Foundations of Quantum Mechanics

Finding out the nature of Planck’s constant is the key that can open the door to understanding quantum mechanics, to writing a complete quantum theory outside the framework of the currently dominant axiomatic approach (recall that the Schrödinger, Klein-Gordon-Fock and Dirac equations were postulated and have not yet been derived from the first principles). Finding out the nature of Planck’s constant is the only way to understand the foundations of quantum theory. This statement is true, since only understanding where Planck’s constant comes from will allow us to derive from the variational principle the equations that describe quantum physics.

A few years ago I managed to find 3 independent ways to calculate Planck’s constant from first principles (i.e. from the geometry of the Universe). Understanding the nature of Planck’s constant made it possible to write out the complete equations of electrodynamics (which also describe quantum phenomena), which are devoid of the known limitations inherent in Maxwell’s equations. Let me briefly mention here some problems of Maxwell’s electrodynamics. The cosmological redshift observed for distant galaxies does not follow from Maxwell’s theory in any way, and we have to introduce it artificially, like the Doppler effect. In fact, the redshift caused by a slow change in the metric tensor should appear in the same equations of electrodynamics written for the expanding universe. This is due to the continuous change in the metric, which leads to a continuous withdrawal of energy from the free electromagnetic field at every point in space. Also, Maxwell’s electrodynamics does not work on micro scales (it does not describe quantum objects), although the electromagnetic field is quantized by itself, as Einstein (1905) and Debye (1910) argued. Moreover, there are a number of well-known paradoxes inherent in Maxwell’s electrodynamics (see, for example, V. Ginzburg’s book “Additional Chapters of Electrodynamics”). All these facts indicate that Maxwell’s electrodynamics is incomplete and needs to be generalized to the case of a changing space metric.

It should be noted that the problems listed above are not independent, as it seems at first glance, and taking into account the non-stationary metric of space, they are all solved simultaneously. The problem of Maxwell’s equations of electrodynamics is caused by the fact that they were written for a static Universe (the metric tensor does not depend on time), which led to the problems mentioned above. That is why Maxwell’s electrodynamics does not allow taking into account the cosmological redshift in the equations themselves. Moreover, it is also not suitable for describing phenomena on microscales (quantum mechanics), when the energy loss of the system is associated with the expansion of the Universe (i.e., with small, adiabatic changes in the metric tensor). In this case, the energy losses (carried out through the electromagnetic field) become comparable in magnitude with the energy of the quantum system itself.

It is interesting to note that the same error occurred here as in the case of dark matter (where classical mechanics and hydrodynamics began to be applied outside their range of applicability, which led to the need to introduce dark matter). The only difference is that physicists did not apply Maxwell’s electrodynamics outside its scope (because it obviously did not work for quantum objects) and were forced to develop a new method of calculation called quantum mechanics.

Here in this paper: https://www.scirp.org/pdf/JAMP_2017030814454579.pdf

Planck’s constant was calculated from first principles, and the correct equations of electrodynamics were obtained in a linear approximation on an adiabatically varying Finsler manifold (here I would like to emphasize that only in Finsler geometry does the cosmological constant arise naturally, while in Riemannian geometry it does not exist and has to be introduced artificially). As I expected, the redshift explanation came from equations. However, a complete surprise for me was the explanation of the Aharonov-Bohm (A-B) effect, which followed from the obtained equations! I must admit that I did not expect this, because I thought that it (the A-B effect) was hidden much deeper. Thus, the resulting theory (generalized electrodynamics on an adiabatically changed manifold) describes both the macro- and microworld, perfectly explains why quantization occurs, and can be used to solve a wide range of problems. This approach not only made it possible to obtain the equations of motion of a quantum system from the variational principle, but also made it possible to solve the problem of wave function collapse (the EPR paradox). As a result, it became possible to solve the problem of the enormous discrepancy between the observed value of the cosmological constant and the calculated value of the vacuum energy density (Vacuum catastrophe), also called “ the worst theoretical prediction in all of physics“.

At the same time, a paper was written in which a third (simplified) version of the calculation of Planck’s constant on a Riemannian manifold was proposed in order to popularize the idea among the widest circle of colleagues – physicists. Article was published in Mod.Phys.Lett.A:

https://www.worldscientific.com/doi/10.1142/S0217732319503152

For your convenience, I will briefly outline the essence of the main part of this work. As you know, at one of the Solvay conferences at the beginning of the 20th century, the following problem was proposed and immediately solved: Suppose we have a pendulum, the thread of which slowly (adiabatically) changes with time. Question: What will be the conserved quantity in this case? It is clear that the energy E is not conserved (because we change the length of the thread).

At the same time (at the congress) they came to the conclusion that the conserved quantity (adiabatic invariant) will be ET = const., where E is the energy of the pendulum, and T is its period. The electromagnetic field is a pendulum (two-dimensional). If a free EM field propagates over an adiabatically varying manifold (in this simplified paper, an adiabatically varying Riemannian manifold was considered), then it is clear that the photon energy will not be conserved (recall the cosmological redshift). Then one can calculate the value of the adiabatic invariant ET = const., and I did it in the article. This can be done using the first volume of Landau and Lifshitz’s course in theoretical physics (section “adiabatic invariants”) or as done in my article mentioned above. As it should be, one obtain ET = h (once again, I note that the cosmological constant does not arise in the Riemannian world, but naturally arises from torsion only in Finsler geometry). For this reason, in this article I did not introduce the cosmological constant (because I did not consider it possible to postulate it as some kind of “external” parameter of the theory) and the obtained value of Planck’s constant differs from the calculated one for the Finsler manifold by exactly the value of the cosmological constant).

Summarizing the obtained results: Planck’s constant is an adiabatic invariant of a free electromagnetic field propagating on an adiabatically (slowly) changing Finsler manifold. In this case, the so-called quantization is immediately obtained from the requirement that the boundary conditions be satisfied. Thus, in the works, not only general equations of electrodynamics were obtained, applicable to describe the so-called. “quantum” systems, but the doors are open to understanding the fundamentals of QM and QED.

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