Quantum Field Theory - Science topic

Physics states that ‘symmetry dictates interaction’ [1][2]; Invariance, symmetry, and conservation are usually approximately the same concepts [3], and the objects of conservation are usually discrete. The basic conservation of energy corresponds to the energy quantum e = hν, the basic conservation of momentum to the momentum quantum P =h/λ, the conservation of charge to the integer charge e, the conservation of the spin number to ℏ/2, the conservation of the particle number to the lepton number, the baryon number [4], and so on.

1) Does Noether's theorem impose a limit on the continuity of energy and momentum [5]?

2) If we regard these discretisations as representing different energy forms, do the symmetries likewise convert when the energy forms convert?

3) Assuming that an abstract energy remains constant in all cases, should there likewise be any symmetries that remain constant all the time to support symmetry evolution?

4) Should these different discretisations have a common origin? If so, how are the relationships between them constructed? Or through what channels are they related?

5) Particle number conservation are all additive and empirical postulates [4], should there be theoretical support behind them?

6) Symmetries are classified into external and internal symmetries [6]; external symmetries are concerned with spacetime coordinate transformations and internal symmetries are concerned with gauge invariance. If they are united, how are inner space symmetries related to external space symmetries?

--------------------------------------

References：

[1] Yang, C. N. (1996). Symmetry and physics. Proceedings of the American Philosophical Society, 140(3), 267-288.

[2] Gross, D. J. (1992). Gauge theory-past, present, and future? Chinese Journal of Physics, 30(7), 955-972.

[3] “Symmetry, Invariance and Conservation (1) - Who is the Primary?”；https://www.researchgate.net/post/NO20Symmetry_Invariance_and_Conservation_1-Who_is_the_Primary

[4] Krieger, P. (2006). Conservation Laws - PHY357_Lecture6. https://www.physics.utoronto.ca/~krieger/PHY357_Lecture6.pdf

[5] Kosmann-Schwarzbach, Y. (2011). The Noether Theorems. In Y. Kosmann-Schwarzbach & B. E. Schwarzbach (Eds.), The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century (pp. 55-64). Springer New York. https://doi.org/10.1007/978-0-387-87868-3_3

[6] Wess, J. (2000). From symmetry to supersymmetry. In The supersymmetric world: the beginnings of the theory (pp. 67-86). World Scientific. https://www.changhai.org/articles/translation/physics/sym_and_supersym3.php （中文版）

‘How big is the proton?"[1] We can similarly ask, “How big is the electron?” “How big is the photon?” CODATA gives the answer [2], proton rms charge radius r_p=8.41 x10^-16m; classical electron radius, r_e=2.81x10^-15m [6]. However, over a century after its discovery, the proton still keeps physicists busy understanding its basic properties, its radius, mass, stability and the origin of its spin [1][4][7]. Physics still believes that there is a ‘proton-radius puzzle’ [3][4], and does not consider that the size of a photon is related to its wavelength.

Geometrically the radius of a circle is clearly defined, and if an elementary particle is regarded as a energy packet, which is unquestionably the case, whether or not it can be described by a wavefunction, can its energy have a clear boundary like a geometrical shape? Obviously the classical electron radius is not a clear boundary conceptually in the field, because its electric field energy is always extending. When physics uses the term ‘charge radius’, what does it mean when mapped to geometry? If there is really a spherical charge [8][9], how is it maintained and formed^*?

----------------------------------------

Notes:

^*“Now if we have a sphere of charge, the electrical forces are all repulsive and an electron would tend to fly apart. Because the system has unbalanced forces, we can get all kinds of errors in the laws relating energy and momentum.” [Feynman Lecture C28]

----------------------------------------

[1] Editorial. (2021). Proton puzzles. Nature Reviews Physics, 3(1), 1-1. https://doi.org/10.1038/s42254-020-00268-0

[2] Tiesinga, E. (2021). CODATA recommended values of the fundamental physical constants: 2018.

[3] Carlson, C. E. (2015). The proton radius puzzle. Progress in Particle and Nuclear Physics, 82, 59-77. https://doi.org/https://doi.org/10.1016/j.ppnp.2015.01.002

[4] Gao, H., Liu, T., Peng, C., Ye, Z., & Zhao, Z. (2015). Proton remains puzzling. The Universe, 3(2).

[5] Karr, J.-P., Marchand, D., & Voutier, E. (2020). The proton size. Nature Reviews Physics, 2(11), 601-614. https://doi.org/10.1038/s42254-020-0229-x

[6] "also called the Compton radius, by equating the electrostatic potential energy of a sphere of charge e and radius with the rest energy of the electron"; https://scienceworld.wolfram.com/physics/ElectronRadius.html

[7] Gao, H., & Vanderhaeghen, M. (2021). The proton charge radius. https://www.researchgate.net/post/NO44_What_is_an_electric_charge_Can_it_exist_apart_from_electrons_Would_it_be_an_effect ;

[8] What is an electric charge? Can it exist apart from electrons? Would it be an effect? https://www.researchgate.net/post/NO44_What_is_an_electric_charge_Can_it_exist_apart_from_electrons_Would_it_be_an_effect ;

[9] Phenomena Related to Electric Charge，and Remembering Nobel Laureate T. D. Lee; https://www.researchgate.net/post/NO46Phenomena_Related_to_Electric_Chargeand_Remembering_Nobel_Laureate_T_D_Lee

When physicists talk about matter and antimatter asymmetries, they always start with the positive and negative electron solutions of the Dirac equation, and do not distinguish between it and positive and negative protons, or between it and positive and negative hydrogen [1]. Should we notice that these are three different levels of things. They were produced at different moments in the evolution of the early universe. The earliest products were positive and negative particles of extremely high energy, which humans were not yet able to produce, and which we may assume to be h+ h-. They would have been a series of unstable particles that could not form a protective mechanism of their own and all annihilated or disintegrated on their own. Then came the q+q- quark series of particles. The independent quarks are still unstable, but the u, d can combine with each other to form a joint protection mechanism. This is the first layer of protection, the baryogenesis epoch in the evolution of the Universe. the imbalance of matter (baryons) and antimatter (antibaryons) in the observed universe was formed during this epoch [2]. Protons and neutrons are of equal energy and are formed almost simultaneously, they further combine to form nuclei, which is the second layer of protection, the Big Bang Nucleosynthesis (BBN) epoch. Then again, electrons are formed and they combine with the nucleus to form the third layer of protection. The initial main condition for these three phases is the high energy spacetime field.

From the above process, can we see the basic principles of the evolution of the universe?

1) Survival of the fittest - when we say ‘Matter and antimatter particles are always produced as a pair’ [5], we should not be referring to protons and antiprotons or the like, but rather pairs of elementary particles produced by the reaction γ γ' →p+p-, [3]. This is a fundamental symmetry. In the subsequent baryons, both positive and negative particles are included. They are not produced in pairs; they are already the result of filtering and division. Therefore, there is an important clue that the ‘protection mechanism’ is the primary condition on which the ‘survival of the fittest’ depends in the evolutionary process of the universe. The protection mechanism is actually a screening process that selectively preserves either positive or negative particles. For example, p+ protects u quarks and d quarks; and -u and -d break up on their own, or form p-. However, at this point the p+ and p-, although equally annihilable, form their respective centres once they separate. Around their respective centres, only the same p survives. As a result of this repetition, the weak imbalance eventually creates a region of separation of two opposite matter particles. We can think of them as the beginnings of a positive and negative universe. This actually foreshadows that our universe should not be a single universe.

2) Consistency of Natural Laws - Natural laws must apply to all things. The nature of dark matter particles predicted by physics should not go beyond the Standard Model. Positively charged particles, negatively charged particles^*, and uncharged particles form just three symmetrical beings. Therefore, viewing uncharged particles as dark matter particles has the best match， and neutrinos are the best option [6][7][8].

3) The necessity of multiple universes - the universe cannot randomly choose between positive and negative matter as its building blocks. Separate multiple universes of positive and negative matter is a much more plausible explanation. Considering our current universe as one of the universes does not detract from its study, but only adds to the understanding of its creation and evolution. Considering the current universe as the only one would introduce many fundamental limitations, such as spacetime boundaries, the origin of energy, future endings, and so on. The Big Bang is the correct explanation, but there is insufficient evidence and justification for treating it as the entire source of the universe.

----------------------------------

^* “According to the standard model of particle physics, however, the opposite charges should be pretty much the only difference: particles and antiparticles should have nearly all the same properties.”[4]

----------------------------------

[1] https://home.cern/science/physics/antimatter.

[2] Springer. (2020). 100 Years of Fundamental Theoretical Physics in the Palm of Your Hand: Integrated Technical Treatment.

[3] Symmetry, Invariance and Conservation (3) - Are Annihilation and Pair Production a Supersymmetric relation? https://www.researchgate.net/post/NO22Symmetry_Invariance_and_Conservation_3-Are_Annihilation_and_Pair_Production_a_Supersymmetric_relation.

[4] https://www.nature.com/articles/d41586-023-03043-0.

[5] https://home.cern/science/physics/matter-antimatter-asymmetry-problem.

[6] Yuan, Y., Abdukerim, A., & etl. (2022). A search for two-component Majorana dark matter in a simplified model using the full exposure data of PandaX-II experiment. arXiv preprint arXiv:2205.08066.

[7] Akhmedov, E. (2014). Majorana neutrinos and other Majorana particles: Theory and experiment. arXiv preprint arXiv:1412.3320.

[8] Adhikari, R., Agostini, M., Ky, N. A., Araki, T., Archidiacono, M., Bahr, M., Baur, J., Behrens, J., Bezrukov, F., & Dev, P. B. (2017). A white paper on keV sterile neutrino dark matter. Journal of Cosmology and Astroparticle Physics, 2017(01), 025.

Everyone, physicist or not, seems to know what forces are, at least for mechanical, gravitational, and electromagnetic forces. And, even physicists take this sense of forces deeper into physics to recognise other forces, even those that may exist. So, what exactly are forces? How many kinds are there? Do we classify forces by their 'strength'? by their 'distance'? by their 'position'? by the 'object'? by their 'roles'? by their 'origin' ? Are forces and matter separate entities? Are force and energy separate entities?

In physics, there are many kinds of mass [1], all of which are called 'mass'; there are many kinds of energy, all of which are called 'energy' [2]; and similarly, physics suggests that there are four basic forces, electromagnetic, weak, strong, and gravitational, all of which are called 'force'. We have been accustomed to treating these things with the same dimension as if they were different, and no longer bother to find out whether the differences are essential or not.

The classical concept of force, with direction, magnitude and point of action, obeys the principle of vector superposition, but there is no concept of propagation and field. Obviously, this force is only a macroscopic equivalence.

The concept of force in QED and QCD is propagation and exchange of 'virtual particles'. The electromagnetic force is an 'virtual photon', the weak force is an 'virtual W boson', the strong force is an 'virtual gluon', and the gravitational force is an ( virtual) 'graviton'. The definition of force chooses to exchange discrete 'virtual particles' with no definite parameters, rather than the real continuous, intersecting 'field' of matter itself.

QFT argues that 'symmetry dictates interaction (force)' [3][11], Symmetry Create a Force [4]. Invariance, symmetry, and conservation are associated and even identical concepts [5][11]. QFT believes that the first three forces have already achieved 'unification', gauge fields based on different Lie groups, and that the current focus of theoretical physics is on quantum gravity. Is this ‘unification’ what we really understand? Can symmetry be understood as field exchange?

I have tried many ways to find an acceptable description of the weak force, but without success. Most physicists simply say that the weak force is a special kind of force^①. It is not attraction or repulsion, it is transformation. Can a transformation that be described by symmetry cannot be described by an intuitive force? It should not. Any transformation must involve a spatio-temporal change between interacting fields, and that should characterise the action of the force field^②. It is just that we are not yet able to specify it.

It is generally assumed that the 'unification' of forces would be at a very high energy level [8], and at the time of the Big Bang, the forces were unified. We think of the Big Bang as the starting point because we are currently in a state that is midway from the Big Bang. But shouldn't the so-called ‘singularity’ of the Big Bang be a result in the first place? There is no reason to deny that it is the end of a previous state of the universe. It should then be assumed that forces are uniform at any stage of the evolution of the universe, and that what is not uniform is only the way they are expressed. Shouldn't the unity here be the same as the unity of QFT?

Is there a process by which force fields are generated? Observe the annihilation process, e+ e- → γ+γ. Does the attraction between the electrons 'disappear' at the end of the reaction? Where does the accompanying force field go? In turn, γ+γ → e+ e-, the photons transform themselves into electron pairs with the help of the field inside the atom^③. The electromagnetic field is not newborn in this process, but has always been there, only transformed in form. Physics considers the nuclear force as the strong force ^④ that maintains the stability of the nuclear structure. According to the cosmic evolutionary process, there is a period of nucleosynthesis [9]. Where is the strong force when there is no nucleus formation? Waiting in the void? Obviously it is impossible. The only force at this time is the force of the quark (assuming it has been created) itself under extreme space-time conditions. The nuclear structure can only be produced by it and maintained by it. Therefore, force must be united with matter [7]; we cannot separate force from matter. All matter is a form of energy-momentum, therefore without energy-momentum there is no force^⑤ . The force field is the expression of the energy field and the matter field when they interact with each other, and there is only the difference between equilibrium and non-equilibrium.

With this line of thought can we answer the following question:

1) Is inertia a force? Are Newton's first, second, and third laws unified? Should all motions, including motion 'at rest' with zero velocity, and the fastest motion, the speed of light, be interpreted in the same way? Isn't light the baseline of inertia? shouldn't the baseline of relativity be equally the baseline of the forces?

2) Is gravitational redshift a 'force'? Is cosmological redshift a 'force'? Is the Doppler effect a 'force'? Aren't they all interacting processes? Aren't they all processes that exchange energy and momentum? If all redshifts are forces, does that mean that gravitational and expanding spacetime are associated with electromagnetic fields?

3) Interference is an interaction, but is interference a force, either in free space or on an interferometer?

4) Is vacuum excitation, if any, a force? Is there a force in the 'probabilistic interpretation' of the wave function? Is there a force in the 'Uncertainty Principle'? Is there a 'force' in the 'fluctuation' of a quantum field? Is 'coupling' a force? They are all manifestations of interaction, how can they be unified?

5) Are the four interacting forces independent of each other? The electromagnetic force is independent of the gravitational force, and there is no interaction between the strong force and the weak force. ......? If they are completely different things, why do we define them all as 'forces'? If there is a commonality, why are they independent of each other? Wouldn't they be the same force in different situations?

6) Forces have always been there, with or without them. If they have an 'origin', what is the 'force' that produces them?

7) Electromagnetic potentials, gravitational potentials, Yukawa potentials, Higgs potentials, are they all expressions of forces? Are they entities [10][12][13][14] or are they distributional 'parameters' of the field? Is the unity of 'force' the unity of potential?

----------------------------

^① “The weak interactions have even a very much shorter range and, so far as we know, are not responsible for holding anything together. They are, however, responsible for nuclear beta decay." Weinberg also said that the weak force is a strange force because it is not described in electrodynamics. It occurs slowly, but causes atomic nuclei to decay. It is hoped that a new and similar theory will be developed to explain it.

^② There is no need to be confused about the fact that the weak force is able to effect a transition within the nucleus, rather than causing a split, simply because it is not strong enough; the ‘transition’ is still in fact a process of splitting to the nearest state. This process maintains the overall structure of the nucleus, but not the state of the nucleus.

^③ Physics considers vacuum excitation.

^④ "But the known forces, gravity and electromagnetism, were insufficient to bind protons and neutrons tightly together into objects as small as the observed nuclei. Physicists were confronted with a new force, the most powerful in nature. "[6]

^⑤ If conservation of energy and momentum is the first principle, the exchange and conservation of energy and momentum is the source of 'force'.

----------------------------

[1] https://www.researchgate.net/post/NO45_What_is_Mass_Must_the_Hierarchy_of_Mass_be_Determined_Simultaneously_by_the_Origin_of_Mass?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InByb2ZpbGUiLCJwYWdlIjoicHJvZmlsZSIsInByZXZpb3VzUGFnZSI6InByb2ZpbGUiLCJwb3NpdGlvbiI6InBhZ2VDb250ZW50In19

[2] https://www.researchgate.net/post/NO10_Can_different_forms_of_energy_be_unified2?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InByb2ZpbGUiLCJwYWdlIjoicHJvZmlsZSIsInByZXZpb3VzUGFnZSI6InByb2ZpbGUiLCJwb3NpdGlvbiI6InBhZ2VDb250ZW50In19

[3] Yang, C. N. (1980). Einstein's impact on theoretical physics. Physics Today, 33(6), 42-49.

[4] Schmitz, W. (2019). Particles, Fields and Forces. Springer.

[5] https://www.researchgate.net/post/NO20Symmetry_Invariance_and_Conservation_1-Who_is_the_Primary?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InByb2ZpbGUiLCJwYWdlIjoicHJvZmlsZSIsInBvc2l0aW9uIjoicGFnZUNvbnRlbnQifX0

[6] Wilczek, F. (2005). "Nobel Lecture: Asymptotic freedom: From paradox to paradigm." Reviews of Modern Physics 77(3): 857.

[7] Wilczek, F. (2016). Unification of force and substance. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374(2075), 20150257.

[8] Dienes, K. R., Dudas, E., & Gherghetta, T. (1999). Grand unification at intermediate mass scales through extra dimensions. Nuclear Physics B, 537(1), 47-108. https://doi.org/https://doi.org/10.1016/S0550-3213(98)00669-5

[9] Allahverdi, R., Amin, M. A., Berlin, A., & etl. (2020). The first three seconds: a review of possible expansion histories of the early universe. arXiv preprint arXiv:2006.16182.

Fields, B. D., Olive, K. A., Yeh, T.-H., & Young, C. (2020). Big-bang nucleosynthesis after Planck. Journal of Cosmology and Astroparticle Physics, 2020(03), 010.

[10] Aharonov, Y., & Bohm, D. (1959). Significance of electromagnetic potentials in the quantum theory. Physical Review, 115(3), 485.

[11] Wu, A., & Yang, C. N. (2006). Evolution of the concept of the vector potential in the description of fundamental interactions. International Journal of Modern Physics A, 21(16), 3235-3277.

[12] Yukawa, H. (1935). On the interaction of elementary particles. I. Proceedings of the Physico-Mathematical Society of Japan. 3rd Series, 17, 48-57.

[13] Agrawal, P., Saha, D., Xu, L.-X., Yu, J.-H., & Yuan, C.-P. (2020). Determining the shape of the Higgs potential at future colliders. Physical Review D, 101(7), 075023.

In the Standard Model, if we ignore the unverifiable property of colour charge and consider neutrinos as ‘dark matter particles’ for the time being [1], then we can consider fermions to have the signature properties of electric charge, spin magnetic moment and mass. We consider the electron as a representative, which differs from other fermions only by its mass size, stability, and position in the composite particle.

‘Charge’ was one of the first properties of particles to be discovered, and it appears to correspond to “mass-charge”, which has a similar behaviour [Weyl][Heaverside]. While we have paid a great deal of attention to the existence of an origin of mass [2] and introduced the Higgs mechanism [9], no one seems to have paid much attention to the existence of an origin of electric charge since the beginning of the last century. In order to establish an electromagnetic worldview [3], physicists at that time worked on determining the electron model [4][5][6] : is it rigid? What is its radius? A most crucial question is how should the charge in it be distributed? To this day, physics still does not know the structure of the electron, and what the charge is, except that there exists e+e- ↔ γ γ . Then，

1) Does electric charge have an origin? The fact that it is capable of annihilation and creation, there must be a process of generation. What determines this process? Doesn't a process need to be described, even if it is vacuum-excited generation?

2) Is electric charge an independent entity? We have never seen a ‘charge’, only electrons.

3) A charge cannot be a ‘point’, how does it manage not to repel itself? Poincaré once postulated the existence of a non-electromagnetic reaction force that balances the repulsion between distributed charges to keep them from splitting [7].

4) Does the electric field of a charge act on itself? Why do we see this as a problem? [10]

5) Why is the charge a discrete (quantised) value?1 or 1/3 ^‡. Is the discrete nature of energy related to the discrete nature of charge? Or furthermore, do all discretisations originate from the discrete nature of energy? 〠

6) How can charges be positive and negative and perfectly equal? What is the physical pathway by which charge is created? How can different positive and negative charges be created at the same time in the same physical picture? And positive and negative charges can cause annihilation of positive and negative electrons, not just positive and negative charges.

7) Is there a relationship between electric and magnetic charge? According to Dirac [8], the electric charge e and the magnetic charge g must co-exist, hc/eg=2 ^*. Why can the spin-magnetic moment (the inner discreative magnetic moment of the electron) [11] not be considered as a result of ‘magnetic charge’? The magnetic charge must be a magnetic monopole [12], can't it be a magnetic dipole ^**? We are looking for magnetic monopoles, why not electric charges? [13]

8) Charge appears to be independent of mass. How can particles with different masses (e, μ, τ; u, c, t; d, s, b) have the same charge? But when e+e- → γ γ occurs, the charge disappears and so does the mass.

9) How can electric charge share a particle with magnetic charge and mass? † Wouldn't this be a good answer if they were all the result of spin [14]?

10) U(1) symmetry produces conserved charge [15]; charge is conserved when interacting. Is conservation of charge independent of conservation of energy? What will it mean if they are not conserved? 〠

11) What should the charge of a black hole be if it is one of its characteristics? Will the charge of the ultimate black hole eventually be the same as that of an electron?

12) The more important question is this: all of these questions, mentioned above, must be answered at the same time for the problem to be truly solved.

-----------------------------------------------------------------

Supplement (2024.8.28)

【NO.46】Phenomena Related to Electric Charge，and Remembering Nobel Laureate Tsung-Dao (T.D.) Lee;

-----------------------------------------------------------------

* Note in particular that the relationship between electric and magnetic charge is related solely to Planck's constant h and the speed of light c. This implies that their roots are the same.

** “If Magnetic Monopoles Would Annihilate Like Positive and Negative Electrons, Would Magnetism Still Exist?”https://www.researchgate.net/post/NO23If_Magnetic_Monopoles_Would_Annihilate_Like_Positive_and_Negative_Electrons_Would_Magnetism_Still_Exist

† The central question of interest here is why should fermions have multiple properties and only these properties? Where do these properties come from? What must be the relationship between these properties? How do they fit together?

‡ Dirac asked, "the reason for the existence of a smallest electric charge."

-----------------------------

[1] Adhikari, R., Agostini, M., Ky, N. A., Araki, T., Archidiacono, M., Bahr, M., Baur, J., Behrens, J., Bezrukov, F., & Dev, P. B. (2017). A white paper on keV sterile neutrino dark matter. Journal of Cosmology and Astroparticle Physics, 2017(01), 025.

[2] Wilczek, F. (2006). The origin of mass. Modern Physics Letters A, 21(9), 701-712.

[3] Battimelli, G. (2005). Dreams of a final theory: the failed electromagnetic unification and the origins of relativity. European Journal of Physics, 26(6), S111.

[4] Waite, T., Barut, A. O., & Zeni, J. R. (1997). The Purely Electromagnetic Electron Re-visited. In J. P. Dowling (Ed.), Electron Theory and Quantum Electrodynamics: 100 Years Later (pp. 223-239). Springer US. https://doi.org/10.1007/978-1-4899-0081-4_18

[5] Williamson, J., & Van der Mark, M. (1997). Is the electron a photon with toroidal topology. Annales de la Fondation Louis de Broglie,

[6] Damour, T. (2017). Poincaré, the dynamics of the electron, and relativity. Comptes Rendus Physique, 18(9), 551-562. https://doi.org/https://doi.org/10.1016/j.crhy.2017.10.006

[7] Poincaré, H. (1905). Sur les Invariants Arithmétiques (On the dynamics of the electron). http://poincare.univ-lorraine.fr/fr/fonds-et-archives； http://www.academie-sciences.fr/fr/Colloques-conferences-et-debats/henri-poincare.html；

[8] Dirac, P. A. M. (1931). Quantised singularities in the electromagnetic field. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 133(821), 60-72. Dirac, P. A. M. (1948). The theory of magnetic poles. Physical Review, 74(7), 817.

[9] Higgs, P. W. (2014). Nobel lecture: evading the Goldstone theorem. Reviews of Modern Physics, 86(3), 851.

[10] Wheeler, J. A., & Feynman, R. P. (1949). Classical electrodynamics in terms of direct interparticle action. Reviews of Modern Physics, 21(3), 425.

[11] Ohanian, H. C. (1986). What is spin? American Journal of Physics, 54(6), 500-505.

Yang, C. N. (1983). The spin. AIP Conference Proceedings,

Sasabe, S., & Tsuchiya, K.-i. (2008). What is spin-magnetic moment of electron? Physics Letters A, 372(4), 381-386.

[12] Rajantie, A. (2012). Introduction to magnetic monopoles. Contemporary Physics, 53(3), 195-211.

Rajantie, A. (2016). The search for magnetic monopoles. Physics Today, 69(10), 40-46.

[13] Aad, G., Abbott, B., Abbott, D. C., Abud, A. A., Abeling, K., Abhayasinghe, D., Abidi, S., AbouZeid, O., Abraham, N., & Abramowicz, H. (2020). Search for magnetic monopoles and stable high-electric-charge objects in 13 TeV proton-proton collisions with the ATLAS detector. Physical Review Letters, 124(3), 031802.

[14] Yang, C. N. (1983). The spin. AIP Conference Proceedings,

[15] Lancaster, T., & Blundell, S. J. (2014). Quantum field theory for the gifted amateur. OUP Oxford.

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.?

-----------------------------------------

* 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]。

-----------------------------------------

[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,

[23] https://www.researchgate.net/publication/377566579_The_Relationship_Between_the_Theory_of_Everything_and_the_Constants_of_Nature_English_Version

When searching for additional insights I found in: Laidlaw A. “An Unspeakable Mechanism”. Intl. J. Adv. Res. Phys. Sci. (2018), 5, 6, 10-28: “local realist field model,” “distributed action” and “Fields at different points in space do not interact with each other. Alternatively, at any given space point, the interaction between two fields depends only on the values of the fields that are present at that point.”

I also found in A. Laidlaw and L.G. van Willigenburg “On the Appearance of Action at a Distance” https://www.researchgate.net/publication/372841182: “If we are to think of the interaction quanta as distributed fields then we must also think of the source and the target quanta as distributed fields. Each of them permeates the entire space, which is also the modern view from Quantum Field Theories. The source and the target are thus always touching, everywhere.”

And “Therefore, what the QED interaction mechanism is describing is a distributed transfer of energy-momentum from one distributed field to another. In other words, it is describing local field-field interactions that are spatially distributed, not atomist particle-particle interactions. It is describing distributed action.”

Proposal

Distributed fields are formed from the primal state of the universe in an epoch. Whether one considers details of the universe as having expanded from some compact primal energy state, or considers that the details have condensed from a universe-scale primal energy state (my favorite), each “distributed field” is of universe scale. On the occasion of two distributed fields interacting, their interaction occurs in their full extent. An observable is a sample of the interacting distributed fields at any space point of that interaction. The location of the space point of an observation is determined by an observer sampling the interacting fields from one of them.

Were we to accept neutrality of the universe, we would find that for each distributed field a complementary distributed field exists. Further, we would require that interacting fields be complementary, like a key and a lock. Then, in the EPR Alice and Bob event, the two interacting distributed fields that individually include Alice’s and Bob's local states would be complementary fields. Observables of the state of Alice's and Bob's complementary distributed fields would occur under the influence of the values of the fields at each observation point, including from which distributed field the observation is made. The observation determines the state of Alice's distributed field, and of necessity, it also determines the state of Bob's complementary distributed field.

Now, it is specifically proposed that Alice's distributed fields are selected from a myriad of distributed fields by the location of Alice's observation. Bob's complementary distributed fields are also selected from a myriad of distributed fields by the location of Bob's observation apparatus. Setting the states of a pair of these fields that include both locations awaits setting of one field state by an observation. At the observation by Alice her distributed field is set and distributed field interaction sets Bob's distributed field to the complement of Alice’s distributed field. How? At the observation by Bob the complementary distributed field is observed, producing for instance, spin opposite.

Replies

Please inform me whether this view is on track for “distributed action.” I have been interested in non-locality for decades with a past bias toward “backward in time” anti-particle communication. I would like to understand the distributed action view also, since it seems more in line with modern treatments of non-locality.

The concept of mass explained by the Higgs mechanism is able to include all concepts of mass, inertial mass, gravitational mass, mechanical mass, electromagnetic mass [1], kinematic mass, static mass, longitudinal mass, transverse mass [2], bare mass ...... ? Is it the Higgs field that leads to the mass-energy equation? How are coupling relationships established? Do the Couplings Transfer Energy-Momentum?

Although there are many different sub-concepts of mass, a distinguishing feature is that the mass of an object is not reflected, recognisable, or measurable when it is not interacting. We can think of all mass as a property of resistance that only presents itself when an object's state of motion changes^§. The so-called "rest mass" can only be regarded as a representation of the amount of static energy, and not vice versa.

Thus, it is clear that masses are essentially the same, differing only in size and form^*. This also implies that no matter how many differences there are in the occasions of interaction, as long as the required dimension is the same, they are the same mass. In this way, the Equivalence Principle in GR need not be regarded as a specific condition.

However, mass is not constant, and the magnitude of an object's mass in SR changes according to the Lorentz transformation. This predicts that the mass of an object is related to the increase or decrease in the energy of the object and is bounded by the speed of light.

Higgs physics suggests [3] that the mass of bosons is given by the Higgs mechanism [4]; that the mass of fermions is also given by the Higgs field [10], although this is still an open question [5]; and that Higgs particles themselves give their own mass [3], although this is not a clear-cut conclusion either [6].The Higgs field is a scalar field that pervades space, and is the same as the other elementary particle fields, electron fields, quark fields, etc., co-existing in the vacuum^**. They all appear to have the same status, except for the Higgs mechanism.

However, the current Higgs mechanism has some obvious explanation missing.

1) Why does the Higgs field selectively couple to bosons? I.e., how does the Higgs field recognise the bosons W^±, Z and γ, g, all of which have energy and perform the same function, and to which the Higgs field selectively assigns mass, or not.

2) The magnitude of the coupling coefficient of the Higgs field determines the mass size of the fermions [10]. Then, the mass hierarchy of the three generations of fermions is determined by the Higgs field^¶.Why should the particles all have different couplings coefficients g_j to the Higgs field? and where do these values come from[7][8]? Before there is mass, fermions have exactly the same quantum number and they are indistinguishable [9]^†. How does the Higgs field recognise these particles? The obvious requirement is that they must have additional parameters, or other physical quantities that do not present . At the same time, The action of the Higgs field on the positive and negative particles (e+,e-; q+,q-; ) is identical. And how does it ignore this difference?

3) If the Higgs field is not coupled to fermions, can fermions really travel at the speed of light like photons without stopping? According to the mass-energy equation E=mc², are all particles energy before there is mass（or none）? So the coupling of the Higgs field is to energy, do they have to exchange energy between them? What is the energy transfer relation here, E=mc²? If m=0 now, is E fully converted to the raw energy of the particle?

4) If the significance of the existence of inertial mass for fermions, W^± can be explained, what is the significance of the Higgs Boson possessing inertial mass itself?Does it really implies the existence of a 'fifth force', mediated by the exchange of Higgs bosons [8]?

5) The shape of the Higgs potential V(Ø) expresses the relationship between the potential and the field strength , V(Ø) ~ Ø [10] ^‡ . Ø is hidden in the vacuum ††. How do different Ø present themselves at a given spatial location? Do they interact with other particles in one way?

6) How does the mathematical explanation of the Higgs mechanism map reasonably to physical reality? Must the Higgs potential be an external field? ^‡‡ Wouldn't it be better if it were the field of the particle itself? [12] Is the Higgs mechanism for mass completely excludes the relation between mass and spin ?[15]

7) Not all mass is caused by Higgs [10], and potential energy (binding energy) gives mass as well. In this case, is mass still consistent? Doesn't mass become a variable?

------------------------------------------

Supplement: Can mass have multiple origins? （2024.9.26）

“The Higgs does seem to be the source of the mass of elementary particles, e.g., the electron; but it is responsible for < 2% of the mass of more complex things, like the proton. The mass of the vast bulk of visible material in the Universe has a different source.”[1] “the Higgs boson is almost irrelevant to the origin of the proton mass. ”[2]

Mass is an important particle property. If mass has surprisingly multiple origins, how do we explain their relationship? Do they produce the same results by similar mechanisms, or completely different ones? Do they all rely on external fields? Is the mass-energy equation, m=E/c^2, a clue to determining the uniform origin of mass? Can a mechanism that does not provide energy provide mass?

Does mass obey the superposition principle? Is it a scalar superposition or a vector superposition? Is it a linear or nonlinear superposition? Let us consider a process in which u, d quarks combine to form a proton p. In the early stages of the evolution of the universe, nothing else in particular existed. u and d automatically combine to form p in such a scenario, like a pair of lovers meeting to form a family. The family is a more stable structure, and the ‘quality’ of life of the family (In Chinese, quality and mass are one word, 质量) has increased. The increased ‘quality’ does not come from outside, but from the union itself.

------------------------------------------

§ Mass is usually thought of as resisting a change in the "state" of matter, but what is the "state"? Why does it resist change? Why can it resist change? My personal reference answer is here [12]: Mass originates from damping the superluminal intent of a spinning light ring and as a result is the fundamental property that distinguishes fermions from bosons.

* Mass is somewhat similar to energy in that it exists in various forms, but the two are fundamentally different.

** Physics doesn't know what parameters to use to describe these fields and doesn't seem to be interested.

‡ “One of the most important open questions in Higgs physics is whether the potential written in that equation is the one chosen by nature. ”[8]

‡‡ "Central to all of Higgs physics is the Higgs potential."[8] C. N. Yang[13]: "Symmetry breaking with the introduction of a field will not be the last theory, although for the time being it is a good theory, like Fermi's theory of beta decay." Expresses his scepticism about the Higgs mechanism.

† With no Higgs field, the electron and electron neutrino would be identical particles, and the W and Z particles, and in fact all standard model fermions, would be massless. [9]

†† The vacuum seems to be the all-powerful vacuum, and physics assigns many functions to the vacuum [14].

¶ The hierarchies among fermion masses and mixing angles, however, remain unexplained.[11]

------------------------------------------

[1] Thomson, J. J. (1881). XXXIII. On the electric and magnetic effects produced by the motion of electrified bodies. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 11(68), 229-249.

[2] Abraham, M. (1902). Principles of the Dynamics of the Electron (Translated by D. H. Delphenich). Physikalische Zeitschrift 4(1b), 57-62.

[3] Ellis, J. (2013). Higgs physics. arXiv preprint arXiv:1312.5672.

[4] Higgs, P. W. (1964). Broken Symmetries and the Masses of Gauge Bosons. Physical Review Letters, 13(16), 508-509. https://doi.org/10.1103/PhysRevLett.13.508

[5] Ghosh, D., Gupta, R. S., & Perez, G. (2016). Is the Higgs mechanism of fermion mass generation a fact? A Yukawa-less first-two-generation model. Physics Letters B, 755, 504-508.

[6] Consoli, M., & Cosmai, L. (2020). The mass scales of the Higgs field. International Journal of Modern Physics A, 35(20), 2050103.

[7] Melia, F. (2021). The origin of rest-mass energy. The European Physical Journal C, 81(8), 707. https://doi.org/10.1140/epjc/s10052-021-09506-w

[8] Salam, G. P., Wang, L.-T., & Zanderighi, G. (2022). The Higgs boson turns ten. Nature, 607(7917), 41-47. https://doi.org/10.1038/s41586-022-04899-4

[9] Lancaster, T., & Blundell, S. J. (2014). Quantum field theory for the gifted amateur. OUP Oxford.

[10] Schmitz, W. (2019). Particles, Fields and Forces. Springer.

[11] Bauer, M., Carena, M., & Gemmler, K. (2016). Creating the fermion mass hierarchies with multiple Higgs bosons. Physical Review D, 94(11), 115030.

[12]

[13] C.N.Yang. (2014). 六十八年心路（1945-2012）. 三联书店.

[14] https://www.researchgate.net/post/NO34How_the_View_of_Space-Time_is_Unified_6-Are_Vacuum_and_Space_Two_Separate_Things?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InByb2ZpbGUiLCJwYWdlIjoicHJvZmlsZSIsInBvc2l0aW9uIjoicGFnZUNvbnRlbnQifX0

[15] C. N. Yang emphasised: in the context of gauge theory, the conjecture of why we need a theory of gravity with spin electrons. Today I remain believing that this is a key to the future conquest of quantum general relativity.

-------------------------------------------------------------------------

The energy operator ih∂/∂t and the momentum operator ihΔ or ih∂/∂x play a crucial role in the derivation of the Schrödinger equation, the Klein-Gordon equation, the Dirac equation, and other physics arguments.

The energy and momentum operators are not differential operators in the general sense; they do play a role in the derivation of the equations for the definition of energy and momentum.

However, we do not find any reasonable arguments or justifications for the use of such operators, and even their meaning can only be speculated from their names. It is used without explanation in textbooks.

The clues we found are:

1) In the literature [ Brown, L. M., A. Pais and B. Poppard (1995). Twentieth Centure Physics (I), Science Press.], "In March 1926, Schrödinger noticed that replacing the classical Hamiltonian function with a quantum mechanical operator, i.e., replacing the momentum p by a partial differentiation of h/2πi with position coordinates q and acting on the wave function, one also obtains the wave equation."

2) Gordon considered that the energy and momentum operators are the same in relativity and in non-relativism and therefore used in his relativistic wave equation (Gordon 1926).

(3) Dirac also used the energy and momentum operators in the relativistic equations with electron spins (Dirac 1928). Dirac called it the "Schrödinger representation", a self-adjoint differential operator or Hermitian operator (Dick 2012). (D).

Our questions are:

Why can this be used? Why is it possible to represent energy by time differential for wave functions and momentum by spatial differential for wave functions? Has this been historically argued or not?

Keywords: quantum mechanics, quantum field theory, quantum mechanical operators, energy operators, momentum operators, Schrödinger equation, Dirac equation.

the collapse of the wavefunction is often said to be a fundamental problem in physics, because it would contradict special relativity. but this is nonsense, because here a relativistic question is asked in a non relativistic theory, quantum mechanics. the question would make sense in quantum field theory, which is lorentz invariant, but here the ''problem'' does not occur, since in qft the wavefunction is an operator.

please comment.

In his article "More is different", Anderson said that new laws of physics "emerge" at each physical level and new properties appear [1]; Wheeler, when claiming that "law without law" and "order comes out of disorder", argued that chaotic phenomena " generate" different laws of physics [2][3]. What they mean is that the laws, parameters, and constants of the upper level of physics appear to be independent of the laws of physics of the lower level. Is this really the case? Are we ignoring the conditions that form the physical hierarchy, thus leading to this illusion?

Let's suppose a model. The conditions for the formation of new levels are at least two: i. Existence of low-level things A,B ...... , the existence of interaction modes a, b,...... ; two, the existence of a sufficient number of low-level things, NxA, MxB....... Then when they are brought together, there are many possible combinations, e.g., (AA), (AAA), (AAA)', ...... , (AB), (BA), (AAB)', (BAB), ........ Then it escalates to [(AA)(AA)], [(AB)(ABA)], ....... What this actually leads to is a change in the structure of things and a corresponding change in the way they interact. The result of the "change" is the appearance of new physical phenomena, new forces, and so on.

Physics is an exact match for math, so let's use math as an example of this phenomenon. Suppose we have a number of strings (threads) that can be regarded as underlying things, then, when a string is curled into a circle, L=2πR, the law of the relationship between the length of the string and its radius, and the irrational constant π appear; when two strings are in cascade, L=l₁+l₂, the law that the total length of the string is equal to the sum of the individual string lengths (Principle of superposition) appears; and, when three strings form a right triangle, the law of Pythagoras, c²=a²+b², the law of sums of interior angles of triangles ∠A + ∠B + ∠C = 180° , and the irrational constant √2 appear ...... ; and the transcendental number e appears when the string length L grows in a fixed proportion (continuous compound interest)[4]^‡ ...... ; when the string vibrates, sine waves (sinωt) appear; when two strings are orthogonal, i appears ...... ; and when more kinds of vibrating strings are superimposed under specific conditions, more phenomena appear ^*.......

All these "qualitative changes" do not seem to be caused by "quantitative changes", but more by the need to change the structure. As mathematical theorems emerge, so must the laws of physics, and it is impossible for physics to transcend mathematics. Therefore, as long as there is a change of structure in physics, i.e. the possibility of symmetry breaking [5]^**, new "symmetries", new "laws", new "forces", new "constants", new "parameters" are almost inevitable.

Can we try to attribute all physical phenomena to emergence under hierarchical structural conditions? For example, the fine structure constant^‡‡and the Pauli exclusion principle emerge because of the formation of atomic structure; the "nuclear force" emerges because of the combination of protons and neutrons; The "strong interaction force" and "weak interaction force" appeared because of the structure of protons and neutrons. We should pay attention to the causal relationship here. Without structure, there would be no new phenomena; it is the more fundamental interactions that form structure, not these new "phenomena".

-----------------------------

* e.g. Blackbody radiation law, Bose statistics, Fermi statistics, etc.

** Should there be "spontaneous symmetry breaking"? Any change in symmetry should have a cause and a condition.

‡ What does it mean in physics if e will appear everywhere and the individual mathematical constants appear so simply? They must likewise appear at the most fundamental level of physics.

‡‡ https://www.researchgate.net/post/NO33_What_Does_the_Dimensionless_Nature_of_the_Fine-Structure_Constant_Mean

-----------------------------

2024-07-27 补充

In addition to the structure and statistics generated by the interactions that result in new laws of physics, the expression of the different orders of differentials and integrals of such generating processes is another important way of making the laws of physics emerge.

Typical examples of such expressions can be seen @ Ingo D. Mane: “On the Origin and Unification of Electromagnetism, Gravitation, and Quantum Mechanics“：

-----------------------------

[1] Anderson, P. W. (1972). More Is Different: broken symmetry and the nature of the hierarchical structure of science.

. Science, 177(4047), 393-396. https://doi.org/doi:10.1126/science.177.4047.393

[2] Wheeler, J. A. (1983). ‘‘On recognizing ‘law without law,’’’Oersted Medal Response at the joint APS–AAPT Meeting, New York, 25 January 1983. American Journal of Physics, 51(5), 398-404.

[3] Wheeler, J. A. (2018). Information, physics, quantum: The search for links. Feynman and computation, 309-336.

[4] Reichert, S. (2019). e is everywhere. Nature Physics, 15(9), 982-982. https://doi.org/10.1038/s41567-019-0655-9;

[5] Nambu, Y. (2009). Nobel Lecture: Spontaneous symmetry breaking in particle physics: A case of cross fertilization. Reviews of Modern Physics, 81(3), 1015.

Free spacetime contains no energy-momentum^*, so when objects m are travelling at constant velocity in it, they do not exchange energy-momentum. Non-free spacetime contains energy-momentum. The Einstein field equation of general relativity,

Rµν - (1/2)gµνR = G*Tµν,

expresses the relationship between the energy-momentum (mass) and the structure of spacetime ( metric) at a point (region) in spacetime^**. Usually we think that "Gravity couples universally to all forms of energy" [1]. Then, we need to ask three basic questions:

1) What is the best way to express the energy-momentum of the gravitational field? or how are the "long-standing problems about energy-momentum localisation in GR" [2][3][4] addressed? The energy-momentum of the gravitational field is the energy-momentum of the spacetime field, which must be localizable. The energy-momentum of the spacetime field must involve only the spacetime parameter xi(i=0,1,2,3), because the independent spacetime field has no other parameter (or it has some other hidden parameter that does not play an explicit role). But it cannot be expressed directly in terms of spatio-temporal coordinates (t,x,y,z) because they must be background independent, nor can it be expressed in terms of time lengths T and space lengths L because we have no way of determining the measurement boundaries. So what are the remaining covariates? The rates of measure change, curvature, and deflection, etc.. which are the most appropriate? Even if we consider space-time as a "medium", what are the properties of the medium? Density, elasticity? What density? What elasticity?

2) By what means are gravitational fields and other forms of energy-momentum exchanged with each other? Obviously it must be through a common covariate, and then the only option available is the spacetime covariate. Does this qualify that all other forms of energy-momentum must contain spacetime covariates? Includes energy-momentum of dark matter (no dark energy involved). And more critically, the form of these spacetime Attributes and the form in which the spacetime energy-momentum is expressed should be the same, i.e., if the energy-momentum of spacetime is expressed in terms of a change of metric, the other forms of energy-momentum must be related to a change in the spacetime metric; and if it is expressed in terms of a curvature, the other forms must be related to a change in the curvature.

3) Is the energy-momentum of the gravitational field conserved[5]? If the energy-momentum of the gravitational field is not conserved, what will become of the gravitation dominated evolution of galaxies?

-------------------------------------------

^* We need to distinguish between the concepts of space-time and vacuum.“Are Vacuum and Space Two Separate Things?”，https://www.researchgate.net/post/NO34How_the_View_of_Space-Time_is_Unified_6-Are_Vacuum_and_Space_Two_Separate_Things；

^** The concept of a strict "point" interaction does not really exist in physics.

-------------------------------------------

[1] Kiefer, C. (2006). Quantum gravity: general introduction and recent developments. Annalen der Physik, 518(1-2), 129-148.

[2] Einstein Ann. d. Phys. 49, 769 (1916).

[3] Hestenes, D. (2021). Energy-Momentum Complex in General Relativity and Gauge Theory. Advances in Applied Clifford Algebras, 31(3), 51.

[4] Møller, C. (1958). On the localization of the energy of a physical system in the general theory of relativity. Annals of Physics, 4(4), 347-371.

[5] Szabados, L. B. (2009). Quasi-local energy-momentum and angular momentum in general relativity. Living Reviews in Relativity, 12(1), 1-163.

If gravity is caused by spacetime, then negative gravity should also be caused by spacetime. If general relativity is correct, then it should be able to describe all spacetime types and describe both positive and negative gravity.

In electromagnetic interactions there are two opposite forces, attractive and repulsive. The direction of the electric force depends on the identity of the "electric charge"; the direction of the magnetic force depends on the polarity of the "magnetic charge"^*. However, in gravitational phenomena we only find attractive forces at the macroscopic level. This seems to be a flaw, somewhat similar to our inability to see antimatter (the gravitational force produced by antimatter is still positive). The concepts of "negative mass" and "negative energy" have been proposed and assumed to give rise to negative gravity [1][2][3]. This seems a somewhat absurd idea.

According to the interpretation of general relativity, gravity is a manifestation of the "curvature" of spacetime. So, if positive curvature of space-time produces "positive gravity", does negative curvature of space-time produce "negative gravity"? Under what conditions and in what places should such a situation leading to negative gravity occur?

Schwarzschild spacetime is a spherically symmetric solution of GR, can spherical symmetry be extended across the "event horizon" to r=0?

The best way to describe it is that we take the "event horizon" (r=2GM) as the dividing line, whose inner and outer spacetimes are symmetric. The external is gravitational force (pointing to the centre of the sphere), which tends to zero at r→∞，and is the macroscopic case; the internal is negative gravitational force (leaving the centre of the sphere), which tends to zero at r→0, and is the microscopic case(This looks like a very good match for elementary particles). However, physics suggests that the interior of a black hole is much more complex [4].

---------------------------------------------------------------------------------

^* We don't think there's a magnetic monopole； Fan, C. (2023). If Magnetic Monopoles Would Annihilate Like Positive and Negative Electrons, Would Magnetism Still Exist? https://www.researchgate.net/post/NO23If_Magnetic_Monopoles_Would_Annihilate_Like_Positive_and_Negative_Electrons_Would_Magnetism_Still_Exist

---------------------------------------------------------------------------------

[1] Bondi, H. (1957). Negative mass in general relativity. Reviews of Modern Physics, 29(3), 423.

[2] Tiwari, R. N., Rao, J. R., & Ray, S. (1991). Gravitational sources of purely electromagnetic origin. Astrophysics and Space Science, 178(1), 119-132. https://doi.org/10.1007/BF00647119

[3] Parikh, M. K., & Wilczek, F. (2000). Hawking radiation as tunneling. Physical Review Letters, 85(24), 5042.

[4] Carroll, S. M. (1999). Lecture Notes on General Relativity. https://www.researchgate.net/publication/2354635_Lecture_Notes_on_General_Relativity

There are over 300 physical constants in physics [1][2], c, h, G, e, α, me, mp, θ, μ0, g, H0, Λ, ...... with different definitions [3], functions and statuses; some of them are measured, some are derived [4] and some are conjectured [5]. There is a recursive relationship between physical constants, capable of establishing, from a few constants, the dimensions of the whole of physics [6], such as SI Units. There is a close correlation between physical constants and the laws of physics. Lévy-Leblond said, any universal fundamental constant may be described as a concept synthesizer expressing the unification of two previously unconnected physical concepts into a single one of extended validity [7], such as, the mass-energy equation E = mc^2. Physics is skeptical that many constants are constant constants [8], even including the speed of light invariance. But "letting a constant vary implies replacing it by a dynamical field consistently" [9], in order to avoid being trapped in a causal loop, we have to admit that there is a set of fundamental constants that are eternally invariant*.

So which physical constants are the most fundamental natural constants? Are they the ones that have invariance, Lorentz invariance, gauge invariance, diffeomorphism invariance [10]? Planck's 'units of measurement' [11], combines the relationship between the three constants Planck constant h, speed of light c, gravitational constant G. "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."[12] This should be the most unignorable reference to the best provenance of these constants, which should be the coefficients of some extremely important equations? [13]

-------------------------------

* They are eternal and unchanging, both at the micro and macro level, at any stage of the evolution of the universe, even at the Big Bang, the Big Crash.

-------------------------------

[1] Group, P. D., P. Zyla, R. Barnett, J. Beringer, O. Dahl, D. Dwyer, D. Groom, C.-J. Lin, K. Lugovsky and E. Pianori (2020). "Review of particle physics." Progress of Theoretical and Experimental Physics 2020(8): 083C001.

[2] Tiesinga, E. (2021). "CODATA recommended values of the fundamental physical constants: 2018."

[3] https://www.nist.gov/programs-projects/fundamental-constants-nature;

[4] DuMond, J. W. (1940). "A Complete Isometric Consistency Chart for the Natural Constants e, m and h." Physical Review 58(5): 457.

[5] Carroll, S. M., W. H. Press and E. L. Turner (1992). "The cosmological constant." Annual review of astronomy and astrophysics 30: 499-542.

[6] Martin-Delgado, M. A. (2020). "The new SI and the fundamental constants of nature." European Journal of Physics 41(6): 063003.

[7] Lévy-Leblond, J.-M. (1977, 2019). "On the Conceptual Nature of the Physical Constants". The Reform of the International System of Units (SI), Philosophical, Historical and Sociological Issues.

[8] Dirac, P. A. M. (1979). "The large numbers hypothesis and the Einstein theory of gravitation " Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 365.1720: 19-30.

Webb, J., M. Murphy, V. Flambaum, V. Dzuba, J. Barrow, C. Churchill, J. Prochaska and A. Wolfe (2001). "Further evidence for cosmological evolution of the fine structure constant." Physical Review Letters 87(9): 091301.

[9] Ellis, G. F. and J.-P. Uzan (2005). "c is the speed of light, isn't it?" American journal of physics 73(3): 240-247.

[10] Utiyama, R. (1956). "Invariant theoretical interpretation of interaction." Physical Review 101(5): 1597.

Gross, D. J. (1995). "Symmetry in physics: Wigner's legacy." Physics Today 48(12): 46-50.

[11] Stoney, G. J. (1881). "LII. On the physical units of nature." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 11(69): 381-390.

Meschini, D. (2007). "Planck-Scale Physics: Facts and Beliefs." Foundations of Science 12(4): 277-294.

[12] Robotti, N. and M. Badino (2001). "Max Planck and the 'Constants of Nature'." Annals of Science 58(2): 137-162.

[13]

General Relativity field equations [1]:

G_µν = G*T_µν...... (EQ.1).

It is a relation between the matter field (energy-momentum field) T_µν and the spacetime field G_µν, where the gravitational constant G is the conversion factor between the dimensions [2].Einstein constructed this relation without explaining why the spacetime field and the matter field are in such a way, but rather assumed that nine times out of ten, they would be in such a way. He also did not explain why the spacetime field G_µν is described by curvature and not by some other parameter. Obviously, we must find the exact physical relationship between them, i.e., why T_µν must correspond to G_µν, in order to ensure that the field equations are ultimately correct.

We know that matter cannot be a point particle, it must have a scale, and matter cannot be a solid particle, it must be some kind of field. The fact that matter has a scale means that it has to occupy space-time; the fact that matter is a field means that it is mixed with space-time, i.e., matter contains space-time. So, when applying Einstein's field equations, how is matter's own spacetime defined? Does it change its own spacetime? If its own energy-momentum and structure have already determined its own spacetime, should the way it determines its own spacetime be the same as the way it determines the external spacetime? If it is the same, does it mean that the spacetime field is actually a concomitant of the matter field?

If one were to consider a gravitational wave, one could think of it as a fluctuating spacetime field that propagates independently of the material source after it has been disconnected from it. They have decoupled from each other and no longer continue to conform to the field equations (EQ.1). Although gravitational waves are the product of a source, the loss of that source prevents us from finding another specific source for it to match it through the equation (EQ.1). Just as after an electron accelerates, the relationship between the radiated electromagnetic wave and the electron is no longer maintained. Does this indicate the independence of spacetime field energies?

-----------------------------

♛ “Does the Energy Tensor T_µν in the Field Equations Contain the Energy-momentum of the Spacetime Field?”：https://www.researchgate.net/post/NO37Doubts_about_General_Relativity_2-Does_the_Energy_Tensor_Tmn_in_the_Field_Equations_Contain_the_Energy-momentum_of_the_Spacetime_Field

♛ “Is the Geometry Interpretation of Gravity a Paradox?”：https://www.researchgate.net/post/NO36_Doubts_about_General_Relativity_1-Is_the_Geometry_Interpretation_of_Gravity_a_Paradox

-----------------------------

[1] Grøn, Ø., & Hervik, S. (2007). Einstein's Field Equations. In Einstein's General Theory of Relativity: With Modern Applications in Cosmology (pp. 179-194). Springer New York. https://doi.org/10.1007/978-0-387-69200-5_8

[2] “The Relationship Between the Theory of Everything and the Constants of Nature”：https://www.researchgate.net/publication/377566579_The_Relationship_Between_the_Theory_of_Everything_and_the_Constants_of_Nature_English_Version

Zero stands for emptiness, for nothing, and yet it is considered to be one of the greatest achievements of humankind. It took a long stretch of human history for it to be recognized and appreciated [1][4]. In the history of mathematics considerable confusion exists as to the origin of zero. There can be no unique answer to the query, "Who first discovered the zero?", for this may refer to any one of several related but distinct historical issues† [2]. A very explicit use of the concept of zero was made by Aristotle, who, speaking of motion in a vacuum, said "there is no ratio in which the void is exceeded by body, as there is no ratio of zero to a number” [3][2]*. He apparently recognized “the Special Status of Zero among the Natural Numbers.”

If we believe that zero is explicitly expressed mathematically, whether in number theory, algebra, or set theory, is the meaning of zero also clear and unified in the different branches of physics? Or can it have multiple meanings? Such as:

1）Annihilation——When positive and negative particles meet [5][6], e+e-=γ+γ'，the two charges disappear, the two masses disappear, and only the energy does not disappear or increase; the momentum of the two electrons, which was 0, now becomes the positive and negative momentum of the two photons. How many kinds of zeros exist here, and what does each mean?

2）Double-slit interference—— The interference pattern in Young's double slit experiment, what exactly is expressed at the dark fringe? And how should it actually be understood? For light waves, it can be understood as the field canceling due to destructive interference and presenting itself as zero. For single photons, single electrons [7], physics considers it to be a probabilistic statistical property [12]. This means that in practice, at the dark fringes of theoretical calculations, the field will also be likely not to be zero‡.

3）Destructive interference——In Mach–Zehnder interferometer [8]，there's always been a question of where the energy in the destructive interference arm went [9]? There seems to be an energy cancellation occurring.

4）Anti-reflection coatings——By coating [10], the reflected waves are completely canceled out to achieve the purpose of increasing transmission.

5）Nodes of Standing Waves——In optical resonant cavity, Laser Resonator. " The resonator cavity's path length determines the longitudinal resonator modes, or electric field distributions which cause a standing wave in the cavity "[13]. The amplitude of the electromagnetic field at the node of the standing wave is zero, but we cannot say that the energy and momentum at this point are zero, which would violate the uncertainty principle.

6）Laser Beam Mode——The simplest type of laser resonator modes are Hermite-Gaussian modes, also known as transverse electromagnetic modes (TEMnm), in which the electric field profile can be approximated by the product of a Gaussian function with a Hermite polynomial. TEMnm，where n is the number of nodes in x direction, m is the number of nodes in y direction [14].

7）Nodes of the Wave Function——Nodes and ends of the Wave Function Ψ in a square potential well have zero probability in quantum mechanics‡ [11]。

8）Pauli exclusion principle—— Fermions are antisymmetric，Ψ(q1,q2)=-Ψ(q1,q2), so Ψ(q1,q2)=0；Here a wave function of zero means that "field" is not allowed to exist, or according to the Copenhagen interpretation, the wave function has zero probability of appearing here?

9）Photon——zero mass, zero charge.

10）Absolute vacuum——Can it be defined as zero energy space?

11）Absolute temperature 0K——Is the entire physical world defined as a zero energy state except for photons?

12）Perfect superconductor—— "The three 'big zeros' of superconductivity (zero resistance, zero induction and zero entropy) have equal weight and grow from a single root: quantization of the angular momentum of paired electrons" [15].

13）......

Doesn't it violate mathematical principles if we may interpret the meaning of zeros in physics according to our needs? If we regard all zeros as energy not existing, or not allowed to exist here, does it mean that energy must have the same expression? Otherwise, we cannot find a unified explanation.

---------------------------------------------

* Ratio was a symmetrical expression particularly favored by the ancient Greeks.

† Symbols(0,...), words (zero, null, void, empty, none, ...), etc..

‡ Note in particular that probability itself is defined as a probability, not an exact value. For example, a probability of 0.5 can occur in physical reality as 0.49999999999, and it is almost never possible to have an accurate probability value such as 0.5. This means that there is no probability value that never occurs, even if the probability is theoretically 0. It is against the principle of probability to assume that a probability of zero means that it will never occur in reality.

---------------------------------------------

[1] Nieder, A. (2016). "Representing something out of nothing: The dawning of zero." Trends in Cognitive Sciences 20(11): 830-842.

[2] Boyer, C. B. (1944). "Zero: The symbol, the concept, the number." National Mathematics Magazine 18(8): 323-330.

[3] the Physics of Aristotle;

[4] Boyer, C. B. (1944). "Zero: The symbol, the concept, the number." National Mathematics Magazine 18(8): 323-330.

[5] https://www.researchgate.net/post/NO8Are_annihilation_and_pair_production_mutually_inverse_processes

[6] https://www.researchgate.net/post/NO22Symmetry_Invariance_and_Conservation_3-Are_Annihilation_and_Pair_Production_a_Supersymmetric_relation

[7] Davisson, C. and L. H. Germer (1927). "Diffraction of Electrons by a Crystal of Nickel." Physical Review 30(6): 705-740.

[8] Mach, L., L. Zehnder and C. Clark (2017). The Interferometers of Zehnder and Mach.

[9] Zetie, K., S. Adams and R. Tocknell (2000). "How does a Mach-Zehnder interferometer work?" Physics Education 35(1): 46.

[10] https://en.wikipedia.org/wiki/Anti-reflective_coating

[11] Chen, J. (2023). From Particle-in-a-Box Thought Experiment to a Complete Quantum Theory? -Version 22.

[12] Born, M. (1955). "Statistical Interpretation of Quantum Mechanics." Science 122(3172): 675-679.

[13]

[14] "Gaussian Beam Optics." from https://experimentationlab.berkeley.edu/sites/default/files/MOT/Gaussian-Beam-Optics.pdf.

[15] Kozhevnikov, V. (2021). "Meissner Effect: History of Development and Novel Aspects." Journal of Superconductivity and Novel Magnetism 34(8): 1979-2009.

The external spacetime field produced by an object of mass M, the Schwarzschild spacetime metric solution, is usually obtained as follows [1]:

1) Assumes a spherically symmetric spacetime metric, and is static and time invariant;

2) Assumes a vacuum conditions outside, with T_µν = 0;

3) Solve the Einstein field equation, R_µν - (1/2)g_µνR=T_µν...... (EQ.1)

4) Utilize the boundary condition: the Newtonian potential ф = -GM/r, which introduces the mass M. Obtain the result:

ds² = -(1-2GM/r)dt² + (1-2GM/r)^-1dr² + r²dΩ²...... (EQ.2)

Overall, the Schwarzschild metric employs a priori derivation steps. The solution is unique according to Birkhoff's theorem.

Einstein does not explain why M leads to ds², our questions are:

a) The spacetime metric is containing the energy-momentum T_spacetime , which can only originate from T_µν and is conserved. Why then must spacetime receive, store, and transmit energy-momentum by curvature^* ?

b) The implication of condition 2) is that the spacetime field energy-momentum is independent of M or can be regarded as such. Comparing this to the electric field of an electron is equivalent to the fact that the energy contained in the electron's electric field is independent of the electron itself. Since T_spacetime is also bound to M, is it not part of M?

c) For complex scenarios, in the T_µν of Einstein's field equation EQ.1, should one include the spacetime energy momentum at the location? With the above Schwarzschild solution, it seems that there is none, otherwise both sides of the equation (EQ.1) become a deadly circle. So, should there be or should there not be? Does the field equation have a provision or treatment that T_µν can only contain non-spacetime energy momentum?

-----------------------------

Notes

* “How the view of space-time is unified (3)-If GR's space-time is not curved, what should it be?” https://www.researchgate.net/post/NO17How_the_view_of_space-time_is_unified_3-If_GRs_space-time_is_not_curved_what_should_it_be

** "Doubts about General Relativity (1) - Is the Geometry Interpretation of Gravity a Paradox?" https://www.researchgate.net/post/NO36_Doubts_about_General_Relativity_1-Is_the_Geometry_Interpretation_of_Gravity_a_Paradox

-----------------------------

References

[1] Grøn, Ø., & Hervik, S. (2007). Einstein's Field Equations. In Einstein's General Theory of Relativity: With Modern Applications in Cosmology (pp. 179-194). Springer New York. https://doi.org/10.1007/978-0-387-69200-5_8

=============================

2024-04-26

Additional information*:

1) In his Karl Schwarzschild Memorial Lecture, Einstein summarized the many scientific contributions of his short life, stating [1], in commenting on Schwarzschild's solution, that “he was the first to succeed in accurately calculating the gravitational field of the new theory”.

(2) Einstein emphasized in his article “Foundations of General Relativity” [1], “We will make a distinction between 'gravitational field' and 'matter', and we will call everything outside the gravitational field matter. Thus the term 'matter' includes not only matter in the usual sense, but also electromagnetic fields.” ; “Gravitational fields and matter together must satisfy the law of conservation of energy (and momentum).”

(3) Einstein, in his article “Description based on the variational principle” [1], “In order to correspond to the fact of the free superposition of the independent existence of matter and gravitational fields in the field theory, we further set up (Hamilton): H=G+M

4) Einstein's choice of Riemannian spacetime as the basis for the fundamental spacetime of the universe, which I have repeatedly searched for in The Collected Papers of Albert Einstein, still leads to the conclusion that he had no arguments, even if only descriptions. In his search for a geometrical description, he emphasized that “This problem was unsolved until 1912, when I hit upon the idea that the surface theory of Karl Friedrich Gauss might be the key to this mystery. I found that Gauss' surface coordinates were very meaningful for understanding this problem.”[2] And, although many physicists also do not understand what Space-Time Curvature is all about, everyone accepted this setup. This concept of `internal curvature', which cannot be mapped to physical reality, is at least a suitable choice from a modeling point of view.

5) Einstein's initial assumptions for the field equations were also very vague, as evidenced by his use of terms such as “nine times out of ten” and “it seems”. He was hoping to obtain the gravitational field equation by analogy with the Poisson equation. Thus, the second-order derivative of the spacetime metric is assumed on the left side of the equation, and the energy-momentum density is assumed on the right side.

-----------------------------------------

* The citations therein are translated from Chinese and may differ from the original text.

[1] University, P. (1997). The Collected Papers of Albert Einstein. Volume 6: The Berlin Years: Writings, 1914-1917. In. Chinese: 湖南科学技术出版社.

[2] Einstein, A. (1982). How I created the theory of relativity(1922). Physics Today, 35(8), 45-47.

Finding out that string theory and such is all about increasing the spatial dimension, is there a temporal dimension?

Does anyone besides me think that the 17 overlapping fields of quantum field theory seem like a chaotic concept that cannot be the foundation of the universe? Every time we discover a new particle or force, we postulate there must be another field. The sole purpose of this new field is to “explain” the existence of the newly discovered particle. When we had only a few fields, this was plausible. However, now we have a chaotic zoo of fields. If we discover more high energy particles, we will happily add more fields.

I have proposed a model of the universe that has only one “Universal field”. However, this question is about whether you defend the model of the universe consisting of many separate fields. To paraphrase Einstein: Everything should be made as simple as possible, but not simpler”. Therefore, perhaps nature really does have 17+ separate fields. What do you think?

Planck Scales (Planck's 'units of measurement') are different combinations of the three physical constants h, c, G, Planck Scales=f(c,h,G):

Planck Time: tp=√ℏG/c^5=5.31x10^-44s ......(1)

Planck Length: Lp=√ℏG/c^3=1.62x10^-35m ......(2)

Planck Mass: Mp=√ℏc/G=2.18x10^-8 kg ......(3)

“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.”[1] And because of the possible relation between Mp and the radius of the Schwarzschild black hole, the possible generalized uncertainty principle [2], makes them a dependent basis for new physics [3]. But what exactly is their natural meaning?

However, the physical constants, the speed of light, c, the Planck constant, h, and the gravitational constant, G, are clear, fundamental, and invariant.

c: bounds the relationship between Space and Time, with c = ΔL/ Δt, and Lorentz invariance [4];

h: bounds the relationship between Energy and Momentum with h=E/ν = Pλ, and energy-momentum conservation [5][6];

G: bounds the relationship between Space-Time and Energy-Momentum, with the Einstein field equation c^4* Gμν = (8πG) * Tμν, and general covariance [7].

The physical constants c, h, G already determine all fundamental physical phenomena‡. So, can the Planck Scales obtained by combining them be even more fundamental than they are? Could it be that the essence of physics is (c, h, G) = f(tp, Lp, Mp)? rather than equations (1), (2), (3). From what physical fact, or what physical imagination, are we supposed to get this notion? Never seeing such an argument, we just take it and use it, and still recognize c,h,G fundamentality. Obviously, Planck Scales are not fundamental physical constants, they can only be regarded as a kind of 'units of measurement'.

So are they a kind of parameter? According to Eqs. (1)(2)(3), c,h,G can be directly replaced by c,h,G and the substitution expression loses its meaning.

So are they a principle? Then who are they expressing? What kind of behavioral pattern is expressed? The theory of quantum gravity takes this as a " baseline ", only in the order sense, not in the exact numerical value.

Thus, Planck time, length, mass, determined entirely by h, c, G, do they really have unquestionable physical significance?

-----------------------------------------

‡ Please ignore for the moment the phenomena within the nucleus of the atom, eventually we will understand that they are still determined by these three constants.

-----------------------------------------

[1] Robotti, N. and M. Badino (2001). "Max Planck and the 'Constants of Nature'." Annals of Science 58(2): 137-162.

[2] Maggiore, M. (1993). A generalized uncertainty principle in quantum gravity. Physics Letters B, 304(1), 65-69. https://doi.org/https://doi.org/10.1016/0370-2693(93)91401-8

[3] Kiefer, C. (2006). Quantum gravity: general introduction and recent developments. Annalen der Physik, 518(1-2), 129-148.

[4] Einstein, A. (1905). On the electrodynamics of moving bodies. Annalen der Physik, 17(10), 891-921.

[5] Planck, M. (1900). The theory of heat radiation (1914 (Translation) ed., Vol. 144).

[6] Einstein, A. (1917). Physikalisehe Zeitschrift, xviii, p.121

[7] Petruzziello, L. (2020). A dissertation on General Covariance and its application in particle physics. Journal of Physics: Conference Series,

[8] https://www.researchgate.net/post/No28The_Relation_Between_Mathematics_and_Physics_4-Could_All_Physical_Constants_be_Unified_to_a_set_of_Fundamental_Constants_of_Nature

[9]

The fine-structure constant is obtained when the classical Bohr atomic model is relativisticized [1][2]. α=e²/ℏc, a number whose value lies very close to 1/137. α did not correspond to any elementary physical unit, since α is dimensionless. It may also be variable [6][7]^*.

Sommerfeld introduced this number as the relation of the “relativistic boundary moment” p₀=e²/c of the electron in the hydrogen atom to the first of n “quantum moments” p_n=nh/2π. Sommerfeld had argued that α=p₀/p₁ would “play an important role in all succeeding formulas,” he had argued ^‡ [5].

There are several usual interpretations of the significance of fine structure constants [3].

a）In 1916, Sommerfeld had gone no further than to suggest that more fundamental physical questions might be tied to this “relational quantity.” In Atomic Structure and Spectral Lines, α was given a somewhat clearer interpretation as the relation of the orbital speed of an electron “in the first Bohr orbit” of the hydrogen atom, to the speed of light [5].

b) α plays an important role in the details of atomic emission, giving the spectrum a "fine structure".

c) The electrodynamic interaction was thought to be a process in which light quanta were exchanged between electrically charged particles, where the fine-structure constant was recognized as a measure of the force of this interaction. [5]

d) α is a combination of the elementary charge e, Planck's constant h, and the speed of light c. These constants represent electromagnetic interaction, quantum mechanics, and relativity, respectively. So does that mean that if G is ignored (or canceled out) it represents the complete physical phenomenon.

Questions implicated here :

1) What does the dimensionless nature of α imply? The absence of dimension means that there is no conversion relation. Since it is a coupling relation between photons and electrons, is it a characterization of the consistency between photons and charges?

2) The various interpretations of α are not in conflict with each other, therefore should they be unified?

3) Is our current interpretation of α the ultimate? Is it sufficient?

4) Is α the most fundamental physical constant^**? This is similar to Planck Scales^† in that they are combinations of other fundamental physical constants.

-----------------------------------

* Spatial Variation and time variability.

‡ Sommerfeld considered α "important constants of nature, characteristic of the constitution of all the elements."[4]

† https://www.researchgate.net/post/NO30The_Relation_Between_Mathematics_and_Physics_6-Are_Planck_Scales_Constants_Parameters_or_Principles

** https://www.researchgate.net/post/No28The_Relation_Between_Mathematics_and_Physics_4-Could_All_Physical_Constants_be_Unified_to_a_set_of_Fundamental_Constants_of_Nature

-----------------------------------

[3] 张天蓉. (2022). 精细结构常数. https://blog.sciencenet.cn/blog-677221-1346617.html

[1] Sommerfeld, A. (1916). The fine structure of Hydrogen and Hydrogen-like lines: Presented at the meeting on 8 January 1916. The European Physical Journal H （2014）, 39(2), 179-204.

[2] Sommerfeld, A. (1916). Zur quantentheorie der spektrallinien. Annalen der Physik, 356(17), 1-94.

[4] Heilbron, J. L. (1967). The Kossel-Sommerfeld theory and the ring atom. Isis, 58(4), 450-485.

[5] Eckert, M., & Märker, K. (2004). Arnold Sommerfeld. Wissenschaftlicher Briefwechsel, 2, 1919-1951.

[6] Wilczynska, M. R., Webb, J. K., Bainbridge, M., Barrow, J. D., Bosman, S. E. I., Carswell, R. F., Dąbrowski, M. P., Dumont, V., Lee, C.-C., Leite, A. C., Leszczyńska, K., Liske, J., Marosek, K., Martins, C. J. A. P., Milaković, D., Molaro, P., & Pasquini, L. (2020). Four direct measurements of the fine-structure constant 13 billion years ago. Science Advances, 6(17), eaay9672. https://doi.org/doi:10.1126/sciadv.aay9672

[7] Webb, J. K., King, J. A., Murphy, M. T., Flambaum, V. V., Carswell, R. F., & Bainbridge, M. B. (2011). Indications of a Spatial Variation of the Fine Structure Constant. Physical Review Letters, 107(19), 191101. https://doi.org/10.1103/PhysRevLett.107.191101

The historical evolution of the concept of "vacuum" [1] can be roughly described as the following.

0) Buddhist Vacuum: the void formlessness, the empty barrier-free. It refers to the place and space where all dharmas exist. There are four meanings: pervasive, immovable, endless, and eternal.

I) Conceptual Vacuum: Aristotle in ancient Greek era believed that " Void separated from the matter does not exist" [2], the void must be filled with matter in order to be able to carry out physical action^*. The concept of vacuum at this stage is void, a state of space.

II) Industrial vacuum: Evangelista Torricelli (1608-1647), secretary and assistant of Galileo Galilei (1564-1642), proved the "vacuum" without an atmosphere using a mercury barometer [3]. The concept of vacuum at this stage was static and overlapped with Newton's absolute space.

III) Ether Vacuum: “......, as the recipient of energy, is to regard it as continuously filling all space, and possessing the mobility of fluid rather than the rigidity of a solid. If whatever possess the property of inertia be matter, then the medium is a form of matter. But away from ordinary matter it is, for obvious reasons, best to call it as usual by a separate name, the ether."[4] "The aether is the solitary tenant of the universe, save for that infinitesimal fraction of space which is occupied by ordinary matter."[5]. The vacuum at this stage is the medium through which electromagnetic waves can travel.

IV) Quantum Vacuum: Along with the development of quantum mechanics, numerous vacuum-related concepts have arisen, the ground state, the various excited states, zero point energy, negative energy sea, spontaneous emission, Vacuum polarization, vacuum fluctuations, etc.. "The vacuum is, in fact, precisely the ground state of the fundamental many-field system. "[9]^† "In a quantum theory, the vacuum is a very busy place. Particle-antiparticle pairs are constantly produced out of nothing, violating the energy-conservation law by borrowing an amount of energy E from the vacuum for a time t such that Et<ℏ, according to Heisenberg's uncertainty principle. "As the Higgs boson propagates in the quantum vacuum, it feels the presence of virtual particles and interacts with them."[6] and theoretically and experimentally identified the Casimir effect for verifying vacuum energy[7][8], and the Lamb shift. The concept of vacuum at this stage provides a self-consistent ground for quantum field theory, where the vacuum is seen as a separate background for spacetime.

V) Relativity Vacuum： Quantum field theory predicts that a uniformly accelerated particle detector sees the vacuum as a thermal bath with temperature T related to its proper acceleration a, i.e., T =a/2π, as a result of the interaction between the detector and the fluctuating vacuum scalar fields, and this is called the Fulling-Davies-Unruh (FDU) effect. Vacuum and space appear to be separate.

VI) Planck Scales Vacuum: Some of the new physics considers the vacuum to be more complex, with the emergence of Quantum foams [11], Spin foams, Quantum spacetime [12], String Network, Lattice structure, Conformal structure [13], and other concepts [14]. Space is discretized and the Vacuum seems to merge with Space again.

VII) Dark Energy Vacuum: It is believed by some people that the vacuum energy is dark energy, and therefore the vacuum is a place with a certain dark energy density. In this case, the vacuum has the effect of the cosmological constant Λ [15], which is the driving force for the accelerated expansion of space-time.

It appears that the relationship between the various vacuums and space is not consistent. Without a clear definition on this most fundamental issue of physics, it may already be a potential obstacle to progress.

1) Is the size of the vacuum the same as the size of cosmic space? When cosmic space inflation or expands, is the cosmic vacuum also inflating or expanding?

2) If the vacuum is not empty, is it uniform? Is it affected by the General Relativity Space-Time Metric (Curvature)? Is the vacuum inside a black hole the same as the vacuum elsewhere?

3) In a particle accelerator, does an electron traveling at high speed see the same vacuum as a stationary electron? Do electrons interact with the vacuum only at the moment of collision?

4) Without vacuum energy, is there no possibility of producing any particles in space? How were the initial elementary particles excited^‡?

5) Would our conception of the vacuum change if we gave up the dynamical function of the uncertainty principle?

--------------------

* Aristotle gives an example, if a ball is thrown up, and it continues to fly after it has been released from the hand, it means that something must be holding it up one after the other, otherwise it would have fallen down. Note that this plain view is not necessarily wrong. Without borrowing the notion of conservation of energy-momentum, our explanation must return to the plain description. In fact, the intuitive interpretation of conservation of energy-momentum itself still requires this plain view.

‡ "What relation subsists between the medium which fills the interstellar void and the condensations of matter that are scattered throughout it?"[5] The relation between vacuum energy and visible energy was questioned 100 years ago.

† In the literature [9] the vacuum is specified, the Higgs vacuum, electromagnetic field vacuum, Dirac electron vacuum, the boson vacuum, the QCD vacuum......

--------------------

[1] 张天蓉. (2022). 真空. https://blog.sciencenet.cn/blog-677221-1342155.html

[2] Aristotle. (1929). The Metaphysics [物理学] (张竹明, Trans.).

[3] https://www.britannica.com/biography/Evangelista-Torricelli

[4] Heaviside, O. (1892). On the forces, stresses, and fluxes of energy in the electromagnetic field. Philosophical Transactions of the Royal Society of London.(A.)(183), 423-480.

[5] Whittaker, E. (1910). A History of the Theories of Aether and Electricity (Vol. Vol. I: The Classical Theories; Vol. II: The Modern Theories, 1900-1926). Courier Dover Publications（1989）极好的早期物理学历史著作。

[6] Kane, G., & Pierce, A. (2008). Perspectives on LHC physics. World Scientific Publishing Co. Pte. Ltd.

[7] Casimir, H. B. (1948). On the attraction between two perfectly conducting plates. Proc. Kon. Ned. Akad. Wet.,

[8] Jaffe, R. L. (2005). Casimir effect and the quantum vacuum. Physical Review D, 72(2), 021301. https://doi.org/10.1103/PhysRevD.72.021301

[9] Aitchison, I. J. R. (1985). Nothing's plenty the vacuum in modern quantum field theory. Contemporary Physics, 26(4), 333-391. https://doi.org/10.1080/00107518508219107

[10] Zhou, W., & Yu, H. (2020). Collective transitions of two entangled atoms and the Fulling-Davies-Unruh effect. Physical Review D, 101(8), 085009.

[11] Misner, C. W., Thorne, K. S., & Zurek, W. H. (2009). John Wheeler, relativity, and quantum information. Physics Today, 62(4), 40-46.

[12] Ashtekar, A., & Singh, P. (2011). Loop quantum cosmology: a status report. Classical and quantum gravity, 28(21), 213001.

Rovelli, C. (2008). Loop Quantum Gravity. Living Reviews in Relativity, 11(1), 5. https://doi.org/10.12942/lrr-2008-5

[13] Penrose, R. (2012). The basic ideas of conformal cyclic cosmology. AIP Conference Proceedings 11,

[14] Addazi, A., Alvarez-Muniz, J., & etl. (2022). Quantum gravity phenomenology at the dawn of the multi-messenger era—A review. Progress in Particle and Nuclear Physics, 125, 103948. https://doi.org/https://doi.org/10.1016/j.ppnp.2022.103948

[15] Peebles, P. J. E., & Ratra, B. (2003). The cosmological constant and dark energy. Reviews of Modern Physics, 75(2), 559.

I. We often say that xx has no physical meaning or has physical meaning. So what is "physical meaning" and what is the meaning of "physical meaning "*?

"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. I claim that all assertions of this kind are uniquely determined for the future as well, i.e., that the causality principle is valid in the following formulation: From knowledge of the fourteen potentials ......, in the present all statements about them in the future follow necessarily and uniquely insofar as they have physical meaning" [1].“Hilbert's answer is based on a more precise formulation of the concept of causality that hinges on the distinction between meaningful and meaningless statements.”[2]

Hawking said [4], "I take the positivist view that a physical theory is nothing more than a mathematical model, and it is pointless to ask whether it corresponds to the real. All one can seek is that its predictions agree with its observations."

Is there no difference between physics and Mathematics? We believe that the difference between physics and mathematics lies in the fact that physics must have a physical meaning, whereas mathematics does not have to. Mathematics can be said to have a physical meaning only if it finds a corresponding expression in physics.

II. We often say, restore naturalness, preserve naturalness, the degree of unnaturalness, Higgs naturalness problem, structural naturalness, etc., so what is naturalness or unnaturalness?

“There are two fundamental concepts that enter the formulation of the naturalness criterion: symmetry and effective theories. Both concepts have played a pivotal role in the reductionist approach that has successfully led to the understanding of fundamental forces through the Standard Model. ” [6]

Judging naturalness by symmetry is a good piece of criteria; symmetry is the only result of choosing stability, and there seems to be nothing lacking. But using effective theories as another criterion must be incomplete, because truncate obscures some of the most important details.

III. We often say that "The greatest truths are the simplest"（大道至简†）, so is there a standard for judging the simplest?

"Einstein was firmly convinced that all forces must have an ultimate unified description and he even speculated on the uniqueness of this fundamental theory, whose parameters are fixed in the only possible consistent way, with no deformations allowed: 'What really interests me is whether God had any choice in the creation of the world; that is, whether the necessity of logical simplicity leaves any freedom at all' ”[6]

When God created the world, there would not have been another option. The absolute matching of the physical world with the mathematical world has shown that as long as mathematics is unique, physics must be equally unique. The physical world can only be an automatic emulator of the mathematical world, similar to a Cellular Automata.

It is clear that consensus is still a distant goal, and there will be no agreement on any of the following issues at this time:

1) Should there be a precise and uniform definition of having physical meaning? Does the absence of physical meaning mean that there is no corresponding physical reality?

2) Are all concepts in modern physics physically meaningful? For example, probabilistic interpretation of wave functions, superposition states, negative energy seas, spacetime singularities, finite and unbounded, and so on.

3) "Is naturalness a good guiding principle?"[3] "Does nature respect the naturalness criterion?"[6]

4) In physics, is simplicity in essence uniqueness? Is uniqueness a necessary sign of correctness‡?

---------------------------------------------------------

* xx wrote a book, "The Meaning of Meaning", which Wittgenstein rated poorly, but Russell thought otherwise and gave it a positive review instead. Wittgenstein thought Russell was trying to help sell the author and Russell was no longer serious [5]. If one can write about the Meaning of Meaning, then one can follow with the Meaning of Meaning of Meaning. In that case, how does one end up with meaning? It is the same as causality; there must exist an ultimate meaning which cannot be pursued any further.

‡ For example, the Shortest Path Principle, Einstein's field equation Gµν=k*Tµν, all embody the idea that uniqueness is correctness (excluding the ultimate interpretation of space-time).

† “万物之始，大道至简，衍化至繁。”At the beginning of all things, the Tao is simple; later on, it evolves into prosperous and complexity. Similar to Leonardo Da Vinci，＂Simplicity is the ultimate sophistication.＂ However, the provenance of many of the quotes is dubious.

------------------------------

[1] Rowe, D. E. (2019). Emmy Noether on energy conservation in general relativity. arXiv preprint arXiv:1912.03269.

[2] Sauer, T., & Majer, U. (2009). David Hilbert's Lectures on the Foundations of Physics 1915-1927: Relativity, Quantum Theory and Epistemology. Springer.

[3] Giudice, G. F. (2013). Naturalness after LHC8. arXiv preprint arXiv:1307.7879.

[4] Hawking, S., & Penrose, R. (2018). The nature of space and time (吴忠超，杜欣欣, Trans.; Chinese ed., Vol. 3). Princeton University Press.

[5] Monk, R. (1990). Ludwig Wittgenstein: the duty of genius. London: J. Cape. Morgan, G. (Chinese @2011)

[6] Giudice, G. F. (2008). Naturally speaking: the naturalness criterion and physics at the LHC. Perspectives on LHC physics, 155-178.

The concept of quantization in physics begins with the expression E=hν, P=h/λ obtained from the blackbody radiation law, where h is the minimum amount of action [1]. Since there is a mass-energy relation E=mc^2 [2], all matter particles (with mass) can and must be equally capable of being expressed ‡ in terms of E=hν, which leads to the fact that the structure and interactions of all matter must be finite, integer multiples of the quantity hν. While the fact that ν can be continuous* does not prevent the fulfillment of occasions where there is a requirement for energy continuity, the discrete nature of the energy levels dictates that the choice of ν is finite.

In quantum mechanics, the state of a particle can be described by its wave function Ψ(r), or there can be described by the momentum representation φ(p). In fact, we can regard Ψ(r) as a time-domain energy packet and φ(p) as a frequency-domain momentum packet; momentum φ(p) and energy Ψ(r) are a pair of Fourier transformations. If the fundamental composition of matter is a variety of quanta E=hνi (i=1,2,3), then the momentum pi implied in all matter is also a variety. The Fourier transform of a continuous function in the time domain produces an infinite multitude in the frequency domain, and vice versa. Physics really cannot express infinite multinomials. Only the Fourier transform DFT of a finitely discrete time-domain function corresponds to a finite number of discrete terms in the frequency domain, which can express the physical reality under certain conditions. The Fourier transform is related in quantum mechanics to wave-particle duality, superposition, the uncertainty principle, measurement, etc. Therefore, we ask:

1) Is the discrete Fourier transformation the only inevitable choice for the quantization of physics?

2) Since everything is expressed by the photon's E=hν, should fermions (electrons, quarks), W bosons, gluons also be expressed by photons?

-------------------------------------------

‡ including all fermions, electrons, quarks, etc. Do we then need to find a direct compositional relation between fermions and E=hν? Since, the composition of quarks is associated with E=hν, why is the interaction not it, but changed to gluons?

* We need to think about the question, what must be the physical meaning of ν in E=hν?

-----------------------------------------

[1] Planck, M. (1900). The theory of heat radiation (1914 (Translation) ed., Vol. 144).

[2] Einstein, A. (1905). Does the inertia of a body depend upon its energy-content. Annalen der Physik, 18(13), 639-641.

[3]

[4]

"What is an elementary particle?" This seemingly simple question has no clear answer; this seemingly unimportant question may be very important.

Weinberg says [1], "Giving this answer always makes me nervous. i would have to admit that no one really knows." in textbooks, the history of the discovery of particles is recounted. From atoms, electrons, protons, neutrons, up to neutrinos and quarks in the Standard Model, however, the definition of elementary particles is usually not given, and various particles are discussed directly, as in the literature [2][3], ignoring the concept of Elementary.

To answer this question, it is necessary to answer what is meant by "particle" and what is meant by "elementary".

"A particle is simply a physical system that has no continuous degrees of freedom except for its total momentum. "[1]. But obviously, whether this definition holds depends on the depth of the researcher's perspective. If we study only dust, then dust is a particle, even though it has a rich internal structure; if we study blackbody radiation, then a photon is a particle, even though we don't know if it has a structure ....... So the concept of "particle" depends only on our perspective and ability to focus.

"what is meant by elementary ?" Elementary is used in many contexts, not only as "elementary particle", but also as elementary fields, elementary electric charge, etc. Whatever the object of description, our understanding of elementary is that as long as the object it qualifies is irreducible, then that object is elementary. Does irreducible mean "nothing could be pulled or knocked out of it"? This is not a reliable answer, because we don't know at what energy level a composite particle would terminate its decomposition. If there are "Kerr black holes as elementary particles" [4], how do we break it up? And it has been found that different particles produce each other in collisions, so which is a composite of which [1]? even different things produce the same output, so "The difference between elementary and composite particles has thus basically disappeared. and that is no doubt the most important experimental discovery of the last fifty years." [Heisenberg 1975]. When we get to the QFT stage, "particles are not fundamental entities" [5], "There are no particles, there are only fields " [6]. "From the perspective of quantum field theory, the basic ingredients of Nature are not particles but fields; particles such as the electron and photon are bundles of energy of the electron and the electromagnetic fields."[1].

Although photons and electrons come from imagined different elementary fields*, they can nevertheless be converted into each other by the annihilation process e+e- → γ γ' and the pair creation process γ γ' → e+e- [7], with the consequent creation or disappearance of the properties of electrons (charge, spin, mass). Physics suggests that this process is not direct, but rather that photons γ γ' produced by electromagnetic fields excite electron fields, from which e+e- is produced. If we remove this intermediate process, the photon has a spacetime symmetry, which corresponds to the Lorentz invariance of SR in "flat spacetime", and the electron has a gauge-invariant Internal spacetime symmetry, which corresponds to the general covariance of GR in "curved spacetime"; the photon is a boson, the electron is a fermion; according to the supersymmetry theory [8], there is a symmetry relationship between bosons and fermions. Since it is a symmetry relation, they must be convertible to each other, that is, different states of one thing. So, shouldn't annihilation and pair production be a kind of supersymmetric transition relationship? Why don't we consider "annihilation" and "pair production" as verification experiments of supersymmetric relations? Do we have another theory and experiment to determine this symmetry relation? If we further define that particles that can be produced by photons through "pair production" are elementary particles, wouldn't that answer all the questions?

Weinberg said. "We will not be able to give a final answer to the question of which particles are elementary until we have a final theory of force and matter. " What does that really mean?

----------------------------------

Notes

* Space-time is filled with dozens of different fields, it is impossible to imagine their rationality and necessity.

----------------------------------

References

[1] Weinberg, S. (1996). "What is an elementary particle." See http://www. slac. stanford. edu/pubs/beamline/27/1/27-1-weinberg. pdf.

[2] Griffiths, D. J. (2017). Introduction to Elementary Particles, WILEY.

[3] Group, P. D. (2016). "Review of particle physics." Chinese Physics C 40(10): 100001.

[4] Arkani-Hamed, N., Y.-t. Huang and D. O’Connell (2020). "Kerr black holes as elementary particles." Journal of High Energy Physics 2020(1): 1-12.

[5] Fraser, D. (2021). Particles in quantum field theory. The Routledge Companion to Philosophy of Physics, Routledge: 323-336.

[6] Hobson, A. (2013). "There are no particles, there are only fields." American journal of physics 81(3): 211-223.

[7] https://www.researchgate.net/post/NO8_Are_annihilation_and_pair_production_mutually_inverse_processes

[8] Wess, J. (2000). From symmetry to supersymmetry. The supersymmetric world: the beginnings of the theory, World Scientific: 67-86.

From the earliest Pythagorean (~570BCE-~490BCE) view that "everything is number" [1], to the founder of modern physics, Galileo (1564-1642), who said "the book of nature is written in the language of mathematics" [2], to attempts by Hilbert (1862-1943) to mathematically "axiomatize" physics [3]，and to the symmetry principle [9], which today is considered fundamental by physics, Physics has never been separated from mathematics, but there has never been a definite answer as to the relationship between them. Thus Wigner (1902-1995) exclaimed [4]: "The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. gift which we neither understand nor deserve."

CN Yang, commenting on Einstein's "On the method of theoretical physics" [5], said, "Was Einstein saying that fundamental theoretical physics is a part of mathematics? Was he saying that fundamental theoretical physics should have the tradition and style of mathematics? The answers to these questions are no "[6]. So what is the real relationship between mathematics and physics? Is mathematics merely a tool that physics cannot do without? We can interpret mathematics as a description of physical behavior, or physics as operating according to mathematical principles, or they are completely equivalent, but one thing is unchangeable, all physics must ultimately be concretely embodied in its physical parameters, regardless of who dominates whom. We need to remember the essential question, "That is, we don't invent mathematical structures - we discover them, and invent only the notation for describing them"[7]. Mathematics is abstract existence, physics is reality. We cannot completely replace physical explanations with mathematical ones. For example, ask "How do light and particles know that they are choosing the shortest path [8]. The answer is that it is determined by the principle of least action. This is the correct mathematical answer, but not the final physical answer. The final physical answer should be, "Light and particles are not searching for shortest paths, they are creating and defining shortest paths". Why this can be so is because they are energy-momentum themselves. The ultimate explanation is just math*，if we can't boil it down to specific, well-defined, measurable physical parameters. Following Pythagoras' inspiring vision that the world can be built up from concepts, algorithms, and numbers [9]. When we discuss the relationship between math and physics, do we need first ask:

1) What are numbers? Shouldn't we first attribute numbers to "fundamental quantities" in mathematics and physics? Are scalars, vectors, and spinors complete expressions of such fundamental quantities? All other quantities are composites of these fundamental quantities, e.g., tensor.

2) Do mathematics and physics have to have these fundamental quantities in common before we can further discuss the consistency between their theorems? That is, the unification of mathematics and physics must begin with the unification of fundamental quantities.

3) Where do these fundamental quantities come from in physics? In what way are they represented?

--------------------------------

Notes：

* And then what do imaginary numbers in physics correspond to? [10][11]

--------------------------------

References：

[1] McDonnell, J. (2017). The Pythagorean World: Why Mathematics Is Unreasonably Effective In Physics Springer.

[2] Kosmann-Schwarzbach, Y. (2011). The Noether Theorems. The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century. Y. Kosmann-Schwarzbach and B. E. Schwarzbach. New York, NY, Springer New York: 55-64.

Einstein, A. (1934). "On the method of theoretical physics." Philosophy of science 1(2): 163-169.

[3] Corry, L. (2004). David Hilbert and the axiomatization of physics (1898-1918): From Grundlagen der Geometrie to Grundlagen der Physik, Springer.

[4] Wigner, E. P. (1990). The unreasonable effectiveness of mathematics in the natural sciences（1960）. Mathematics and Science, World Scientific: 291-306. 【这个说法本身可能是存在问题的，不是数学在物理学中的有效性，而是不能够区分物理学准则和数学算法。】

[5] Einstein, A. (1934). "On the method of theoretical physics." Philosophy of science 1(2): 163-169.

[6] Yang, C. N. (1980). "Einstein's impact on theoretical physics." Physics Today 33(6): 42-49.

[7] Russell, B. (2010). Principles of mathematics （1903）, Routledge.

[8] https://www.researchgate.net/post/NO4_How_do_light_and_particles_know_that_they_are_choosing_the_shortest_path

[9] Wilczek, F. (2006). "The origin of mass." Modern Physics Letters A 21(9): 701-712.

[10] Chian Fan, e. a. (2023). "How to understand imaginary numbers (complex numbers) in physics." from https://www.researchgate.net/post/NO6_How_to_understand_imaginary_numbers_complex_numbers_in_physics.

[11] Baylis, W. E., J. Huschilt and J. Wei (1992). "Why i?" American Journal of Physics 60(9): 788-797. 【复数、虚数、波函数】

I well come to discuss on recent trend in physics" A Postquantum Theory of Classical Gravity?" by Jonathan Oppenheim

Noether's theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: for one, it is not applicable to dynamics wherein the system interacts with an environment; furthermore, even in the case where the system is isolated, if the quantum state is mixed then the Noether conservation laws do not capture all of the consequences of the symmetries[1].

In SR, force-free motion in an inertial frame of reference takes place along a straight-line path with constant velocity. Viewed from a non-inertial frame, on the other hand, this path of motion will be a geodesic curve in a flat spacetime. Einstein made the plausible assumption that this geodesic motion also holds in the non-flat case, i.e. in a spacetime region for which it is impossible to find a coordinate system that leads to the Minkowski metric in SR[2].

All spacetime models can be expressed in terms of the gμν = {4x4} matrix, differing only in the distribution of matrix elements. The gμν of Minkowski spacetime is the unit diagonal matrix {1 -1 -1 -1}; the gμν of Riemann spacetime is { X }. If a new spacetime model is introduced gμν={a0,-a1,-a2,-a3}, which is a non-unit diagonal matrix. (ds)^2=(a0)^2+(a1)^2+(a2)^2+(a3)^2, always holds, interpreting it as a non-uniformly flat spacetime, generalised Minkowski spacetime, and no longer a curved spacetime. Should Noether's theorem maintain its validity in this case.

----------------------------------

References

[1] Marvian, I., & Spekkens, R. W. (2014). Extending Noether's theorem by quantifying the asymmetry of quantum states. Nature Communications, 5(1), 3821. https://doi.org/10.1038/ncomms4821 ;

[2] Rowe, D. E. (2019). Emmy Noether on energy conservation in general relativity. arXiv preprint arXiv:1912.03269.

Do we need to find a motivation for symmetry: {?} → {invariance} → {conservation} → {symmetry} →

Should there be an ultimate symmetry that is identical to the conservation, structure invariance, and interaction invariance of the energy-momentum primitives and that determines all other symmetries?

Symmetry, invariance, and conservation are, in a sense, the same concept [1][2][3] and will generally be described in this order, as if symmetry were dominant.

As commonly understood, energy-momentum conservation was the first physics concept to be developed. It exists as a matter of course in mechanics, thermodynamics, and electricity. However, after physics entered the twentieth century, from quantum mechanics to general relativity, the conservation of energy-momentum has been repeatedly encountered with doubts [5][6][7][8][9][10], and so far it still can't be determined as a universal law by physics. Some of the new physics is insisting on "something out of nothing"[11][12][13][14] or spontaneous vacuum fluctuations[15], which equals to the rejection of energy-momentum conservation. The important reasons for this may be: First, Energy-momentum conservation cannot be proved† . Second, energy-momentum in physics has never been able to correspond to a specific thing, expressed by a unified mathematical formula‡, and it can only be the "equivalence" of various physical forms that are converted and transferred to each other [16]. Third, we have a biased understanding of the status of energy-momentum conservation, such as "These symmetries implied conservation laws. Although these conservation laws, especially those of momentum and energy, were regarded to be the most important of all. Although these conservation laws, especially those of momentum and energy, were regarded to be of fundamental importance, these were regarded as consequences of the dynamical laws of nature rather than as consequences of the symmetries that underlay these laws."[17]. Conservation of energy-momentum was relegated to a subordinate position. Fourth, it is believed that the Uncertainty Principle can be manifested as a " dynamics ", which can cause various field quantum fluctuations in the microscopic domain, and does not have to strictly obey the energy-momentum conservation.

"Symmetry" refers to the "invariance under a specified group of transformations" of the analyzed object [4]. Symmetry is always accompanied by some kind of conservation, but conservation does not only refer to the conservation of energy-momentum, but also, under different conditions, to the conservation of other physical quantities, such as charge, spin, or the conservation of other quantum numbers. Thus, "conservation" is usually the constant invariance of something at some level, and Wigner divided symmetries into classical geometrical symmetries and dynamical symmetries, which are associated with specific types of interactions, every interaction has a dynamical invariance group. "It may be useful to discuss first the relation of phenomena, laws of nature, and invariance principles to each other. This relation is not quite the same for the classical invariance principles, which will be called geometrical, and the new ones, which will be called dynamical."[1]. According to Wigner, we can define the "geometric invariance" of everything as the manifestation of interactions filtered through the absoluteness of the spatio-temporal background. This interaction exhibits itself whenever you assume an observer*. displacement invariance, Lorentz invariance are typical. We can define all "dynamical invariance" as manifestation when the background absolutes of the potential field are filtered out. gauge invariance, the diffeomorphism invariance are typical manifestations." from a passive role in which symmetry is the property of interactions, to an active role in which symmetry serves to determine the interactions themselves --a role that I have called symmetry dictates interaction." "Einstein's general relativity was the first example where symmetry was used" actively to determine gravitational interaction" [2]. This expresses the same idea, that the role of symmetry is elevated to the status of "force". Gross says that the secret of nature is symmetry. The most advanced form of symmetries we have understood are local symmetries-general coordinate invariance and gauge symmetry. The most advanced form of symmetries we have understood are local symmetries-general coordinate invariance and gauge symmetry. unified theory that contains both as a consequence of a greater and deeper symmetry of which these are the low energy remnants [18]. He regards the unification of general relativity and quantum field theory as a unification of symmetries. He regards the unification of general relativity and quantum field theory as a unification of symmetries. If we define generalized invariance as the completeness of the structure, properties, and laws of interaction of the analyzed objects when they interact, i.e., the undecomposability of the whole as a whole, the conservation of the properties (charge, spin, other quantum numbers, etc.), and the consistency of the interaction relations (laws), it is clear that the invariance in this case is special invariance, which means only the invariance of the laws of interaction.

While symmetry, conservation, and invariance are almost equivalent expressions at the same level, there are subtle but important differences. If unbounded, it is the order in which the three are expressed, who actually determines whom, and who ultimately determines the laws of physics. In any case, when we currently speak of symmetry, it must correspond to specific invariance and conservation, not to broad invariance and conservation. This in fact greatly limits the claim that "symmetry dictates interaction", since interaction is much more general. There is no such thing as a failure of interaction, but there is often a failure of symmetry, unless we decide that there will be an ultimate symmetry that determines all other symmetries.

"A symmetry can be exact, approximate, or broken. Exact means unconditionally valid; approximate means valid under certain conditions; broken can mean different things, depending on the object considered and its context. different things, depending on the object considered and its context."[19] "It is not clear how rigorous conservation laws could follow from approximate symmetries"[1]. This reflects the uncertainty of the relationship between conservation currents ( charges) and symmetries, and if we know that conservation currents can still be maintained even with approximate symmetries, it should be understood that this must be a function of the fact that conservation currents have a more universal character. From a reductionist point of view, the conservation charge at all levels will gradually decompose with the decomposition of matter, until finally it becomes something that cannot be decomposed. Such a thing can only be the most universal energy-momentum and at the same time be the ultimate expression that maintains its conservation as well as the invariance of interactions. Otherwise, we will pursue the questions:

1) If energy-momentum conservation is not first, where does the power to move from one symmetry to another, symmetry breaking [11] [12], come from? How can symmetry violations [13] in physics be explained?

2) If symmetry fully expresses interactions, how do we evaluate "symmetry implies asymmetry", "imperfect symmetry", " approximate symmetry", " hidden symmetry"? hidden symmetry"?

3) One of the implications of energy-momentum conservation is that they have no origin, are a natural existence, and do not change with scale and energy level or temperature; symmetry has an origin, and is related to scale, temperature and energy level. How are they equivalent to each other?

4) Must there be an ultimate symmetry which will determine everything and be consistent with conservation and invariance?

--------------------------------------------------------------------------------------------

Notes

† We will analyze this separately, which is its most important physical feature [20].

‡ Can different forms of energy be unified?[16]

* We can define the actual observer to be the object of action and the abstract observer to be the object of action for analysis. For example, when we analyze the Doppler effect, we are analyzing it in the abstract; if you don't actually detect it, no Doppler effect occurs in the object of analysis.

--------------------------------------------------------------------------------------------

References

[1] Wigner, E. P. (1964). "Symmetry and conservation laws." Proceedings of the National Academy of Sciences 51(5): 956-965.

[2] Yang, C. N. (1996). "Symmetry and physics." Proceedings of the American Philosophical Society 140(3): 267-288.

[3] Yang, C. N. (1980). "Einstein's impact on theoretical physics." Physics Today 33(6): 42-49.

[4] Brading, K., E. Castellani and N. Teh (2003). "Symmetry and symmetry breaking."

[5] Bohr, N., H. A. Kramers and J. C. Slater (1924). "LXXVI. The quantum theory of radiation." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 47(281): 785-802.

[6] Dirac, P. A. M. (1927). "The quantum theory of dispersion." Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 114(769): 710-728.

[7] Carroll, S. M. and J. Lodman (2021). "Energy non-conservation in quantum mechanics." Foundations of Physics 51(4): 83.

[8] Bondi, H. (1990). "Conservation and non-conservation in general relativity." Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 427(1873): 249-258.

[9] Maudlin, T., E. Okon and D. Sudarsky (2020). "On the status of conservation laws in physics: Implications for semiclassical gravity." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 69: 67-81.

[10] Pitts, J. B. (2022). "General Relativity, Mental Causation, and Energy Conservation." Erkenntnis 87.

[11] Hoyle, F. (1948). "A new model for the expanding universe." Monthly Notices of the Royal Astronomical Society, Vol. 108, p. 372 108: 372.

[12] Vilenkin, A. (1982). "Creation of universes from nothing." Physics Letters B 117(1): 25-28.

[13] Josset, T., A. Perez and D. Sudarsky (2017). "Dark energy from violation of energy conservation." Physical review letters 118(2): 021102.

[14] Singh Kohli, I. (2014). "Comments On: A Universe From Nothing." arXiv e-prints: arXiv: 1405.6091.

[15] Tryon, E. P. (1973). "Is the Universe a Vacuum Fluctuation?" Nature 246(5433): 396-397.

[16] Chian Fan, https://www.researchgate.net/post/NO10_Can_different_forms_of_energy_be_unified

[17] Gross, D. J. (1996). "The role of symmetry in fundamental physics." Proceedings of the National Academy of Sciences 93(25): 14256-14259.

[18] Gross, D. J. (1992). "Gauge theory-past, present, and future?" Chinese Journal of Physics 30(7): 955-972.

[19] Castellani, E. (2003). "On the meaning of symmetry breaking." Symmetries in physics: Philosophical reflections: 321-334.

[20] https://www.researchgate.net/publication/369890893_Summary_Table_of_Light_String_and_Light_Ring_Properties_Supersymmetry

The Hubble radius is defined as the distance from our location where particles (galaxies) are receding from us at the speed of light. Our “Hubble radius” is currently about 13.8 billion light years. Beyond the Hubble radius, particles are receding faster than the speed of light. This apparent violation of the cosmic speed limit is usually explained as being possible because space itself is expanding and space has no speed limit. Particles in this volume of space are not traveling faster than the local photons.

However, this explanation creates a problem. It implies that the space beyond our Hubble radius is fundamentally different from our local space. For a thought experiment, imagine that we could instantly teleport an electron anywhere in the universe. If we teleported an electron to a volume of space beyond our Hubble radius, the electron that we consider to be stationary, would be moving faster than the speed of light propagating in the volume of space beyond our Hubble radius. Obviously, the electron we consider to be stationary cannot exist in the quantum vacuum beyond our Hubble radius. Omni-directional gravitational waves emanating from a point in space that is beyond our Hubble radius would appear to us to have a velocity distribution that is symmetrical to the local CMB rest frame there. This implies to me that space is a sonic medium with a privileged frame of reference. What do you think?

When God built the world, he needed an absolute ruler to measure space, an absolute clock to measure time. This is light. Then the light was kneaded together in space-time and became matter. Space-time is not a container for matter, not a stage for matter, but "you are in me and I am in you", becoming part of matter. Light is their dominator. Therefore, when we say that virtual particles are transmitting interactions [1], they are actually interactions mediated by light and space-time, and virtual particles are only a kind of "pronoun".

We should be aware of the special nature of light. Many physicists believe that photons have no special characteristics compared to other elementary particles [2]. Why do we choose to ignore the basic facts?

1) The speed of light is independent of the inertial system in which the observer is located, and becomes the basis of Special Relativity‡, the limiting criterion of motion. This alone is sufficient to declare that the photon is not in the same position as any other particle.

2) The speed of light is independent of the inertial system in which the light source is located*, and the speed of light seen by the observer remains the same no matter at what speed (and in what direction) the light source is moving. This one determines the absoluteness of light's own background spacetime, and provides a reference standard for relative spacetime. The speed of motion of any other particle is closely related to the reference frame.

3) Photons have an infinite variety of continuity (ν→∞), while any other particle in the Standard Model [1] has only one. Or group them together, in symmetrical terms, a finite number of generations. A more symmetrical statement would be that a continuous infinite number of photons corresponds to a discrete infinite number of matter particles. But there are only a few kinds of matter particles that can exist stably. If we haven't missed it, the distribution of discrete matter particles, from lowest to highest, should be, x → neutrinos (three generations) → x → electrons (three generations) → x → quarks (three generations) → x → ....... Where x represents particles that are undiscoverable in their very short lifetimes, or their energies are too high to have been discovered yet. We believe that black holes line up in this series[4].

4) Photons express energy-momentum from infinitely small to infinitely large without limit. The energy of any elementary particle in the Standard Model is determined.

5) Light is in eternal motion and cannot be accelerated, which determines that photons are particles without mass. This is the essence that distinguishes photons from other particles [3].

6) A free photon has no gravitational field**, or its gravitational field potential is 0. Any other particle has a gravitational field.

7) The polarization of a photon is different from the spin of a particle.

8) Light is the only particle that does not interact with its own kind, they only interfere superpositionally, and any interference disappears as soon as it does not interact with other matter (e.g. the screen). Any other particle interacts with its own kind.

9) Any two photons of the same frequency are absolutely identical in absolute space. However, any two electrons cannot overlap, and the difference in spatial location causes them not to be absolutely identical†.

10) The speed of light is constant in any spacetime context and in any medium¶. This point determines that the spacetime of GR, the spacetime of SR, and the spacetime of QM must be the same spacetime[5]. And any other particle will change its velocity not only when interacting, but also in a gravitational field.

Please feel free to add to this and welcome different points of view.

--------------------------------------------------------------------------

* The process of photon emission: from a light source in a particular inertial system to a photon in absolute space, where the interface can only be light itself.

† I am not sure how this differs from the all-homogeneity that determines statistical properties, Bose statistics, Fermi statistics.

‡ Any "relativity", relative space-time, relative energy-momentum, arises because of interactions and the need for conservation of energy-momentum during the interactions.

¶ The change in the velocity of light in a medium is only the result of an external observer's observation; it is the result of a change in space-time within the medium. Nowhere does light appear to change its velocity.

** If a photon is in a gravitational field, its energy owns the gravitational field as it matches it. This is compatible with GR.

--------------------------------------------------------------------------

[1] Schmitz, W. (2019). Particles, Fields and Forces, Springer.

[2] Weinberg, S. (2020). Dreams of a Final Theory, Hunan Science and Technology Press.

[3] The only possibility for a photon to manifest mass is from the non-axial action of matter particles on it. That is, any action that exists at an angle to the direction of propagation of light, z, is capable of experiencing the mass of the photon. Note that our criterion for determining mass is the presence or absence of "damping" in its own motion. The structure and motion of the photon have a definite directionality, and other particles do not have to distinguish between the directionality of their structure and the directionality of their motion (or we don't know that yet), and their structure can be considered isotropic. So using E=mc^2 applied to photons is not correct, because when there is no interaction, the photon must not have mass. When there is an interaction, the mass of the photon is simply the mass felt by the other. The photon does not hold. Whereas any other particle will hold a changed mass after the interaction. For example, when an electron is accelerated, his mass changes according to the Lorentz transformation.

[4] Similar point of view, “The assumption is made that black holes should be subject to the same rules of quantum mechanics as ordinary elementary particles or composite systems. ”‘t Hooft, G. (1985). "On the quantum structure of a black hole." Nuclear Physics B 256: 727-745.

[5] https://www.researchgate.net/publication/373717939_Convergent_and_Disperse_Cyclic_Multiverse_Model;

If the transition is instantaneous, the moment the photon appears must be superluminal.

In quantum mechanics, Bohr's semi-classical model, Heisenberg's matrix mechanics, and Schödinger's wave function are all able to support the assumption of energy levels of atoms and coincide with the spectra of atoms. It is the operating mode of most light sources, including lasers. This shows that the body of their theories is all correct. If they are merged into one theory describing the structure image, it must have the characteristics of all three at the same time. Bohr's ∨ Heisenberg's ∨ Schödinger's, will form the final atomic theory*.

The jump of an electron in an atom, whether absorbed or radiated, is in the form of a single photon, and taking the smallest energy unit. For the same energy difference ΔE, jumping chooses a single photon over multiple photons with lower frequency ν, suggesting that a single photon structure has a more reasonable match between atomic orbital structures**.

ΔE=hν ......(1)

ΔE=Em-En ......(2)

It is clear that without information about Em, En at the same time, generating a definite jump frequency ν is impossible. "Rutherford pointed out that Rutherford pointed out that if, as Bohr did, one postulates that the frequency of light ν, which an electron emits in a transition, depends on the difference between the initial energy level and the final energy level, it appears as if the electron must "know" the frequency of light ν. level and the final energy level, it appears as if the electron must "know" to what final energy level it is heading in order to emit light with the right frequency."[1].

Bohr's postulate of Eq. (1)(2) energy level difference is valid [2]. But it does not hold as axiomatic postulate. This is not just because all possible reasons have not been ruled out. For example, one of the most important reasons is that the relationship between the "wave structure" of the electron and the electromagnetic field has not been determined†. Only if this direct relationship is established can the transition process between them be described. It is also required that the wave function and the electromagnetic field are not independent things, and it is required that the wave function is a continuous field distribution, not a probability distribution [5]. More importantly, Eqs. (1)(2) do not fulfill the axiomatic condition of being axiomatic postulate, which is not capable of ignoring the null information‡.

Doing it as a comparison of questions is the same as when we ask how the photon controls its speed [3] and where the photon should reach next. They are both photon behaviors that must rest on a common ground.

Considering the electron transition as a source of light, it is equally consistent with the principle of Special Relativity, and the photons radiated must be at the speed of light c and independent of the speed of the electrons††. However, if the light-emitting process is not continuous, the phenomenon of superluminal speed occurs.

We decompose the light-emitting process into two stages. The first stage, from "nothing" to "something", is the transition stage; the second stage, from something to propagation, is the normal state. According to classical physics, if the light emission is instantaneous, i.e., it does not occupy time and space. Then we can infer that the photon from nothing to something is not a continuous process, but an infinite process, and the speed at which the photon is produced is infinity. We cannot believe that the speed of propagation of light is finite and the speed at which light is produced is infinite. There is no way to bridge from the infinite to the finite, and we believe that this also violates the principle of the constancy of the speed of light.

There is no other choice for the way to solve this problem. The first is to recognize that all light emitting is a transitional "process" that occupies the same time and space, and that this transitional process must also be at the speed of light, regardless of the speed of the source of light (and we consider all forms of light emitting to be sources of light). This is guaranteed by and only by the theory of relativity. SR will match the spacetime measure to the speed of light at any light source speed. Secondly, photons cannot occur in a probabilistic manner, since probability implies independence from spacetime and remains an infinity problem. Third, photons cannot be treated as point particles in this scenario. That is, the photon must be spatially scaled, otherwise the transition process cannot be established. Fourth, in order to establish a continuous process of light emission, the "source" of photons, whether it is an accelerated electron, or the "wave function" of the electron jump, or the positive and negative electron annihilation, are required to be able to, with the help of space and time, continuous transition to photons. This will force us to think about what the wave function is.

Thinking carefully about this question, maybe we can get a sense of the nature of everything, of the extensive and indispensable role of time and space.

Our questions are:

1) Regardless of the solution belonging to which theory, where did the electron get the information about the jump target? Does this mean that the wave function of the electron should span all "orbitals" of the atom at the same time.

2) If the jump is a non-time-consuming process, should it be considered a superluminal phenomenon¶ [4]?

3) If the jump is a non-time consuming process, does it conflict with the Uncertainty Principle [5]?

4) What relationship should the wave function have to the photon to ensure that it produces the right photon?

-------------------------------------------------------------------------

Notes:

* Even the theory of the atomic nucleus. After all, when the nucleus is considered as a "black box", it presents only electromagnetic and gravitational fields.

* * It also limits the possibility that the photon is a mixed-wavelength structure. "Bohr noticed that a wave packet of limited extension in space and time can only be built up by the superposition of a number of elementary waves with a large range of wave numbers and frequencies [2].

† For example, there is a direct relationship between the "electron cloud" expressed by the wave function of the hydrogen steady state, and the radiating photons. With this direct relationship, it is possible to determine the frequency information between the transition energy levels.

‡ If a theory considers information as the most fundamental constituent, then it has to be able to answer the questions involved here.

†† Why and how to achieve independence from the speed of light cannot be divorced from SR by its very nature, but additional definitions are needed. See separate topic.

¶ These questions would relate to the questions posed in [3][4][5].

-------------------------------------------------------------------------

References:

[1] Faye, J. (2019). "Copenhagen Interpretation of Quantum Mechanics." The Stanford Encyclopedia of Philosophy from <https://plato.stanford.edu/archives/win2019/entries/qm-copenhagen/>.

[2] Bohr, N., H. A. Kramers and J. C. Slater (1924). "LXXVI. The quantum theory of radiation." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 47(281): 785-802. This was an important paper known as "BSK"; the principle of conservation of energy-momentum was abandoned, and only conservation of energy-momentum in the statistical sense was recognized.

[3] “How does light know its speed?”；

https://www.researchgate.net/post/NO3_How_does_light_know_its_speed;

[4] “Should all light-emitting processes be described by the same equations?”；

https://www.researchgate.net/post/NO11_Should_all_light-emitting_processes_be_described_by_the_same_equations；

[5] “Does Born's statistical interpretation of the wave function conflict with ‘the Uncertainty Principle’?” https://www.researchgate.net/post/NO13_Does_Borns_statistical_interpretation_of_the_wave_function_conflict_with_the_Uncertainty_Principle；

A body at rest has rest Energy, so it should also have rest Momentum.

Lao Tzu said, “Gravity is the root of lightness; stillness, the ruler of movement”(重为轻根，静为躁君)*. The meaning of this statement can be extended in physics to mean that "big-G determines how light or heavy an object is, and rest-m determines how easy or difficult it is to move".

According to the mass-energy equation** [1], E=mc^2, any object with mass m has "rest energy" [1], regardless of its inertial frame†. Note that E here is meant to be the energy lost when radiating the photon γ, which is absolute and unchangeable in any inertial frame. The mass-energy equation has been experimentally verified [2] as the correct relation.

According to special relativity [3], the mass of the same object is different in different inertial frames, m' = βm. Therefore, the energy of conversion of m of an object into photon γ is different in different inertial frames. This issue has been discussed in [4], but there is no consensus. Our view is that the "rest energy" is theoretically not Lorentz invariant, and the existence of a minimum value is a reasonable result. The most rational explanation for this is that the minimum corresponds to an absolutely static spacetime, i.e., absolute spacetime(Later we will show that absolute space-time and relative space-time are not in conflict). Analytically, this is one of the reasons why absolute spacetime should exist. The constant speed of light is another reason.

In all cases in physics, energy and momentum coexist and have a fixed relationship, not independent metrics. The energy-momentum ‡ of a photon, E=hν[5], P=h/λ[6]; the energy-momentum relation of Newtonian mechanics, E=P^2/2m; and the relativistic energy-momentum relation, E^2=c^2p^2+m^2c^4. Therefore, it is assumed that if there is a body of mass m that has "rest energy", then it should also have "rest momentum". There is a "rest momentum", and the rest momentum cannot be zero. The rest energy is not intuitive, and the rest momentum should not be intuitive too. The calculation of the rest momentum is the same as the calculation of the rest energy. The nature of mass looks more like momentum; after all, energy is a sign of time, while momentum is a sign of movement. Therefore, instead of calling it the principle of equivalence of inertial mass and rest-energy[1], it should be called the principle of equivalence of inertial mass and rest-momentum.

When positive and negative electrons meet and annihilate [7], -e+e→γ+γ, radiating two photons in opposite directions. Their energy is conserved and so is their momentum. Energy is a scalar sum, while momentum is a vector sum. It seems that the "rest momentum" inside the object should be zero. However, one could argue that it is actually the momentum of the two photons that is being carried away, but in opposite directions. The momentum of the two photons should not come out of nothing, but rather there should be momentum of the two photons, also in some balanced way, and probably playing a very important role, such as the binding force.

Our questions are:

1) Since energy and momentum cannot be separated, should an object with "rest energy" necessarily have "rest momentum".

2) Elementary particles can be equated to a " energy packet ", and energy is time dependent. If an elementary particle is also equivalent to a "momentum packet", the momentum in the packet must be related to space. Does this determine the spatio-temporal nature of the elementary particles? And since momentum is related to force, is it the force that keeps the "energy packet" from dissipating?

------------------------------------------------------------------------------

Notes：

* Lao Tzu，Tao-Te-Ching，~500 BCE. This quote is a translation of someone else's. There are some excesses that I don't entirely agree with. Translating classical Chinese into modern Chinese is just as difficult as translating classical Chinese into English.

** There is a historical debate about the process of discovery of the mass-energy equation, and digging into the history shows that there were discoverers and revisers both before and after Einstein, see literature [8][9]. Important contributions came from Poincaré, F. Hasenöhrl, Planck et al. Their derivations do not have the approximation of Einstein's mass-energy equation. And there is also a debate about the interpretation of the mass-energy equation. Notable debates can be found in the literature[10].

† There is a question here, i.e., is the rest mass Lorentz invariant? That is, is the rest mass the same in different inertial systems? Why?

‡ Einstein questioningly emphasized that energy and momentum seem to be inseparable, but did not explain it.

------------------------------------------------------------------------------

References：

[1] Einstein, A. (1905). "Does the inertia of a body depend upon its energy-content." Annalen der physik 18(13): 639-641.

Einstein, A. (1935). "Elementary derivation of the equivalence of mass and energy." Bulletin of the American mathematical society 41(4): 223-230.

[2] Rainville, S., J. K. Thompson, E. G. Myers, J. M. Brown, M. S. Dewey, E. G. Kessler, R. D. Deslattes, H. G. Börner, M. Jentschel, P. Mutti and D. E. Pritchard (2005). "A direct test of E=mc2." Nature 438(7071): 1096-1097.

[3] Einstein, A. (1905). "On the electrodynamics of moving bodies." Annalen der physik 17(10): 891-921.

[4] Is there a minimum value of m in the mass-energy equation E=mc^2? https://www.researchgate.net/post/NO7_Is_there_a_minimum_value_of_m_in_the_mass-energy_equation_Emc2；

[5] Planck, M. (1900). " " Verh. Deutsh. Phys. Ges 2: 237.

[6] Einstein, A. (1917). Physikalisehe Zeitschrift xviii: p.121

[7] Li, B. A. and C. N. Yang (1989). "CY Chao, Pair creation and Pair Annihilation." International Journal of Modern Physics A 4(17): 4325-4335.

[8] Ives, H. E. (1952). "Derivation of the mass-energy relation." JOSA 42(8): 540-543.

[9] Sharma, A. (0000). "The past present and future of the Mass Energy Equation DE =Dmc2." http://www.mrelativity.net/Papers/8/Sharma4.htm.

[10] Peierls, R., J. Warren and M. Nelkon (1987). "Mass and energy." Physics Bulletin 38(4): 127.

The fallacy of the aether was that its only function was to propagate light waves. This question goes much further and probes whether space (the vacuum) is an elastic medium that propagates waves at the speed of light. For example, do gravitational waves propagate in the elastic fabric of space? If space is assumed to be an elastic wave propagation medium, then gravitational wave equations imply this medium has enormous impedance of c³/G = 4 x 10³⁵ kg/s.

This is a discussion question, and I am going to take the position that spacetime is an elastic medium with “spacetime foam” properties first proposed by John Wheeler. He determined that the uncertainty principle and vacuum zero-point energy implied space has Planck length oscillations at Planck frequency. This would make spacetime a physical medium that propagates waves at the speed of light with impedance of c³/G. This impedance is so enormous that a rotating wave with Planck length amplitude and an electron’s Compton radius would have an electron’s energy.

I am taking the position that the quantum vacuum is a sonic medium that propagates waves at the speed of light. This medium gives the vacuum its “intrinsic” properties such as vacuum permittivity ε_o, vacuum permeability μ_o, impedance of free space Z_o, virtual particle formation, etc. If spacetime is not a physical medium, why does it have finite values for ε_o, μ_o and Z_o? The following link has more information about my opinion and model. What is your opinion?

Quantum field theory has a named field for each particle. There is an electron field, a muon field, a Higgs field, etc. To these particle fields the four force fields are added: gravity, electromagnetism, the strong nuclear force and the weak nuclear force. Therefore, rather than nature being a marvel of simplicity, it is currently depicted as a less than elegant collage of about 17 overlapping fields. These fields have quantifiable values at points. However, the fundamental physics and structure of fields is not understood. For all the praise of quantum field theory, this is a glaring deficiency.

Therefore, do you expect that future development of physics will simplify the model of the universe down to one fundamental field with multiple resonances? Alternatively, will multiple independent fields always be required? Will we ever understand the structure of fields?

God said, "Let there be light."

So, did God need to use many means when He created light? Physically we have to ask, "Should all processes of light generation obey the same equation?" "Is this equation the 'God equation'?"

Regarding the types of "light sources", we categorize them according to "how the light is emitted" (the way it is emitted):

Type 0 - naturally existing light. This philosophical assumption is important. It is important because it is impossible to determine whether it is more essential that all light is produced by matter, or that all light exists naturally and is transformed into matter. Moreover, naturally existing light can provide us with an absolute spacetime background (free light has a constant speed of light, independent of the motion of the light source and independent of the observer, which is equivalent to an absolute reference system).

Type I - Orbital Electron Transition[1]: usually determines the characteristic spectra of the elements in the periodic table, they are the "fingerprints" of the elements; if there is human intervention, coherent optical lasers can be generated. According to the assumptions of Bohr's orbital theory, the transitions are instantaneous, there is no process, and no time is required*. Therefore, it also cannot be described using specific differential equations, but only by probabilities. However, Schrödinger believed that the wave equation could give a reasonable explanation, and that the transition was no longer an instantaneous process, but a transitional one. The wave function transitions from one stable state to another, with a "superposition of states" in between [2].

Type II - Accelerated motion of charged particles emitting light. There are various scenarios here, and it should be emphasized that theoretically they can produce light of any wavelength, infinitely short to infinitely long, and they are all photons. 1) Blackbody radiation [3][4]: produced by the thermal motion of charged particles [5], is closely dependent on the temperature, and has a continuous spectrum in terms of statistical properties. This is the most ubiquitous class of light sources, ranging from stars like the Sun to the cosmic microwave background radiation [6], all of which have the same properties. 2) Radio: the most ubiquitous example of this is the electromagnetic waves radiated from antennas of devices such as wireless broadcasting, wireless communications, and radar. 3）Synchrotron radiation[7]，e+e− → e+e−γ；the electromagnetic radiation emitted when charged particles travel in curved paths. 4）bremsstrahlung[8]，for example, e+e− → qqg → 3 jets[11]；electromagnetic radiation produced by the acceleration or especially the deceleration of a charged particle after passing through the electric and magnetic fields of a nucleus，continuous spectrum. 5）Cherenkov Radiation[9]：light produced by charged particles when they pass through an optically transparent medium at speeds greater than the speed of light in that medium.

Type III：Partical reactions、Nuclear reactions：Any physical reaction process that produces photon (boson**) output. 1）the Gamma Decay；2）Annihilation of particles and antiparticles when they meet[10]: this is a universal property of symmetric particles, the most typical physical reaction；3）Various concomitant light, such as during particle collisions；4）Transformational light output when light interacts with matter, such as Compton scattering[12].

Type IV: Various redshifts and violet shifts, changing the relative energies of light: gravitational redshift and violet shift, Doppler shift; cosmological redshift.

Type V: Virtual Photon[13][14]?

Our questions are:

Among these types of light-emitting modes, type II and type IV light-emitting obey Maxwell's equation, and the type I and type III light-emitting processes are not clearly explained.

We can not know the light-emitting process, but we can be sure that the result, the final output of photons, is the same. Can we be sure that it is a different process that produces the same photons?

Is the thing that is capable of producing light, itself light? Or at least contains elements of light, e.g., an electric field E, a magnetic field H. If there aren't any elements of light in it, then how was it created? By what means was one energy, momentum, converted into another energy hν, momentum h/λ?

There is a view that "Virtual particles are indeed real particles. Quantum theory predicts that every particle spends some time as a combination of other particles in all possible ways"[15]. What then are the actual things that can fulfill this interpretation? Can it only be energy-momentum?

We believe everything needs to be described by mathematical equations (not made-up operators). If the output of a system is the same, then the process that bridges the output should also be the same. That is, the output equations for light are the same, whether it is a transition, an accelerated moving charged particle, or an annihilation process, the difference is only in the input.

------------------------------------------------------------------------------

* Schrödinger said：the theory was silent about the period s of transition or 'quantum jumps' (as one then began to call them). Since intermediary states had to remain disallowed, one could not but regard the transition as instantaneous; but on the other hand, the radiating of a coherent wave train of 3 or 4 feet length, as it can be observed in an interferometer, would use up just about the average interval between two transitions, leaving the atom no time to 'be' in those stationary states, the only ones of which the theory gave a description.

** We know the most about photons, but not so much about the nature of W, Z, and g. Their mass and confined existence is a problem. We hope to be able to discuss this in a follow-up issue.

------------------------------------------------------------------------------

Links to related issues:

【1】"How does light know its speed and maintain that speed?”;

https://www.researchgate.net/post/NO3_How_does_light_know_its_speed；

【2】"How do light and particles know that they are choosing the shortest path?”

【3】"light is always propagated with a definite velocity c which is independent of the state of motion of the emitting body.";

【4】“Are annihilation and pair production mutually inverse processes?”； https://www.researchgate.net/post/NO8_Are_annihilation_and_pair_production_mutually_inverse_processes;

------------------------------------------------------------------------------

Reference:

[1] Bohr, N. (1913). "On the constitution of atoms and molecules." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 26(151): 1-25.

[2] Schrödinger, E. (1952). "Are there quantum jumps? Part I." The British Journal for the Philosophy of science 3.10 (1952): 109-123.

[3] Gearhart, C. A. (2002). "Planck, the Quantum, and the Historians." Physics in perspective 4(2): 170-215.

[4] Jain, P. and L. Sharma (1998). "The Physics of blackbody radiation: A review." Journal of Applied Science in Southern Africa 4: 80-101. 【GR@Pushpendra K. Jain】

[5] Arons, A. B. and M. Peppard (1965). "Einstein's Proposal of the Photon Concept—a Translation of the Annalen der Physik Paper of 1905." American Journal of Physics 33(5): 367-374.

[6] PROGRAM, P. "PLANCK PROGRAM."

[7] https://www.nist.gov/pml/sensor-science/what-synchrotron-radiation

[8] 韧致辐射；

[9] Neutrino detection by Cherenkov radiation：" Super-Kamiokande(超级神冈)." from https://www-sk.icrr.u-tokyo.ac.jp/en/sk/about/. 江门中微子实验 "The Jiangmen Underground Neutrino Observatory (JUNO)." from http://juno.ihep.cas.cn/.

[10] Li, B. A. and C. N. Yang (1989). "CY Chao, Pair creation and Pair Annihilation." International Journal of Modern Physics A 4(17): 4325-4335.

[11] Schmitz, W. (2019). Particles, Fields and Forces, Springer.

[12] Compton, A. H. (1923). "The Spectrum of Scattered X-Rays." Physical Review 22(5): 409-413.

[13] Manoukian, E. B. (2020). Transition Amplitudes and the Meaning of Virtual Particles. 100 Years of Fundamental Theoretical Physics in the Palm of Your Hand: Integrated Technical Treatment. E. B. Manoukian. Cham, Springer International Publishing: 169-175.

[14] Jaeger, G. (2021). "Exchange Forces in Particle Physics." Foundations of Physics 51(1): 13.

[15] Are virtual particles really constantly popping in and out of existence? Or are they merely a mathematical bookkeeping device for quantum mechanics? - Scientific American.

Mach said [1], the principle of minimum xxxx, are they the natural purpose?

Born said in his "Physics in My Generation"[2], that while it is understandable that a particle chooses the straightest path to travel at a given moment, we cannot understand how it can quickly compare all possible motions to reach a point and pick the shortest path —— a question that makes one feels too metaphysical.

Speaking of the Hamiltonian principle and the minimum light path, Schrödinger recognizes the wonder of this problem [3]: Admittedly, the Hamilton principle does not say exactly that the mass point chooses the quickest way, but it does say something so similar - the analogy with the principle of the shortest travelling time of light is so close, that one was faced with a puzzle. It seemed as if Nature had realized one and the same law twice by entirely different means: first in the case of light, by means of a fairly obvious play of rays; and again in the case of the mass points, which was anything but obvious, unless somehow wave nature were to be attributed to them also. And this, it seemed impossible to do. Because the "mass points" on which the laws of mechanics had really been confirmed experimentally at that time were only the large, visible, sometimes very large bodies, the planets, for which a thing like "wave nature" appeared to be out of the question.

Feynman had a topic of minimum action in his "Lecture of Physics" [4]. It discusses how particle motion in optics, classical mechanics, and quantum mechanics can follow the shortest path. He argues that light "detects" the shortest path by phase superposition, but when a baffle with a slit is placed on the path, the light cannot check all the paths and therefore cannot calculate which path to take, and the phenomenon of diffraction of light occurs. Here, Feynman defined the path of light in two parts, before and after the diffraction occurs. If we take a single photon as an example, then before diffraction he considered that the photon travels along the normal geometric optical path, choosing the shortest path. After diffraction occurs, the photon loses its ability to "find" the shortest path and takes a different path to the diffraction screen, with different possibilities. This leads to the concept of probability amplitude in quantum mechanics.

To explain why light and particles can choose the "shortest path", the only logical point of view should be that light and particles do not look for the shortest path, but create it and define it, whether in flat or curved spacetime. Therefore, we should think about what light and particles must be based on, or what they must be, in order to be able to define the shortest paths directly through themselves in accordance with physics.

[1] Ernst Mach, Popular Scientific Lectures.

[2] Born, M. (1968). Physics in My Generation, Springer.

[3] Schrödinger, E. (1933). "The fundamental idea of wave mechanics. Nobel lecture " 12 (1933).

[4] Feynman, R. P. (2005). The Feynman Lectures on Physics(II), Chinese ed.

Keywords: light, Fermat principle of the shortest light time, Hamilton principle, Feynman path integral， Axiomatic

Does energy have an origin or root?

When Plato talks about beauty in the "Hippias Major", he asks: "A beautiful young girl is beautiful", "A sturdy mare is beautiful", "A fine harp is beautiful", "A smooth clay pot is beautiful" ....... , So what exactly is beauty? [1]

We can likewise ask, Mechanical energy is energy, Heat energy is energy, Electrical and magnetic energy is energy, Chemical and internal energy is energy, Radiant energy is energy, so what exactly is "energy"?[2]

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". Thus, Feynman introduced energy as an abstract quantity from the beginning of his university teaching [3].

However, the universal concept of energy in physics states that energy can neither be created nor destroyed, but can only be transformed. If energy cannot be destroyed, then it must be a real thing that exists, because it makes no sense to say that we cannot destroy something that does not exist. If energy can be transformed, then, in reality, it must appear in a different form. Therefore, based on this concept of energy, one can easily be led to the idea that energy is a real thing, a substance. This concept of energy is often used, for example, that energy can flow and that it can be carried, lost, stored, or added to a system [4][5].

Indeed, in different areas of physics, there is no definition of what energy are, and what is consistent is only their Metrics and measures. So, whether energy is a concrete Substance**, or is just heat, or is the capacity of doing work, or is just an abstract cause of change, was much discussed by early physicists. However, we must be clear that there is only one kind of energy, and it is called energy. It is stored in different systems and in different ways in those systems, and it is transferred by some mechanism or other from one system to another[9].

Based on a comprehensive analysis of physical interactions and chemical reaction processes, energy is considered to be the only thing that communicates various phenomena. Thus, "Energism" was born*[8]. Ostwald had argued that matter and energy had a “parallel” existence, he developed a more radical position: matter is subordinate to 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”[6]. This view has expressed the idea of considering "pure energy" as a "unity" and has assumed the process of energy interaction. However, because of the impossibility to determine what energy is, it has been rejected by both scientific and philosophical circles as "metaphysics" and "materialism"[10].

The consistency and transitivity of energy and momentum in different physical domains have actually shown that they must be linked and bound by something fundamental. Therefore, it is necessary to re-examine the "Energism" and try to promote it.

The relationship between energy and momentum, which are independent in classical mechanics, and their conservation are also independent. the momentum of the particle does not involve its energy. but In relativity, the conservations of momentum and energy cannot be dissociated. The conservation of momentum in all inertial frames requires the conservation of energy and vice versa. space and time are frame-dependent projections of spacetime[7].

Our questions are:

1) What is energy, is it a fundamental thing of entity nature**, or is it just a measure, like the property "label" of "beauty", which can be used by anyone: heat, light, electricity, machinery, atomic nuclei. Do the various forms of energy express the same meaning? Can they be expressed mathematically in a uniform way? Is there a mathematical definition of "energy"? ***

2) Is the conservation of energy a universal principle? How does physics ensure this conservation?

3) Why is there a definite relationship between energy and momentum in all situations? Where are they rooted?

4) If the various forms of energy and momentum are unified, given the existence of relativity, is there any definite relationship between them and time and space?

-------------------------------------------------------------------------

* At the end of the nineteenth century, two theories were born that tried to unify the physical world, "electromagnetic worldview" and "Energism". We believe that this is the most intuitive and simple view of the world. And, probably the most beautiful and correct view of the world.

** If it is an entity, then it must still exist at absolute zero. Like the energy and momentum of the photon itself, it does not change because of the temperature, as long as it does not interact with each other.

*** We believe that this is an extremely important issue, first mentioned by Sergey Shevchenko（ https://www.researchgate.net/profile/Sergey-Shevchenko ）in his reply to a question on Researchgate, see https://www.researchgate.net/post/NO1_Three-dimensional_space_issue; SS's reply.

-------------------------------------------------------------------------

Referencs

[1] Plato.

[2] Ostwald 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 (heat, chemical, electrical, volume, etc.) is assigned an intensity. And formulated two fundamental laws of energetics. The first expresses the conservation of energy in the process of transfer and conversion; the second explains in terms of intensity equilibrium what can start and stop the transfer and conversion of energy.

[3] Duit, R. (1981). "Understanding Energy as a Conserved Quantity‐‐Remarks on the Article by RU Sexl." European journal of science education 3(3): 291-301.

[4] Swackhamer, G. (2005). Cognitive resources for understanding energy.

[5] Coelho, R. L. (2014). "On the Concept of Energy: Eclecticism and Rationality." Science & Education 23(6): 1361-1380.

[6] Holt, N. R. (1970). "A note on Wilhelm Ostwald's energism." Isis 61(3): 386-389.

[7] Ashtekar, A. and V. Petkov (2014). Springer Handbook of Spacetime. Berlin, Heidelberg, Springer Berlin Heidelberg.

[8] Leegwater, A. (1986). "The development of Wilhelm Ostwald's chemical energetics." Centaurus 29(4): 314-337.

[9] Swackhamer, G. (2005). Cognitive resources for understanding energy.

[10] The two major scientific critics of Energism are Max Planck and Ernst Mach. The leading critic of the political-philosophical community was Vladimir Lenin (the founder of the organization known as Comintern). But he criticized not only Ostwald, but also Ernst Mach.

I am trying to learn modern physics and frequently encounter the phrase "gauge theory". I look up the definition and find that it is a theory in which a Lagrangian is invariant under a certain class of transformations. That sounds to me like we are using Noether's theorem to find constants of motion. I learned enough math to know several ways of finding constants of motion. One way is Noether's theorem. Another way is to find operators that commute with a Hamiltonian. A third way is to derive implications directly from the given governing equations. Which, if any of these methods, are called "gauge theory"? And why?

It is commonly believed that the concept of electron spin was first introduced by A.H. Compton (1920) when he studied magnetism. "May I then conclude that the electron itself, spinning like a tiny gyroscope, is probably the ultimate magnetic particle?"[1][2]; Uhlenbeck and Goudsmit (1926) thought so too [4], but did not know it at the time of their first paper (1925) [3]. However, Thomas (1927) considered Abraham (1903) as the first to propose the concept of spinning electron [5]. Compton did not mention Abraham in his paper "The magnetic electron" [2], probably because Abraham did not talk about the relationship between spin and magnetism [0]. In fact, it is Abraham's spin calculations that Uhlenbeck cites in his paper [4].

Gerlach, W. and O. Stern (1921-1922) did the famous experiment* on the existence of spin magnetic moments of electrons (even though this was not realized at the time [6]) and published several articles on it [7].

Pauli (1925) proposed the existence of a possible " two-valuedness " property of the electron [8], implying the spin property; Kronig (1925) proposed the concept of the spin of the electron to explain the magnetic moment before Uhlenbeck, G. E. and S. Goudsmit, which was strongly rejected by Pauli [9]. Uhlenbeck, G. E. and S. Goudsmit (1925) formally proposed the concept of spin[3], and after the English version was published[4], Kronig (1926), under the same title and in the same journals, questioned whether the speed of rotation of an electron with internal structure is superluminal**[10]. Later came the Thomas paper giving a beautiful explanation of the factor of 2 for spin-orbit coupling[11]. Since then, physics has considered spin as an intrinsic property that can be used to explain the anomalous Seeman effect.

The current state of physics is in many ways the situation: "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."[11]. With this in mind, C. N. Yang briefly reviewed how spin became a part of physics. For spin, he summarized several important issues: 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. All of these played essential roles in the early understanding of the concept of spin, but that was not so clearly appreciated at the time [11].

Speaking about the understanding of spin, Thomas said [5]: "I think we must look towards the general relativity theory for an adequate solution of the problem of the "structure of the electron" ; if indeed this phrase has any meaning at all and if it can be possible to do more than to say how an electron behaves in an external field. Yang said too: "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 [11]. I believe that all unified theories must take this into account.

What exactly is spin, F. J. Belinfante argued that it is a circular energy flow [12][15] and that spin is related to the structure of the internal wave field of the electron. A comparison between calculations of angular momentum in the Dirac and electromagnetic fields shows that the spin of the electron is entirely analogous to the angular momentum carried by a classical circularly polarized wave [13]. The electron is a photon with toroidal topology [16]. At the earliest, A. Lorentz also used to think so based on experimental analysis. etc.

1) Is the spin of an electron really spin? If spin has classical meaning, what should be rotating and obeying the Special Relativity?

2) What should be the structure of the electron that can cause spin quantization and can be not proportional to charge and mass?

3) If spin must be associated with General Relativity, must we consider the relationship between the energy flow of the spin and the gravitational field energy?

------------------------------------------------------------------- -------

* It is an unexpectedly interesting story about how their experimental results were found. See the literature [17].

** Such a situation occurs many times in the history of physics, where the questioned and doubted papers are published in the same journal under the same title. For example, the debate between Einstein and Bohr, the EPR papers [18] and [19], the debate between Wilson and Saha on magnetic monopoles [20] and [21], etc.

--------------------------------------------------------------------------

Reference：

[0] Abraham, M. (1902). "Principles of the Dynamics of the Electron (Translated by D. H. Delphenich)." Physikalische Zeitschrift 4(1b): 57-62.

[1] Compton, A. H. and O. Rognley (1920). "Is the Atom the Ultimate Magnetic Particle?" Physical Review 16(5): 464-476.

[2] Compton, A. H. (1921). "The magnetic electron." Journal of the Franklin Institute 192(2): 145-155.

[3] Uhlenbeck, G. E., and Samuel Goudsmit. (1925). "Ersetzung der Hypothese vom unmechanischen Zwang durch eine Forderung bezüglich des inneren Verhaltens jedes einzelnen Elektrons." Die Naturwissenschaften 13.47 (1925): 953-954.

[4] Uhlenbeck, G. E. and S. Goudsmit (1926). "Spinning Electrons and the Structure of Spectra." Nature 117(2938): 264-265.

[5] Thomas, L. H. (1927). "The kinematics of an electron with an axis." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 3(13): 1-22.

[6] Schmidt-Böcking, H., L. Schmidt, H. J. Lüdde, W. Trageser, A. Templeton and T. Sauer (2016). "The Stern-Gerlach experiment revisited." The European Physical Journal H 41(4): 327-364.

[7] Gerlach, W. and O. Stern. (1922). "Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld. " Zeitschrift f¨ur Physik 9: 349-352.

[8] Pauli, W. (1925). "Über den Einfluß der Geschwindigkeitsabhängigkeit der Elektronenmasse auf den Zeemaneffekt." Zeitschrift für Physik 31(1): 373-385.

[9] Stöhr, J. and H. C. Siegmann (2006). "Magnetism"(磁学), 高等教育出版社.

[10] Kronig, R. D. L. (1926). "Spinning Electrons and the Structure of Spectra." Nature 117(2946): 550-550.

[11] Yang, C. N. (1983). "The spin". AIP Conference Proceedings, American Institute of Physics.

[12] Belinfante, F. J. (1940). "On the current and the density of the electric charge, the energy, the linear momentum and the angular momentum of arbitrary fields." Physica 7(5): 449-474.

[13] Ohanian, H. C. (1986). "What is spin?" American Journal of Physics 54(6): 500-505. 电子的自旋与内部波场结构有关。

[14] Parson, A. L. (1915). Smithsonian Misc. Collections.

[15] Pavšič, M., E. Recami, W. A. Rodrigues, G. D. Maccarrone, F. Raciti and G. Salesi (1993). "Spin and electron structure." Physics Letters B 318(3): 481-488.

[16] Williamson, J. and M. Van der Mark (1997). Is the electron a photon with toroidal topology. Annales de la Fondation Louis de Broglie, Fondation Louis de Broglie.

----------------------------------------------------------------------------

[17] Friedrich, B. and D. Herschbach (2003). "Stern and Gerlach: How a bad cigar helped reorient atomic physics." Physics Today 56(12): 53-59.

[18] Bohr, N. (1935). "Can quantum-mechanical description of physical reality be considered complete?" Physical review 48(8): 696.

[19] Einstein, A., B. Podolsky and N. Rosen (1935). "Can quantum-mechanical description of physical reality be considered complete?" Physical review 47(10): 777.

[20] Wilson, H. (1949). "Note on Dirac's theory of magnetic poles." Physical Review 75(2): 309.

[21] Saha, M. (1949). "Note on Dirac's theory of magnetic poles." Physical Review 75(12): 1968.

The holographic principle was first proposed by Gerard 't Hooft. It was given a precise string-theory interpretation by Leonard Susskind who said, “The three-dimensional (3D) world of ordinary experience––the universe filled with galaxies, stars, planets, houses, boulders, and people––is a hologram, an image of reality coded on a … two-dimensional (2D) surface." The prime example of holography is the AdS/CFT correspondence, first proposed by Juan Maldacena in late 1997. In theoretical physics, the anti-de Sitter/conformal field theory correspondence, sometimes called Maldacena duality or gauge/gravity duality, is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter spaces (AdS) which are used in theories of quantum gravity, formulated in terms of string theory or M-theory. On the other side of the correspondence are conformal field theories (CFT) which are quantum field theories, including theories similar to the Yang–Mills theories that describe elementary particles.

A 3D cube can be regarded as an image of reality coded on a 2D surface (a projection from a square). The cubic shape would be a linear projection resulting from adding, in one direction, multiple layers of the information in the square. The 2D square would be a nonlinear (angular) projection resulting from adding 4 lines, each one being separated from those adjoining it by 90 degrees. A one-dimensional line is a set of points obeying a linear relationship. A point’s an exact position or location. It’s important to understand that a point is not a thing, but a place. It possesses zero size and no matter how far we zoomed in, it’d remain dimensionless with no width. Instead of programming a set of points to follow a straight line, suppose they’re represented curvilinearly as a waveform described by Fourier analysis or v=f(lambda).

The plane figure with 4 lines - a square or other parallelogram – could then have a pair of intersecting sides represent the vector of photons and the vector of gravitons i.e. electromagnetic (EM) waves and gravitational (G) waves. The momentum of interacting photons and gravitons would produce a pressure identified as mass (this interaction would be similar to a gravitational field refracting passing light, or the pressure of sunlight propelling the mass of solar sails).

Also, interacting photons and gravitons produce the quantum spin of the produced mass e.g. the photon’s quantum spin of 1 could interact with the graviton’s quantum spin of 2 to create one divided by two (½ is the spin of every particle of matter).

Another example is photonic spin 1 could inversely interact with gravitonic spin 2 to create two divided by one (2/1 is the spin of particles comprising the gravitational field of massive black holes).

Referring to the two above examples – When William Rowan Hamilton devised quaternions back in 1843, he defined them as the quotient of two vectors. So, matter particles and black holes can both be described by quaternions.

Yet another example is – spin 1 means the particle has to be turned round completely (360 degrees) to look the same. Spin 2 means the particle has to be turned 180 degrees to look the same. What happens if time reversal is incorporated into this interaction of particles in space? The photon’s complete spin of 1 is added to the graviton’s half spin of 180 degrees then the graviton’s time reversal subtracts half a spin. This gives 1+1/2-1/2 which equals the spin of the strong nuclear force’s gluon as well as the spin of the weak force’s W and Z bosons.

An intriguing fact is that matter particles need to be completely turned round twice (720 degrees) to look the same. And a Mobius strip has to be travelled around twice to reach the start. Does this imply that the hard and solid objects we touch daily are actually immaterial things composed of the Mobius and its topological mathematics?

Should the time reversal above be confirmed experimentally, it means gravitation and electromagnetism are the only truly fundamental forces. The strong and weak forces are products of G and EM. Also, the Higgs boson and field would not be responsible for generation of mass. The two parallelogram lines depicting the gravitational vector and electromagnetic vector would have graviton-photon interaction displayed by the diagonal of the parallelogram. The scalar Higgs boson may be positioned as a point on this diagonal because tensor calculus changes the coordinates of the vectors and diagonal into those of the Higgs (relating the Higgs field to the supposedly unrelated gravitational field). When the mass produced is 125 GeV/c^2 and the quantum spin is zero, Higgs is the result.

Perhaps it was concluded that the Higgs is responsible for mass because the calculations of Peter Higgs and others go a significant part of the way to the conclusions of Vector-Tensor-Scalar Geometry and its parallelogram. But the connection with gravitation (and electromagnetism) was overlooked. Interestingly, these two forces were suggested as playing a role in the formation of elementary particles – and, as it turns out, in the formation of the nuclear forces not discovered until the 1930s - in a 1919 paper published by Albert Einstein.

Are annihilation and pair production mutually inverse processes?

p+p− → γ γ'

“Annihilation can happen when all the quantum numbers of two colliding particles add up to zero. It might be electron on positron, proton on antiproton, neutron on antineutron, quark on antiquark etc. The force responsible depends on the possible interactions of the annihilating particles.” “Annihilation does not require the presence of other fields.”[x]

“In particular, one concludes that the two photons resulting from the annihilation of slow positrons in matter always have their planes of polarization perpendicular to each other. This has been pointed out by Wheeler who also proposed a possible experimental verification.”[2]

γ γ' →p+p−

It is often assumed that the concept of pair generation was first introduced by Breit and Wheeler, ω1+ω2→e+e-; however, in their paper [1], "pair generation" appears as an old term and cites the paper by Weizsäcker, CF, Z (1934), and Williams' formula。

Perrin (1933) (in French) was probably the first to introduce the concept of 'pair production'. He had a paper entitled "The possibility of materialization by the interaction of photons and electrons."

Regarding pair production: 1）At first sight light-light scattering seems to be impossible because in classical electrodynamics (linear Maxwell equations) the process does not occur. The resulting wave is everywhere given by the sum of the two incoming waves. 2）In quantum mechanics however the situation is quite different. Due to the uncertainty principle a photon of energy E can fluctuate into states of charged particle pairs (with mass mpair.）Experimentally it is very difficult to collide high energy photon beams. A very elegant way of avoiding this difficulty is again to use virtual particles, this time the quantum fluctuation of an electron into an electron photon state.[3]

The identification of pairs is usually a result of statistical findings[4][5][7][8][9]. e.g.

The identification of γ γ → pp events is mainly based on three artificial neural networks, used to separate antiprotons from e−, µ− and h−, where h− represents either a π− or K−[4]

QCD predictions for large-momentum transfer cross sections of the type ‘γγ→ BB' are given, for B and B' any members of the baryon octet or decuplet, and all possible helicity combinations for photons and baryons[8].

An electron enters the laser beam from the left, and collides with a laser photon to produce a high-energy gamma ray. The electron is deflected downwards. The gamma ray then collides with four or more laser photons to produce an electron-positron pair [9].

1) The process of "pair production" and the process of annihilation of positive and negative particles are not mutually invertible. Just as the mass-energy equation is not reciprocal (E=mc^2, which is irreversible for photons), p+p- → γ γ' and γ γ' → p+p- are not γ γ' = p+p-. This is one of the differences between the mathematical equations and the physical equations.

(2) The process of "annihilation" does not require special conditions, while the process of " pair production" must require auxiliary conditions, the presence of other particles being necessary. What is the essential function of these auxiliary conditions? What are the conditions under which photons can "collide" and not just interfere?

3) Is the process of "pair production" one or two processes? Must the " pair of particles" be produced in pairs at the same time, or with equal probability for positive and negative particles? Or is it both. The literature [6] describes pairs of positive and negative particles as being produced simultaneously. This question is very important because it determines the mechanism of the "photon-particle" transition and even their structure.

(4) The colliding positive and negative particles do not necessarily annihilate into photons, but essentially depend on whether the magnitude of the energy reaches the energy value of a certain particle, e+e-→µ+µ-. Here is the root of the problem of the level difference of the three generations of particles implied, just as the energy level difference of orbiting electrons. Can quantum field theory give a concrete, or directional, explanation?

5) Where do the properties of the original positive and negative particles go after annihilation occurs? Charge, spin-magnetic moment, mass, and the spacetime field of the elementary particle. Can the origin of the properties be inferred from this? That is, if the properties are somehow conserved, then by reversibility, do the annihilated photons imply all the properties of the elementary particles. The total charge is conserved after the annihilation of the positive and negative electrons. But where does the positive charge go and where does the negative charge go? The following issues are involved here: https://www.researchgate.net/post/How_Fermions_combine_four_properties_in_one

[1]【Breit, G. and J. A. Wheeler (1934). "Collision of two light quanta." Physical Review 46(12): 1087】

[2]【Yang, C.-N. (1950). "Selection rules for the dematerialization of a particle into two photons." Physical Review 77(2): 242】

[3]【Berger, C. and W. Wagner (1987). "Photon photon reactions." Physics Reports 146(1-2): 1-134】

[4]【Achard, P., O. Adriani, M. Aguilar-Benitez and etl. (2003). "Proton–antiproton pair production in two-photon collisions at LEP." Physics Letters B 571(1-2): 11-20】

[5]【de Jeneret, J., V. Lemaitre, Y. Liu, S. Ovyn, T. Pierzchala, K. Piotrzkowski, X. Rouby, N. Schul and M. V. Donckt (2009). "High energy photon interactions at the LHC." arXiv preprint arXiv:0908.2020.】

[6]【Michaud, A. (2013). "The Mechanics of Electron-Positron Pair Creation in the 3-Spaces Model." International Journal of Engineering Research and Development 6: 2278-2800】* Researchgate Link：

Minimum mass issues are involved here:

https://www.researchgate.net/post/Is_there_a_minimum_value_of_m_in_the_mass-energy_equation_Emc2

[7]【Klein, S. R. and P. Steinberg (2020). "Photonuclear and two-photon interactions at high-energy nuclear colliders." Annual Review of Nuclear and Particle Science 70: 323-354.】

[8]【Farrar, G. R., E. Maina and F. Neri (1985). "QCD Predictions for γγ Annihilation to Baryons." Nuclear Physics B 259(4): 702-720】

[9]【SLAC. (1970). "SLAC Experiment E144 Home Page." from https://www.slac.stanford.edu/exp/e144/.】

【Burke, D. L., R. C. Field, G. Horton-Smith, J. E. Spencer, D. Walz, S. C. Berridge, W. M. Bugg, K. Shmakov, A. W. Weidemann, C. Bula, K. T. McDonald, E. J. Prebys, C. Bamber, S. J. Boege, T. Koffas, T. Kotseroglou, A. C. Melissinos, D. D. Meyerhofer, D. A. Reis and W. Ragg (1997). "Positron Production in Multiphoton Light-by-Light Scattering." Physical Review Letters 79(9): 1626-1629】

【Schwarzschild, B. (1998). "Gamma Rays Create Matter Just by Plowing into Laser Light." Physics Today 51(2): 17-18】

————————————————————————————————————

2023-06-25

For the "pair production" experiment, the 2021 STAR Collaboration collectively published a paper "Measurement of e+ e- momentum and angular distributions from linearly polarized photon collisions" [4].

"At RHIC, scientists accelerate gold ions to 99.995% of the speed of light in two accelerator rings. If the speed is high enough, the strength of the circular magnetic field can be equal to the strength of the perpendicular electric field," Xu said. perpendicular electric and magnetic fields of equal strength is exactly what a photon is-a quantized "particle "So, when the ions are moving close to the speed of light, there are a bunch of photons surrounding the gold nucleus. As the ions pass one another without colliding, two photons (γ) from the electromagnetic cloud surrounding the ions can interact with each other to create a matter-antimatter pair: an electron (e-) and positron (e+) [5]. [The headline of the media report is more interesting [5][6][7]]

The history of the discovery of the physics of particle production and annihilation is presented in paper [1]; paper [3] is an analysis of the experimental phenomena by Anderson, the discoverer of positrons, in which four possibilities are proposed for each result, "pair production" being one of them. He finally determined that "pair production" was the real case. The results provided by André Michaud [9] should be similar [see his replies for details].

Comparing the STAR experiment [5] and the E114 experimental method [8], they produce photon "collisions" in a very different way. These two experiments are in turn different from experiments [2] and [3]. It is commonly believed that there are three possible interactions [4]: the collisions of two virtual photons (as calculated by Landau and Lifshitz, giving the total cross section for e+e- production predominantly at the pair threshold), of one virtual and one real photon (Bethe-Heitler process ), or of two real photons-the Breit-Wheeler process.

Question: Yang[1] and Andeson considered that Chao [2] and Anderson [3] are both electron pair generation processes, so is this a "photon-photon" collision "γγ → e+e- " process? If so, are the photons real or virtual, and what is the difference between them and the experiments [4][8]? If not, then there are no "photon-photon" collisions in the experiments of Chao [2] and Anderson [3], but only "photon-particle" collisions?

------------------------------------------------------------------------------