The Algebra of the Pseudo-Observables I: Why Quantum Mechanics is the ultimate description of Reality

TL;DR

This paper introduces a new algebraic framework called the algebra of pseudo-observables, providing a minimal and logically consistent foundation for quantum mechanics, explaining its core structures and asserting its uniqueness as the ultimate description of reality.

Contribution

It develops a new algebraic approach to quantum mechanics based on pseudo-observables, offering clear physical interpretations and a logical foundation that supports the uniqueness of quantum theory.

Findings

Provides a minimal algebraic structure for quantum observables

Explains the origin of complex and matrix structures in quantum mechanics

Argues for the uniqueness of quantum mechanics as the fundamental theory

Abstract

This paper is the first of several parts introducing a new powerful algebra: the algebra of the pseudo-observables. This is a C*-algebra whose set is formed by formal expressions involving observables. The algebra is constructed by applying the Occam's razor principle, in order to obtain the minimal description of physical reality. Proceeding in such a manner, every aspect of quantum mechanics acquires a clear physical interpretation or a logical explanation, providing, for instance, in a natural way the reason for the structure of complex algebra and the matrix structure of the formulation of Werner Heisenberg of quantum mechanics. Last but not least, the very general hypotheses assumed, allow one to state that quantum mechanics is the unique minimal description of physical reality.