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.?
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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.
https://www.researchgate.net/post/Why-did-the-Lorenz-interpretation-prevail-over-Maxwells-in-defining-Electrodynamics
“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]。
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References
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[2] Einstein, A. (1917). Physikalisehe Zeitschrift, xviii, p.121
[3] Sipe, J. (1995). Photon wave functions. Physical Review A, 52(3), 1875. //
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[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.
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[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.
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[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,
[23] https://www.researchgate.net/publication/377566579_The_Relationship_Between_the_Theory_of_Everything_and_the_Constants_of_Nature_English_Version