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arXiv:2301.04180 · International Journal of Theoretical Physics

A Holographic Principle for Non-Relativistic Quantum Mechanics

Russell B. Thompson

Published Feb 4, 2023• 5 citations
arXivHTMLPDF
DOI
10.1007/s10773-022-05274-9

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In quantum mechanics without application of any superselection rule to the set of the observables, a closed quantum system temporally evolves unitarily, and this Lorentzian regime is characterized by von Neumann entropy of exactly zero. In the holographic theory in the classicalized ground state, we argue that the unitary real-time evolution of a non-relativistic free particle with complex-valued quantum probability amplitude in this Lorentzian regime can be temporally analytically continued to an imaginary-time classical stochastic process with real-valued conditional probability density in the Euclidean regime, where the von Neumann entropy of the classicalized hologram and the information of a particle trajectory acquired by the classicalized hologram are positive valued. This argument could shed light on the Euclidean regime of the holographic Universe.
This paper introduces the Geometric Resource Limit Interpretation (GRLI) of quantum mechanics, proposing that wavefunction collapse is an objective, deterministic event triggered when a system's informational complexity exceeds the local holographic capacity of spacetime. By grounding the collapse mechanism in the Bekenstein Bound and Susskind’s holographic complexity framework, GRLI eliminates the coordinate paradoxes of non-relativistic collapse models and achieves Einsteinian covariance. The author outlines three distinct, falsifiable experimental proposals in photonic interferometry and quantum computing to test for non-thermal, complexity-linked dephasing artifacts.