Gravitationally induced uncertainty relations in curved backgrounds

• URL: http://arxiv.org/abs/2101.05552v1
• Date: Thu, 14 Jan 2021 11:19:17 GMT
• Title: Gravitationally induced uncertainty relations in curved backgrounds
• Authors: Luciano Petruzziello and Fabian Wagner
• Abstract summary: In particular, we assume the quantum wave function to be confined to a geodesic ball on a given space-like hypersurface whose radius is a measure of the position uncertainty. We concurrently work out a viable physical definition of the momentum operator and its standard deviation in the non-relativistic limit of the 3+1 formalism. For the sake of illustration, we apply our general result to a number of examples arising in the context of both general relativity and extended theories of gravity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper aims at investigating the influence of space-time curvature on the uncertainty relation. In particular, relying on previous findings, we assume the quantum wave function to be confined to a geodesic ball on a given space-like hypersurface whose radius is a measure of the position uncertainty. On the other hand, we concurrently work out a viable physical definition of the momentum operator and its standard deviation in the non-relativistic limit of the 3+1 formalism. Finally, we evaluate the uncertainty relation which to second order depends on the Ricci scalar of the effective 3-metric and the corresponding covariant derivative of the shift vector. For the sake of illustration, we apply our general result to a number of examples arising in the context of both general relativity and extended theories of gravity.

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