Response to Comment on "A Loophole of All "Loophole-Free" Bell-Type Theorems", by J.P. Lambare

TL;DR

This paper argues that Bell's inequalities do not hold under non-Newtonian calculus with non-Diophantine arithmetic, providing a counterexample that challenges the standard assumptions of Bell-type theorems.

Contribution

It introduces non-Newtonian calculus as a framework where Bell's inequalities fail, offering a new perspective on hidden-variable models.

Findings

Bell's inequality is a property of limited hidden-variable models.

Standard proofs of Bell's inequalities fail under non-Newtonian calculus.

An explicit counterexample to Bell's theorem is constructed.

Abstract

Contrary to what Lambare [arXiv:2008.00369] assumes, in non-Newtonian calculus (a calculus based on non-Diophantine arithmetic) an integral is typically given by a nonlinear map. This is the technical reason why all the standard proofs of Bell-type inequalities fail if non-Newtonian hidden variables are taken into account. From the non-Newtonian perspective, Bell's inequality is a property of a limited and unphysical class of hidden-variable models. An explicit counterexample to Bell's theorem can be easily constructed.