To bypass Lehmann’s theorem against Heisenberg’s “Unified Field Theory of Elementary Particles,” requiring a Hilbert space with an indefinite metric, which is in conflict with the quantum mechanical probability interpretation, it was proposed by the author that Lorentz invariance, on of the fundamental assumptions made by Heisenberg, is a dynamic symmetry, approximately only valid for energies small compared to the Planck energy of ~10^19 GeV, with the fundamental symmetry of nature the Galilei group, in agreement with Mach’s principle. There then Heisenberg’s theory can be reformulated as an exactly non-relativistic quantum field theory with a positive definite metric in Hilbert space. With the Hamiltonian operator in such a theory commuting with the particle number operator, Heisenberg’s ground state of the vacuum is permitted to be a zero temperature plasma made up of positive and negative Planck mass particles which are one Planck mass per Planck length volume, interacting with the Planck force over a Planck length. Making for this Planck mass plasma the Hartree-Foch approximation, one obtains the Landau-Ginzburg equation of a super-fluid, and from the Boltzmann equation the quantum potential of the Madelung transformed Schrodinger equation. Quantum mechanics is thereby explained as a completely deterministic theory, as required by Kant’s law of causality. This paper was inspired by a remarkable paper recently published by I. Licata [1], who compared the work by the author for a deterministic interpretation of quantum mechanics to the work of ‘t Hooft with the same goal.
The purpose of the article is to show that quantum mechanics is a synthesis of the old classical concepts and the new non-classical concepts (physics and mathematics). To illustrate the relationship of continuity between classical physics and quantum mechanics, the materials of Planck, Broglie, Schrodinger, Bohr and Dirac are considered. The author begins with a comparative study of the fundamental principles of classical and quantum physics, and concludes that, despite their opposition and irreducibility, scientists tried to adopt the principles of classical physics for constructing quantum mechanics. Survey of Planck's papers showed that Planck's formula for the blackbody spectrum containing the quantum of action is obtained as a synthesis of classical concepts and quantum concepts. Survey of Broglie's papers showed that the quantum-mechanical concept of Broglie emerged as a synthesis of the provisions of the classical (variation principles) and quantum physics (Planck's constant). Survey of Schrodinger's papers showed great generality of quantum theory in comparison with classical mechanics. Survey of Bohr's papers showed that Bohr was able to prove the basic concepts of quantum physics with the help of methodological principles. Survey of Dirac's papers showed that Dirac discovered the equivalence of Schrodinger's and Heisenberg's theories, showed that they go back to the same physical and algebraic principles, and that they can be formulated as variants of the quantum-mechanical system. The author considers the methodological features of quantum mechanics and fixes a number of methodological principles by which quantum mechanics is significantly different from classical physics. The category of quantum mechanics, on which an attempt to reconstruct the physical picture of the world based on quantum theory, is briefly discussed. On the basis of this reconstruction, there are the world picture broad categories: mass-field and space-time. The categories are related by the formula: wave-like particle moves in the classical space-time background. The first association the particles and interactions is from quantum mechanics, the second space and time from the special theory of relativity. In conclusion, a list of basic relations of quantum mechanics with classical physics is made. The development of quantum ideas resulted from direct influence of classical physics, so the main heuristic techniques to construct quantum theory are two ideas, namely, the idea of continuity and the idea of conformity which Bohr's methodological principles express. At the same time, quantum theory requires the use of classical concepts for support and verification. This is due to the restrictions imposed by the experimental technique. Thus, the author claims that quantum mechanics is a synthesis of the old classical concepts and the new non-classical concepts (physics and mathematics).