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arXiv · 2411.07961

Quantum Mechanics from General Relativity and the Quantum Friedmann Equation

Marco Matone·Nikolaos Dimakis
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Abstract

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.

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Marco Matone, Nikolaos Dimakis. 2025-11-01. Quantum Mechanics from General Relativity and the Quantum Friedmann Equation. https://doi.org/10.1140/epjc%2Fs10052-025-14930-3

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