On Monday, March 9, 2020 at 6:42:41 AM UTC-5, Bruno Marchal wrote: > > > On 6 Mar 2020, at 12:40, Lawrence Crowell <[email protected] > <javascript:>> 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. > > > The Digital Mechanist thesis enforces that physics is derivable from > Gödel’s and Löbs’ theorem, and indeed we find quantum logic exactly were > expected. > > All computations are executed/emulated, in the mathematical sense of the > Logicians, in arithmetic. The physical appearances have to be justified by > the calculus of the 1p (plural) indeterminacy in arithmetic. > > There is a natural, canonical “many-wold” interpretation of arithmetic, > developed by the “majority of universal numbers in arithmetic. > > > I will have to write more if possible. I am not sure that all of physics is derived from Gödel’s theorem. I see is as more that from classical to quantum mechanics there is a sort of forcing, to borrow from set theory, to extend a model with undecidable propositions. Where this undecidable matter enters in is with the problem of measurement and decoherence.
As for an earlier comment, Turing's model is in a grey zone between mathematics often seen as pure and with physics. The tape and reader, appearing a bit like a sort of cart on a track, is a model of a physical system. That system is a computer. LC > > > 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. > > > Sure. > > > Bruno > > > > > 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] <javascript:>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/0d684c57-3761-4867-8baf-5f2807d2af9f%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/0d684c57-3761-4867-8baf-5f2807d2af9f%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > > -- 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/ab75db4c-a76b-4af5-afea-5c2416b8ccd0%40googlegroups.com.
