Einstein, Podolsky and Rosen (1935) suggested hidden variables unexplained by standard quantum mechanics, and postulated local interaction only. In 1964 Bell introduced an inequality whose violation was thought to provide evidence against _local_ hidden variable theories. Violation tests are inconclusive as yet - see chain of papers starting maybe with Aspect et al, PRL 49, p. 91 and 1804, 1982; and Franson's counter argument: PR D, p 2529, 1985, and numerous more recent papers. Many physicists now believe in nonlocality, but the issue is not settled yet.
Is Bell's inequality relevant to algorithmic TOEs? It is about locality assumptions - but ATOEs do not even insist on locality. There are computable universes whose light speed exceeds ours, or where there is no light at all, where there is global interaction among distant particles, or where there are no particles as we know them, etc. The point of ATOEs is: as long as the computability assumptions hold, any complex universe is unlikely, no matter whether Bell's inequality makes sense in it or not. >From this point of view Bell's inequality and locality are not the real issues. The issue is more general. It is determinism vs nondeterminism. There is NO experimental data proving the universe is truly nondeterministic. If it were, where would the unexplained randomness come from? As pointed out by Saibal Mitra, non-crackpots such as 't Hooft (physics Nobel 1999) endorse hidden variable theory and determinism, e.g.: http://xxx.lanl.gov/abs/hep-th/0105105 http://xxx.lanl.gov/abs/hep-th/0104219 Sure, there is a lot of data that at first glance suggests probabilistic aspects of particle behavior, but many pseudorandom generators produce data that match Gaussian or other well-known distributions. I think nobody has ever bothered to systematically check existing data for pseudorandomness. (Note that decorrelation does not imply independence.) Suppose the history of some universe is indeed generated by a deterministic computer program. In principle this would make everything predictable for anybody who knows the program. This does not at all imply, however, that an observer evolving within the universe could predict exactly what is happening light years away, for several reasons: 1. He may never get full access to the current hidden variables, i.e., the current state of the program, because of: 1a. some sort of prewired uncertainty principle that holds for local observers (but not for outsiders such as the Great Programmer). 1b. a maximal universe-specific speed that prevents the observer from collecting precise information about distant parts of his universe. 2. Even if the observer had full access to the state, to make predictions he would need a predictor built within his universe. In general, this machine will run much slower than the universe itself, unable to predict it in time. (But perhaps able to postdict parts of it.) To illustrate 2: there are pseudorandom generators that run extremely slowly but produce extremely convincing results such as the enumerable but effectively random number Omega. The speed prior, however, suggests our universe's pseudorandom generator is much faster than the Omega generator. Juergen http://www.idsia.ch/~juergen/ http://www.idsia.ch/~juergen/everything/html.html http://www.idsia.ch/~juergen/toesv2/