On Saturday, June 6, 2020 at 5:25:23 PM UTC-5, Philip Thrift wrote: > > > As for Hossenfelder's fav quantum mechanics semantics, she has stated many > times on her blog, it's superdeterminism. > > > https://arxiv.org/abs/1912.06462 > > > "A superdeterministic theory is one which violates the assumption of > Statistical Independence (that distributions of hidden variables are > independent of measurement settings). Intuition suggests that Statistical > Independence is an essential ingredient of any theory of science (never > mind physics), and for this reason Superdeterminism is typically discarded > swiftly in any discussion of quantum foundations. The purpose of this paper > is to explain why the existing objections to Superdeterminism are based on > experience with classical physics and linear systems, but that this > experience misleads us. Superdeterminism is a promising approach not only > to solve the measurement problem, but also to understand the apparent > nonlocality of quantum physics. Most importantly, we will discuss how it > may be possible to test this hypothesis in an (almost) model independent > way." > > @philipthrift >
Superdeterminism is just a form of hidden variable theory. This invariant set theory of Palmer and Hossenfelder as a means of connecting nonlinearity with QM is interesting. The approach with Cantor sets connects with incomputability. I prefer a more standard definition of incomputability than what P&H appeal to. This works invariant set theory does imply a violation of statistical independence, but it does so as a hidden variable. The complement of a fractal set is undecidable. A fractal set is recursively enumerable, which means we can compute it in a finite automata up to some point, and “in principle” a Turing machine that runs eternally could compute the whole thing. The complement of this is not computable. The complement of a recursive set is recursive, but the complement of a recursively enumerable set is not recursively enumerable and is incomputable. The invariant set in this superdeterminism is a form of Cantor set or related to a fractal. The results of Matiyasevich showed that p-adic sets have no global solution method, where p-adic sets are equivalent to Diophantine equations. This means that dynamical maps from one point to another on the Cantor set are not given by the same quotient group and in general there is no single decidable system for such maps. In effect this means it is not observable. So, while superdeterminism violates statistical independence this is all a nonlocal hidden variable and thus unobservable. In ways this is where I depart from Hossenfelder and Palmer, where Palmer uses a different concept of incomputability, based on the idea of Smale et al on the need to compute a fractal an infinite amount. I appeal to the complement of a fractal, a fractal being a recursively enumerable set and computable in a standard sense, but where the complement is not computable. The fractal emerges from QM in a singular perturbation series and the complement comes with the dual of a convex set with measure L^p is L^q with 1/p + 1/q = 1. 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/affd7fd8-26f9-4cca-983c-aa038a542739o%40googlegroups.com.
