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arXiv:1810.11840 · International Journal of Theoretical Physics

Some Clarifications on the Relation Between Bohmian Quantum Potential and Mach’s Principle

Faramarz Rahmani, Mehdi Golshani

Published Jul 8, 2017• 5 citations
arXivHTMLPDF
DOI
10.1007/s10773-017-3476-6

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One of the important and famous topics in general theory of relativity and gravitation is the problem of geodesic deviation and its related singularity theorems. An interesting subject is the investigation of these concepts when quantum effects are considered. Since the definition of trajectory is not possible in the framework of standard quantum mechanics (SQM), we investigate the problem of geodesic equation and its related topics in the framework of Bohmian quantum mechanics in which the definition of trajectory is possible. We do this in a fixed background and we do not consider the backreaction effects of matter on the space–time metric.
A new Bohmian quantum-relativistic model, in which from the Klein-Gordon equation a generalization of the standard Zitterbewegung arises, is explored. It is obtained by introducing a new independent time parameter, whose relative motions are not directly observable but cause the quantum uncertainties of the observables. Unlike Bohm's original theory, the quantum potential does not affect the observable motion, as for a normal external potential, but it only determines that one relative to the new time variable, of which the Zitterbewegung of a free particle is an example. The model also involves a relativistic revision of the uncertainty principle.