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Published July 12, 2021 | Submitted
Journal Article Open

Non-relativistic geometry and the equivalence principle

Abstract

We describe a geometric and symmetry-based formulation of the equivalence principle in non-relativistic physics. It applies both on the classical and quantum levels and states that the Newtonian potential can be eliminated in favor of a curved and time-dependent spatial metric. It is this requirement that forces the gravitational mass to be equal to the inertial mass. We identify the symmetry responsible for the equivalence principle as the remnant of time-reparameterization symmetry of the relativistic theory. We also clarify the transformation properties of the Schrödinger wave-function under arbitrary frame changes.

Additional Information

© 2021 IOP Publishing Ltd. Received 23 January 2021; Revised 13 April 2021; Accepted 6 May 2021; Published 1 June 2021. MT is grateful to the Caltech SURF program for providing a research opportunity. This research was supported in part by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. AK was also supported by the Simons Investigator Award. Data availability statement: No new data were created or analysed in this study.

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Created:
August 20, 2023
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October 23, 2023