Concerning an old (but still quite alive) rebuttal of the theorem of John Bell

TL;DR

This paper critically reexamines Lochak's old rebuttal of Bell's theorem, clarifying misconceptions about hidden variables and non-locality in quantum mechanics, and demonstrates that Lochak's conclusions are incorrect.

Contribution

It provides a detailed analysis showing Lochak's arguments against Bell's definition of hidden variables are flawed, reaffirming the standard interpretation of Bell's theorem.

Findings

Lochak's claim conflicts with quantum formalism is incorrect

Bell's definition of hidden variables remains consistent with quantum mechanics

Non-locality is still necessary to explain Bell inequality violations

Abstract

In a old paper by G. Lochak, it is claimed that the Bell definition of a hidden variable is in conflict with the formalism of quantum mechanics. This result implies that it is not necessary to invoke non locality to explain the violation of the Bell inequality. A careful analysis of the concept of probability for hidden variables, as defined differently by Bell and Lochak, show that the reasoning and main conclusions of are not correct.