A Simple Proof of Locality in Quantum Mechanics

TL;DR

This paper demonstrates that quantum mechanics inherently respects locality at the level of physical effects, using a straightforward proof involving commuting operators, aligning with principles in relativistic quantum field theories.

Contribution

It provides a simple, general proof of locality in quantum mechanics within the standard interpretation, connecting quantum and relativistic notions of locality.

Findings

Quantum mechanics respects locality at the level of physical effects.

Commuting Hermitian operators can be used to prove locality.

The proof aligns quantum mechanics with relativistic quantum field theory principles.

Abstract

While quantum mechanics allows spooky action at a distance at the level of the wave-function, it also respects locality since there is no instantaneous propagation of real physical effects. We show that this feature can be proved in the standard interpretation of quantum mechanics by a simple general result involving commuting Hermitian operators corresponding to distant (causally disconnected) observables. This is reminiscent of satisfying the locality condition in relativistic quantum field theories.