On Monday, March 9, 2020 at 7:52:00 PM UTC-5, Lawrence Crowell wrote: > > > 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. > > > There is nothing in any quantum mechanics theory that goes beyond a formulation in terms of a quantum Turing machine.
https://en.wikipedia.org/wiki/Quantum_Turing_machine Quantum Turing machines can be related to classical and probabilistic Turing machines in a framework based on transition matrices <https://en.wikipedia.org/wiki/Stochastic_matrix>. That is, a matrix can be specified whose product with the matrix representing a classical or probabilistic machine provides the quantum probability matrix representing the quantum machine. This was shown by Lance Fortnow <https://en.wikipedia.org/wiki/Lance_Fortnow>. [ https://arxiv.org/abs/quant-ph/0003035 ] Actually it can all be reduced to the SKIP calculus. *SKIP: Probabilistic SKI combinator calculus* <https://poesophicalbits.blogspot.com/2013/06/skip-probabilistic-ski-combinator.html> Add to the *S*, *K*, and *I* combinators of the SKI combinator calculus <http://en.wikipedia.org/wiki/SKI_combinator_calculus> the *P* combinator: *S**xyz* = *xz*(*yz*) *K**xy* = *x* *I**x* = *x* *P* = *K* or *KI* with equal probability (0.5) It follows that *P**xy* evaluates to *K**xy* or *KI**xy*, then to *x* or *I* *y* = *y* with equal probability. There is nothing "uncomputable" in any of this. @philipthrift -- 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/ccadde6f-d7be-4add-a6df-b8df60aa7252%40googlegroups.com.
