🚀 go-pugleaf

In article <1992Oct1.125305.13437@oracorp.com>, daryl@oracorp.com (Daryl McCullough) writes:
> In article <297@mtnmath.UUCP>, paul@mtnmath.UUCP (Paul Budnik)
> writes:

> The EPR-like correlations are certainly strange, but as far as I know
> there is no experimental evidence contradicting the predictions of QM.

I never said there was. I only claim that the predictions are unlikely
to be true and not justified by any reasonable theoretical argument.

> It seems clear to me that the wave function is not a physical field,
> in the sense of the classical electromagnetic field. The problem shows
> up when you consider the quantum mechanics of more than one particle;
> the wave function becomes a function of position in configuration
> space, rather than space-time. That is, in general the wave function
> is of the form Psi(r1,r2,...,rn,t), where rj is the position vector
> for the jth particle. As far as I know, there is no way to interpret
> such a thing as a field---what is its value at the North Pole, for
> instance? There is no such thing as the value of the wave function
> at a particular space-time point, so it doesn't make much sense to
> talk about that value collapsing.

I am surprised that someone has not raised this issue a lot sooner in this
discussion. Ofcourse you are correct. A physical wave function cannot be
the same thing as the multiparticle Psi of quantum mechanics. It is only
the single particle wave function for which such an identity is possible.
Let me first give an intuitive explanation of what I think may be going
on and then talk about how it can be handled in the existing formalism.

I believe that space-time and state vectors defined at points in space-time
are discrete. This allows for results that can approximate differential
equations to a high accuracy at a large enough scale.
There is an entirely new class of effects at smaller scales. Among these
effects is a minimum `energy' to create a stable structure. An initial
disturbance cannot diffuse indefinitely. It will ultimately break up
into independent `particles' or go through some some repeated sequence
of states as a stable structure.

In a continuous model it is impossible to reproduce this affect of independent
dynamically stable structures using ordinary space-time. One has to
give a probability for any combination of properties of all the particles
that are part of a model. This includes a separate position for each
particle. Hence the need for Psi as you described it. I think that there
is a wave function for each individual particle that represents the
probability of this particle interacting. These functions can overlap
in physical space and these stable structures can still retain their
structural integrity. This cannot be modeled directly using continuous
structures.

If this is what is happening physically, what does it mean in the
conventional formalism of quantum mechanics? In this physical model
there are no jumps. A particle is not created or destroyed instantaneously.
It is a `continuous' process in a discrete manifold. There is no
way to evolve Psi in a continuous way when a particle is created or
destroyed. The number of coordinates change. One must plead ignorance.
No one knows in detail what is happening when an interaction between
particles occurs. All experimental observations involve interactions.
The QM state vector will eventually be a correct reflection of
physical reality, but this will not be true immediately.
Thus QM should be though of as a theory that has explicit holes in it.
We do not yet have a model of what is happening at these transitions.

Regardless of what level of credibility you give my intuitive model,
I believe this is the correct assumption to make about quantum mechanics.
We have an excellent model of what happens with the linear evolution of
the state vector. We do not have any reasonable model of what happens
with the nonlinear changes that are an equally important and universal
aspect of physical reality. The most reasonable assumption
is that the size of these holes in time is large enough to prevent
locality from being violated.

Paul Budnik