Derivation of Quantum Mechanics algebraic structure from invariance of the laws of Nature under system composition and Leibniz identity

TL;DR

This paper derives the algebraic structure of quantum and classical mechanics from invariance principles and Leibniz identity, highlighting how these foundations distinguish quantum from classical physics through Bell's inequalities.

Contribution

It introduces a novel derivation of quantum and classical mechanics algebraic structures based on invariance under system composition and Leibniz identity.

Findings

Quantum and classical algebraic structures are derived from invariance principles.

Violations of Bell's inequalities distinguish quantum from classical mechanics.

The interplay of products, coproducts, and tensor products underpins the derivation.

Abstract

Products and tensor products are linked by a universal property. Imposing the invariance of the laws of Nature under tensor composition along with Leibniz identity determines quantum and classical mechanics algebraic structure through the interplay between products, coproducts, and the tensor product. Violations of Bell's inequalities distinguishes quantum from classical mechanics.