Quantum Mechanics from Symmetry

TL;DR

This paper introduces a classical probabilistic framework called GIV theory that generalizes quantum mechanics by focusing on symmetry-based incompatible variables, showing that quantum properties naturally emerge from symmetry considerations.

Contribution

It demonstrates that quantum mechanics can be derived from a broader symmetry-based probabilistic framework, reducing the postulates to symmetry properties.

Findings

Quantum properties like uncertainty and interference arise in classical systems with incompatible variables.

QM emerges naturally when variables are symmetry elements, specifically from the Poincare group.

The commutator and Born postulates are shown to follow automatically from symmetry considerations.

Abstract

Several recent studies have suggested that incompatible variables, which play an essential role in quantum mechanics (QM), are, somewhat surprisingly, not necessarily unique to QM. To investigate this possibility and obtain a better understanding of two central postulates of QM, namely the commutator postulate and the Born postulate, we introduce a classical probabilistic theoretical framework which is more general than QM and contains QM as a special case. We call this framework the General Incompatible Variables (GIV) theory, and we show that not only QM systems but also any probabilistic systems (classical or quantal) that possess incompatible variables will exhibit the quantal properties of uncertainty and interference, and we illustrate this with a roulette-like classical system (which we call the Arrow) that shows precisely these properties. We show that QM emerges naturally from the GIV framework when the fundamental variables are taken to be symmetries, so that the incompatibility of the QM variables is actually just the incompatibility of the corresponding symmetries (or their generators). Specifically, when the variables are taken to be the elements of the Poincare group (the symmetry of spacetime) we find that the commutator postulate and the Born postulate follow automatically, and are therefore no longer postulates. QM thus emerges as a special case of GIV theories for which the variables are symmetries.