From: paul@mtnmath.UUCP (Paul Budnik)
Newsgroups: sci.crypt

Subject: Re: Are there truly random phenomena?
Summary: The nondeterminism of quantum collapse is the issue.
Message-ID: <149@mtnmath.UUCP>
Date: 6 Aug 91 19:21:50 GMT
References: <> <> <148@mtnmath.UUCP>
Organization: Mountain Math Software, P. O. Box 2124, Saratoga, CA 95070
Lines: 63

In article , (Hugh Miller) writes:
>        Roger Penrose:
>    Only _one_ of the
>    alternatives survives into the actuality of physical experience,
>    according the the process _R_ (called reduction of the state-vector
>    or collapse of the wave-function; completely different from _U_).  It
>    is here, and only here, that the non-determinism of quantum theory
>    makes its entry....
>    How would you propose to use, say, a Geiger counter strapped to a
> beta-emitter or the hiss of a hot resistor without performing a state
> reduction?  And, if so, you introduce randomness.

Just because most physicists assert that quantum collapse is
a nondeterministic process does not make it so. There is good reason to doubt
this assertion. About the same time Bell refuted von Newman's claim that
no more complete theory could be consistent with quantum mechanics he proved
that quantum mechanics is not a local theory. This non locality comes from
the assumption that wave function collapse has no hidden structure and
occurs instantaneously. If current theory is completely correct, vast
quantities of information are being transmitted *instantaneously* over
billions of light years. One cannot use this effect for faster than light
communication.  It is as if nature encrypts the information with quantum
uncertainty.  One can do an experiment where changing the state of a
polarizer will instantaneously effect the results obtained at an arbitrarily
large distance.  One can measure the time when the effect occurs and the
time when the polarizer changes state and one can prove that information was
transferred instantly. However the latter step requires comparing observations
at the remote and local sites and this information cannot be transferred
at faster than light speeds.

This is an active area of experimental investigation. Claims have been made
that locality has been violated but Franson showed that Aspect's widely
reported experiment did not have accurate enough timing to confirm that
locality is violated. To my knowledge no later experiment has
adequately addressed Franson's arguments. I think it far more likely
that quantum collapse is a local Lorentz invariant process just like every
other known physical process. If so, quatnum mechanics must be an
incomplete theory as Einstein insisted. It may well be that quantum
collapse is a deterministic process based on some new level of physical
structure that we do not yet understand. This seems to me far more likely
that the universe is not local. The question of locality may be decided
experimentally within the decade.

> >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 recursivel y
>    Why is `the set of all predictions of quantum mechanics' (?) a
> recursively denumerable set?
[recursively enumerable *not* recursively denumerable]

The set of all computable predictions from any theory is recursively
enumerable assuming the set of initial conditions is recursively enumerable.
Quantum mechanics does make any noncomputable predictions. The set of all
possible initial conditions for a quantum mechanical system of finite size
and energy is finite. The set of all such possible initial conditions is
recursively enumerable.

Paul Budnik