Symmetry as a foundational concept in Quantum Mechanics

TL;DR

This paper argues for treating symmetry as a fundamental concept in quantum mechanics, proposing new postulates that clarify ambiguities and could advance quantum cosmology and gravity theories.

Contribution

It introduces a novel set of postulates emphasizing symmetry as fundamental, linking them to standard quantum mechanics and enhancing conceptual understanding.

Findings

Reformulation clarifies ambiguities in standard quantum mechanics.

Symmetry-based postulates align with existing axioms.

Potential applications in quantum cosmology and gravity.

Abstract

Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a fundamental concept in the construction of physical systems. Based on this idea, we propose a series of postulates for describing quantum systems, and establish their relation and correspondence with axioms of standard quantum mechanics. Through some examples we show that this reformulation helps better understand some of ambiguities of standard description. Nonetheless its application is not limited to explaining confusing concept and it may be a necessary step toward a consistent model of quantum cosmology and gravity.