Quantum collapse as undecidable proposition in an Everettian multiverse

TL;DR

The work addresses how Gödel-style undecidability and quantum measurement behave inside an Everettian multiverse to describe the Universe as a self-referential, semantically closed system. It frames the Universe with symbolic languages and a von Neumann universal constructor, and situates physical limits through the Bekenstein bound $S \leq \frac{2\pi k R E}{\hbar c \ln 2}$ and Bremermann's limit, within a Deutsch-extended Church–Turing view. Undecidable propositions arise intrinsically in the Universe's structure and require a meta-universe (Everettian metastructure) to interpret measurement outcomes; Born frequencies are interpreted as asymptotic multiverse densities rather than simple amplitudes. This work links computation, logic, and quantum cosmology, offering a framework to reason about the limits of language-driven descriptions and the need for semantically closed quantum-language formalisms to model the cosmos.

Abstract

Our representation of the Universe is built with sequences of symbols, numbers, operators, rules and undecidable propositions defining our mathematical truths, represented either by classical, quantum and probabilistic Turing Machines containing intrinsic randomness. Each representation is at all effects a physical subset of the Universe, a metastructure of events in space and time, which actively participate to the evolution of the Universe as we are internal observers. The evolution is a deterministic sequence of local events, quantum measurements, originated from the local wavefunction collapse of the complementary set of the observers that generate the local events in the Universe. With these assumptions, the Universe and its evolution are described in terms of a semantically closed structure without a global object-environment loss of decoherence as a von Neumann's universal constructor with a semantical abstract whose structure cannot be decided deterministically a-priori from an internal observer. In a semantically closed structure the realization of a specific event writing the semantical abstract of the constructor is a problem that finds a "which way" for the evolution of the Universe in terms of a choice of the constructor's state in a metastructure, the many-world Everett scenario from the specific result of a quantum measurement, a classical Gödel undecidable proposition for an internal observer, exposing the limits of our description and possible simulation of the Universe.