# The Noncommutative Values of Quantum Observables

## TL;DR

This paper explores the concept of noncommutative values for quantum observables, proposing a new way to represent their values beyond classical real numbers, using infinite sets of complex numbers.

## Contribution

It introduces the idea of noncommutative values for quantum observables and discusses their theoretical and practical feasibility.

## Key findings

- Noncommutative values can be represented as infinite sets of complex numbers.
- The proposed representation makes sense both theoretically and practically.
- Challenges classical notions of observable values in quantum mechanics.

## Abstract

We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural phenomena than its classical analog. Getting from the algebra of physical observables to their values on a fixed state is, at least for classical physics, really a homomorphic map from the algebra into the real number algebra. The limitation of the latter to represent the values of quantum observables with noncommutating algebraic relation is obvious. We introduce and discuss the idea of the noncommutative values of quantum observables and its feasibility, arguing that at least in terms of the representation of such a value as an infinite set of complex number, the idea makes reasonable sense theoretically as well as practically.