Equivalence Principle for Quantum Mechanics in the Heisenberg Picture
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917664772849664 |
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| author | Kong, Otto C. W. |
| author_facet | Kong, Otto C. W. |
| contents | We present an exact quantum observable analog of the weak equivalence principle for a `relativistic' quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant classical Hamiltonian evolution picture, with the proper identification of the canonical momentum variables as $p_μ$, rather than $p^μ$. We discuss the meaning of the equations in relation to projective measurements as well as equations with solution curves as ones in the noncommutative geometric picture of spacetime, and a plausible approach to quantum gravity as a theory about quantum observables as physical quantities including the notion of quantum coordinate transformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03095 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Equivalence Principle for Quantum Mechanics in the Heisenberg Picture Kong, Otto C. W. General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Physics We present an exact quantum observable analog of the weak equivalence principle for a `relativistic' quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant classical Hamiltonian evolution picture, with the proper identification of the canonical momentum variables as $p_μ$, rather than $p^μ$. We discuss the meaning of the equations in relation to projective measurements as well as equations with solution curves as ones in the noncommutative geometric picture of spacetime, and a plausible approach to quantum gravity as a theory about quantum observables as physical quantities including the notion of quantum coordinate transformation. |
| title | Equivalence Principle for Quantum Mechanics in the Heisenberg Picture |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2309.03095 |