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Non-Local Quantum Theory is Fourier-Transformed Classical Mechanics. Planck's Constant as Adiabatic Invariant Characterized by Hubble's and Cosmological Constants

A. A. Lipovka

Published Dec 1, 2013• 0 citations
OpenAlex

Abstract

In the present work we suggest a non-local generalization of quantum theory which include quantum theory as a particular case. On the basis of the idea, that Planck constant is an adiabatic invariant of free electromagnetic field, we calculate the value of Plank constant from first principles, namely from the geometry of our Universe. The basic nature of the quantum theory is discussed. The nature of the dark energy is revealed.

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In the present work we suggest a non-local generalization of quantum theory which include quantum theory as a particular case. On the basis of the idea, that Planck constant is an adiabatic invariant of free electromagnetic field, we calculate the value of Plank constant from first principles, namely from the geometry of our Universe. The basic nature of the quantum theory is discussed. The nature of the dark energy is revealed.
The generator aspect of observables in classical mechanics leads naturally to a generalized classical mechanics, of which quantum mechanics is shown to be a particular case. Basic features of quantum mechanics follow, such as the identification of observables with self-adjoint operators, and canonical quantization rules. This point of view also gives a new insight on the geometry of quantum theory: Planck's constant is related for instance to the curvature of the quantum-mechanical space of states, and the uniqueness of quantum mechanics can be proved. Finally, the origin of the probabilistic interpretation is discussed.
We trace the historical appearance of Planck's constant in physics, and we note that initially the constant did not appear in connection with quanta. Furthermore, we emphasize that Planck's constant can appear in both classical and quantum theories. In both theories, Planck's constant sets the scale of atomic phenomena. However, the roles played in the foundations of the theories are sharply different. In quantum theory, Planck's constant is crucial to the structure of the theory. On the other hand, in classical electrodynamics, Planck's constant is optional, since it appears only as the scale factor for the (homogeneous) source-free contribution to the general solution of Maxwell's equations. Since classical electrodynamics can be solved while taking the homogenous source-free contribution in the solution as zero or non-zero, there are naturally two different theories of classical electrodynamics, one in which Planck's constant is taken as zero and one where it is taken as non-zero. The textbooks of classical electromagnetism present only the version in which Planck's constant is taken to vanish.
Arguments are gived for the plausibility that quantum mechanics is a stochastic theory and that many quantum phenomena derive from the existence of a real noise consisting of vacuum fluctuations of all fundamental fields existing in nature. Planck's constant appears as the parameter fixing the scale of the fluctuations. Hints for an intuitive explanation are offered for some typical quantum features, like the uncertainty principle or the particle behaviour of fields. It is proposed that the recent discovery of dark energy in the universe is an argument for the reality of the vacuum fluctuations. A study is made of the compatibility of the model with the results of performed tests of Bell\'{}s inequalities.
Quantum mechanics is traditionally formulated in terms of postulates inferred from experimentalobservations. Here we propose that the statistical regularities of quantum mechanics arise as macro-scopic manifestations of stochastic fluctuations of dynamical parameters in microscopic systems gen-erated by a non-inertial physical background. Although the specific nature of this background mayvary, the universality of quantum statistics is ensured by invariant properties of stochastic dynam-ics - analogous to the role of the equivalence principle in general relativity - and by the existence ofa fundamental action scale, Planck constant h. By extending classical mechanics to include higher-order derivatives induced by non-inertial fuctuations and imposing a stability condition on admissibletrajectories, the minimal action scale h naturally emerges. In this framework quantum mechanicsappears as an effective statistical description of systems embedded in a fluctuating non-inertial envi-ronment while preserving all standard predictions of the theory.