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arXiv · 2411.02082

Ramsey Approach to Quantum Mechanics

Edward Bormashenko·Nir Shvalb
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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.

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Edward Bormashenko, Nir Shvalb. 2024-11-04. Ramsey Approach to Quantum Mechanics. https://arxiv.org/abs/2411.02082

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