“Is Spacetime Emergent? New Paper Uses Gödel, Tarski & Chaitin to Challenge Simulation Hypothesis”

Reference: Faizal, M., Krauss, L. M., Shabir, A., & Marino, F. (2025). Consequences of Undecidability in Physics on the Theory of Everything. Journal of Holography Applications in Physics, 5(2), 10–21. doi:10.22128/jhap.2025.1024.1118

Mir Faizal, Lawrence M. Krauss, Arshid Shabir, and Francesco Marino have a new physics paper out in the Journal of Holography Applications in Physics this year. The theory posits a novel Theory of Everything scaffolding. The big idea is an extrapolation of the constraints for a possible Theory of Everything. (Repeat: This is not a Theory of Everything or a Grand Unified Theory. It is a proposal for the possible structure of a final theory, outlining potential expectations.)

A final theory should produce spacetime rather than assume it, in this theoretical scaffolding. Spacetime and quantum fields become emergent from these deeper rules and so are not fundamental to the universe. The degree to which this becomes deeper will depend on the final theory and the best-fit candidate for it.

The starting point of this new theory is to treat quantum gravity as a deeper set of rules from which quantum fields and spacetime can emerge. They make some bold starting points. John Wheeler’s “It from Bit” or pure computation is rejected outright as fundamental. This has significant implications for many theoretical constructs trying to implicate computation as foundational. It has implications that extend beyond the direct interpretation of the statement.

The authors posit that any candidate quantum-gravity theory can be cast as effectively axiomatized, an algorithmically formal system. It has a finite or at least recursively enumerable list of axioms and computable inference rules. Spacetime and quantum fields becomes a derived construct. All within the larger aforementioned system. Some points of contact are Gödel, Tarski, and Chaitin. What did they show?

Gödel proved: If any formal system is consistent and powerful enough to encode arithmetic, then factual statements exist in the intended interpretation, but cannot be proved within that system. No algorithmic system can be consistent and complete.

Tarski showed that a system cannot internally capture its own notion of truth. Truth must be handled in a “larger” language. Chaitin showed that some actual mathematical facts are beyond proof because they are too complex. These together address incompleteness, the requirements of a larger context for attaining the truth of a system, and the concept of truth in mathematics beyond proof due to complexity: incompleteness (Gödel), a larger language (Tarski), and complexity (Chaitin).

If the system is consistent and firm enough to represent arithmetic rules, then Gödel’s incompleteness, Tarski’s undefinability, and Chaitin’s results imply that algorithms cannot capture all truths. Truth requires a large scaffolding outside of algorithms.

The result of these is that an algorithmic ToE cannot capture all truths. The proposal is to add an ‘external’ truth predicate or an externalizing predicate to truth, to recognize true but unprovable facts that are missed by computable cores. These moves introduce a stacked explanatory system, ranging from non-algorithmic understanding to computable laws of quantum gravity, to an emergent spacetime and matter.

Therefore, the first step is not reducible to computation, but it does lead to computation. Science maintains its integrity while grounded in a non-algorithmic layer in this stack. Simulations are algorithmic. Therefore, a universe grounded in a non-algorithmic layer is not a simulation.

Exotic hypercomputation is unaddressed.

Scott Douglas Jacobsen is the publisher of In-Sight Publishing (ISBN: 978-1-0692343) and Editor-in-Chief of In-Sight: Interviews (ISSN: 2369-6885). He writes for The Good Men Project, International Policy Digest (ISSN: 2332–9416), The Humanist (Print: ISSN 0018-7399; Online: ISSN 2163-3576), Basic Income Earth Network (UK Registered Charity 1177066), A Further Inquiry, and other media. He is a member in good standing of numerous media organizations.