Physical finiteness of the universe restricts the applicability of Church-Turing and Gödel theorems.
The retrieved literature touches upon physical constraints on computation and cosmological modeling involving Turing machines and Gödel constructions, but does not fully establish that the physical finiteness of the universe restricts the applicability of both theorems.
rails:sufficiency:partial_only:for=0+2p:against=0+0p | v55:multi_partial_one_side:lean=lean_partial:for:one_sided
The Physical Church-Turing Thesis: Computation as a Fundamental Physical Process. 2025. https://doi.org/10.20944/preprints202509.0116.v1
We propose a fundamental revision of the Church-Turing thesis that recognizes computation as an inherently physical process constrained by the laws of thermodynamics, quantum mechanics, and relativity. The classical Church-Turing thesis states that any effectively calculable function can be computed by a Turing machine, but this formulation ignores the physical substrate required for computation. We establish the Physical Church-Turing Thesis: any effectively calculable function that can be physically computed must respect the fundamental constraints imposed by physical law. We develop a rigorous framework based on erasure complexity and reversible computation that leads to provable energy lower bounds for computational problems. Our analysis shows that physical computability can form a proper subset of Turing computability under explicit resource constraints, as formalized by our erasure-based framework. We provide concrete theorems connecting time-space-coherence trade-offs to unavoidable bit erasures, yielding quantitative energy bounds via Landauer's principle. The framework unifies computation theory with fundamental physics and provides practical guidance for energy-efficient algorithm design.
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Quantum Collapse and Computation in an Everett Multiverse - PMC. https://pmc.ncbi.nlm.nih.gov/articles/PMC11675084/
ecessary environment for the evolution of the pure state that represents the object universe when described in terms of classical (or pseudo-classical) formal propositions with the possibility of building a Gödel symbolic construction (or a Turing Machine) to describe the evolution of the universe and the interaction between subsets up to the interaction with “classical” (or pseudo-classical) observers, which leads to the problem of a quantum measurement to be related to an undecidable proposition inside the linguistic representation of the universe itself. The implication is to have as mandatory the existence of a metastructure as a “linguistic” meta-universe. Being that this representation of the meta-universe is a class of universes in the evolution of our universe and at the same time built with physical events in the universe, the class should be a subset of the universe by definition or coincide with the universe, recalling Russell’s paradox. The mandatory requirement of the existence of a universe of universes shows that our classical language is inadequate for describing the state universe as a whole self-object unless we employ a self-bootstrapped structure, in which the laws of physics self-sustain one another through their mutual consistency [ 81 ]. 3. Conclusions In our formal language, the universe can be described in different ways. Each single bit of information is the result of a physical process inside the universe. An example is an end game modeling a self-referential system with a semantically closed structure containing intrinsic randomness, as any of its representations is a subset where there is not a global object-environment loss of decoherence but interactions with its subsets, indicating that its evolution, including the mathematical truths, undecidable propositions and quantum measurement problem, are metastructures inside the universe built with interactions between subsets. Our formal language is based on mathematical truths and any form
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