Mathematical Physics - Science topic

Tetraquarks are 4 particle quark states since 3^4 = 3×3×3×3 = 81. In trying to organize the 6 known quarks, charm, truth, beauty, up, down, and strange in the weight diagram of SU(3), does the description of and the properties of the X(3872), X(4140), X(5568), X(6900) exotic Hadron tetraquarks fit into the (2,2) + (2,2) + (2,2) = 27 + 27 + 27 = 81 highest weight representation of SU(3) and the (2,2) highest weight representation of SU(3) be a basis from which one could make predictions about the existence of undiscovered tetraquarks?

See B. Hall, Lie Groups, Lie Algebras and Representations, p 151 for a description of the (2,2) highest weight diagram.

Is there any evidence in the data from Fermi Lab or CERN for 3 particle quark Baryon states or 2 particle Meson quark in the 21 dimensional 2,2 highest weight representation of SU(3) with any of the 6 known quarks charm, truth, beauty, up, down, or strange?

In quantum physics, bosons are elementary particles that can occupy the same place in space, but to not accumulate like classical particles, as having been shown in recent experiments on photons where tens of thousands of particles behave as a single quantum particle. Please see the attached link.

This result can be interpreted mathematically if we use a mathematics in which 1+1=1. And from this we obtain 1+1+1+1...=1, in other words ∞→1. For clarity, it should be mentioned here that this kind of mathematics has the form of a Boolean algebra. We can hardly use it, but as shown by the experiments on photons, bosons can.

If these are also true for Higgs boson then the state of an infinite density of matter cannot be achieved because Higgs boson is considered to be the particle that gives masses to other particles. How can  a black hole be formed?

On the other hand, fermions can be considered to follow a mathematics in which 1+1=0.

Actually, the inverse process is more interesting because it can be used to explain the wave mechanics. If tens of thousands of quantum particles can occupy the same place in space and behave as a single quantum particle, i.e., ∞→1, then there is no reason why a single quantum particle cannot make copies of itself to form a medium, i.e., 1→∞, so it can manifest as a wave.

Quantum physics is weird as long as we don't understand it. This statement seems to be obvious as 1+1=2. However, if we follow Einstein's way of thoughts, it's even weirder if we have the ability to understand it at all. 

Recently, I have been able to construct spacetime structures of quantum particles entirely in terms of geometry and topology which shows that the concept of infinite density matter seems to be irrelevant. Please refer to my work entitled  SPACETIME STURCUTURES OF QUANTUM PARTICLES and  A DERIVATION OF THE RICCI FLOW for more details.

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.

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* 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.

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[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.

Our entire description of photons is based on energy Eo=hν [1], momentum Po=h/λ [2], and Helicity and Massless. we are not sure of the wave function Ψo(t,x) of photons, although there have been many different ideas and attempts to do so [3][4][5][6]. Experiments have shown that photons have wave-particle duality; two-photon interference can occur between them [7], and single-photon interference can occur by itself [8]; low energy photons can make electrons jump, photoelectric effect occurs [9], and the energy is converted to free "photoelectrons" in the matter; mid-level energy photons can collide with electrons and produce Compton scattering [10], so that the photon energy is reduced; High-energy photons can generate "pair-production" [11][12] with the help of atomic nuclei, e.g. γ+γ→e+e-.

Classical field theory is based entirely on the Maxwell's Equations, which consists of Faraday‘s Law, Ampere's Law, Gauss's Law, and Coulomb's Law, where both Faraday's equations and Ampere's equations in free space describe electromagnetic waves. We believe that electromagnetic waves consist of two orthogonal, synchronized, time-varying fields, the electric field E and the magnetic field H. Maxwell's equations is a synthesis of experimental results, not a result of mathematical derivation.

We believe that "All beams of electromagnetic radiation are made of photons" [4], including Laser beams, but "A key question is, can we view light as being comprised of particles called photons, or must one view light as a field, and the 'number of photons' only as the name we give to quantum states of the electromagnetic field [5]? electromagnetic field [5]? We know that cosmic microwave background (CMB) is electromagnetic, and that it needs to be detected with a radar antenna because the wavelength is too long; we know that blackbody radiation is electromagnetic, and that it needs to be detected with a photodetector because the wavelength is too short. We know that X-rays, gamma rays, millimeter waves, meter-wave radio waves, and radio astronomy telescopes detect photons.

However, "What is a photon" [4], should a photon have a scale? Is a bridge needed between the classical Maxwell equations and the photon? We have described them both correctly yet cannot connect them directly. The barrier between photons and electromagnetic waves may never be broken if we remain entangled in the probabilistic interpretation of the wave function [17], photon localizability [18], and Negative-energy solution [19], and such quantum mechanical problems.

Nature does not exist without a reason, and there must be a profound reason why an electromagnetic wave consists of two orthogonal, synchronized, time-varying fields, an electric field E and a magnetic field, rather than one field [23]. This reason either is the cause of its existence, something else causing the phenomenon, or it is the result of its existence, the phenomenon having to constrain the form of existence of something else. In any case, there must be a consistent "ecological chain" between the various forms of existence. This is precisely why the E of an electromagnetic wave is identical to the E of electron charge, the E of W±, the E of quarks, and why the H of an electromagnetic wave is identical to the H of a magnet, the H of a spin magnetic moment. If the electric field, E, and the magnetic field, H, of the electromagnetic wave, surprisingly do not exist in its constituent unit, the photon, then how was it created?

Questions:

1) The wave equation does not require two physical quantities, but why are there two quantities, E and H, in the electromagnetic wave equation? And they are not independent*, they must be orthogonal and synchronized [20]**.

2) What kind of photon equation (wave function) is possible to construct a deterministic Maxwell electromagnetic wave equation? It is reasonable to assume that a photon should never be a point particle and must itself have an electric field E and a magnetic field H. The Maxwell equation formed should not be its Probability density‡.

3) Where is the energy of an electromagnetic wave stored? Is it merely a superposition of photon energies? This question has been asked again and again, from Maxwell to Feynman [15] [16], with no answer so far. Is it possible to localize the energy-momentum of a gravitational field if it is not possible to localize the energy-momentum of an electromagnetic wave?

3) How does the Space-Time Curvature act on the electric field E and the magnetic field H of an electromagnetic wave when light is bent in a gravitational field?

4) Why does the physical world follow the invariance principle? How many invariants should there be in physics? What is the relationship between them? Do Maxwell's equations have all invariants? Lorentz invariance, gauge invariance [21], and general covariance [22], etc.?

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* 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]。

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[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

Paradox 1 - The Laws of Physics Invalidate Themselves, When They Enter the Singularity Controlled by Themselves.

Paradox 2 - The Collapse of Matter Caused by the Law of Gravity Will Eventually Destroy the Law of Gravity.

The laws of physics dominate the structure and behavior of matter. Different levels of material structure correspond to different laws of physics. According to reductionism, when we require the structure of matter to be reduced, the corresponding laws of physics are also reduced. Different levels of physical laws correspond to different physical equations, many of which have singularities. Higher level equations may enter singularities when forced by strong external conditions, pressure, temperature, etc., resulting in phase transitions such as lattice and magnetic properties being destroyed. Essentially the higher level physics equations have failed and entered the lower level physics equations. Obviously there should exist a lowest level physics equation which cannot be reduced further, it would be the last line of defense after all the higher level equations have failed and it is not allowed to enter the singularity. This equation is the ultimate equation. The equation corresponding to the Hawking-Penrose spacetime singularity [1] should be such an equation.

We can think of the physical equations as a description of a dynamical system because they are all direct or indirect expressions of energy-momentum quantities, and we have no evidence that it is possible to completely detach any physical parameter, macroscopic or microscopic, from the Lagrangian and Hamiltonian.

Gravitational collapse causes black holes, which have singularities [2]. What characterizes a singularity? Any finite parameter before entering a spacetime singularity becomes infinite after entering the singularity. Information becomes infinite, energy-momentum becomes infinite, but all material properties disappears completely. A dynamical equation, transitioning from finite to infinite, is impossible because there is no infinite source of dynamics, and also the Uncertainty Principle would prevent this singularity from being achieved*. Therefore, while there must be a singularity according to the Singularity Principle, this singularity must be inaccessible, or will not enter. Before entering this singularity, a sufficiently long period of time must have elapsed, waiting for the conditions that would destroy it, such as the collision of two black holes.

Most of these singularities, however, can usually be resolved by pointing out that the equations are missing some factor, or noting the physical impossibility of ever reaching the singularity point. In other words, they are probably not 'real'.” [3] We believe this statement is correct. Nature will not destroy by itself the causality it has established.

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Notes

* According to the uncertainty principle, finite energy and momentum cannot be concentrated at a single point in space-time.

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References

[1] Hawking, S. (1966). "Singularities and the geometry of spacetime." The European Physical Journal H 39(4): 413-503.

[2] Hawking, S. W. and R. Penrose (1970). "The singularities of gravitational collapse and cosmology." Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 314(1519): 529-548.

[3] https://www.livescience.com/what-is-singularity.

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补充 2023-1-14

Russell once wrote a letter to Ludwig Wittgenstein while visiting China (1920 - 1921) in which he said "I am living in a Chinese house built around a courtyard *......" [1]. The phrase would probably mean to the West, "I live in a house built around the back of a yard." Russell was a logician, but there is clearly a logical problem with this expression, since the yard is determined by the house built, not vice versa. The same expression is reflected in a very famous poem "A Moonlit Night On The Spring River" from the Tang Dynasty (618BC - 907BC) in China. One of the lines is: "We do not know tonight for whom she sheds her ray, But hear the river say to its water adieu." The problem here is that the river exists because of the water, and without the water there would be no river. Therefore, there would be no logic of the river saying goodbye to its water. There are, I believe, many more examples of this kind, and perhaps we can reduce these problems to a structural logic pradox †.

Ignoring the above logical problems will not have any effect on literature, but it should become a serious issue in physics. The biggest obstacle in current physics is that we do not know the structure of elementary particles and black holes. Renormalization is an effective technique, but offers an alternative result that masks the internal structure and can only be considered a stopgap tool. Hawking and Penrose proved the Singularity Theorem, but no clear view has been developed on how to treat singularities. It seems to us that this scenario is the same problem as the structural logic described above. Without black holes (and perhaps elementary particles) there would be no singularities, and (virtual) singularities accompany black holes. Since there is a black hole and there is a singularity, how does a black hole not collapse today because of a singularity, will collapse tomorrow because of the same singularity? Do yards make houses disappear? Does a river make water disappear? This is the realistic explanation of the "paradox" in the subtitle of this question. The laws of physics do not destroy themselves.

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* One of the typical architectural patterns in Beijing, China, is the "quadrangle", which is usually a square open space with houses built along the perimeter, and when the houses are built, a courtyard is formed in the center. Thus, before the houses were built, it was the field, not the courtyard. The yard must have been formed after the house was built, even though that center open space did not substantially change before or after the building, but the concept changed.

† I hope some logician or philosopher will point out the impropriety.

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

We tried to start the development of this topic, but given the large number of mysteries related to the mind, its appearance and evolution - noogenesis, etc., we feel that it is necessary to combine efforts, exchange experiences and advice on further development in various directions, coordinates, aspects.

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]

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* 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.

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[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]

Hello,

The sum of Kinetic energy Ke(t) and Potential energy Pe(t) in a physical system is referred to as Total energy Te(t)=Ke(t)+Pe(t), what can we say about the difference Ke(t)-Pe(t) and what can we call it?

I asked this question because I have found polynomial decay of the sum and exponential decay of the difference!

Thank you in advance!

Khaldi Said

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?

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‡ 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.

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[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

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.

Are you a talented young mathematician and would like to continue your mathematics studies at the PhD program under my supervision at University of Ljubljana, Faculty of Mathematics and Physics? Are you simultaneously interested in the young researcher position at the Institute of Mathematics, Physics and Mechanics in Ljubljana?

If the answers to the above question are affirmative, you may contact me at aljosa.peperko(at)fs.uni-lj.si

More information about my reseach interests:

Kind regards, Aljoša Peperko

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]

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】

In the solution of time-dependent schrodinger partial differential equation it is assumed that The minimum energy of quantum particle is hf/2 but not zero.

The question arises is there any rigorous mathematical physics proof?

As for example, light beam attenuation is described by the differential equation

dS/dx = -S

which solution is S~e(-x).

But what physical processes could be described by the differential equation:

dS/dt = -t*S or dS/dx = -x*S

which solution is S~e(-t^2) or S~e(-x^2), with t as time and x as distance.

Do you have ideas?

Thank you very much in advance,

Algis

1. The Logic of PhysicsPhysics students begin with meso-world experiments and theories. Naturally, at the young age, they get convinced that the logic they follow at that level is identical with the ideal of scientific method. Convictions on scientific temper may further confirm them in this. This has far-reaching consequences in the concept of science and of the logic of science.

But, unquestionably, the logic behind such an application of the scientific method is only one manner of realizing (1) the ideal of scientific method, namely, observe, hypothesize, verify, theorize, attempt to falsify for experimental and theoretical advancements, etc., and (2) the more general ideal of reason.

But does any teacher or professor of physics (or of other sciences) instruct their students on the advantages of thinking and experimenting in accordance with the above-mentioned fundamental fact of all scientific practice in mind, or make them capable of realizing the significance of this in the course of time? I think, no.

This is why physicists (and for that matter all scientists) fail at empowering their students and themselves in favour of the growth of science, thought, and life. The logic being followed in the above-said mode of practice of scientific method, naturally, becomes for the students the genuine form of logic, instead of being an instantiation of the ideal of logic as reason. This seems to be the case in most of the practices and instruction of all sciences till today. A change of the origin, justification, and significance of the use of logic in physics from the very start of instruction in the sciences is the solution for this problem. The change must be in the foundations.

All humans equate (1) this sort of logic of each science, and even logic as such, with (2) reason as such. Reason as such, in fact, is more generic of all kinds of logic. Practically none of the professors (of physics as well as of other sciences) terms the version of logic of their science as an instantiation of reason, which may be accessed ever better as the science eventually grows into something more elaborate and complex. Physicist gets more and more skilled at reasoning only as and when she/he wants to grow continuously into a genuine physicist.

As the same students enter the study of recent developments in physics like quantum physics, relativity, nano-physics (Greek nanos, “dwarf”; but in physics, @ 10-9), atto-physics (@ 10-18), etc., they forget to make place for the strong mathematical effects that are due by reason of the conceptual and processual paradoxes due to epistemological and physical-ontological difference between the object-sizes and the sizes of ourselves / our instruments. The best examples are the Uncertainty Principle, the Statistical Interpretation of QM, Quantum Cosmology, etc.

They tend to believe that some of these and similar physics may defy our (meso-physical) logic – but by this mistakenly intending that all forms of reasoning would have to fail if such instances of advanced physics are accepted in all of physics. As a result, again, their logic tends to continue to be of the same level as has been taken while they did elementary levels of physics.

Does this not mean that the ad hoc make-believe interpretations of the logic of the foundations of QM, Quantum Cosmology, etc. are the culprits that naturally make the logic of traditional physics inadequate as the best representative of the logic of nature? In short, in order to find a common platform, the logic of traditional and recent branches of physics must improve so to adequate itself to nature’s logic.

Why do I not suggest that the hitherto logic of physics be substituted by quantum logic, relativity logic, thermodynamic logic, nano-logic, atto-logic, or whatever other logic of any recent branch of physics that may be imagined? One would substitute logic in this manner only if one is overwhelmed by what purportedly is the logic of the new branches of physics. But, in the first place, I wonder why logic should be equated directly with reason. The attempt should always be to bring the logic of physics in as much correspondence with the logic of nature, so that reason in general can get closer to the latter. This must be the case not merely with physicists, but also with scientists from other disciplines and even from philosophy, mathematics, and logic itself.

Therefore, my questions are: What is the foundational reason that physicists should follow and should not lose at any occasion? Does this, how does this, and should this get transformed into forms of logic founded on a more general sort of physical reason? Wherein does such reason consist and where does it exist? Can there be a form of logic in which the logical laws depend not merely on the size of objects or the epistemological level available at the given object sizes, but instead, on the universal characteristics of all that exist? Or, should various logics be used at various occasions, like in the case of the suggested quantum logic, counterfactual logic, etc.?

Just like logic is not to be taken as a bad guide by citing the examples of the many logicians, scientists, and “logical” human beings doing logic non-ideally, I believe that there is a kernel of reason behind physics, justified solely on the most basic and universal characteristics of physical existents. These universals cannot belong solely to physics, but instead, to all the sciences, because they belong to all existents.

This kernel of reason in physics is to be insisted upon at every act of physics, even if many physicists (and other scientists and philosophers) may not ensure that kernel in their work. I shall discuss these possibly highest universals and connect them to logic meant as reason, when I elaborate on: 3. The Ontology of Physics (in a forthcoming discussion in RG)

The matter on which physicists do logical work is existent matter-energy in its fundamental implications and the derivative implications from the fundamental ones. This is to be kept in mind while doing any logically acceptable work physics, because existent matter-energy corpora in processuality delineate all possible forms of use of logic in physics, which logic is properly to be termed nature’s reason.

Moreover, conclusions are not drawn up by one subject (person) in physics for use by the same subject alone. Hence, we have the following two points to note in the use of logic in physics and the sciences: (1) the intersubjectively awaited necessity of human reason in its delineation in logical methods should be upheld at least by a well-informed community, and (2) the need for such reason behind approved physics should then be spread universally with an open mind that permits and requires further scientific advancements.

These will make future generations further question the genuineness of such logic / specific realization of reason, and constantly encourage attempts to falsify theories or their parts so that physics can bring up more genuine instantiations of human reason. But is such human reason based on the reason active in nature?

Although the above arguments and the following definition of logic in physics might look queer or at least new and unclear for many physicists, for many other scientists, for many mathematicians, and even for many logicians, I define here logic for use in physics as the fundamental aspect of reason that physics should uphold constantly in every argument and conclusion due from it:

Logic in physics is (1) the methodological science (2) of approaching the best intersubjectively rational and structural consequences (3) in what may be termed thought (not in emotions) (4) in clear terms of ever higher truth-probability achievable in statements and conclusions (5) in languages of all kinds (ordinary language, mathematics, computer algorithms, etc.) (6) based on the probabilistically methodological use, (7) namely, of the rules of all sensible logics that exemplify the Laws of Identity, Non-contradiction, and Excluded Middle, (8) which in turn must pertain to the direct and exhaustive physical implications of “to exist”.

Here I have not defined logic in physics very simply as “the discipline of the rules of thought”, “the discipline of the methodological approach to truths”, etc., for obvious reasons clarified by the history of the various definitions of logic.

But here comes up another question: Is the reason pertaining to physical nature the same as the most ideal form of human reason? From within the business of physics, how to connect the reason of physical nature with that of humans? I may suggest some answers from the epistemological and ontological aspects. But I would appreciate your responses in this regard too.

I'm supposed to be able to figure this out and am embarrassed to be having a mental block right now. The answer is probably simple.

Consider a loop or ring made of some rigid material. The loop has tick marks that are uniformly spaced and spaced closely enough so that sections of the round loop between tick marks are approximately straight line segments. The loop is now made to spin around its axis. The Lorentz length contraction should make the distance between tick marks shrink, so the loop circumference should shrink. However, the Lorentz length contraction should not affect the loop diameter measured in a direction perpendicular to the motion of the tick marks. This says that the loop should not shrink. Does it shrink?

When I look up the definition of a Lie group I find that it is a differential manifold. When I look up the definition of a manifold I find that it is a space that is locally Euclidean. My understanding is that a manifold is not required to have a metric tensor or distance measure so "Euclidean" cannot be referring to the Pythagorean theorem for triangles. So what does Euclidean mean? I look up the definition of a Euclidean space and find that it is a space defined through axiomatic theory. So I put all of these statements together to obtain the definition of a Lie group? We invent an axiomatic theory to obtain a manifold, then arrange for it to be differentiable (whatever that means) and now we have a Lie group. This makes no sense to me. Can somebody please give more understandable definitions of Lie group, manifold, and Euclidean space?

I took a first course in abstract algebra where a group was defined without any mention of a manifold. It seems to me that reference to a manifold in the definition of a Lie group is unnecessary and makes the definition unnecessarily difficult to understand. Even if so, I am still looking for an easy-to-understand definition of a manifold.

We assume the answer is no because a minus sign appears to the left:

-h^2/2m (d^2Ψ(x,t)/dx^2]partial)+V(x,t)Ψ(x,t)=ihdΨ(x,t)/dt]partial

And,

-h^2/2m (d^2Ψ*(x,t)/dx^2]partial)+V(x,t)Ψ*(x,t)=-ihdΨ*(x,t)/dt]partial

The question is what is the mathematical/physical meaning of the minus sign?

I found the solutions of the equations D_1(z)=0, D_3(z)=0, D_5(z)=0, D_7(z)=0 and D_9(z)=0 which are x=2logφ=0.9624, x=2.03185, x=2.89218, x=3.68896, x=4.46019 respectively. D_odd(z) functions are the well known Bloch Wigner Ramakrishnan functions introduced by Zagier and z=exp(-x). Do you know if these solutions are related to each other?

Bifurcation is a fascinating concept found in various fields, including mathematics, physics, and biology.

The really important breakthrough in theoretical physics is that the Schrödinger Time Dependent Equation (STDE) is wrong, that it is well understood why is it wrong, and that it should be replaced by the correct Deterministic Time Dependent Equation (DTDE). Unitary theory and its descendants, be they based on unitary representations or on probabilistic electrodynamics, will have to go away. This of course runs against the claims about string and similar theories made in the video. But our claims are a dense, constructive criticism with many consequences. Taken into account if you are concerned about the present and the near future of Theoretical Physics.

Wave mechanics with a fully deterministic behavior of waves is the much needed and sought --sometimes purposely but more often unconsciously-- replacement of Quantism that will allow the reconstruction of atomic and particle physics. A rewind back to 1926 is the unavoidable starting point to participate in the refreshing new future of Physics. Many graphical tools currently exists that allow the direct visualization of three dimensional waves, in particular of orbitals. The same tools will clearly render the precise movement and processes of the waves under the truthful deterministic physical laws. Seeing is believing. Unfortunately there is a large, well financed and well entrenched quantum establishment that stubbornly resists these new developments and possibilities.

When confronted with the news they do not celebrate, nor try to renew themselves overcoming their quantum prejudices. Instead the minds of the quantum establishment refuse to think. They negate themselves the privilege of reasoning and blindly assume denial, or simply panic. The net result is that they block any attempt to spread the results. Accessing funds to recruit and direct fresh talents in the new direction is even harder than spreading information and publishing.

Painfully, this resistance is understandable. For these Quantists are intelligent scientists (yes, they are very intelligent persons) that instinctively perceive as a menace the news that debunk the Wave-Particle duality, the Uncertainty Principle, the Probabilistic Interpretation of wave functions and the other quantum paraphernalia. Their misguided lifelong labor, dedication and efforts --of themselves and of their quantum elders, tutors, and guides-- instantly becomes senseless. I feel sorry for such painful human situation but truth must always prevail. For details on the DTDE see our article

Hopefully young physicists will soon take the lead and a rational wave mechanics will send the dubious and troublesome Quantism to its crate, since long waiting in the warehouse of the history of science.

With cordial regards,

Daniel Crespin

In my paper in Phys. Letts..vol 68A (1978)409-411, I have discussed a metric

projectively related to Friedman/R-W metric with identical geodesics.Questions:

Are there other such solutions for this case or for other conformaly flat

spaces? One such solution defines an infinite succession. Is there a computer

program to find infinite succession of (covariant)Einstein tensors.; the

change represents the erruption of matter-energy in assumed spontaneous

projective change. on approach to a singularity. Physically the change is

caused by intervention of Gauge fields to avoid gravity-induced collapse.

The point is that addition to Christofell connection of a term (Identity tensor

times Vector) leaves a system of geodesics unchanged,and is in accord

with equivalence principle. This way one can relate both gauge field and

Q.M. with G .R..Details on request.See also Matsience Report no92(1978)/

paper 9,14pp (www.imsc.res.in/Library)-Black Body Structure of a Black

Hole. And  Lie Structure of Quasiconformal Maps in R*(*=N). And Physics of

String Theory in Quantum Field Theory. QM,& Optics- Ed VV Dodonov &

V I Manko , Moscow (1990) Nova Publishers (N,Y)vol 187 of Proc 0f Lebedev Phy. Inst.Acad. 0f Sciences 0f the USSR./pp113-116..

Qm is the ultimate realists utilization of the powerful differential equations, because the integer options and necessities of solutions correspond to nature's quanta.

The same can be said for GR whose differential manifolds, an sdvanced concept or hranch in mathematics, have a realistic implementation in nature compatible motional geodesics.

1 century later,so new such feats have been possible, making one to think if the limit of heuristic mathematical supplementation in powerful ways towards realist results in physics in reached.

We assume that the statistical weight SW for free nodes in a geometric shape is of extreme importance in mathematics and theoretical physics but is still absent.

However, SW, which is a dimensionless mathematical/physical quantity attached to the importance of the position of the node, can be well defined via the normal/Gaussian distribution curve or equivalently via the B-matrix transition chains.

Both approaches give exactly the same result, which shows that SW is uniquely defined.

I am trying to derive weak-field Schwarzschild metric using Linearized Einstein's field equations of gravity:

[]h_μν – 1/2 η_μν []h = -16πG/ c4 Tμν

For static, spherically symmetrical case, the Energy- momentum tensor:

T_μν = diag { ρc² , 0, 0, 0 }

Corresponding metric perturbations for static ortho-normal coordinates:

h_μν = diag { h_tt , h_xx , h_yy , h_zz }

With one index rised using flat space-time Minquoskwi metric η^μν= { -1 , 1, 1, 1 }:

h^μ_ν = diag { -h_tt , h_xx , h_yy , h_zz }

Trace of the metric:

h = h^γ_γ = - h_tt + h_xx + h_yy + h_zz

The four equations:

1) []h_tt – 1/2 η^tt []h = -16πG/ c⁴ T_tt

=> []h_tt + 1/2 []( - h_tt + h_xx + h_yy + h_zz )= -16πGρ/ c²

=> 1/2 []( h_tt + h_xx + h_yy + h_zz )= -16πGρ/ c²

2) []h_xx – 1/2 η^xx []h = -16πG/ c⁴ T_xx

=> []h_xx - 1/2 []( - h_tt + h_xx + h_yy + h_zz )= 0

=> 1/2 []( h_tt + h_xx - h_yy - h_zz )= 0

Similarly:

3) 1/2 []( h_tt - h_xx + h_yy - h_zz )= 0

4) 1/2 []( h_tt - h_xx - h_yy + h_zz )= 0

Adding equations 2), 3) & 4) to 1) respectively, yield:

[]( h_tt + h_xx ) = []( h_tt + h_yy ) = []( h_tt + h_zz )= -16πGρ/ c²

Solving the equations using:

[] ≈ ▼² ≈ 1/R² d/ dR ( R² d/ dR ) for static spherically symmetric case; we get:

( h_tt + h_xx ) = ( h_tt + h_yy ) = ( h_tt + h_zz )= -8πGρR² / 3c² – K₁/ R + K₂

Similar solutions for vacuum case, with Tμν= 0 would be:

( h_tt + h_xx ) = ( h_tt + h_yy ) = ( h_tt + h_zz )= – K'₁/ R + K'₂

For the metric to be asymptotically flat:

K₂ = K'₂ = 0

For the solutions to be continuous at boundary, R= r, the radius of spherically symmetric matter:

- 8πGρr² / 3c² ≈ - 2Gm/ rc²

The remaining two constants must be:

K₁ = 0 & K'₁ = 2Gm/ Rc²

Therefore, my solution comes:

( h_tt + h_xx ) = ( h_tt + h_yy ) = ( h_tt + h_zz )= - 2Gm/ Rc²

But, as per the literature, the weak field Schwarzschild metric must come out to be:

h_tt = h_xx = h_yy = h_zz = 2Gm/ Rc²

Thus the solutions must come out to be:

( h_tt + h_xx ) = ( h_tt + h_yy ) = ( h_tt + h_zz )= + 4Gm/ Rc²

I am not able to make out where I am making mistake. Can anybody please help?

Thanks.

Nikhil

This is to provide updates on my research as a backup communication channel for my project Multidimensional Integrable Systems

should Researchgate go through with its plan to discontinue the project feature altogether on March 31, 2023.

For the previous update log please see this snapshot

made on April 1, 2023.

You are welcome to follow this question, especially if you are interested in my research, and/or have already followed or intend to follow the above project.

For now, here are the links

0) to my lab

1) to the presentation explaining the most important research results in the project

2) to the key paper of the project

and to the other works in the project

which is now a spotlight, see

Physics is Stalled by Politics - Paper with solutions to 64 significant problems published in #3 journal but rejected by arXiv.org. The new paper entitled, Measurement Quantization, published Jan. 25, 2023 in the Intl. J. Geom. Methods Mod. Phys., lays out the foundations of quantum behavior using existing classical expressions, expanded to account for the discrete internal frame of the universe. The paper presents predictions of a length contraction effect unrelated to that described by Einstein and then presents measurement data to support the approach. It then derives the physical constants and the laws of nature from first principles. It unifies gravity with electromagnetism and writes both SR and GR anew from first principles, therein leading to a derivation of the equivalence principle. It presents simple classical solutions to dark energy, dark matter and a no free parameter description of early universe events. But we should restate, this paper is classical mechanics, offering 530 equations describing phenomena across the entire measurement domain. While extensive support is offered, additional support rests on a long history of support for classical mechanics. In regards to posts regarding the heated debate about the absurdity of new research being filtered, I agree! Even though this paper is published in the #3 mathematical physics journal in the world (by SJR ranking) and is indexed to NASA’s ADS, it was rejected by arXiv.org. I then sought the assistance of a top five ranked astrophysicist in the world. The case was reopened, reconsidered and then rejected a second time, as though classical mechanics was of questionable scientific merit. The point is, classical mechanics is worthy of arXiv.org. We must conclude that the paper was rejected because of a higher cultural mandate, that breakthroughs that impact the existing funding model cannot appear as though they enjoy support by the community. For insight, see this post by Avi Loeb: https://avi-loeb.medium.com/how-to-navigate-academia-6e8c4feea460 I will state, this paper presents solutions to 82.5% of all outstanding problems in cosmology among many other classical and quantum problems. If community leaders really want to effect change, they would use well-vetted publications as example of this cultural absurdity and the need for change. And the best way to affect that change is to begin by supporting breakthroughs in existing classical mechanics on their blogs, in videos, in presentations and at conferences. Community leaders should not be posting literature as unanswered (i.e., dark matter, dark energy) where existing classical mechanics offers insight with straight-forward calculations. Otherwise, such individuals mimic the same cultural bias they are arguing against.

There are a few point to consider in this issue

Points pro current emphasis

1. Math is the backbone of a physical theory. Good representation, good quantities of a theory, phenomena but bad math makes for bad theory

2. There is a general skepticism for reconsidering role of mathematized approach in physics Masters syllabi/upgrading role of literature/essay

2. Humans communicate, learn, think & develop construct via language

Arguments Con

1. Math is the elements in theory and "physics product" that is responsible for precision& prediction. Indespensible though, it exists in the mind of some individuals & function as well, in parallel with conception, physical arguments

2. Not all models in physics are mathematical. Some are conceptual

3. Formulations of solutions to physics problems via math techniques and methods is def of mathematical physics. However, this is a certain % of domain of skills.

But syllabus focuses 100% on this

I am asking if such a hypothetical particle can effectively formerly described by mathematics as a non-Euclidean space object having more than three normal spatial dimensions and at normal time thus speed no more than c.

Ultimately, I'm asking if hypothetical superluminous phenomena can be formerly translated as extra dimensions and vice versa.

For example, can Hilbert space describe superluminous phenomena?

My interest is because I am intrigued by the idea that extra dimensions could be possible apparent effects caused by possible physical superluminous quanta phenomena in our normal three-spatial dimensions space.

And can you reference articles or texts giving answers to this question?

This is briefly considered in https://arxiv.org/abs/0804.1924 which is on RG as https://www.researchgate.net/publication/314079736_Entropy_and_its_relationship_to_allometry_v17.

Reviewing the literature would be helpful before considering whether to updatie the 2015 ideas.

We see many theories in physics, mathematics, etc. becoming extremely axiomatic and rigorous. But are comparisons between mathematics, physics, and philosophy? Can the primitive notions (categories) and axioms of mathematics, physics and philosophy converge? Can they possess a set of primitive notions, from which the respective primitive notions and axioms of mathematics, physics, and philosophy may be derived?

Raphael Neelamkavil

Dear Sirs,

In the below I give some very dubious speculations and recent theoretical articles about the question. Maybe they promote some discussion.

1.) One can suppose that every part of our reality should be explained by some physical laws. Particularly general relativity showed that even space and time are curved and governed by physical laws. But the physical laws themself is also a part of reality. Of course, one can say that every physical theory can only approximately describe a reality. But let me suppose that there are physical laws in nature which describe the universe with zero error. So then the question arises. Are the physical laws (as an information) some special kind of matter described by some more general laws? May the physical law as an information transform to an energy and mass?

2.) Besides of the above logical approach one can come to the same question by another way. Let us considers a transition from macroscopic world to atomic scale. It is well known that in quantum mechanics some physical information or some physical laws dissapear. For example a free paricle has a momentum but it has not a position. Magnetic moment of nucleus has a projection on the external magnetic field direction but the transverse projection does not exist. So we can not talk that nuclear magnetic moment is moving around the external magnetic field like an compass arror in the Earth magnetic field. The similar consideration can be made for a spin of elementary particle.

One can hypothesize that if an information is equivalent to some very small mass or energy (e. g. as shown in the next item) then it maybe so that some information or physical laws are lossed e.g. for an electron having extremely low mass. This conjecture agrees with the fact that objects having mass much more than proton's one are described by classical Newton's physics.

But one can express an objection to the above view that a photon has not a rest mass and, e.g. rest neutrino mass is extremely small. Despite of it they have a spin and momentum as an electron. This spin and momentum information is not lost. Moreover the photon energy for long EM waves is extremely low, much less then 1 eV, while the electron rest energy is about 0.5 MeV. These facts contradict to a conjecture that an information transforms into energy or mass.

But there is possibly a solution to the above problem. Photon moves with light speed (neutrino speed is very near to light speed) that is why the physical information cannot be detatched and go away from photon (information distribution speed is light speed).

3.) Searching the internet I have found recent articles by Melvin M. Vopson

which propose mass-energy-information equivalence principle and its experimental verification. As far as I know this experimental verification has not yet be done.

I would be grateful to hear your view on this subject.

I am working on topology optimization for photonic devices. I need to apply a custom spatial filter on the designed geometry to make it fabricable with the CMOS process. I know there exist spatial filters to remove the pixel-by-pixel and small features from the geometry. However, I have not seen any custom analytical or numerical filters in the literature. Can anyone suggest a reference to help me through this?

Thanks,

Is paraphrasing necessary in such cases, or is direct quotation with appropriate citation sufficient?

Mathematical physics conditions are necessary.

I am studying integral transforms (Fourier, Laplace, etc), to apply them in physics problems. However, it is difficult to get books that have enough exercises and their answers. I have found that in particular the Russian authors have excellent books where there are a lot of exercises and their solutions.

Greetings,

Ender

Dear All,

Recently, I have looked into the Web in search for some works on Search And Rescue or guarding strategies. I have found some works related to UAV exploration in urban environment or SAR disaster site exploration. But, it was not what I really meant.

I wonder if there is any up-to-date literature (analytical, mathematical, physical, simulations maybe?) devoted to search and rescue or guarding, e.g., on the sea. I recall the stories from the time of WWII when allied vessels, after loosing contact with the submarine, started to move in circles with increasing radius. Also, there were special books prepared by mathematicians describing sequences of random turns to avoid being hit by a torpedo.

Do you know if there were any advances in the topic since then? Where the strategies using by modern SAR service are taken from?

Regards,

Michal

Here we discuss about one of the famous unsolved problems in mathematics, the Riemann hypothesis. We construct a vision from a student about this hypothesis, we ask a questions maybe it will give a help for researchers and scientist.

I came across this question (attached below). I tried to solve it but got stuck in the portion where we need to calculate the inverse tranform. I found a solution of this question (also attached below) but there, in the encircled portion, I couldn't get how they took a 2x factor out and change the limits from (-∞, +∞) to [0,+∞ ). I know that we can do this changing of limits only if it's an even function and can take the limiting points [0,+∞ ) iff the function is of the form y = ax² . But here the term inside the exponential function is of the form y = ax² + bx + cix, where i =complex number, and accordingly the limit should change to some random [m,+∞ ) in place of [0,+∞ ). Also, the 2x factor would not be there because the limiting point is changing from [0,+∞ ) to [m,+∞ ) and the graph will not be symmetrical across X=0 Axis.

I will be highly grateful if you can kindly clarify my doubt or let me know where I am making a mistake in understanding the question.

The Nilsson diagram is obtained by solving the Schrodinger equation. If the deformation parameters are continuous, I wonder the orbits should be continuous as well. If the Pauli exclusion principle is the reason, the nilsson quantum number are not always equal, such as 5/2[402] and 5/2[642], why?

Dear Sirs,

The elevator example in general relativity is used to show that gravitational force and an inertial force are not distinguishable. In other words the 2nd Newton's law is the same in the two frames: inertial frame with homogenous gravitational field and the elevator's frame without gravitational field which has constant acceleration in respect to the inertial frame.

But every one knows that an inertial force is a force which does not obey the 3rd Newton's law. For example such forces are cetrifugal force and Coriolis force existing in the Earth reference frame. Gravitational force satisfies the 3rd Newton's law. So one can conclude that the gravitational force is not inertial.

Could you clarify the above controversy.

I am by no means an expert on this subject, but a few papers on this subject sparked an interest into whether instantons give rise to a non-zero vacuum expectation value or could be involved in the generation of the Higgs field.

Instantons in mathematical physics arise as solutions to a set of non-linear differential equations than minimize the Yang-Mills functional for a non-abelian gauge theory. This is part of the differential geometric way of writing classical fields in terms of a connection and the curvature of a connection. The classical electromagnetic field is a U(1) connection and the curvature form of this connection is an anti-symmetric matrix that whose entries are the electric and magnetic fields. For non-abelian groups such as SU(2) and SU(3), the connection and curvature of the connection formalism give rise to the weak force of the Z and W-, W+, and the 8 gluons of the SU(3) strong force. The instanton number can be thought of as describing the number of instantons present and is an expression of how "twisted" or topologically non-trivial the vector bundle or underlying space is.

The Higgs field is what gives spin 1/2 particles mass as well as giving mass to the Z and W-, W+ particles. The masses of spin 1/2 particles are determined by something called the Yukawa coupling. My question is how can instantons contribute to a non-zero vacuum expectation value and are there theories that say the Higgs field is built up in this way?

Dear Sirs,

Everyone knows the derivation of Lorentz transformations from electromagnetic wave front propagation. But Lorentz transformations are the basis of the general mechanics theory. It seems to me it is logically correct to derive the transformations from purely mechanical grounds. But how to do this? Mechanical (sound) waves are not of course applicable here. Or there is only purely mathematical approach? I The later is also not good in physics. Could it be derived from gravitational wave propagation? If it is so is there any controversy because General relativity is based on special relativity? I would be grateful for your suggestions.

Operator product expansion is made in the deep ultraviolet region. In thermal field theory, it is explicitly shown , that the UV divergence in the quantum corrections does not depend on temperature. Hence, temperature shouldn't play any essential role in OPE, in thermal field theory(TFT). On the other hand, TFT is not Lorentz invariant. Hence, in the mixing of scalar operators in OPE, the matrix of anomalous dimensions should vary with quantum corrections due to the non- Lorentz invariant. Hence , I cannot understand the relevance of OPE in thermal field theory.

Good day,

In standard PDE literature, there are a lot of solution approaches for the 1-D wave equation initial-boundary value problem. One way is with separation of variables. Below I describe the problem, the standard solution, and then I ask about a more complicated problem.

Given:

Wave Equation u_tt = c²u_xx.; x ∈ (0, 1), t> 0 with

c=1,

u(0, t) = u(1, t)=0, t> 0,

u(x, 0) = f(x),

x ∈ (0, 1).

u(x, t) =summation over k=1..∞ of [ a_k sin (k π x) * cos (k π t) ]

a_k determinted by Fourier analysis of the function f(x).

My question is about an obstacle.

Let's say there is an obstacle of infinitesimal length of time and space, at x=x₂ and t=t₂, such that u(x₂,t₂)=d₂.

1. How does the solution u(x,t) change after time t₂?

2. How does the answer to 1 change if the obstacle is extended for a finite time?

3. How does the answer to 1 change if the obstacle is extended for a finite space?

4. How does the answer to 1 change if d₂ = 0?

5. Can you point me to some references where I can find the solutions for 1-4? In my opinion, this is related to string vibration as well as electromagnetic wave propagation, for example if a propagating wave encounters a conductor. I hope to be able to find at least some elementary references on this topic.

Thank you in advance..

Dear Sirs,

I would like to find out whether galilean relativity principle (which means the same

form of three Newton's laws in all inertial frames) is derived from the three Newton's laws or

any other classical mechanics statements.

The document: DOI: 10.13140/RG.2.1.4285.9289

Mathematically the question is to determine all the transformations realized between some coordinate systems which have a physical reality for the experimenters: each of these four-dimensional coordinate systems is formed by a cartesian and rectangular coordinate system of a three-dimensional Euclidean physical space, and by a particular temporal parameter which is qualified as cartesian and whose construction is specified. We obtain then a group of nonlinear transformations that contains the Poincaré group and is described by about fifteen real numbers.

Interpretation:

1 / The paradox of Ehrenfest:

If the elements of a family of observers are not motionless the ones with recpect to the others, in other words if their world lines are not elements of a unique physical space, then even in the context of classical kinematics, how they can manage to put end to end their infinitesimal rules to determine the length of a segment of curve of their reference frame (each will naturally ask his neighbor not to move until measurement is ended) ? this is the basis for the proposed solution to Ehrenfest paradox. Inspired by the expression of the law of Hubble, every theory must provide explicit or implicit assumptions to compare "the proper distance" D (which can vary over time) which separates an arbitrarily chosen experimenter P from a certain object, and "the proper distance" D' which separates another arbitrarily selected experimenter P' from the same object and this because it is admitted that this concept of proper distance has a physical meaning even in a non-comoving reference frame.

2 / The authorized relative motions are quantified:

I establish an Eulerian description of the construction of all the physical spaces of the "classical kinematics" and an Eulerian description of the construction of all the physical spaces of nature in the context of the new theory. In classical kinematics all the authorized relative motions between observers can be described by two arbitrary functions of the universal temporal parameter (one of the rotation and one of the translation) and in the context of the new theory, all the authorized relative motions between observers are described by at most 15 real numbers. A notion of expansion of the universe is established as being a structural reality and a rigorous formulation of the experimental law of Hubble is proposed.

Thank you.

Is it possible to formulate the Ricci-flow as the Euler-Lagrange equations of some system? What would be the corresponding action functional?

As you may be aware, the quest to construct a 3x3 magic square using 7, 8, or 9 distinct square integers poses a captivating challenge (refer to pages 17 and 18 of the provided paper). Furthermore, it is intriguing to note the profound connections between magic squares and various physical phenomena (see pages 18 to 23 of the aforementioned paper). The crucial inquiry then arises: How can we harness the tools of physics to unravel these enigmas?

Math relates numbers to other numbers. But this is insufficient for physics. Physics models which include a cause-and-effect are more useful and result in bettter human understanding. For example, current models are time reversable. If cause-and-effect is part of the calculation, the model would not be time reversable without another equation showing how energy (entropy) is expended. Further, any proposed model that was only mathematical manupliation would not be considered physics.

The total energy of two bodies in gravitational interaction must be

(m1 + m2) c^2 - G m1 m2 / r ,

where r is the distance between them. When r is  G/c^2 times the reduced mass, the total energy and hence the total mass vanish! It is the Schwarzschild radius, so a black hole may form. Does it necessarily have zero mass? Is this not contradictory?

A conical surface in a Riemannian manifold M is the union of all the geodesics that connects a fixed point p (the vertex) and any point on some curve in M which doesn't contain the point p. If we define the same in the Riemannian product space S² times R in the analogous way, how can such surfaces be parametrized? In which way can they be visualized?

I got a question (in a Question paper) as follows:-

The answer say's 6 conserved quantities are there, but how is it possible? Can anyone kindly explain.

I have attached there some equations which is needed to be solved by keller box method.but I have faced problems with block elimination portion because of here momentum equation starts with f'' instead of f'''.I have also attached here sample matrix when equation starts with f'''.what will happen when it starts with f''?what will be iteration of converges for this?