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arXiv:math-ph/0301040

Time evolutions in Quantum mechanics and (Lorentzian) geometry

Paschke, Mario

Published Jan 29, 2003• 2 citations
arXivHTMLPDF

Abstract

As R.Feynman has shown to F. Dyson -- who published it then in 1990 under the name of "Feynman's proof of Maxwell's equations" -- the only interactions compatible with the canonical uncertainty relation (for scalar particles on flat $\R^3$) are the Lorentz covariant electromagnetic interactions. We generalize Feynman's argument to arbitrary configuration spaces, thereby clarifying its hidden assumptions as well as its geometrical significance. In addition, our result establishes a correspondence between globally hyperbolic spacetimes and solutions to our (algebraically formulated) axioms for nonrelativistic quantum mechanics.

DOI
10.48550/arxiv.math-ph/0301040

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As R.Feynman has shown to F. Dyson -- who published it then in 1990 under the name of "Feynman's proof of Maxwell's equations" -- the only interactions compatible with the canonical uncertainty relation (for scalar particles on flat R3\R^3R3) are the Lorentz covariant electromagnetic interactions. We generalize Feynman's argument to arbitrary configuration spaces, thereby clarifying its hidden assumptions as well as its geometrical significance. In addition, our result establishes a correspondence between globally hyperbolic spacetimes and solutions to our (algebraically formulated) axioms for nonrelativistic quantum mechanics.
A paper by Dyson, published nearly two decades ago, describing Feynman’s proof of Maxwell equations, has generated many comments, analysis, discussions and generalizations of the proof. Feynman’s derivation is assumed to be based on two main sets of equations. One is supposed to be the second law of Newton and the other a set of basic commutation relations from quantum physics.Here we present a new comment on this paper, focusing mainly on the initial arguments and applying a new method of analysis and interpretation of physics, named observational realism. The present discussion does not alter the technical steps of Feynman, but do clarify their basis. We show that Newton’s physics is not a starting point in Feynman’s derivation, neither is quantum physics involved in it, but the foundations of relativity only.
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