Quantum Mechanics from General Relativity and the Quantum Friedmann Equation

• URL: http://arxiv.org/abs/2411.07961v1
• Date: Tue, 12 Nov 2024 17:37:32 GMT
• Title: Quantum Mechanics from General Relativity and the Quantum Friedmann Equation
• Authors: Marco Matone, Nikolaos Dimakis,
• Abstract summary: We show that the recently introduced linear form of the Friedmann equations corresponds to the first-order WKB expansion of a quantum cosmological equation. A detailed example within the radiation-dominated context illustrates how these quantum solutions connect to Seiberg-Witten theory.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we demonstrate that the recently introduced linear form of the Friedmann equations corresponds to the first-order WKB expansion of a quantum cosmological equation, indicating that both General Relativity (GR) contains aspects of Quantum Mechanics (QM) and that GR itself is part of a more general theory. Solutions of this quantum Friedmann equation are built in terms of a quantum scale factor that encapsulates the quantum effects on a free-falling particle. The quantum-modified scale factor reshapes the dynamics of the universe, removing the singularity due to the vanishing of the scale factor. A detailed example within the radiation-dominated context illustrates how these quantum solutions connect to Seiberg-Witten theory, recently applied to black holes, and incorporate resurgence phenomena and complex metrics as developed by Kontsevich, Segal, and Witten. As a result, this reveals an invariance of time parametrization under $\Gamma(2)$ transformations of the wave function.

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