Ramsey Approach to Quantum Mechanics
How to cite: Bormashenko, E.; Shvalb, N. Ramsey Approach to Quantum Mechanics. Preprints 2024, 2024100893. https://doi.org/10.20944/preprints202410.0893.v1 Bormashenko, E.; Shvalb, N. Ramsey Approach to Quantum Mechanics. Preprints 2024, 2024100893. https://doi.org/10.20944/preprints202410.0893.v1
Abstract
Ramsey theory enables re-shaping of the basic ideas of the quantum mechanics. Quantum observables, represented by linear Hermitian operators are seen as the vertices of the graph. Relation of commutation define 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, 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 the numerous examples, including the motion of a particle in a centrally symmetrical field.
Keywords
quantum mechanics, Ramsey theorem; observables; operators, complete graph; Ramsey number; centrally symmetrical field.
Subject
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)