Consequences of Undecidability in Physics on the Theory of Everything
Mir Faizal 1 Lawrence M Krauss 2 Arshid Shabir 3 Francesco Marino 4
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.
https://jhap.du.ac.ir/article_488.html
I just saw this article, which on the face of it, looks highly
relevant to this group. I haven't read it, so can't comment yet.
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