Quantum Mechanics from General Relativity and the Quantum Friedmann Equation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918180875665408 |
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| author | Matone, Marco Dimakis, Nikolaos |
| author_facet | Matone, Marco Dimakis, Nikolaos |
| contents | We demonstrate that the recently introduced linear equation, reformulating the first Friedmann equation, is the first-order WKB expansion of a quantum cosmological equation. This result shows a deeper underlying connection between General Relativity and Quantum Mechanics, pointing towards a unified framework. Solutions of this equation are built in terms of a scale factor encapsulating quantum effects on a free-falling particle. The quantum scale factor reshapes cosmic dynamics, resolving singularities at its vanishing points in several cases of interest. As an explicit example, we consider the radiation-dominated era and show that the quantum equation is dual to the one in Seiberg-Witten formulation, recently applied to black holes, and incorporates resurgence phenomena and complex metrics, as developed by Kontsevich, Segal, and Witten. This links to the invariance of time parametrization under $Γ(2)$ transformations of the dual wave function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_07961 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Mechanics from General Relativity and the Quantum Friedmann Equation Matone, Marco Dimakis, Nikolaos High Energy Physics - Theory General Relativity and Quantum Cosmology Quantum Physics We demonstrate that the recently introduced linear equation, reformulating the first Friedmann equation, is the first-order WKB expansion of a quantum cosmological equation. This result shows a deeper underlying connection between General Relativity and Quantum Mechanics, pointing towards a unified framework. Solutions of this equation are built in terms of a scale factor encapsulating quantum effects on a free-falling particle. The quantum scale factor reshapes cosmic dynamics, resolving singularities at its vanishing points in several cases of interest. As an explicit example, we consider the radiation-dominated era and show that the quantum equation is dual to the one in Seiberg-Witten formulation, recently applied to black holes, and incorporates resurgence phenomena and complex metrics, as developed by Kontsevich, Segal, and Witten. This links to the invariance of time parametrization under $Γ(2)$ transformations of the dual wave function. |
| title | Quantum Mechanics from General Relativity and the Quantum Friedmann Equation |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Quantum Physics |
| url | https://arxiv.org/abs/2411.07961 |