Does a Quantum Particle Know its Own Energy?

TL;DR

This paper explores the nature of quantum reality through a path-integral reformulation, comparing classical and quantum descriptions of particle trajectories, and investigates how quantum states relate to possible particle paths.

Contribution

It introduces a novel perspective on quantum reality using path integrals and analyzes particle trajectories in simplified models to distinguish quantum from classical behavior.

Findings

Quantum reality differs from classical in the set of possible trajectories.

Path-integral reformulation provides insights into quantum states and their classical counterparts.

Model analysis reveals differences in trajectories for ground and excited states.

Abstract

If a wave function does not describe microscopic reality then what does? Reformulating quantum mechanics in path-integral terms leads to a notion of "precluded event" and thence to the proposal that quantal reality differs from classical reality in the same way as a set of worldlines differs from a single worldline. One can then ask, for example, which sets of electron trajectories correspond to a Hydrogen atom in its ground state and how they differ from those of an excited state. We address the analogous questions for simple model that replaces the electron by a particle hopping (in discrete time) on a circular lattice.