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arXiv · 2310.09218

Adherence and violation of the equivalence principle from classical to quantum mechanics

Joseph Balsells·Martin Bojowald
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Abstract

Investigation into the applicability of the equivalence principle in quantum mechanics has taken many forms, with varying conclusions. Here, a dynamical semi-classical description of a wave packet in terms of its center of mass and higher quantum fluctuations is applied to the case of a quantum particle in gravitational free fall. The analysis provides an intuitive account of the origin of mass-dependence in quantum-gravitational dynamics through an effective potential that enforces the uncertainty principle. This potential has two implications: (i) The lowest order quantum fluctuations encoding the width and spreading of the wave packet obey an uncertainty relation whose observance is mass-dependent. (ii) In an inhomogeneous gravitational field tidal effects couple the center of mass motion to the quantum fluctuations. The combined effect results in a clear demonstration of how some conceptions of the weak equivalence principle, based on mass dependence, are violated. The size of this violation is within sensitivities of current Eotvos and clock-based return time experiments.

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Joseph Balsells, Martin Bojowald. 2023-10-13. Adherence and violation of the equivalence principle from classical to quantum mechanics. https://doi.org/10.1103/physrevd.108.084030

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