Edward Bormashenko, Nir Shvalb
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 the graph. Relation of commutation defines coloring of the edges linking the vertices: if the operators commute, they are connected with the red link; if they do not commute, they are connected with the green link. Thus, a bi‐colored, complete, Ramsey graph emerges. According to the Ramsey 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, which could or, alternatively, could not be established simultaneously in a given quantum system. The Ramsey approach to the quantum mechanics is illustrated with numerous examples, including the motion of a particle in a centrally symmetrical field.
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title={Ramsey Approach to Quantum Mechanics},
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