Ramsey Approach to Quantum Mechanics

TL;DR

This paper introduces a novel approach to quantum mechanics using Ramsey theory, modeling quantum observables as vertices in a bi-colored graph where edges represent commutation relations, revealing fundamental constraints on observable triads.

Contribution

It applies Ramsey theory to quantum mechanics, providing a new graph-based framework to analyze commutation relations among observables and their simultaneous measurability.

Findings

Ramsey's theorem implies unavoidable monochromatic triangles in the graph.

The approach visualizes quantum relations as a bi-colored complete graph.

It offers a new perspective on the structure of quantum observables.

Abstract

Ramsey theory enables re-shaping of the basic ideas of quantum mechanics. Quantum observables represented by linear Hermitian operators are seen as the vertices of a graph. Relations of commutation define the coloring of edges linking the vertices: if the operators commute, they are connected with a red link; if they do not commute, they are connected with a green link. Thus, a bi-colored complete Ramsey graph emerges. According to Ramsey's theorem, a complete bi-colored graph built of six vertices will inevitably contain at least one monochromatic triangle; in other words, the Ramsey number \( R(3,3) = 6 \). In our interpretation, this triangle represents the triad of observables that could or could not be established simultaneously in a given quantum system. The Ramsey approach to quantum mechanics is illustrated.