Free fall in KvN mechanics and Einstein's principle of equivalence

Abstract

The implementation of Einstein's principle of equivalence in Koopman-von Neumann (KvN) mechanics is discussed. The implementation is very similar to the implementation of this principle in quantum mechanics. This is not surprising, because KvN mechanics provides a Hilbert space formulation of classical mechanics that is very similar to the quantum mechanical formalism. Both in KvN mechanics and quantum mechanics, a propagator in a homogeneous gravitational field is simply related with a free propagator. As a result, the wave function in a homogeneous gravitational field in a freely falling reference frame differs from the free wave function only in phase. Fisher information, which quantifies our ability to estimate mass from coordinate measurements, does not depend on the magnitude of the homogeneous gravitational field, and this fact constitutes the formulation of Einstein's principle of equivalence, which is valid both in quantum mechanics and KvN mechanics.

arXiv comment46 pages, no figures, to be published in Annals of Physics

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Cited by in corpus (8)

• Eisenhart lift of Koopman-von Neumann mechanics
• Decoherence-Free Entropic Gravity: Model and Experimental Tests
• The wave operator representation of quantum and classical dynamics
• Gravitational time dilation, free fall, and matter waves
• The Schwinger action principle for classical systems
• Mass-energy equivalence in gravitationally bound quantum states of the neutron
• Operational classical mechanics: Holonomic Systems
• Non-local imprints of gravity on quantum theory