Szangolies [ J. Szangolies, "Epistemic Horizons and the Foundations of Quantum Mechanics," https://arxiv.org/abs/1805.10668 ] works a form of the Cantor diagonalization for quantum measurements. As yet a full up form of the CHSH or Bell inequality violation result is waiting. There are exciting possibilities for connections between quantum mechanics, in particular the subject of quantum decoherence and measurement, and Gödel’s theorem.
If we think of all physics as a form of convex sets of states, then there are dualisms of measures p and q that obey 1/p + 1/q = 1. For quantum mechanics this is p = ½ as an L^2 measure theory. It then has a corresponding q = ½ measure system that I think is spacetime physics. A straight probability system has p = 1, sum of probabilities as unity, and the corresponding q → ∞ has no measure or distribution system. This is any deterministic system, think completely localized, that can be a Turing machine, Conway's <i>Game of life</i> or classical mechanics. A quantum measurement is a transition between p = ½ for QM and ∞ for classicality or 1 for classical probability on a fundamental level. What separates these different convex sets are these topological obstructions, such as the indices given by the Kirwan polytope. The distinction between entanglements is also given by these topological indices or obstructions. How these determine a measurement outcome, or the ontology of an element of a decoherent sets is not decidable. This is where Gödel’s theorem enters in. A quantum measurement is a way that quantum information or qubits encode other qubits as Gödel numbers. The prospect spacetime, or the entropy of spacetime via event horizon areas, is a condensate or large N-entanglement of quantum states then implies there is a connection between quantum computation and information accessible in spacetime configurations. These configurations may either be the Bekenstein bound S = kA/4ℓ_p^2, or quantum modified version S = kA/4ℓ_p^2 + quantum corrections. Then the quantum processing or quantum Church-Turing thesis is I think equivalent to the information processing of spacetime as black holes and maybe entire cosmologies. These are exciting developments. LC -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/0d684c57-3761-4867-8baf-5f2807d2af9f%40googlegroups.com.
