The quantum theory of the electromagnetic field in the Weyl-Wigner representation as a local realistic model

TL;DR

This paper revisits the Weyl-Wigner representation of the quantum electromagnetic field, proposing a classical local realistic model based on a vacuum field, contrasting it with non-relativistic quantum mechanics and analyzing entangled light experiments.

Contribution

It introduces a local realistic interpretation of the electromagnetic field within the Weyl-Wigner framework, challenging traditional views on quantum nonlocality and Bell inequalities.

Findings

Wigner representation suggests a classical Maxwell theory with a vacuum field.

Non-relativistic quantum mechanics does not admit a similar realistic interpretation.

Provides a local model for entangled light experiments and critiques Bell's definition of local realism.

Abstract

I revisit the Wigner (or Weyl-Wigner, WW) representation of the quantum electromagnetic field. I show that, assuming that Fock states are just mathematical concepts devoid of physical reality, WW suggests a realistic interpretation which turns out to be (classical) Maxwell theory with the assumption that there is a random radiation filling space, the vacuum field. I elucidate why, in sharp constrast, non-relativistic quantum mechanics of particles does not admit a realistic interpretation via WW. I interpret experiments involving entangled light beams within WW, in particular optical tests of Bell inequalities. I show that WW provides clues in order to construct local model for those experiments. I give arguments why Bell defintion of local realism is not general enough.