Ramsey Approach to Quantum Mechanics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913576370831360 |
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| author | Bormashenko, Edward Shvalb, Nir |
| author_facet | Bormashenko, Edward Shvalb, Nir |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_02082 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ramsey Approach to Quantum Mechanics Bormashenko, Edward Shvalb, Nir Mathematical Physics Quantum Physics 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. |
| title | Ramsey Approach to Quantum Mechanics |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2411.02082 |