> On 10 Mar 2020, at 01:52, Lawrence Crowell <goldenfieldquaterni...@gmail.com> > wrote: > > On Monday, March 9, 2020 at 6:42:41 AM UTC-5, Bruno Marchal wrote: > >> On 6 Mar 2020, at 12:40, Lawrence Crowell <goldenfield...@gmail.com >> <javascript:>> wrote: >> >> Szangolies [ J. Szangolies, "Epistemic Horizons and the Foundations of >> Quantum Mechanics," https://arxiv.org/abs/1805.10668 >> <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.
That might not be the case, but it has to be so when we assume the digital mechanist hypothesis? Of course it is not a direct derivation from Gödel, but from all nuances that incompleteness impose to the provability notion. Incompleteness gives sense to the Theatetus-like variant of the rational opinion/belief, namely: TRUTH (p, God, the One, …) BELIEF ([]p, provability, Incompleteness forbids to see this as a knowledge) KNOWLEDGE ([]p & p, true belief, the soul, the first person, the owner of consciousness) And the “two matters”: INTELLIGIBLE MATTER ([]p & <>t) (with p restricted to sigma_1 propositions, the partial computable one) SENSIBLE MATTER ([]p & <>t & p) (idem) The soul provides an intuitionist logic, the two matters and the soul provides quantum logics when p is restricted on the partial computable (sigma_1) propositions (the true and the false one, which makes things more complex). See may papers for more on this. This needs some understanding of the existence of all computations in the models of arithmetic). > 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. With mechanism, physics must become a study of the relative computational histories statistics. > > 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. A computer is universal implemented in the physical reality, but with mechanism, the physical reality is what emerge statistically from the first person points of view of the computer executed in the arithmetical reality (or in any reality related to any universal machine). I use numbers only because most people are familiar with them. I sum up 40 years of work, in a taboo domain, and all this is build on not so well known, or understood, theorem in mathematical logic, so ask any question, and maybe read also the papers. The first thing to understand is the incompatibility between (very weak form of) Digital Mechanism and (very weak form of ) Materialism or Physicalism. Bruno > > 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 everyth...@googlegroups.com <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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/ab75db4c-a76b-4af5-afea-5c2416b8ccd0%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/ab75db4c-a76b-4af5-afea-5c2416b8ccd0%40googlegroups.com?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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