Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau
Discussion
Started 16 September 2024
The need of a paradigm shift in physics
The need of a paradigm shift in physics
Is it possible in a world as fragmented as ours to present a new concept of Unity in which Science, Philosophy and Spirituality or Ontology can be conceived working in Complete Harmony?
In this respect the late Thomas S. Kuhn wrote in his
The Structure of Scientific Revolutions
"Today research in parts of philosophy, psychology, linguistic, and even art history, all converge to suggest that the traditional paradigm is somehow askew. That failure to fit is also increasingly apparent by the historical study of science to which most of our attention is necessarily directed here."
And even the father of Quantum Physics complained strongly in his 1952 colloquia, when he wrote:
"Let me say at the outset, that in this speech, I am opposing not a few special statements claims of quantum mechanics held today, I am opposing its basic views that has been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody. It has been worked out in great detail to form a scheme of admirable logical consistency which has since been inculcated in all young students of theoretical physics."
Where is the source of this "crisis of physics" as has been called?
Certainly the great incompatibility between General Relativity and Quantum Mechanics is in a certain sense, one of the reasons, of that great crisis, and that shows clearly the real need of a paradigm shift.
As one that comes from the Judeo-Christian tradition, that need of a real paradigm shift was of course a real need too. Philosophers such as Teilhard de Chardin, Henry Bergson, Charles Pierce and Ken Wilber, all of them worked for it!.
Ken Wilber said that goal of postmodernity should be the Integration of the Big Three, Science, Philosophy and Spirituality, and a scientist as Eric J. Lerner in his The Big Bang Never Happened, show clearly in it, how a paradigm shift was in cosmology is a real need too.
My work about that need started in 1968, when I found for the first time, an equation that was declared the most beautiful equation of mathematics, I mean Euler's relation found by him in 1745, when working with infinite series. It was this equation that took me in 1991, to define what I now call a Basic Systemic Unit, that has the most remarkable property to remain the same in spite of change, exactly the same definition of a Quantum as defined by professor Art Hobson in his book The Tales of Quantum, and that the University of Ottawa found when working with that strange concept that frightened Einstein, the entanglement concept, that seemed to violate Special Relativity.
Where is the real cause of the incompatibility between GR and QM?
For GR Tensor Analysis was used, a mathematical tool based on real numbers, and with it there was the need to solve ten functions representing the gravitational field:
"Thus, according to the general theory of relativity, gravitation occupies an exceptional position with regards to other forces, particularly the electromagnetic forces, since the ten functions representing the gravitational field at the same time define the metrical properties of the space measured."
THE FOUNDATION OF THE GENERAL THEORY OF RELATIVITY
By A. Einstein
Well the point is that, in that metrics that define the GR, time is just another variable, just as space, and as so with the same symmetrical properties, at the point that is can take both signs positive and negative, so time travel could be conceived just as a space travel, and any direction, in fact Stephen Hawking in his A BRIEFER HISTORY OF TIME, writes:
"It is possible to travel to the future. That is, relativity shows that it is possible to create a time machine that will jump you forward in time." Page 105
This is exactly the point that has made physics some sort of metaphysics, and as so created the great crisis of physics. While QM is based on the complex Schrödinger's wave equation or on complex numbers, in which the symbol sqr(-1), is a symbol to separate two different orders of reality, such as Time and Space, GR is based just on real numbers.
The Basic Systemic Unit concept, based on Euler's relation is in fact the definition of a Quantum, and as so it can be used to deduce all fundamental equations of physics as can be seen in my paper... resolving in this way that great crisis of physics
Quantum Physics
Edgar Paternina
retired electrical engineer
Most recent answer
All replies (15)
Naresuan University
This article is very intriguing! It raises important questions about the inconsistency between General Relativity and Quantum Mechanics, which has been a long-standing problem that scientists and philosophers alike have been trying to resolve. The idea of integrating science, philosophy, and spirituality holds great potential for creating a new paradigm that could fundamentally change how we understand the world.
Consultancy of the World
Dear Edgar,
Your thought-provoking question on the need for a paradigm shift in physics resonates deeply with the growing acknowledgment that the current frameworks—particularly General Relativity (GR) and Quantum Mechanics (QM)—face profound limitations. The ongoing struggle to reconcile GR and QM, especially their treatment of time and space, underscores a core issue: the reductionist view that physics can be confined to real numbers in GR and complex numbers in QM may no longer suffice for the holistic understanding we seek.
A genuine paradigm shift, as you rightly highlight, could lie in uniting Science, Philosophy, and Spirituality. The concept of a "Basic Systemic Unit" based on Euler's relation, which bridges change and constancy, holds intriguing promise. This idea touches on a potential resolution: if we consider time and space not merely as mathematical variables but as expressions of deeper ontological structures, a more unified understanding of reality might emerge. This could lead to a model that embraces the entanglement and non-locality of QM, while still respecting the metrical rigidity of GR.
The shift requires us to transcend disciplinary silos and engage with the metaphysical dimensions that both physicists like Einstein and philosophers like Teilhard de Chardin sensed but did not fully integrate. Your reference to Ken Wilber's call for the integration of the "Big Three" is apt—perhaps the next scientific revolution lies not just in new equations, but in a broader ontological framework where science, philosophy, and spirituality converge harmoniously.
Best regards,
Sandeep Jaiswal
1 Recommendation
Dear Sandeep and Surat
You Sandeep wrote:
"perhaps the next scientific revolution lies not just in new equations, but in a broader ontological framework where science, philosophy, and spirituality converge harmoniously."
Yes definitively, and in fact, that ontological framework already exist in a book, that present even a new cosmology that is in certain sense, very far from what we know about the cosmos and of the Universe as a whole, and in that book science, philosophy and spirituality converge harmoniously, that book is called The Urantia Book that you can load freely from the web, https://www.urantia.org/urantia-book/read-urantia-book-online.
It is really a hard nut to crack as it presents such a different paradigm from all we have known up to now, but if you are really opened minded, I highly recommend it... as it will "fundamentally change how we understand the world" as Surat wrote.
My Best Regards
Edgar
Dear Edgar
Look up on internet John Thompson "Why has physics failed to completely explain the universe: a philosophical approach to a final theory". and John Thompson "The universe: a philosophical derivation of a final theory". These will, I hope completely explain everything you ask about. The first explains where mathematics falls down and the second produces a complete final theory that can be tested mathematically to give predictions of all the major constants; the test is included at the end. Particularly take note of the section on special relativity also in the last chapter. Regards John Thompson
Independent Researcher
Quote: "Where is the real cause of the incompatibility between GR and QM?"
The historical cause seems to have been that both were separately grounded on different sets of incompatible grounding premises established after confirmed electromagnetic properties of the electrons were ignored and remained undocumented in textbooks of the era as Special Relativity theory was adopted, a fact that came to light only indirectly in 1982 with the publication of Einstein's biography by Abraham Pais.
The historical unfolding of this major disconnect with experimental reality is presented in this article:
The neglected electromagnetic properties of the electron that were confirmed even before 1907 are explained in this article:
1 Recommendation
Dear André,
Excellent work yours!
But not being a physicist, my point of view has been around the fundamental equations of physics, based as you know on complex numbers, such that they are all seen under a same unified framework, and most all, with that concept of unit we have a clear differentiation of Time and Space,as in GR time was as reduced to a similar space dimension, with the same symmetric property, at the point time travel was conceived possible, just as space in which you can travel in any direction, and as so physics entered a in some sort of metaphysics...
My Best Regards
Edgar
1 Recommendation
Independent Researcher
Dear Edgar,
Thank you for your appreciation. The fact that you are familiar with complex numbers/geometry is what I think gives you such a clear perspective on these issues.
Indeed, it was an attempt at demystifying complex numbers/planes/geometry and to make these so-called "complex" aspects of geometry more easily understandable to beginners, that induced me to write this article, that emphasized anew Wessel's discovery of the fact that i=√(-1)= 1∠90°, the latter term removing the minus sign so disconcerting to many, and even causes them to shy away from studying in depth this so important aspect of mathematics:
Best Regards, André
1 Recommendation
Dear André,
Thanks for sharing the paper in which sqr(-1), is exactly in this case, a rotation of 90 degrees, so in this way, the complex plane is generated, in which the so called real axis, that one not affected by sqr(-1), is the one associated with the Cosine function in which we have only one solution as
Cos(theta) = Cos(theta)
Cos(-theta) = Cos(theta)
so in the complex metrics of the Basic Systemic Unit concept, this is associated with Time, that can take the negative sign
and the one associated with space is the Sine function that can take both signs as
Sin(theta) = Sin(theta)
Sin(-theta) = -Sin(theta)
so the symmetry of space, and that we assume in that metric that the three dimensions can be represented by just one.
This exactly that metric that permits to deduce all the fundamental equations under a unified framework, which gives reason of the validity of that metric, see attatchment.
Best regards
Edgar
1 Recommendation
In fact in IE in Power Systems, when dealing with three phase systems, we reduced them to one phase system, and for the power system to work properly in steady state the three phases must be balanced to avoid blackout.
1 Recommendation
Independent Researcher
It is barely credible how extensive the understanding of physical processes can be by means of these complex considerations.
Are you familiar with the book "Practical Electronics for Inventors" By Paul Scherz?
I found that this reference provides the clearest explanation of how complex math can be applied to electronic designs.
I also recall that Minkowski came up with his 4D spacetime geometry by relating sqr(-1) to the "time dimension"
Regarding the need of a Paradigm shift Teilhard de Chardin wrote in his The Phenomenon of man:
"THE WITHIN OF THINGS
On the scientific plane, the quarrel between materialist and the upholder of a spiritual interpretation, between finalist and determinists, still endures...
I am convinced that the two points of view require to be brought into union, and that they soon will unite in a kind of phenomenology or generalized physic in which the internal aspect of things as well as the external aspect of the world will be taken into account. Otherwise, so it seems to me, impossible to cover the totality of the cosmic phenomenon by one coherent explanation such as science must try to construct."
Edgar
Independent Researcher
I agree.
For this to be accomplished however it seems to me that as many people as possible must reach a complete understanding of the only tool at our disposal to analyze and understand all aspects of physical reality: learning first to understand how this tool operates: the 6-layer neural network of our neocortex.
If interested, here is an overview of the current state of understanding of how conceptual thinking is generated and supported by the verbal areas of the neocortex:
Dear André,
What I've found is that the third mode: "the mathematical thinking mode by idealized concepts association", is really that mode that I've found with Euler's relation that include not just all numbers but a symbol to differentiate two different orders of reality(Time and Space):
the within and the without of things(not reducible the one to the other), as Teilhard put it, so in this way we can have that "generalized physic", that solve not only the crisis of physics but the crisis of mankind.
My best regards
Edgar
It is quite difficult to achieve even personally a paradigm shift, in fact it is perhaps as “painful” as leaving the womb. But once achieved, it is so satisfying that the wonder of seeing a new panorama all at once is something that opens up a new world to us, such that its beauty impels us to share it. This is what happened in 1991, after having verified the beauty and the simplifying power of complex numbers, which led me to the concept of Basic Systemic Unit, which allowed me to deduce the fundamental equations of physics, in a new conceptual frame of reference, whose main characteristic is precisely the “surprising vision” of the whole in which the great incompatibility that we have experienced between QM and GR no longer exists.
In this sense Harry Lass in his book
ELEMENTS
OF
PURE AND
APPLIED
MATHEMATICS
wrote:
“Let us hope that the reader does not feel that it is absolutely necessary to visualize a vector in a four-dimensional space in order to speak of such a vector. He may feel that an abstract idea can have no place in the realm of science. This is not the case. No one can visualize a four-dimensional space. Yet the general theory of relativity is essentially a theory of a four-dimensional Riemannian geometry”.
It is at this point of having reduced time to a spatial dimension, with its same symmetrical characteristics, that definitely separates us radically from the general theory of relativity, since the concept of Basic Systemic Unit, by allowing us to define a metric based on the Euler relation, has allowed us to define a unit, constituted by two different but complementary entities; different insofar as they are clearly differentiated by sqr(-1), which is in fact a symbol of radical separation, such that in this case Time cannot be reduced to Space.
Moreover, since Time is associated with the cosine function in which
Cos(-q) = Cos()
Y
Cos(-q) = Cos(q)
Which tells us that it has only one always positive solution, which is in agreement with what we know about time, that it is always flowing from the past, to the present towards the future; to think that a flow towards the past can be given, for example, is a chimera of science fiction, which has only been conceivable since in the metric of general relativity, time being assimilated to a spatial dimension, allows us to think of the possibility of time travel in any direction and that in fact its flow can be stopped at a point, just like space. But we know that time once measured is no longer the same. The question is, can physicists accept a paradigm shift like the one we have proposed in my paper Quantum Physics, which solves definitively the great incompatibility between QM and GR, by allowing with the same mathematical concept based on Euler's relation, to derive all those fundamental equations of physics, such as:
- That of the pendulum in which by equating the weighing mass and the inertial mass at a point of equilibrium has allowed to deduce that equation of the pendulum that normal science had had to eradicate as pointed out by Thomas S. Kuhn in Structure of Scientific Revolutions.
- That of Special Relativity, in which the complex plane is that canvas on which the speed of light and the invariance of momentum allow us to deduce, almost intuitively, the formula of mass and energy.
- Those of General Relativity in which following a mathematical procedure and that of Kepler's Laws, allows us to deduce both the equation of the normal planets and that of the Planet Mercury, evidently based both on Einstein's work and also especially on the solution due to Schwarshild, but using the same concept of UBS and not the tensor analysis, whose main difference is that time is not reduced in this case to a spatial dimension.
- And finally the Wave Equation that Erwin Schrödinger presented in 1926 as a postulate, thus solving the Wave-particle duality, since the concept of UBS, being not a spatial type trajectory, but a basic system constituted by a two-components entity, whose state cannot be determined since it has no laws of relation between those two components, which defines the Uncertainty Principle on the one hand, and on the other hand the same concept of Quantum, by remaining, those two components inseparable in the complex plane, which is the plane in which the quantum drama develops, and as in special relativity the invariance of momentum, allowed defining energy as the fundamental entity of the universe, since mass is a concept derived from it. In fact, in the case of the pendulum, the complex plane was the invariant frame, even with respect to the fixed stars, as was demonstrated with Faucault's pendulum.
Edgar Paternina
Retired electrical engineer
Similar questions and discussions
【NO.49】Must dark energy exist? Is it discrete? Does it have symmetry with energy?
Should there be a cosmological constant Λ term in the GR field equations? Is the Λ term symmetric with Gμν?
"According to Einstein's theory of General Relativity, gravity should lead to a slowing of the cosmic expansion. Yet, in 1998, two teams of astronomers studying distant supernovae made the remarkable discovery that the expansion of the universe is speeding up. To explain cosmic acceleration, cosmologists are faced with two possibilities: either 70% of the universe exists in an exotic form, now called dark energy, that exhibits a gravitational force opposite to the attractive gravity of ordinary matter, or General Relativity must be replaced by a new theory of gravity on cosmic scales."[1] In order to match the phenomenon of cosmic expansion, the general theory of relativity introduced the cosmological constant term and various speculations on its cause have been made [2]. However, these studies have rarely addressed the possible solutions in the structural aspects of the universe [3].
If there is only gravitational force, it looks like there is a deficiency. We believe that if there is a gravitational force, there is a corresponding repulsive force. But who should cause it and under what circumstances? It is important to know that in electromagnetic interactions, both positive and negative forces are formed by charges, and our goal is to unify the electromagnetic and gravitational forces. Would dark energy be a repulsive force symmetrical to gravity? Where does their symmetry come into play? If the result is to be symmetrical, the cause must first have symmetry. According to the assumptions of modern physics, the dark energy that causes the expansion of the universe is background and not symmetrical with the energy in GR. Regular energies are floating above the dark energy background, so they cannot have symmetry. In Einstein's gravitational field equation, Gµν + Λgµν = G*Tµν, the energy Tµν leads to an unmeasurable intrinsic Space-Time Curvature Gµν [4] while Λgµν is assumed to be a measurable extrinsic Space-Time Expansion due to the universal energy [5]. Specific and background, intrinsic and extrinsic, curvature and expansion do not have any symmetrical meaning. It would then not be appropriate to arrange them in a GR field equation.
Philosophically speaking, there should be no difference with ‘existence’ at this time and the other time, this place and the other place, i.e., when space and time are considered as background *, ‘existence’ does not depend on space-time coordinates. Therefore, the equations of the universe should not require boundary and initial conditions. Physics, by analysing observational data, has proposed the ‘Big Bang Theory’ and the ‘Accelerated Expansion Theory’ of the Universe, both of which are inconsistent with this. Therefore, the hypothesis of dark energy based on this foundation is questionable.
Our Questions:
Does the existence of ‘energy’ necessitate the existence of ‘dark energy’ or ‘anti-energy’? The hypothesis of the existence of dark energy is based only on the observation of the expansion of the universe. Is it the only explanation for the expansion of the universe? [6]
The function of energy is to drive interactions, and energy is presented in discrete forms, which can be manifested in a variety of forms, including gravity. Is the function of dark energy only to cause negative gravity? Is there only one form of dark energy?
Conservation of energy is an important physical principle, is dark energy conserved?
If gravity and negative gravity cancel each other out, why can't energy and dark energy cancel each other out directly?
-----------------------------------
Notes
* We believe that existence itself has a space-time parameter, but not a coordinate parameter.
-----------------------------------
References
[1] Dark Energy Survey, Collaboration. https://www.darkenergysurvey.org/the-des-project/overview/
[2] Peebles, P. J. E., & Ratra, B. (2003). The cosmological constant and dark energy. Reviews of Modern Physics, 75(2), 559.
[3] Fan, C. (2023). Convergent and Disperse Cyclic Multiverse Model (CDCMM). https://www.preprints.org/manuscript/202309.0784/v2
[4] Doubts about General Relativity (7) - Is Space-Time Bend a Motion? https://www.researchgate.net/post/NO42Doubts_about_General_Relativity_7-Is_Space-Time_Bend_a_Motion；
Doubts about General Relativity (5) - Should there be "negative gravity" in General Relativity?，https://www.researchgate.net/post/NO40Doubts_about_General_Relativity_5-Should_there_be_negative_gravity_in_General_Relativity.
[5] Doubts about General Relativity (3) - Are Space-Time Curvature and Expansion Two Different Geometrical Mechanical Properties? https://www.researchgate.net/post/NO38Doubts_about_General_Relativity_3-Are_Space-Time_Curvature_and_Expansion_Two_Different_Geometrical_Mechanical_Properties.
[6] Is there a reasonable alternative to the theory of the expanding universe?
【NO.31】The Relation Between Mathematics and Physics (7) - Why do Electromagnetic Waves Consist of Two Fields, Electric Field E and Magnetic Field H?
How did Photons Construct Light?
Our entire description of photons is based on energy Eo=hν [1], momentum Po=h/λ [2], and Helicity and Massless. we are not sure of the wave function Ψo(t,x) of photons, although there have been many different ideas and attempts to do so [3][4][5][6]. Experiments have shown that photons have wave-particle duality; two-photon interference can occur between them [7], and single-photon interference can occur by itself [8]; low energy photons can make electrons jump, photoelectric effect occurs [9], and the energy is converted to free "photoelectrons" in the matter; mid-level energy photons can collide with electrons and produce Compton scattering [10], so that the photon energy is reduced; High-energy photons can generate "pair-production" [11][12] with the help of atomic nuclei, e.g. γ+γ→e+e-.
Classical field theory is based entirely on the Maxwell's Equations, which consists of Faraday‘s Law, Ampere's Law, Gauss's Law, and Coulomb's Law, where both Faraday's equations and Ampere's equations in free space describe electromagnetic waves. We believe that electromagnetic waves consist of two orthogonal, synchronized, time-varying fields, the electric field E and the magnetic field H. Maxwell's equations is a synthesis of experimental results, not a result of mathematical derivation.
We believe that "All beams of electromagnetic radiation are made of photons" [4], including Laser beams, but "A key question is, can we view light as being comprised of particles called photons, or must one view light as a field, and the 'number of photons' only as the name we give to quantum states of the electromagnetic field [5]? electromagnetic field [5]? We know that cosmic microwave background (CMB) is electromagnetic, and that it needs to be detected with a radar antenna because the wavelength is too long; we know that blackbody radiation is electromagnetic, and that it needs to be detected with a photodetector because the wavelength is too short. We know that X-rays, gamma rays, millimeter waves, meter-wave radio waves, and radio astronomy telescopes detect photons.
However, "What is a photon" [4], should a photon have a scale? Is a bridge needed between the classical Maxwell equations and the photon? We have described them both correctly yet cannot connect them directly. The barrier between photons and electromagnetic waves may never be broken if we remain entangled in the probabilistic interpretation of the wave function [17], photon localizability [18], and Negative-energy solution [19], and such quantum mechanical problems.
Nature does not exist without a reason, and there must be a profound reason why an electromagnetic wave consists of two orthogonal, synchronized, time-varying fields, an electric field E and a magnetic field, rather than one field [23]. This reason either is the cause of its existence, something else causing the phenomenon, or it is the result of its existence, the phenomenon having to constrain the form of existence of something else. In any case, there must be a consistent "ecological chain" between the various forms of existence. This is precisely why the E of an electromagnetic wave is identical to the E of electron charge, the E of W±, the E of quarks, and why the H of an electromagnetic wave is identical to the H of a magnet, the H of a spin magnetic moment. If the electric field, E, and the magnetic field, H, of the electromagnetic wave, surprisingly do not exist in its constituent unit, the photon, then how was it created?
Questions:
1) The wave equation does not require two physical quantities, but why are there two quantities, E and H, in the electromagnetic wave equation? And they are not independent*, they must be orthogonal and synchronized [20]**.
2) What kind of photon equation (wave function) is possible to construct a deterministic Maxwell electromagnetic wave equation? It is reasonable to assume that a photon should never be a point particle and must itself have an electric field E and a magnetic field H. The Maxwell equation formed should not be its Probability density‡.
3) Where is the energy of an electromagnetic wave stored? Is it merely a superposition of photon energies? This question has been asked again and again, from Maxwell to Feynman [15] [16], with no answer so far. Is it possible to localize the energy-momentum of a gravitational field if it is not possible to localize the energy-momentum of an electromagnetic wave?
3) How does the Space-Time Curvature act on the electric field E and the magnetic field H of an electromagnetic wave when light is bent in a gravitational field?
4) Why does the physical world follow the invariance principle? How many invariants should there be in physics? What is the relationship between them? Do Maxwell's equations have all invariants? Lorentz invariance, gauge invariance [21], and general covariance [22], etc.?
-----------------------------------------
Notes
* Are E and H fixed relationships, or are they independent? "The electric field for one inertial observer is a particular combination of the electric and magnetic fields of the other observer. and similarly for the magnetic field. It follows that the electric and magnetic fields do not, in this sense, have a separate existence but rather are observer-dependent manifestations of a single electromagnetic field" [13][14]. This phenomenon is very significant in that it actually implies the inseparability of E and H.
** On the question of the synchronization of the electric field E and the magnetic field H, @André Michaud initiated a discussion a long time ago and received a wide range of responses.
“To summarize the issue, Ludvig Lorenz interpreted both E and B fields of free moving electromagnetic energy as peaking to maximum synchronously at the same time, which is an interpretation that Maxwell disagreed with; while Maxwell's was that both fields have to mutually induce each other while being 180 degrees out of phase for the electromagnetic energy to even exist and propagate, in permanent oscillation on a plane transverse with respect to the direction of motion of the energy in vacuum.”
‡ It is usually described as such, e.g. "energy-density photon wave function", "position probability density amplitude", "probability density of the photon"[4][6][19]。
-----------------------------------------
References
[1] Planck, M. (1900). The theory of heat radiation (1914 (Translation) ed., Vol. 144).
[2] Einstein, A. (1917). Physikalisehe Zeitschrift, xviii, p.121
[3] Sipe, J. (1995). Photon wave functions. Physical Review A, 52(3), 1875. //
[4] Bialynicki-Birula, I., & Bialynicka-Birula, Z. (2006). Beams of electromagnetic radiation carrying angular momentum: the Riemann–Silberstein vector and the classical–quantum correspondence. Optics communications, 264(2), 342-351. //
[5] Smith, B. J., & Raymer, M. (2007). Photon wave functions, wave-packet quantization of light, and coherence theory. New Journal of Physics, 9(11), 414.
[6] Cugnon, J. (2011). The photon wave function. Open Journal of Microphysics, 1.
[7] Pfleegor, R. L., & Mandel, L. (1967). Interference of Independent Photon Beams. Physical Review, 159(5), 1084-1088. https://doi.org/10.1103/PhysRev.159.1084
[8] De Broglie, L., & Silva, J. A. E. (1968). Interpretation of a Recent Experiment on Interference of Photon Beams. Physical Review, 172(5), 1284-1285. https://doi.org/10.1103/PhysRev.172.1284
[9] Einstein, A. (1905). 关于光的产生和转换的一个启发性观点 (Chinese ed., Vol. 4).
[10] Compton, A. H. (1923). The Spectrum of Scattered X-Rays. Physical Review, 22(5), 409-413. https://doi.org/10.1103/PhysRev.22.409
[11] Breit, G., & Wheeler, J. A. (1934). Collision of two light quanta. Physical Review, 46(12), 1087.
[12] Burke, D. L., Field, R. C., Horton-Smith, G., Spencer, J. E., Walz, D., Berridge, S. C., Bugg, W. M., Shmakov, K., Weidemann, A. W., Bula, C., McDonald, K. T., Prebys, E. J., Bamber, C., Boege, S. J., Koffas, T., Kotseroglou, T., Melissinos, A. C., Meyerhofer, D. D., Reis, D. A., & Ragg, W. (1997). Positron Production in Multiphoton Light-by-Light Scattering. Physical Review Letters, 79(9), 1626-1629. https://doi.org/10.1103/PhysRevLett.79.1626
[13] Hall, G. (2008). Maxwell's electromagnetic theory and special relativity. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 366(1871), 1849-1860.
[14] Feynman, R. P. (2005). The Feynman Lectures on Physics(III) [费恩曼物理学讲义] (Chinese ed., Vol. III).
[15] Maxwell, J. C. (1865). VIII. A dynamical theory of the electromagnetic field. Philosophical transactions of the Royal Society of London(155), 459-512.
[16] Feynman, R. P. (2005). The Feynman Lectures on Physics(II) [费恩曼物理学讲义] (Chinese ed., Vol. II).
[17] Born, M. (1926). Quantum mechanics of collision processes. Uspekhi Fizich.
[18] Zhi-Yong, W., Cai-Dong, X., & Ole, K. (2007). The first-quantized theory of photons. Chinese Physics Letters, 24(2), 418.
[19] Kobe, D. H. (1999). A Relativistic Schrödinger-like Equation for a Photon and Its Second Quantization. Foundations of Physics, 29(8), 1203-1231. https://doi.org/10.1023/A:1018855630724
[20] Michaud, A. (2021). Mise en évidence de l'interprétation initiale de Maxwell de l'électromagnétisme (Republication augmentée PI).
[21] Yang, C. N. (2014). The conceptual origins of Maxwell's equations and gauge theory. Physics Today, 67(11), 45.
[22] Petruzziello, L. (2020). A dissertation on General Covariance and its application in particle physics. Journal of Physics: Conference Series,
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