The Quantum Theory of the Electromagnetic Field in the Weyl–Wigner Representation as a Local Realistic Model

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 contrast, 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 models for those experiments. I give arguments why Bell definition of local realism is not general enough.