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From: aboulang@bbn.com (Albert Boulanger)
Newsgroups: comp.ai,sci.physics
Subject: Re: Quasicrystals and hidden variables (Chaos and AI)
Message-ID: <54872@bbn.COM>
Date: 13 Apr 90 23:38:19 GMT
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In-reply-to: kp@uts.amdahl.com's message of 13 Apr 90 18:53:18 GMT

In article <965p02gf9cNw01@amdahl.uts.amdahl.com> kp@uts.amdahl.com (Ken Presting) writes:


   Penrose does cite David Deutch, "Quantum thoery, the Church-Turing
   pinciple, and the universal quantum computer", Proc. Roy. Soc. (1985)
   A400, 97-117.  Apparently, a quantum device can exhibit some of the
   *speed* properties of a non-deterministic TM.  As far as I know, there
   is no (well-founded) suggestion that non-recursive functions can be
   computed by these devices.

Well, Deutch does suggest that a quantum computer could determine
once-and-for-all that the Many Worlds interpretation is the correct
interpretation. I have not figured out whether this implies that it
computes a non-recursive function -- but probably so since all
recursive-functions obey classical causality. To put it another way,
the "extra" power of a quantum computer would come from its ability to
use non-local interactions and is not just an issue of computational
speed else one could use a normal TM to determine that the Many Worlds
interpretation is corect.

   This is very interesting.  Discreteness in the spectrum of energy states
   is not by itself sufficient - there is no problem in having a denumerable
   infinity of discrete states within a finite interval.

   If a real system can depend in a macroscopically observable way on
   how close it gets to (eg) an ionization energy, then chaotic behavior
   might be observable in QM.  How are the mathematical examples constructed?

The issue of chaos in the correpondence limits of quantum systems is a
hot topic.  For those interested in the issue of quantum chaos, I
strongly suggest:

"Classical Mechanics, Quantum Mechanics, and the Arrow of Time"
T. A. Heppenheimer, Mosiac, Volume 20, No 2, Summer 1989, 2-11

Also, Rod Jensen has been doing work on the stadium problem in the
quantum domain. Very intersing stuff.


Still pondering nonlocality,
Albert Boulanger
BBN Systems & Technologies Corp.
aboulanger@bbn.com