Consequences of Undecidability in Physics on the Theory of Everything

[Russell Standish]

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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Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders hpc...@hpcoders.com.au
http://www.hpcoders.com.au
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[Giulio Prisco]

On Fri, Oct 31, 2025 at 6:47 AM Russell Standish <li...@hpcoders.com.au> wrote:
>
>
> 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.
>

Interesting. Here's a press release:
https://news.ok.ubc.ca/2025/10/30/ubco-study-debunks-the-idea-that-the-universe-is-a-computer-simulation/

I agree that the whole of reality is computationally undecidable but I
don't think this "proves" that the universe cannot be a simulation,
the question is not even well posed.

> --
>
> ----------------------------------------------------------------------------
> Dr Russell Standish Phone 0425 253119 (mobile)
> Principal, High Performance Coders hpc...@hpcoders.com.au
> http://www.hpcoders.com.au
> ----------------------------------------------------------------------------
>

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[Brent Meeker]

So maybe we should conclude that it's not infinite or it's not algorithmic because it includes true randomness.  Either or both seem entirely plausible.

Brent

[Russell Standish]

On Fri, Oct 31, 2025 at 02:06:44PM -0700, Brent Meeker wrote:
> So maybe we should conclude that it's not infinite or it's not algorithmic
> because it includes true randomness.  Either or both seem entirely plausible.
>

But then there is Bruno Marchal's point that first person
indeterminism as seen inside a universal dovetailer shows that an
algorithm can generate true randomness, as seen by conscious entities
generated by the algorithm.

[Brent Meeker]

On 10/31/2025 2:40 PM, Russell Standish wrote:

On Fri, Oct 31, 2025 at 02:06:44PM -0700, Brent Meeker wrote:

So maybe we should conclude that it's not infinite or it's not algorithmic
because it includes true randomness.  Either or both seem entirely plausible.

But then there is Bruno Marchal's point that first person
indeterminism as seen inside a universal dovetailer shows that an
algorithm can generate true randomness, as seen by conscious entities
generated by the algorithm.

So the proof of Goedel's theorem would not fail in the presence of "as seen by" randomness that was actually algorithmic.  But it would always seem to be false, i.e. it would empirically be false (which is the only kind of false that matters).

Brent