Foundations of Quantum Mechanics

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

Several years ago, I managed to find 3 independent ways to calculate the 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, devoid of the known limitations inherent in Maxwell’s equations. Let me note here in brief some of the problems of Maxwell’s electrodynamics. The redshift observed for distant galaxies does not follow from Maxwell’s theory in any way, and we have to introduce it artificially. In reality, the redshift caused by a slow change in the metric tensor should have been present in the very equations of electrodynamics written out for the expanding Universe. In addition, Maxwell’s electrodynamics does not work on microscales (quantum objects) although the electromagnetic field is quantized by itself as it was argued by Einstein (1905) and by Debye (1910). Moreover, there are a number of well-known paradoxes inherent in Maxwell’s electrodynamics (see for example V. Ginzburg’s book “Additional Chapters”). All these facts argue that Maxwell’s electrodynamics is incomplete and needs to be generalized to the case of a changing metric of space.

It should be noted that the problems listed above are not independent, as it seems at first glance, and with due regard for the time-dependent 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 the Maxwell’s electrodynamics not makes it possible to take into account the cosmological redshift (when the metric tensor depends on time). Moreover, it also is not suitable for describing phenomena on microscales (Quantum Mechanics), when the loss of energy by 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 loss (realized through the electromagnetic field) becomes comparable in magnitude with the energy of the (quantum) system itself.

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

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

The Planck constant was calculated from first principles, and the correct equations of electrodynamics were obtained in a linear approximation on an adiabatically changing Finsler manifold (I would like to emphasize here that only in Finslerian geometry does the cosmological constant arise in a natural way, while in Riemannian geometry it is absent and it has to be introduced artificially). As I expected, an explanation for the redshift emerged from the equations. However, it came as a complete surprise to me the explanation of the Aharonov-Bohm effect, which followed from the obtained equations! I must confess that I did not expect this, since I believed that it (the A-B effect) is hidden much deeper. Thus, the resulting theory (generalized electrodynamics on an adiabatically changed manifold) describes both the macro and micro-world, perfectly explains why quantization arises 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 the collapse of the wave function (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 “ the worst theoretical prediction in all of physics“.

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

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

For your convenience, I will briefly summarize 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 whose thread 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 (adiabatically invariant) value will be ЕТ = const., Where Е is the energy of the pendulum, and Т is its period.

The electromagnetic field is a pendulum (two-dimensional). If a free EM field propagates over an adiabatically changing manifold (in this simplified work an adiabatically changing 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., which I did in the article. This can be done using the first volume of the course of theoretical physics by Landau and Lifshitz (the section “adiabatic invariants”) or as done in my article mentioned above. As I expected, I got ET = h (I note here again that a cosmological constant does not arise in the Riemannian world, but it naturally arises from torsion only in Finslerian geometry). For this reason, in this paper I did not introduce the cosmological constant (because one may not do this) and the resulting value of Planck’s constant differs from the calculated one for a Finsler manifold exactly by the value of the cosmological constant).

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

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