Three attempts at two axioms for quantum mechanics

TL;DR

This paper explores the possibility of formulating quantum mechanics based on nonlocality as a fundamental axiom, proposing three different theories that extend or modify standard quantum mechanics.

Contribution

It introduces three alternative theories derived from nonlocality and causality axioms, offering new perspectives on the foundations of quantum mechanics.

Findings

Three different theories: maximal nonlocal correlations, jamming, modular energy.

Quantum mechanics' position within these theories is analyzed.

Proposes inverting the logical hierarchy of axioms in quantum theory.

Abstract

The axioms of nonrelativistic quantum mechanics lack clear physical meaning. In particular, they say nothing about nonlocality. Yet quantum mechanics is not only nonlocal, it is twice nonlocal: there are nonlocal quantum correlations, and there is the Aharonov-Bohm effect, which implies that an electric or magnetic field h e r e may act on an electron t h e r e. Can we invert the logical hierarchy? That is, can we adopt nonlocality as an axiom for quantum mechanics and derive quantum mechanics from this axiom and an additional axiom of causality? Three versions of these two axioms lead to three different theories, characterized by "maximal nonlocal correlations", "jamming" and "modular energy". Where is quantum mechanics in these theories?