From: paul@mtnmath.UUCP (Paul Budnik)
Newsgroups: sci.physics
Subject: Hidden variable theories, was: Uncertainty Principle
Date: 7 Sep 92 16:00:07 GMT
Organization: Mountain Math Software, P. O. Box 2124, Saratoga. CA 95070

In article <1992Sep7.001518.525@prim>, prim!dave@germany.eu.net (Dave Griffiths) writes:
> In article <1992Sep5.071519.16554@asl.dl.nec.com> terry@aslws01.asl.dl.nec.com (Terry Bollinger) writes:
> 
> Can you (hopefully without getting too technical!) explain what is meant by
> "hidden variables"? I have seen it mentioned many times, but without a
> precise definition of the class of theories it represents.
> 
Quantum mechanics has the seemingly paradoxical property that the conservation
laws are absolute, but prediction about conserved quantities are often
probabilistic. This is what led Einstein to conclude that quantum mechanics
is an incomplete theory. There must be some objective reality corresponding
to conserved quantities such as energy. I believe Einstein was
correct in this conclusion. In 1935 Einstein and his coauthors published EPR
in which they claimed to prove this must be the case. Bohr's response was
that quantum mechanics says nothing about the intrinsic character of
quantum mechanical systems, but only about their interaction with experimental
apparatus.

In 1932 (even before the publication of EPR) von Neuman published a proof that
no more complete theory could give predictions consistent with quantum
mechanics. Bohr's argument and von Neuman's proof were convincing to most
physicists. 

In 1952 Bohm published a deterministic non-local model that was consistent
with the predictions of quantum mechanics. Clearly something was amiss with
von Neuman's proof. In 1966 Bell published a refutation of von Neuman's proof.
He showed that the proof made certain assumptions that "appear reasonable
when results of measurements are loosely identified with properties of
isolated systems. They are are seen to be quite unreasonable when one
remembers with Bohr `the impossibility of any sharp distinction between
the behavior of atomic objects and the interaction with the measuring
instruments which serve to define the conditions under which the
phenomena appear'". Bell's concluding remark in this paper was "It would
therefore be interresting, perhaps, to pursue some further `impossibility
proof,' replacing the arbitrary axioms objected to above by some conditions
of locality, or of separability of distant systems."

In a paper written later but published first Bell did just that. He showed
that quantum mechanics is not a local theory. There are experimentally
observable effects predicted by quantum mechanics that involve instantaneous
action at a distance. This result says *nothing* about the completeness of
quantum mechanics. It simply implys that any theory that is consistent with
quantum mechanics must be nonlocal.

At this point the critical question became, not the completeness of quantum
mechanics but its correctness. Most physicists do not talk about it
in this way, but this is the situation. Most of quantum mechanics has
been validated to an extraordinary degree. However, most of quantum mechanics
is a local theory. Nonlocal effects come entirely from the collapse
postulate, i. e. the assumption then when an observation is made the
wave function instantaneously collapses to a state consistent with that
observation. Several series of experiments were performed to determine if
these nonlocal effects were real. One series by Aspect concluded
with a result published in 1982 that most physicists considered decisive. 
In 1985 Franson published a paper showing that the timing constraints in
Aspect's experiment were inadequate to prove locality was violated.
More recent experimental results continue to be consistent with quantum
mechanics, but none of them, to my knowldege, provide conclusive proof
that locality is violated. They fail to measure directly the times when
an event occurs and its nonlocal effect occurs. 

Current theory predicts that vast quantities of information are being
transmitted instantaneously over billions of light years. Eberhard has
shown that, in effect, this information is encrypted by quantum uncertainty
and thus cannot be used to send a faster than light signal. He also showed
that one can retain Lorentz invariance if one is willing to give up causality.
This is the approach that most physicists writing in this area have accepted.

Since there is not a shred of evidence that the predicted nonlocal effects
exist, I believe, that quantum mechanics is almost certainly wrong.
I suspect that quantum collapse has a local Lorentz invariant structure
and it is this structure that constitutes the `hidden variables' that
determine the precise outcome of experiments. 

Paul Budnik
Newsgroups: sci.physics