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On the equivalence principle and relativistic quantum mechanics. (English) Zbl 1456.83008

Summary: Einstein’s Equivalence Principle implies that the Lorentz force equation can be derived from a geodesic equation by imposing a certain (necessary) condition on the electromagnetic potential [the author, “On the equivalence principle and electrodynamics of moving bodies”, Preprint, arXiv:1503.05577]. We analyze the quantization of that constraint and find the corresponding differential equations for the phase of the wave function. We investigate these equations in the case of Coulomb potential and show that physically acceptable solutions do not exist. This result signals an inconsistency between Einstein’s Equivalence Principle and Relativistic Quantum Mechanics at an atomic level.

MSC:

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C47 Methods of quantum field theory in general relativity and gravitational theory
78A25 Electromagnetic theory (general)
83B05 Observational and experimental questions in relativity and gravitational theory
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