Some Mutant Forms of Quantum Mechanics

TL;DR

This paper introduces a novel finite-field quantum mechanics model that exhibits non-classical correlations without violating Bell's inequality, challenging traditional notions of quantum nonlocality.

Contribution

It constructs a mutant quantum mechanics framework over GF(q) and analyzes its correlation properties, providing new insights into quantum foundations.

Findings

Correlations do not violate CHSH inequality in the model

Discretized quantum mechanics cannot be explained by hidden variables

Proposes an alternative mutation of quantum mechanics

Abstract

We construct a `mutant' form of quantum mechanics on a vector space over the finite Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discretized quantum mechanics cannot be reproduced with any hidden variable theory. An alternative `mutation' is also suggested.