Path: cactus.org!milano!cs.utexas.edu!sdd.hp.com!wupost!hsdndev!adm!smoke!gwyn From: email@example.com (Doug Gwyn) Newsgroups: sci.crypt Subject: Re: Are there truly random phenomena? Message-ID: <firstname.lastname@example.org> Date: 6 Aug 91 03:31:58 GMT References: <email@example.com> <firstname.lastname@example.org> <148@mtnmath.UUCP> Organization: U.S. Army Ballistic Research Laboratory, APG, MD. Lines: 29 In article <148@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes: -In article <email@example.com>, firstname.lastname@example.org (Steven Bellovin) write s: -> Here's a hint, though: virtually all modern physicists think you're -> wrong. And it's not because no one argued the point. -Physicists have a pretty bad record on this point. In the 1930s von Neuman -published a famous proof that claimed no more complete model could produce -predictions consistent with quantum mechanics. This was widely accepted -until the mid 60's when Bell published a refutation. There is no basis -for the widely accepted belief that randomness is fundamental to quantum -mechanics. As a theoretical physicist (who happens to follow Einstein in this and thus is not overly sympathetic to the consensus view), I feel obliged to point out that Budnick's arguments misrepresent the situation and indeed to the contrary, Bell's work, plus recent experimental results, have firmly established that the known phenomena of quantum physics are incompatible with local determinism. I.e., the "probability amplitudes" that embody fundamental quantum properties are NOT simply "probability" in the classical sense of uncertainty reflecting incomplete information. -If you think about this as a problem in the theory of recursive functions -you can see how difficult it would be to come up with a theoretical argument -or experimental results that prove this. You are asking is there a recursively -enumerable set that includes all the predictions of quantum mechanics (a -recursively enumerable set) and all the observed results of experiments -(a finite set). Since the union of a finite and recursively enumerable set -is a recursively enumerable set the answer is yes. Recursive function theory has nothing to do with physics.