While programming/computing in (hypothetical) infinite domains is interesting ...
*Computing in Cantor’s Paradise With λ_ZFC* https://jeapostrophe.github.io/home/static/toronto-2012flops.pdf how any of this relates *in any way* to physical reality (the *stuff of nature *that is *actually around us* in the universe, vs. just some theoretical, mathematical concoction someone may come up with) is dubious. (Things like consciousness is another thing, or subject: It may be "beyond" Turing, bit in a way that has nothing to do with "super" or "hyper" Turing or Cantor or Godel.) @philipthrift On Friday, March 6, 2020 at 5:40:08 AM UTC-6, Lawrence Crowell wrote: > > 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/5dbd538d-bdcd-4935-b22d-ac3f1d94662d%40googlegroups.com.
