arbitrary) potentials at all, rather than working in terms of invariants.”
2
“As far as the causality principle is concerned, if the physical quantities and their time derivatives are known in
the present in any given coordinate system, then a statement will only have physical meaning if it is invariant with
respect to those transformations for which the coordinates used are precisely those for which the known present
values remain invariant.” That's a good definition of "physical meaning."
38
Index
Ａ
annihilation, 13, 15, 18, 19, 34, 36
Axiomatic, 1, 17
axiomatic equation, 16, 26
axioms, 5, 7, 14, 21, 26, 27
Ｂ
boson, 31, 34
Ｃ
constant
gravitational constant, 11
Planck constant, 1, 4, 11, 14, 15, 16, 24, 37
speed of light, 1, 10, 11, 14, 15, 16, 22, 31,
32, 33, 34, 36, 37, 41, 43, 45
Ｅ
electric charge, 1, 12, 18, 21, 35, 37
Ｆ
Faraday
Faraday field equation, 22, 23, 24, 25, 26,
29, 31, 32, 33, 34, 36, 37
fermion, 1, 6, 14, 21, 24, 26, 27, 28, 32, 34, 35,
37
force, 2, 3, 5, 6, 12, 13, 14, 25, 29, 34, 35
maintain force, 12
Ｇ
God
, 2, 37, 40, 44
God Equation, 37
God number, 37
God quantities, 37
Goldstone theorem, 31
Ｈ
Helmholtz decomposition, 27
Higgs, 5, 31, 32, 37, 42, 48
Ｉ
invariance
diffeomorphism invariance, 25
gauge invariance, 24, 36
Lorentz invariant, 13, 28
invariant, 5, 8, 13, 14, 15, 22, 23, 25, 26, 28, 29,
31, 36, 37, 41
Ｌ
light ring, 1, 20, 24, 43, 45
Euler light ring, 33
Light String, 1, 20, 24, 43, 45
Lorentz transformation, 14, 15
Ｍ
magnetic charge, 1, 27, 28, 33
mass charge, 31, 35
Maxwell's equations, 17, 20, 21, 26, 27, 28, 35,
36, 37, 46
Ｎ
natural constants, 1, 3, 9, 10, 13, 14, 16, 17, 18,
33, 37
Ｐ
pair production, 14
Planck scales, 10, 11, 17, 37
39
Ｒ
reductionism, 3, 6, 12, 17, 40
Renormalization, 25
Ｓ
singularities, 4, 8, 9, 10, 26, 35, 36, 47
spacetime
spacetime curvature, 6, 16, 19, 23, 30
spacetime density, 23, 30
spacetime energy, 9, 23, 24, 25
spacetime metric, 16, 22, 23, 29, 30, 31, 35,
36
spin, 8, 24, 26, 27, 28, 29, 30, 31, 37, 47
spin quantum number, 28
symmetry
supersymmetry, 35
symmetry break, 31
Ｔ
theory of everything
, 2, 4, 6, 7, 8, 9, 17, 21, 26,
37, 40
Ｕ
Unified Equation, 1, 8, 9, 17, 20
Ｖ
virtual particle, 5, 35
40
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