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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2504.09806 |
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| _version_ | 1866910913876983808 |
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| author | Schwarz, Albert |
| author_facet | Schwarz, Albert |
| contents | We consider classical theories described by Hamiltonians $H(p,q)$ that have a non-degenerate minimum at the point where generalized momenta $p$ and generalized coordinates $q$ vanish. We assume that the sum of squares of generalized momenta and generalized coordinates is an integral of motion. In this situation, in the neighborhood of the point $p=0, q=0$ quadratic part of a Hamiltonian plays a dominant role. We suppose that a classical observer can observe only physical quantities corresponding to quadratic Hamiltonians and show that in this case, he should conclude that the laws of quantum theory govern his world. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09806 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum theory from classical mechanics near equilibrium Schwarz, Albert Quantum Physics High Energy Physics - Theory Mathematical Physics 81 We consider classical theories described by Hamiltonians $H(p,q)$ that have a non-degenerate minimum at the point where generalized momenta $p$ and generalized coordinates $q$ vanish. We assume that the sum of squares of generalized momenta and generalized coordinates is an integral of motion. In this situation, in the neighborhood of the point $p=0, q=0$ quadratic part of a Hamiltonian plays a dominant role. We suppose that a classical observer can observe only physical quantities corresponding to quadratic Hamiltonians and show that in this case, he should conclude that the laws of quantum theory govern his world. |
| title | Quantum theory from classical mechanics near equilibrium |
| topic | Quantum Physics High Energy Physics - Theory Mathematical Physics 81 |
| url | https://arxiv.org/abs/2504.09806 |