Spin Correlations in $e^{+}e^{-}$ Pair Creation by Two-Photons and Entanglement in QED

TL;DR

This paper derives energy-dependent spin correlation probabilities for electron-positron pairs produced by photon collisions, demonstrating violations of Bell's inequality across all energies, thus supporting quantum field theory in relativistic regimes.

Contribution

It provides explicit, energy-dependent formulas for spin correlations in $e^{+}e^{-}$ pair creation, highlighting quantum entanglement and Bell inequality violations in QED.

Findings

Explicit energy-dependent spin correlation probabilities derived.

Demonstrates violation of Bell's inequality at all energies.

Supports quantum field theory in relativistic regimes.

Abstract

Spin correlations of $e^{+}e^{-}$ pair productions of two colliding photons are investigated and explicit expressions for their corresponding probabilities are derived and found to be \textit{energy} (speed) dependent, for initially \textit{linearly} and \textit{circularly polarized} photons, different from those obtained by simply combining the spins of the relevant particles, for initially \textit{polarized} photons. These expressions also depend on the angles of spin of $e^{+}$ (and/or of $e^{-}$), for initially {\it linearly polarized} photons, but not for {\it circularly polarized} photons, as a function of the energy. It is remarkable that these explicit results obtained from quantum field theory show a clear violation of Bell's inequality of Local Hidden Variables theories at all {\it energies} beyond that of the threshold one for particle production, in support of quantum field theory in the relativistic regime. We hope that our explicit expression will lead to experiments, of the type described in the bulk of this paper, which can monitor energy (and speed) in polarization correlation experiments.