Chian Fan

East China University of Science and Technology | ECUST

Physics believes that macroscopic matter consists of microscopic matter; the macroscopic physical world described by classical mechanics is causal, and the microscopic world described by quantum mechanics is non-causal [1][2]; the wave function that describes a quantum is interpreted as the probability of the quantum's appearance at a certain location. The wave function, then, is the bridge between randomness and causality, the dividing line between the micro and macro worlds. Either according to the Schrödinger equation (1), or the Dirac equation (2),

iħ ∂/∂t {Ψ} = H{Ψ} (1)

(iħγ'∂μ - mc){Ψ} = 0 (2)

The changes of the wave function are all deterministic. What governs this determinism? For example, how does the derivative of the probability ∂/∂t {Ψ}, i.e., the rate of change of the probability in time, occur and by whom?

The essence of an equation is its invariance, and no matter how many solutions there are, the common feature of the solutions is that they maintain the invariance of the equation. In equation (1), (2), it is required that the total probability of the amplitude of the wave function is conserved and the energy-momentum is conserved. If there are more than one conserved quantity in a process at the same time, there must be a definite relationship between them, or one conserved quantity must dominate and the others are additives. If we must assume that the probabilistic interpretation is correct, what is the relationship between energy-momentum and probability?

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

[2] Bassi, A., K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht. 2013. Models of wave-function collapse, underlying theories, and experimental tests. Reviews of Modern Physics 85 (2):471.

"Moreover, the theory does not explain why during a quantum measurement, deterministic evolution is replaced by probabilistic evolution, whose random outcomes obey the Born probability rule."

According to the standard model, the proton consists of three quarks (uud). The three quarks are bound together by the strong force. u quarks have a 2/3 charge and d quarks have a -1/3 charge, so the proton carries an equivalent positive charge [1]. The electromagnetic force is realised by exchanging virtual photons and the strong force is realised by exchanging virtual gluons. If we move a proton by electromagnetic force, it is equivalent to moving three quarks bound together by the strong force, and the strong force needs to change at the same time. So how is the electromagnetic force transferred to the strong force, or how is it converted to the strong force?

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References

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

In electromagnetism the Coulomb force F=q1q2/r^2, the Lorentz force F=q(E+νxB), are computed treating spacetime as flat, and we are measuring what is actually a macroscopic phenomenon, not at the microscopic level. But this does not mean that the principle fails completely at the microscopic level.

Consider particles with mass such as electrons, which should have both electromagnetic and gravitational forces (we cannot rule out the validity of GR at tiny masses). Looking at an electron from the outside, it expresses electric field, magnetic moment, and mass. The Stern-Gerlach experiment fully expressed these covariates [1]. The electron involves only 4 factors, time t, space x, electric field E, and magnetic field H. We express the electron in the set e={Δt, Δx, ΔE, ΔH}, where the elements are all variables. This then implies that the external electromagnetic force, gravitational force, and mass, should all be able to be described by these components, since we can only act on the electron through these components.

Mass then could be exclusively electromagnetic mass [2][3], me={Δt, Δx, ΔE, ΔH}, regardless of the mechanism by which it is produced [4]. The electric field force can likewise be expressed only in terms of Fe=α{Δt, Δx, ΔE, ΔH}, and the gravitational force in terms of the set Fg=G{Δt, Δx}. Obviously, this is their simplest expression.

We need not consider what the electron is. It can be inferred from the set that its electric and gravitational forces overlap, since they share the same part of spacetime expression. This can also be seen by comparing Coulomb's law with Newton's law of gravity. As for neutral massive particles, they can be regarded as cancelling out the electromagnetic field [5] leaving only the Fg = G{Δt, Δx} part. In this way, the gravitational force is naturally unified to the electromagnetic force, and they are coupled together by the spacetime {Δt, Δx}, and automatically incorporated into the gauge field theory; the 'graviton' can be regarded as the spacetime product of the 'photon'. As for gravitational waves, they can be regarded as a part of space-time detached from accelerated motion, like electromagnetic waves radiated by accelerated electrons. This is exactly what Poincaré envisaged [6].

"After Einstein developed his theory of general relativity, in which a dynamical role was given to geometry, Herman Weyl conjectured that perhaps the scale of length would also be dynamical. He imagined a theory in which the scale of length, indeed the scale of all dimensional quantities, would vary from point to point in space and in time. His motivation was to unify gravity and electromagnetism, to find a geometrical origin for electrodynamics. [7, 8]" Wouldn't Weyl have been right if, instead of searching for a geometrical origin of electromagnetism, he had searched for an electromagnetic origin of gravity? Wouldn't electromagnetism be equally geometrical if one considered that the electromagnetic force Fe = α{Δt, Δx, E, H} is essentially the same as that resulting from variations of {Δt, Δx} therein?

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References

[1] Schmidt-Böcking, H., Schmidt, L., Lüdde, H. J., Trageser, W., Templeton, A., & Sauer, T. (2016). The Stern-Gerlach experiment revisited. The European Physical Journal H, 41(4), 327-364. https://doi.org/10.1140/epjh/e2016-70053-2

[2] 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.

[3] What is Mass? Must the Hierarchy of Mass be Determined Simultaneously by the Origin of Mass? https://www.researchgate.net/post/NO45_What_is_Mass_Must_the_Hierarchy_of_Mass_be_Determined_Simultaneously_by_the_Origin_of_Mass

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

[5] The Relation Between Mathematics and Physics (2) - Is the Meaning of Zero Unified in Different Situations in Physics? https://www.researchgate.net/post/NO26The_Relation_Between_Mathematics_and_Physics_2-Is_the_Meaning_of_Zero_Unified_in_Different_Situations_in_Physics

[6] H. Poincaré

[7] Straub, W. O. (2009). Weyl's 1918 Theory Revisited. Pasadena, California. Disponível em: http://www. weylmann. com/revisited. pdf.

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

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?

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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^*?

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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]

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[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

The possible combinations of "limits" and "boundaries" in nature are [1]: 1) "limited and bounded'; 2) “limited and unbounded”; 3) "unlimited and bounded”; 4) “unlimited and unbounded”. Here the object of "limit”can be geometric size, matter, energy, etc., and the object of “boundary”can be regarded as space-time boundary. We need to pay attention to two points here, first, what is the 'space-time boundary'; second, the static 'boundary' and dynamic 'boundary' of the essential difference. For the first point, usually the boundary of space can only be constituted by geometric points, lines and surfaces [2], which ensures that there is no indeterminate space on both sides of the boundary. If set time is the boundary in another dimension, the endpoints of such a boundary are zero-dimensional if they exist at all. For the second point, the Koch snowflake, a fractal curve, is often used in mathematics to express 'infinite perimeter, finite area', which presupposes that the 'boundary' is dynamically progressing infinitely. But once it is stationary at a fixed N(≠∞) [3], it becomes 'limited and bounded’.

‘Symmetry dictates interaction’is a motto of modern physics [4]. Symmetry is in some sense invariance. Coordinate symmetry reflects energy conservation, momentum conservation [5]; charge conservation reflects gauge invariance [6] ....... If time Displacement invariance, and space Displacement invariance, are globally applicable to any individual, do they thereby determine that the entire universe must be unconditionally time Displacement and space Displacement symmetric? Does this dictate that the entire universe must be unbounded in time and space? If there are boundaries to the universe, how can symmetry be maintained at such special places as boundaries? If the universe is anything like "limited and unbounded" [7], how does it support the finiteness of space if conservation of momentum applies globally, when the universe is viewed as a whole object? If conservation of energy is globally applicable, how does it support the finiteness of time? Either way we have to deal with some kind of 'boundary' violation. And if time is cyclic, then the universe must form an 'Ouroboros' [8]. Therefore, if the laws of nature are required to apply globally, it is impossible to face any 'boundary'.

Suppose a finite set, whatever its nature, can we always assign it a centre, as with a tangible entity, we can define its centroid, centre of mass, center of gravity, and so on. Can a finite universe then avoid the existence of a centre? If there is a centre, the universe must have boundaries. At this point, are the time and space boundaries symmetrical? And if we assume that the universe is, infinite in space, infinite in time, and infinite in energy, what would be the catastrophe for our cosmology, or would it be a convenient and useful gateway for research?

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Notes

* It has been said that the universe is limited and unbounded similar to the surface of the Earth, where clearly no boundaries are defined.

** Multiverse theories are receiving more and more attention, and it is more appropriate to think of them as subuniverses within an entire universe.

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References

[1] Chian Fan, "Supersymmetry : Light String and Light Ring". https://www.researchgate.net/publication/369527872_Supersymmetry-Light_String_and_Light_Ring.

[2] Can This Be an Argument for 3-D Space? https://www.researchgate.net/post/NO1_Can_This_Be_an_Argument_for_3-D_Space2.

Yang, J. (2016). The Boundary of A Boundary is Null. https://jeffycyang.github.io/the-boundary-of-a-boundary-is-null/index.html .

[3] Weisstein, Eric W. "Koch Snowflake." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KochSnowflake.html.

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

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

[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] Brading, K. A. (2002). Which symmetry? Noether, Weyl, and conservation of electric charge. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 33(1), 3-22. https://doi.org/https://doi.org/10.1016/S1355-2198(01)00033-8 .

[7] Einstein, A. The Collected Papers of Albert Einstein [爱因斯坦文集] .

Hawking, S. W., & Hertog, T. (2018). A smooth exit from eternal inflation? Journal of High Energy Physics, 2018(4), 147. https://doi.org/10.1007/JHEP04(2018)147

Taming the multiverse: Stephen Hawking’s final theory about the big bang, https://www.cam.ac.uk/research/news/taming-the-multiverse-stephen-hawkings-final-theory-about-the-big-bang#:~:text=Hertog%20and%20Hawking%20used%20their%20new%20theory%20to%20derive%20more

[8] https://mythology.net/others/concepts/ouroboros/