Can quantum gravity be both consistent and complete?

Year: 2025

Authors: Faizal M., Krauss L.M., Shabir A., Marino F., Pourhassan B.

Autors Affiliation: Univ British Columbia Okanagan, Irving K Barber Sch Arts & Sci, Kelowna, BC V1V 1V7, Canada; Canadian Quantum Res Ctr, 204-3002 32 Ave, Vernon, BC V1T 2L7, Canada; Univ Durham, Dept Math Sci, Stockton Rd, Durham DH1 3LE, England; Hasselt Univ, Fac Sci, Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium; Origin Life Fdn, Phoenix, AZ 85018 USA; CNR, Ist Nazl Ott, Via Sansone 1, I-50019 Sesto Fiorentino, FI, Italy; INFN, Via Sansone 1, I-50019 Sesto Fiorentino, FI, Italy; Damghan Univ, Sch Phys, Damghan 3671645667, Iran; Khazar Univ, Ctr Theoret Phys, 41 Mehseti St, AZ-1096 Baku, Azerbaijan.

Abstract: General relativity, despite its profound successes, fails as a complete theory due to presence of singularities. While it is widely believed that quantum gravity has the potential to be a complete theory, in which spacetime consistently emerges from quantum degrees of freedom through computational algorithms, we argue that this goal could be fundamentally unattainable. We examine how this limitation could emerge in various contexts, depending on whether or not every mathematically valid result is physically realized. In the first case, G & ouml;del’s incompleteness theorems, along with related results by Tarski and Chaitin, imply that no theory formulated as a formal axiomatic system can be complete, and that within any computational framework, a fully consistent internal truth predicate is impossible. In the second case, if only a subset of mathematical truths is realized in nature, we argue that this selection cannot be determined by any purely computational process. Hence, a meta-theoretical approach based on nonalgorithmic understanding is indispensable in every case. We discuss some possible consequences of this observation for describing physical systems and note that a nonalgorithmic approach should be essential for any theory of everything.

Journal/Review: INTERNATIONAL JOURNAL OF MODERN PHYSICS D

More Information: This essay received an Honorable Mention in the 2025 Essay Competition of the Gravity Research Foundation.
KeyWords: Quantum gravity; G & ouml;del´s incompleteness theorems; undecidability
DOI: 10.1142/S0218271825440171