Title : Geometrical origin of quantization
Abstract:
It is well known that historically the motion of charged baryonic matter was quantized first (Schrödinger's equation), and only more than 20 years later the Gupta-Bleuler formalism was proposed, which formally described the quantization of the electromagnetic (EM) field. However, up to the present time the foundations of the constructed orthodox quantum theory were not clear, since it is based on two postulates: namely, the value of Planck's constant was postulated and the existence of the wave function was also postulated. This axiomatic approach leads to a misunderstanding of the foundations of quantum mechanics and this is the reason for the existence of a dozen different interpretations of quantum mechanics. However, back in the early 20th century, Einstein and Debye convincingly showed that the EM field is quantized by itself, regardless of the presence or absence of charged baryonic matter.
In this paper, it is proved that Planck's constant is an adiabatic invariant of a free electromagnetic field propagating along a Finsler manifold characterized by an adiabatically time-varying curvature (see Lipovka DOI: 10.4236/jamp.2017.53050). It is shown that on a Finsler manifold, characterized by an adiabatically variable geometry, the classical electromagnetic field is quantized geometrically (quantization arises from the requirement to satisfy inhomogeneous boundary conditions), in such a way that the adiabatic invariant of the electromagnetic field is Planck's constant: ET = h (here E is energy of the free EM field and T is period).
Direct calculation based on cosmological parameters (Hubble constant and cosmological constant) gives the value of Planck's constant ET = h = 6x10 (-27) (erg s), which coincides with the experimental one up to the measurement errors of cosmological parameters. It is also shown that Planck's constant (and therefore all other fundamental constants that depend on h) changes over time due to changes in the geometry of the manifold. As an example, the change in the fine structure constant is calculated. The obtained relative variation for the fine structure constant is ((da/dt)/a) = 1.0x10(-18) (1/s).
In the work under discussion, the equations of complete electrodynamics on an adiabatically varying Finsler manifold are derived. It is shown that quantization arises naturally, directly from these equations of complete electrodynamics and is due to the adiabatically variable geometry of the manifold. Two effects are discussed that immediately follow from the obtained equations: 1) the cosmological displacement of photons and 2) the Aharonov - Bohm effect. Moreover, the explanation of the Aharonov - Bohm effect was made for the first time and from first principles. It is shown that the quantization of systems consisting of electromagnetic fields and a charged baryon component (like atoms) has a simple and clear explanation within the framework of the obtained complete electrodynamics.
