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Can quantum gravity be both consistent and complete?

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Title: Can quantum gravity be both consistent and complete?
Authors: Faizal, Mir1,2,3,4 (AUTHOR) mirfaizalmir@gmail.com, Krauss, Lawrence M.5 (AUTHOR) lawrence@originsproject.org, Shabir, Arshid2 (AUTHOR) aslone186@gmail.com, Marino, Francesco6 (AUTHOR) francesco.marino@ino.cnr.it, Pourhassan, Behnam7,8 (AUTHOR) b.pourhassan@du.ac.ir
Source: International Journal of Modern Physics D: Gravitation, Astrophysics & Cosmology. Dec2025, Vol. 34 Issue 16, p1-16. 16p.
Subjects: Quantum gravity, Incompleteness theorems, Perspective (Philosophy), General relativity (Physics), Unified field theories, Algorithms, Mathematical singularities, Contextualism (Philosophy)
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, Gödel'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. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Modern Physics D: Gravitation, Astrophysics & Cosmology is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="AR" term="%22Faizal%2C+Mir%22">Faizal, Mir</searchLink><relatesTo>1,2,3,4</relatesTo> (AUTHOR)<i> mirfaizalmir@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Krauss%2C+Lawrence+M%2E%22">Krauss, Lawrence M.</searchLink><relatesTo>5</relatesTo> (AUTHOR)<i> lawrence@originsproject.org</i><br /><searchLink fieldCode="AR" term="%22Shabir%2C+Arshid%22">Shabir, Arshid</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> aslone186@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Marino%2C+Francesco%22">Marino, Francesco</searchLink><relatesTo>6</relatesTo> (AUTHOR)<i> francesco.marino@ino.cnr.it</i><br /><searchLink fieldCode="AR" term="%22Pourhassan%2C+Behnam%22">Pourhassan, Behnam</searchLink><relatesTo>7,8</relatesTo> (AUTHOR)<i> b.pourhassan@du.ac.ir</i>
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  Data: <searchLink fieldCode="DE" term="%22Quantum+gravity%22">Quantum gravity</searchLink><br /><searchLink fieldCode="DE" term="%22Incompleteness+theorems%22">Incompleteness theorems</searchLink><br /><searchLink fieldCode="DE" term="%22Perspective+%28Philosophy%29%22">Perspective (Philosophy)</searchLink><br /><searchLink fieldCode="DE" term="%22General+relativity+%28Physics%29%22">General relativity (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Unified+field+theories%22">Unified field theories</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+singularities%22">Mathematical singularities</searchLink><br /><searchLink fieldCode="DE" term="%22Contextualism+%28Philosophy%29%22">Contextualism (Philosophy)</searchLink>
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  Data: 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, Gödel'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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of International Journal of Modern Physics D: Gravitation, Astrophysics & Cosmology is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1142/S0218271825440171
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      – Code: eng
        Text: English
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        PageCount: 16
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      – SubjectFull: Quantum gravity
        Type: general
      – SubjectFull: Incompleteness theorems
        Type: general
      – SubjectFull: Perspective (Philosophy)
        Type: general
      – SubjectFull: General relativity (Physics)
        Type: general
      – SubjectFull: Unified field theories
        Type: general
      – SubjectFull: Algorithms
        Type: general
      – SubjectFull: Mathematical singularities
        Type: general
      – SubjectFull: Contextualism (Philosophy)
        Type: general
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      – TitleFull: Can quantum gravity be both consistent and complete?
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            NameFull: Faizal, Mir
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            NameFull: Krauss, Lawrence M.
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              M: 12
              Text: Dec2025
              Type: published
              Y: 2025
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