Towards Noncommutative Quantum Reality

TL;DR

This paper explores quantum mechanics as a noncommutative form of classical reality, emphasizing the role of noncommutativity in understanding physical quantities and realism.

Contribution

It offers a mathematical perspective that interprets quantum mechanics as fundamentally about noncommutative physical reality, bridging classical and quantum views.

Findings

Quantum reality can be viewed as a noncommutative extension of classical reality.

Noncommutativity is central to understanding the physical quantities in quantum mechanics.

The approach provides a new perspective on the interpretation of quantum theory.

Abstract

The implications of the physical theory of quantum mechanics on the question of realism is much a subject of sustaining interest, while the background questions among physicists on how to think about all the theoretical notion and `interpretation' of the theory remains controversial. Through a careful analysis of the theoretical notions with the help of modern mathematical perspectives, we give here a picture of quantum mechanics, as the basic theory for `nonrelativistic' particle dynamics, that can be seen as being as much about the physical reality as classical mechanics itself. The key is to fully embrace the noncommutativity of the theory and see it as a notion about the reality of physical quantities. Quantum reality is then just a noncommutative version of the classical reality.