paper

The Madelung Picture as a Foundation of Geometric Quantum Theory

arXiv:1509.00467 · doi:10.1007/s10701-017-0112-5

Abstract

Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but this has not resolved the problem. In this article we argue that a quantum theory recoursing to quantization algorithms is necessarily incomplete. To provide an alternative approach, we argue that the Schroedinger equation is a consequence of three partial differential equations governing the time evolution of a given probability density. These equations, discovered by E. Madelung, naturally ground the Schroedinger theory in Newtonian mechanics and Kolmogorovian probability theory. A variety of far-reaching consequences for the projection postulate, the correspondence principle, the measurement problem, the uncertainty principle, and the modelling of particle creation and annihilation are immediate. We also give a speculative interpretation of the equations following Bohm, Vigier and Tsekov, by claiming that quantum mechanical behavior is possibly caused by gravitational background noise.

55 pages, 1 figure; Keywords: Geometric Quantization, Interpretation of Quantum Mechanics, Geometric Quantum Theory, Madelung Equations, Classical Limit; The final publication is available at http://www.doi.org/10.1007/s10701-017-0112-5

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