A dynamic programming interpretation of quantum mechanics
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913189099208704 |
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| author | Brownstein, Adam |
| author_facet | Brownstein, Adam |
| contents | We introduce a transformation of the quantum phase $S'=S+\frac{\hbar}{2}\logρ$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of stochastic particles. We show that the quantum potential can be removed from the transformed quantum Hamilton-Jacobi equations if they are solved as stochastic Hamilton-Jacobi-Bellman equations. The system of equations provide a local description of quantum mechanics, which is enabled by the inherently retrocausal nature of stochastic Hamilton-Jacobi-Bellman equations. We also investigate the stochastic transformation of the classical system, where is it shown that quantum mechanics with the quantum potential reduced by a factor of $\frac{1}{2}$ has a classical representation, which may have interesting implications. Finally, we discuss the notion of a subsystem correspondence principle, which constrains the ontology of the total quantum system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A dynamic programming interpretation of quantum mechanics Brownstein, Adam Quantum Physics History and Philosophy of Physics We introduce a transformation of the quantum phase $S'=S+\frac{\hbar}{2}\logρ$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of stochastic particles. We show that the quantum potential can be removed from the transformed quantum Hamilton-Jacobi equations if they are solved as stochastic Hamilton-Jacobi-Bellman equations. The system of equations provide a local description of quantum mechanics, which is enabled by the inherently retrocausal nature of stochastic Hamilton-Jacobi-Bellman equations. We also investigate the stochastic transformation of the classical system, where is it shown that quantum mechanics with the quantum potential reduced by a factor of $\frac{1}{2}$ has a classical representation, which may have interesting implications. Finally, we discuss the notion of a subsystem correspondence principle, which constrains the ontology of the total quantum system. |
| title | A dynamic programming interpretation of quantum mechanics |
| topic | Quantum Physics History and Philosophy of Physics |
| url | https://arxiv.org/abs/2401.04085 |