Quantum mechanics from invariance principles

TL;DR

This paper derives quantum mechanics from invariance principles similar to relativity, using minimal assumptions and a Jordan-Lie algebraic framework, with Bell inequality violation as a key experimental postulate.

Contribution

It introduces a novel axiomatization of quantum mechanics based on invariance principles and algebraic structures, highlighting the role of Bell inequality violation.

Findings

Quantum mechanics derived from invariance principles

Jordan-Lie algebraic formulation established

Bell inequality violation as a defining postulate

Abstract

Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell inequalities.