Journal of Holography Applications in Physics
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.
10.22128/jhap.2025.1024.1118
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
- Non-Algorithmic Understanding
- Quantum Gravity
- It from Bit
- Gödel’s incompleteness theorems
- Tarski’s undefinability theorem
- Chaitin’s information-theoretic incompleteness
Main Subjects
Article PDF
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Volume 5, Issue 2
June 2025Pages 10-21
- Receive Date: 06 June 2025
- Revise Date: 18 June 2025
- Accept Date: 17 June 2025