Quantum Mechanics reconstruction from invariance of the laws of nature under tensor composition

TL;DR

This paper derives quantum and classical mechanics from four fundamental invariance principles, emphasizing the role of tensor composition and relational laws, with quantum mechanics distinguished by Bell inequality violations.

Contribution

It introduces a novel reconstruction of quantum mechanics based on invariance principles, highlighting tensor composition and relationality as core foundations.

Findings

Quantum mechanics derived from invariance principles

Classical mechanics emerges under specific conditions

Bell inequality violation uniquely characterizes quantum mechanics

Abstract

Quantum and classical mechanics are derived using four natural physical principles: (1) the laws of nature are invariant under time evolution, (2) the laws of nature are invariant under tensor composition, (3) the laws of nature are relational, and (4) positivity (the ability to define a physical state). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.