From: paul@mtnmath.UUCP (Paul Budnik)
Newsgroups: sci.physics
Subject: Re: Hidden variable theories
Date: 13 Sep 92 03:43:22 GMT
Organization: Mountain Math Software, P. O. Box 2124, Saratoga. CA 95070

In article <1992Sep12.194540.16125@galois.mit.edu>, jbaez@riesz.mit.edu (John C. Baez) writes:
> ... 
> >	3. In an experimental tests of Bell's inequality manipulations of a local
> >	polarizer must instantaneously influence results obtained by a distant
> >	observer or Bell's inequality cannot be violated.
> 
> Nope.  That'd be true in a classical theory, but not in a quantum
> theory.  At least that's how I talk about it.  Since you have not
> defined "instantaneously influence" we can argue all day without ever
> getting anywhere.

Having redefined causality are physicists now in the process of redefining
influence? Of course its true that you can only give a mathematically
precise definition of these terms from within a mathematically
precise model. However the model that is appropriate for discusing experimental
tests of Bell's inequality is classical. After all the purpose of the
experiment is to test the correctness of quantum mechanics and it is only
macroscopic observations (that classical theory deals well with)
that are relevant to the experiment. Within this model I believe
these terms have well defined and accepted meanings.

> There is a precise sense in which nothing done in
> any region can influence what's going on in any spacelike separated
> region.  This precise sense is what has been formalized in axiomatic
> quantum field theory as "causality", or the "diamond property" (see my
> previous post and the references).  When I talk about causality and
> say there are no instantaneous influences in quantum field theory,
> this is the sense I mean.  

So you *have* redefined influence! What you have done is assumed Bell's
inequality is violated and redefined these conventional terms in the
context of quantum field theory so that there is no instantaneous influence
or conflict between causality and Lorentz invariance. Marvelous! However,
how is the relevant to our discussion? If I am correct about Bell's inequality
not being violated these new definitions will be in the dustbin of history
before you know it. Always keep in mind that the rich and elegant
mathematics that you are working with is different from physical reality.
You do not not know what physical reality is `really like' nor does anyone else.

> By the way, for those of you who are wondering why the heck I'm
> dragging quantum field theory into this mess, it's not out of some
> love of needless erudition.  It's just because when you try to combine
> special relativity and quantum theory, which is what we're doing here,
> you get quantum field theory.  To talk about this stuff in a mathematically
> precise manner, you need to use the language of quantum field theory. 

Nonsense. The proof of Bell's inequality uses elementary mathematics and
applys to macroscopic observable events. Testing Bell's inequality is
testing the correctness of quantum field theory. You do not need to use the
machinery of the theory to describe these macroscopic experiments. Doing
so is dangerous. It can produce circular arguments where you prove the
theory is correct because you assumed that it was correct.

> 
>...
> 
> I never said the violation of Bell's inequality was insignificant.  I
> think it's very interesting.  Since it does not violate causality or
> Lorentz invariance *in the sense of mathematically rigorous quantum
> field theory* I don't think it's anything "bad".  In other words, it's
> weird and wonderful but it does not indicate any inconsistency in the
> currently accepted approach to quantum field theory.

There is a philosophical disagreement that underlys our disagreement
about specific questions. There are certain aspects of physical phenomena
that no current theory can explain in a way consistent with conventional
notions of determinism, mechanistic models etc. Most physicists
have concluded that therefore there must be no explanations in those
terms and they are free to redefine fundamental concepts related to these
classes of models in a way that best suits their current theories. I think
you are jumping the gun. You certainly haven't considered all possible
models or even all plausible models.

What we know to be true are experimental results in a macroscopic universe.
In those terms Bell's inequality presents us with a result that seems
most improbable. We cannot assume that observations made at one site
are independent of manipulations made at a distant site. This is true
even if the observations and manipulations are separated by billions
of light years. Yet there is not a shred of experimental evidence
to suggest that this affect occurs. The theoretical basis for
it is the instantaneous collapse postulate, which was simply asserted
to be true, possibly because anything else would have implied that quantum
mechanics is an incomplete theory. Isn't it possible that you are
taking your models too seriously?

> >>Why is there any need to introduce new definitions of a term that has
> >>a well established meaning? 
> 
> To quantum field theorists, who spend all day thinking about
> relativity and quantum theory and their relationships, the definitions I
> gave ARE the "well established" definitions of causality, and your
> definition, which by the way you have never given (certainly not
> with any mathematical precision) - is the "new" one.  I have no
> problem with multiple definitions of the same word so long as they are
> precise and explicitly stated.  It's only when one tosses around words
> like "causality" and "influence" claiming that they are well
> understood but not providing precise definitions that things get
> confusing.  

I think you agree that these are well understood in the classical domain
in which real experiments are performed. Is not this the correct domain
to discuss such experiments especially given that it is the correctness
of quantum field theory itself that is being tested?

>... 
> 
> Now I am really confused.  Are you saying that you think Bell's
> inequality is violated or is not?

Sorry. Let me rephrase that.

I will be happy to bet you $50 that by the year 2005 there will be
substantial experimental evidence that that the correlated events
observed in tests of Bell's do not have a space-like separation.

Paul Budnik
Newsgroups: sci.physics,sci.math