Classical Maxwellian polarization entanglement

TL;DR

This paper presents a classical electromagnetic theory explanation for polarization entanglement based on Maxwell's equations, Lorentz transformations, and avoiding Coulomb gauge, suggesting classical origins for quantum-like correlations.

Contribution

It introduces a classical Maxwellian framework for polarization entanglement, showing how relativistic wave transformations and field coupling can produce entanglement phenomena.

Findings

Classical electromagnetic waves can exhibit entanglement-like correlations.

Lorentz transformations relate forward and reverse waves in a single frame.

The theory aligns with special relativity and explains entanglement at arbitrary angles.

Abstract

An explanation of polarization entanglement is presented using Maxwells classical electromagnetic theory.Two key features are required to understand these classical origins.The first is that all waves diffract and weakly diffracting waves,with a principal direction of propagation in the laboratory frame, travel along that direction at speeds ever so slightly less than c.This allows nontrivial Lorentz transformations that can act on selected forward F waves or selected waves R traveling in the opposite direction to show that both can arise from a single zero momentum frame where all the waves are transverse to the original principal direction.Such F and R waves then both belong to a single relativistic entity where correlations between the two are unremarkable.The second feature requires the avoidance of using the Coulomb gauge.Waves, tending to plane waves in the limit of zero diffraction,can then be shown to be composed of two coupled sets of E and B fields that demonstrate the classical entanglement of F and R waves.Being derived from Maxwells equations,the theory is compatible with special relativity.This is used to account for entanglement between waves traveling at arbitrary angles from a source.In spite of a classical explanation,selection of appropriate F and R waves means entanglement is likely to remain a quantum phenomenon.