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How to cite:
Harvey-Tremblay, A. Fundamental Physics as the General Solution to a Maximization Problem on the Shannon Entropy of All Measurements. Preprints2024, 2024041009. https://doi.org/10.20944/preprints202404.1009.v2
Harvey-Tremblay, A. Fundamental Physics as the General Solution to a Maximization Problem on the Shannon Entropy of All Measurements. Preprints 2024, 2024041009. https://doi.org/10.20944/preprints202404.1009.v2
Harvey-Tremblay, A. Fundamental Physics as the General Solution to a Maximization Problem on the Shannon Entropy of All Measurements. Preprints2024, 2024041009. https://doi.org/10.20944/preprints202404.1009.v2
APA Style
Harvey-Tremblay, A. (2024). Fundamental Physics as the General Solution to a Maximization Problem on the Shannon Entropy of All Measurements. Preprints. https://doi.org/10.20944/preprints202404.1009.v2
Chicago/Turabian Style
Harvey-Tremblay, A. 2024 "Fundamental Physics as the General Solution to a Maximization Problem on the Shannon Entropy of All Measurements" Preprints. https://doi.org/10.20944/preprints202404.1009.v2
Abstract
We present a novel approach to quantum theory construction that involves maximizing the Shannon entropy of quantum measurements relative to their initial preparation. By constraining the maximization problem with a phase that vanish under measurements, we obtain quantum mechanics (vanishing U(1)-valued phase), relativistic quantum mechanics (vanishing Spin^c(3,1)-valued phase), and quantum gravity (vanishing ${\rm SL(4,\mathbb{R})}$-valued phase). The first two cases are equivalent to established theory, whereas the later case yields a quantum theory of accelerated reference frames, in which a quantized version of the Einstein field equation lives. Specifically, the spacetime interval is promoted to an observable, effectively building the metric tensor from the underlying quantum structure. Subsequently, the Schrödinger equation generates metric tensor diffeomorphisms and SO(3,1) transformations. Remarkably, the quantized Einstein Field Equations are provably non-perturbatively finite. Moreover, the SU(3)xSU(2)xU(1) gauge symmetries of the Standard Model arise naturally without additional assumptions. Finally, the solution is consistent only with 3+1 spacetime dimensions, as it encounters obstructions in all other dimensional configurations. This framework integrates quantum mechanics, relativistic quantum mechanics, quantum gravity, spacetime dimensionality, and particle physics gauge symmetries from a simple entropy maximization problem constrained by a vanishing phase, yielding the most parsimonious formulation of fundamental physics to date.
Keywords
foundations of quantum physics
Subject
Physical Sciences, Quantum Science and Technology
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
