Towards a Deterministic Interpretation of Quantum Mechanics: Insights from Dynamical Systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916231797276672 |
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| author | Rahman, Aminur |
| author_facet | Rahman, Aminur |
| contents | Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical dependence, however it necessitates the existence of "ghost waves". This manuscript develops a deterministic dynamical system with local interactions. The aggregate behavior of the trajectories are reminiscent of a quantum particle evolving under the Schrödinger equation and reminiscent of Feynman's path integral interpretation in three canonical examples: motion in free space, double slit diffraction, and superluminal barrier traversal. Moreover, the system bifurcates into various dynamical regimes including a classical limit. These results illustrate a deterministic alternative to probabilistic interpretations and aims to shed light on the transition from quantum to classical mechanics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_00707 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards a Deterministic Interpretation of Quantum Mechanics: Insights from Dynamical Systems Rahman, Aminur Quantum Physics Dynamical Systems Classical Physics 81Q50, 70Kxx Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical dependence, however it necessitates the existence of "ghost waves". This manuscript develops a deterministic dynamical system with local interactions. The aggregate behavior of the trajectories are reminiscent of a quantum particle evolving under the Schrödinger equation and reminiscent of Feynman's path integral interpretation in three canonical examples: motion in free space, double slit diffraction, and superluminal barrier traversal. Moreover, the system bifurcates into various dynamical regimes including a classical limit. These results illustrate a deterministic alternative to probabilistic interpretations and aims to shed light on the transition from quantum to classical mechanics. |
| title | Towards a Deterministic Interpretation of Quantum Mechanics: Insights from Dynamical Systems |
| topic | Quantum Physics Dynamical Systems Classical Physics 81Q50, 70Kxx |
| url | https://arxiv.org/abs/2405.00707 |