From: paul@mtnmath.UUCP (Paul Budnik)
Newsgroups: sci.physics
Subject: Re: Hidden variable theories, was: Uncertainty Princi
Date: 11 Sep 92 14:16:36 GMT
Organization: Mountain Math Software, P. O. Box 2124, Saratoga. CA 95070

Paul Budnik writes:
>In article <1992Sep11.015614.28674@galois.mit.edu>, jbaez@riesz.mit.edu (John C. Baez) writes:
>> In a down-to-earth vein, I would only say information was being
>> transmitted by such a device if I could use it tell my grandma what I
>> was having for dinner, or at least do so with some statistically
>> significant chance (i.e., I'll accept a noisy channel as long as it's
>> not 100% noise).  It would only be if someone did THIS with quantum
>> trickery that I would get nervous.  But of course one can't.

>You are free to redefine information in any way you choose (at least
>in a posting) but what you are defining here is normally regarded as
>sending a signal. Information is often transferred in ways that no
>human being can control.

Fine.  I have no attachment to terminology in this issue as long as we
agree on what one can and can't do.  Typically, 99% of argument about
measurement in QM concerns the right way to talk about what happens,
rather than what actually happend, which is why I find it so boring. 
Your latest post confirms that we have no argument over facts, just
massive disagreements about vocabulary, which reassures me that I can
let the matter rest.

>> ... you
>> are using the word "causality" in a certain way, which I think is the
>>"wrong" way, but in any case, that there's another sensible usage of it
>> such that causality is not violated.

>I would appreciate some references. In everything I have read in respected
>journals there is no disagreement that either causality or Lorentz invariance
>is violated. There is a lot of garbage written in popular accounts
>of this subject. 

See any book which explains the various axiomatic approaches to quantum
field theory.  The best for this purpose is "An Introduction to Axiomatic 
Quantum Field Theory" by Bogoliubov, Todorov, and Shirkov (there's also
a new book by roughly the same authors).  There are various axiom schemes, 
notably the Garding-Wightman axioms for quantum fields as operator-valued 
distributions on Minkowski space, the Haag-Kastler axioms for quantum fields in
terms of local algebras of observables, and the Osterwalder-Schroeder
axioms for Euclidean quantum field theory.  All these axioms schemes
contain axioms for causality and Lorentz invariance.  The point is,
what quantum field theorist mean by causality is quite different from
what you seem to mean!  There's not really any contradiction.  There
are, in fact, two distinct notions of causality in quantum field
theory, "microscopic causality," which is called "Local commutativity" on
p. 597 of the book cited above, and another sort of causality
sometimes called the "diamond property," also discussed on the same
page.  These notions are easiest to get ahold of in the Haag-Kastler
axiom scheme.   The first says that the operator algebras living on
spacelike separated open sets commute.  The second says that if one
open set is in the causal shadow of another (see my recent post for a
definition of that term), its operator algebra is contained in the
operator algebra of the other.   Roughly speaking, the latter says
that information, or signals, or whatever you want to call 'em, can't
propagate faster than the speed of light.  More precisely, the state in a 
given open set is completely determined by the state in open set of which it's 
in the causal shadow.  Here I'm using the word "state" in the usual
sense of (mathematical) quantum theory: a positive linear functional on a 
C*-algebra.

If you can't get the above book, which is really very nice, I
recommend the original article

Haag and Kastler
An Algebraic Approach to Quantum Field Theory
Journal of Math. Phys.
5 (1964) p. 848.

Realize, however, that there is a vast literature on the subject since.
There is a book called "An Introduction to Algebraic Quantum Field
Theory" which treats some of the newer stuff - I forget the author -
not to be confused with "An Introduction to Algebraic and Constructive 
Quantum Field Theory" by Segal, Zhou and myself; we have a discussion of 
causality but do not treat the Haag-Kastler axioms (or any others) as such.

>Regarding the rest of your message, there is no absolute contradiction
>in quantum mechanic only some very unlikely predictions.

Unlikely, eh?  Care to state odds at which you'd bet some real money? 
I'm already looking forward to 50 bucks from Dave Ring when his
"solid evidence for supersymmetry" fails to materialize.  (Say - I
forget when the deadline on this bet was!  I don't want to let him
weasel out via indefinite postponement!)  I look forward to the day
when an improved Aspect-type experiment rules out a Lorentz-invariant
wavefunction collapse theory by giving a real violation of Bell's
inequalities - but I'd look forward to it even more if I knew I would
make some money off it!


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