Colliders are Testing neither Locality via Bell's Inequality nor Entanglement versus Non-Entanglement

Abstract

Recently there has been an increased interest in possible tests of locality via Bell's inequality or tests of entanglement at colliders, in particular at the LHC. These have involved various physical processes, such as $t \bar t$, or $\tau^+\tau^-$ production, or the decay of a Higgs boson to 2 vector bosons $H\to VV^*$. We argue that \textit{none} of these proposals constitute a test of locality via Bell's inequality or a test of quantum entanglement versus non-entanglement. In all cases what is measured are the momenta of the final state particles. Using the construction proposed by Kasday (1971) in a different context, and adapted to collider scenarios by Abel, Dittmar, and Dreiner (1992), it is straightforward to construct a local hidden variable theory (LHVT) which exactly reproduces the data. This construction is only possible as the final state momenta all commute. This LHVT satisfies Bell's inequality and is by construction \textit{not} entangled. Thus a test of locality via Bell's inequality or a test of entanglement versus non-entanglement is inherently \textit{not} possible.