The equivalence principle in classical mechanics and quantum mechanics

TL;DR

This paper explores the equivalence principle across classical and quantum mechanics, demonstrating its foundational role in both and clarifying its implications for particle trajectories in gravitational fields.

Contribution

It provides a unified analysis showing the equivalence principle's validity in quantum mechanics and its foundational importance for classical particles.

Findings

The equivalence principle holds for quantum particle trajectories.

The principle's validity explains its expectation in classical mechanics.

Quantum and classical cases are fundamentally connected through the principle.

Abstract

We discuss our understanding of the equivalence principle in both classical mechanics and quantum mechanics. We show that not only does the equivalence principle hold for the trajectories of quantum particles in a background gravitational field, but also that it is only because of this that the equivalence principle is even to be expected to hold for classical particles at all.