- #1
- 20,750
- 28,173
- TL;DR
- The authors invoke Gödel and Tarski and investigate the algorithmic nature of the universe. A philosophical play with words far from reality, or a serious contribution to the possibility of a holographic universe?
I came across the following paper by Mir Faizal, Lawrence M Krauss, Arshid Shabir, and Francesco Marino from BC.
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.
Source: https://jhap.du.ac.ir/article_488.html
Comment: Judging the seriousness of this paper is beyond my capabilities. My first thought, therefore, was a philosophical one: how can the simulation know that it is no simulation? It appeared to me that the authors tripped over their own self-reference with Gödel and Tarski.
Consequences of Undecidability in Physics on the Theory of Everything
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.
Source: https://jhap.du.ac.ir/article_488.html
Comment: Judging the seriousness of this paper is beyond my capabilities. My first thought, therefore, was a philosophical one: how can the simulation know that it is no simulation? It appeared to me that the authors tripped over their own self-reference with Gödel and Tarski.
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