Dear Chian Fan .

It would be better if quantization in physics began with the expressions h=E/ν and h=Pλ. Then the entire discreteness of the surrounding world would be determined by the quantum of action h. And there would be no need to talk about rest energy, its connection with massless photons and all sorts of formal “Planck scales”. At the same time, engaging in casuistry and voluntarily driving oneself into an epistemological dead end.

Mikhail Dulin.

Dear Mikhail N Dulin

you said, "the entire discreteness of the surrounding world would be determined by the quantum of action h. " It really is a wonderful sight.

Best Regards, Chian Fan

The history of a technical subject isn't a good guide to is logic. The statement that the structure and interactions of matter particles must be integer multiples of hv is not correct. It was used as a guide by de Broglie for deducing wave/particle duality, that any quantum particle must display wave-like properties, also.

Answers to the direct questions.

1) No. It's possible to define quantum evolution operators for any element of the symplectic group, upon constructing the corresponding metaplectic representation. Cf. for example

Article Modular discretization of the AdS2/CFT1 Holography

Article Holomorphic Quantization on the Torus and Finite Quantum Mechanics

2) No. E = hv doesn't imply anything about the spin or statistics.

Quantization implies finding the quantum system, upon having fixed the classical limit.

The mathematical ``determinants" of the fact that a physical system is subject to quantum fluctuations are the properties of the corresponding probability distribution.

“…..If the quantization of nature is inevitable, what are its mathematical determinants?....The mathematical ``determinants" of the fact that a physical system is subject to quantum fluctuations are the properties of the corresponding probability distribution.…”

- why the quantization of nature is inevitable it is quite clearly explained in the Shevchenko-Tokarevsky’s Planck scale informational physical model , in this case it is enough to read

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics- though that was rigorously shown yet more 2500 years ago by Zeno in his really outstanding aporias.

That happens since the absolutely fundamental phenomenon “Change” is logically self-inconsistent, and so deterministic continuous changes of everything are logically prohibited. Correspondingly to overcome this prohibition it is necessary (i) – to spend some portion of absolutely fundamental phenomenon/Quantity “Energy”, and (ii) – at that, nonetheless, on some level of changing the state of any/every changing object/system is uncertain – “illogical”.

Again, that happens at every change of any object/system, and that has no any relation to mathematics, which is changing at its development also in accordance with the point above.

If we tell about the informational system “Matter”, which is based fundamentally on a simple, completely rigorous, and universal, binary reversible logics, at description and analysis of what exists and happens in Matter mathematics is extremely effectively applicable, however it is fundamentally nothing else than extremely effective tool,

- which principally practically nothing determines in Matter, including in what exists and happens in Matter there cannot be, and so aren’t some specific “mathematical determinants”, besides very rare exclusions.

“…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]…”

- that the EM radiation of heated material structures is quantized, and energies and momentums of EM quanta that are radiated at relaxation of excited discreet atomic electrons states are E=hν, P=h/λ, that was indeed one of utmost fundamental physical results, which was obtained by Planck.

However that

“. 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… fundamental composition of matter is a variety of quanta E=hνi (i=1,2,3),...”

- is fundamentally wrong, since the above relates only to de Brogile waves and corresponding 3DXYZ momentums. Nonetheless yeah, in mainstream physics such hypothesis exists as hypothesis of “Zitterbewegung” seems from last 1920s, i.e. that having rest mass particles somehow oscillate so the E=mc2=ћω. However the hypothesis exists as some quite natural generalization of Planck relation for EM quanta,

- and though Zitterbewegung was rather probably really experimentally observed in 2008; the hypothesis really hasn’t scientifically rational grounds in mainstream physics [the Planck relation hasn’t also, though, till now it has only experimental grounds].

And it cannot have, since in the mainstream, say, Matter’s spacetime is 4D Minkowski space with metrics (ict, X,Y,Z) , where ictis the time dimension, which really is imaginary mathematically.

[Nobody and never, of course, observed till now imaginary mathematically either space or time, but that is in standard in mainstream physics SR, and that is an example how “mathematical determinants” really work in mainstream physics].

The post is rather long already, so now

Cheers

So let’s continue.

In the SS post above it is pointed that the quite natural scientific extrapolation of the Planck’s relation E=ћω, which quite convincingly is confirmed at experiments with 3DXYZ EM waves and particles “photons”, really is impossible in the mainstream physics, where Matter’s spacetime has 4D metrics (ict, X,Y,Z);

- thought really that is impossible since in mainstream physics not only “space” and “time”, but everything in Matter, including “particles” is/are fundamentally transcendent/uncertain/irrational at all.

Rigorous scientific definitions of fundamentally necessary in this case fundamental phenomena/notions “Space”, “Time”, “Energy”, “Matter”, and so rigorously scientifically rational clarifications what are “Matter’s spacetime”, “particles”, “fundamental Nature forces” – and so “fields”, etc.,

- are possible, and are done, only in framework of the Shevchenko-Tokarevsky’s initial Planck scale informational physical model, in this case it is enough to read a couple of main papers -

“The Informational Conception and the Base of Physics”

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics , and

“The Informational Physical Model and Fundamental Problems in Physics”

https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics .

More see the links above, here only briefly:

- Matter is informational system that is based on binary reversible logics;

- correspondingly the ultimate base of Matter is/are binary reversible, and so at least 4D, fundamental logical elements [FLE], which compose the at least 4D dense FLE- lattice, and everything in Matter are some disturbances in the lattice;

- the lattice is placed in corresponding Matter’s utmost universal fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, [5]4D spacetime with metrics (cτ,X,Y,Z,ct), where the really specific space cτ-dimension in mainstream physics is the time dimension, while really the time dimension is ct-dimension in the metrics above;

- FLE “size” and “FLE binary flip time” are Planck length, lP, and Planck time, tP, so all [disturbance always constantly move in the 4D space only with 4D velocities that have identical absolute values be equal to the speed of light, c= lP/tP;

- particles and their compositions so have 4D momentums P=mc [bold means 4D vector], and energies E=Pc, m is inertial mass.

So photons that are created by 3DXYZ space directed momentums move only in the 3D space with the speeds of light, particles that are created by momentums [“T-particles” in the model] that are directed along cτ-axis, if are at rest in the absolute 3D space, move only in the cτ-dimension with the speed of light;

- if a T-particle is impacted by some 3D space momentum, it moves also in 3D space with some speed V, correspondingly its speed in cτ-dimension decreases in Lorentz factor; and, finally here:

If a 4D space momentum P is infinitesimal, it creates a 4D disturbance in lattice “a FLE flipping point” that propagates as sequential FLE-by-FLE flipping with the speed of light along a 4D straight line.

However if P isn’t infinitesimal, since any disturbance in lattice cannot propagate with speed more than the speed of light [more correctly with speed c√2, see below, but that isn’t too essential], FLEs in the FLE-flipping point start to precess, and so the FLE-flipping point’s trajectory in 4D space is corresponding 4D “helix”,

- while the corresponding cyclically repeating concrete certain FLE-sequences forms a cyclically running with frequency ω algorithm – which is just a particle, that has energy E=Pc=ћω;

- and just that really is the observable “Zitterbewegung”.

The post is rather long already, so more see the linked papers, now

Cheers

Dear Stam Nicolis

Thank you very much for your comments and the references provided!

E=hν is not just history, it is the basis of the whole of physics. There exists no place where it is denied, nor is there any place where it can be separated from h. Not only is there h in spin, but it is even contained in black hole temperatures. the de Broglie concept of matter-waves indicates that all matter has the properties of a wave, which not only does not conflict with discretization, but shows an inseparable and intrinsic relationship with E=hν.

"Quantization implies finding the quantum system, upon having fixed the classical limit" I don't quite understand what this means. There are many quantum operators used in quantum field theory, and isn't that justified by the idea that the quantum is invariant and its own structure can be ignored? For example, annihilation and generation operators.

Regarding the Fourier transform, if it is not the only restriction, then it should still be physically realizable even if there are other expressions. I still need to study the information you provided to verify this.

Best Regards, Chian Fan

There are too many errors in these statements. E = hv is simply the relation between the energy of the particle, the superpositions of which describe a wave, and the frequency of the wave. It doesn't imply anything particular about the spin of the particle, nor does it imply anything about whether the spectrum is discrete-the frequency takes discrete values-or continuous (the frequency can take continuous values). Contrary to popular accounts, quantum energy spectra can be continuous and classical energy spectra can be discrete (the energy spectrum of a quantum particle in a non-compact space is continuous and the modes in a waveguide have a discrete energy spectrum, nonetheless they describe the propagation of classical waves).

``The quantum is invariant'' just doesn't make sense as a sentence. The quantum operators that are used in quantum field theory create states (hence the name ``creation operator'') or annihilate states (hence the name ``annihilation operator''). What these names really mean, however, is that any theory is defined by its space of states, starting from the vacuum state-no particles-and going on to the 1-particle state, 2-particle state and so on.

So the quantities of interest are the transition probabilities from a state of n particles,each with given labels, to a state of k particles with some other labels. These are infinite-dimensional probability distributions and the object of theoretical investigations is how to characterize them in a way that can b used to design experiments. One way is by starting from the classical limit of the quantum theory and trying to take into account the fluctuations. That's what quantization is about.

With respect to „… nor does it imply anything about whether the spectrum is discrete-the frequency takes discrete values-or continuous (the frequency can take continuous values). …“

The frequency could then - and only then - take also continuous value, if both E (energy) and v (frequency) are assumed to be physically continuum, as h (or hBar) is quantized for sure.

But as iSpace theory was recently able to show (mathematically derived and prooven beyond reasonable doubt) that time is discrete in quantum steps of 1/6961 iSpaceSecond (independent of any used unit system to express this by identifying the exact (iSpace-IQ) quantum part and the (iSpace-SI) human artefact part of any (SI of otherwise) unit system based time definition), the allowed possible physical frequencies are likewise discrete (being just the inverse of time).

As a consequence of most simple exact E = h * v multiplicative relation energy E is hence now also necesserily a discrete entity, which can also be seen in the trivial fact (mostly ignored and hidden away in regular textbooks) that the emission and with this also absorption of light due to energy conservation is taking place without any involvement of often pronounced justification of continuum by experimental results involving Heisenberg uncertainty relation (in other words, light is emitted by an exact frequency based energy with zero uncertainty):

Preprint iSpace - Quantization of Time in iSpace-IQ Unit-System by 1/...

Complete discritness needs quantisation of the moment of inertia.

Constants h and c are insuffisant for a theory of everything.

Alaya Kouki For a complete discrete (3D/4D) spacetime such might be so, but iSpace persues a hybrid 10D model, 3D of which are fine grananular (extreme "continuum style" yet still descrete), while all quantum operations run in a (6D/7D) sub-spacetime as derived from logical symmetry reasoning of the derived iSpace-SI and iSpace-IQ equations able to reflect current measured constants of nature with extrem, perfect compatibilty to SI measurement results (which cannot ever be accidental, by reasoning of Occam's razor).

The existence of a quantum of time is undenyable for everyone having read - just really following line by line of most simple Mathematica code - below given link of "iSpace - Quantization of time in iSpace-IQ unit system ..." until the proof appears right in from of their eye: if the human artefact (itBHA or iSpace BaseTime SI time human artefact factor) is devided out by the power of the exponent of SI seconds used by the physical result equation, in all cases just 1/6961 iSpaceSecond is all that remains time wise numerically in the equations.

This works for A*s (or Coulomb) to the power of 1, for V*A*s^2 (or Planck-constant) for the power of 2, for V*A*s^3/m^2 (or electron mass in kilogram) for the power of 3 and 4 respective, depending on the result equation used), and for power of 2 for electron mass in eV/c^2 (ElectronVolt per speed of light squared as mass entity). What is due to the complexity not shown in the really short (max. 100 lines) paper as given its RG link below again, is the method does even work in relation to SI Newtonian G, where the itBHA factor is built into G with the power of 8 (!).

All such is never accidental, demonstrated to work "pixel-perfect" (up to the last LSB integer bit of the value) over a value range of nearly 10^42 (!) orders of magnitude. And it has to do with such precision, either its fully correct model or its just accidental (with repect to 100% full current SI measurement precision compatibility). Choose yourself, but choose wisely.

Preprint iSpace - Quantization of Time in iSpace-IQ Unit-System by 1/...

Method iSpace - Quick check of α and Φ0 from Markoulakis & Antonidakis

Article New novel physical constants metric and fine structure const...

I don't understand your frame work and what is its relation to physics.

Instead of your time 1/6961 iSpaceSecond please try 1/0.7 E12 iSpaceSecond and tell me it is good or not for calculation of physics constants.

Alaya Kouki Dear Alaya,

I have to most openly confess I do not understand your last reply to this thread either: "Instead of your time 1/6961 iSpaceSecond please try 1/0.7 E12 iSpaceSecond and tell me it is good or not for calculation of physics constants." Please see my explaination just given on your related (much simpler) question given directly in the comment section of my paper.

I have not time to discuss this, but it might be interesting to elaborate at least a bit in what form "1/0.7 E12" (whatever that is) could be helpful here?

I do not know (at all) what your mentioning of "E12" could possibly mean, nor how (really self explainable!) some restriction to a 2-digit (max. !) only result of a pocket calculator style floating point division might help to understand physics of constants of nature.

Thank you and kind regards,

Christian

Christian G. Wolf It is interessent your calculation of h & e . 47[V] I had see it in an article of a french physicist speaking about wave function and this constant is a ratio (I can't remember now the article-or 27 [V]).

Howeever your calculation signify that there is something hidden in physics.

I mean by 0.7 E12 a frequency equal to 0.7 times 10 power 12 Hz and it is for me the fundamental frequency of quantum field in its fundamental state.

Dear Stam Nicolis

“There are too many errors in these statements....... ”——

I am with COVID-19, although I have passed the period of high fever, I still feel twice as weak.

COVID-19 symptoms must correspond to specific physiological processes in the body, whether it is fever, sore throat, or coughing, they are all specific reflections. Physics should be the same; everything described by mathematics should have a physical counterpart, and nowhere can it fall short. Although the goal of physics is in fact to find such concrete correspondences, this is not unanimously accepted. A significant number of physicists believe that it is sufficient to be able to explain physical phenomena mathematically, without having to look into the real workings of the physics behind them.

Often we can describe physics in mathematical approximation, but this must not be the case with real physics. What I mean is that physics cannot express all discrete phenomena continuously. To express all discrete phenomena, only a finite number of discrete terms can be used. For example, if two electrons collide, if it is described by δ(t), it cannot be realistic because it contains infinitely many momentum terms and it cannot be physically presented. Therefore, the energy exchange at collision must be a sum of finite terms of momentum. This must require that the electrons are intrinsically equally finite term, so that even if the motion of the electrons is continuous, their output exchange is discrete.

The math-physics relationship is, in fact, temporarily abandoned to one side in the study of true physics, just as the structure of elementary particles is abandoned to one side. Seeing mathematics as a tool is a temporary notion of necessity, and the problem arises when we ask why physics should choose mathematics as a "tool" rather than something else. You know, you can choose to eat with a knife and fork, you can also choose chopsticks, but physics can only choose math.

In any case, this is a question worth exploring, and it can be done slowly, as long as physicists are not in a hurry.

Best Regards, Chian Fan

Chian Fan

Best wishes for a speedy recovery!

Once more: Quantization means constructing the quantum theory, whose classical limit is a given classical theory. If the classical theory is a relativistic field theory, the classical equations of motion describe waves (inear for a free theory, nonlinear for an interacting theory). In the quantum theory their states can be understood as multiparticle states, where the particles can be massless or massive. For the free theory, the dispersion relation can be shown to be hω=h|k| E = |p|c for massless particles and

(hω)2 = (hk)2 + m2c4 E2 =|p|2c2 + m2c4 for massive particles.

So a massless particle doesn't display dispersion, since the phase velocity is equal to the group velocity of the wave, which is described by the coherent superposition of one-particle states, whereas the massive particle does display dispersion, since the phase velocity isn't equal to the group velocity.

The quantities that are relevant for describing a quantum field theory are the transition probabilities from any state of n particles, with given properties (energy, momentum, angular momentum, internal charges) to any state of n' particles with given properties. How to compute these is what quantization is about.

Dear Stam Nicolis and all others

Thank you very much for your kindness and comments! I will continue to try to understand your words from a professional perspective.

Today is Chinese New Year's Eve and I wish you and all peoples here a Happy Dragon Year!

Best Regards， Chian Fan

Stam Nicolis

"whereas the massive particle does display dispersion, since the phase velocity isn't equal to the group velocity."

So I can conclude for equation of motion of a massive particle that there is friction in space. Don't worry about friction, we can associate to space a negative pressure to compensate the friction and it is like that there is no friction.

With this idea QM can have a new direction.

Dispersion≠friction! Nor does it have anything to do with any ``negative pressure''. It doesn't make sense to just throw words around at random.

It would be a good idea to actually study quantum mechanics.

A quantum particle is a classical particle, in equiibrium with a bath of quantum fluctuations. The scale of these fluctuations is set by Planck's constant, so they're significant, when the classical action becomes comparable to Planck's constant, while they're negligible when the classical action is much greater than Planck's constant.

Dispersion appears when taking into account wave/particle duality in quantum mchanics and is a property of the wave, as it propagates.