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Consequences of Undecidability in Physics on the Theory of Everything

Document Type : Letter

Authors

¹ Irving K. Barber School of Arts and Sciences, University of British Columbia Okanagan, Kelowna, BC V1V 1V7, Canada; Canadian Quantum Research Center, 204-3002 32 Ave, Vernon, BC V1T 2L7, Canada; Department of Mathematical Sciences, Durham University, Upper Mountjoy, Stockton Road, Durham DH1 3LE, UK; Faculty of Sciences, Hasselt University, Agoralaan Gebouw D, Diepenbeek, 3590 Belgium.

² Origin Project Foundation, Phoenix, AZ 85018, USA.

³ Canadian Quantum Research Center, 204-3002 32 Ave, Vernon, BC V1T 2L7, Canada.

⁴ CNR-Istituto Nazionale di Ottica and INFN, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy.

Abstract

General relativity treats spacetime as dynamical and exhibits its breakdown at singularities‎. ‎This failure is interpreted as evidence that quantum gravity is not a theory formulated {within} spacetime; instead‎, ‎it must explain the very {emergence} of spacetime from deeper quantum degrees of freedom‎, ‎thereby resolving singularities‎. ‎Quantum gravity is therefore envisaged as an axiomatic structure‎, ‎and algorithmic calculations acting on these axioms are expected to generate spacetime‎. ‎However‎, ‎Gödel’s incompleteness theorems‎, ‎Tarski’s undefinability theorem‎, ‎and Chaitin’s information-theoretic incompleteness establish intrinsic limits on any such algorithmic program‎. ‎Together‎, ‎these results imply that a wholly algorithmic “Theory of Everything’’ is impossible‎: ‎certain facets of reality will remain computationally undecidable and can be accessed only through non-algorithmic understanding‎. ‎We formalize this by constructing a “Meta-Theory of Everything’’ grounded in non-algorithmic understanding‎, ‎showing how it can account for undecidable phenomena and demonstrating that the breakdown of computational descriptions of nature does not entail a breakdown of science‎. ‎Because any putative simulation of the universe would itself be algorithmic‎, ‎this framework also implies that the universe cannot be a simulation‎.

Keywords

Main Subjects

Physics

References

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