🚀 go-pugleaf

In article <1992Oct2.015248.25672@unixg.ubc.ca>, ramsay@unixg.ubc.ca (Keith Ramsay) writes:
> In article <298@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes:
> > Interpretations exist for quantum mechanics because the theory is not
> >formalizable. One cannot define a model for a quantum mechanical system
> >in ZFC. ...
> 
> I think this is somewhat misleading. I don't see what ZFC particularly
> has to do with it, nor "formalizability". The ambiguities in the
> interpretation lie mainly in what the terms, as formalized (which can
> be done in a variety of ways), should be taken to mean. It is not so
> much a mathematical or theoretical problem as a philosophical problem.

In QM there is a disconnect between the theory, which talks only about
probabilities, and experimental observations. It is this disconnect
that is the source of the problems of interpretation. One literally
does not know what one is talking about when one starts discussing
inherently random processes, as opposed to statistical models that result
from incomplete knowledge or an incomplete model. Saying that one
cannot formalize this in ZFC is a way of saying, in a precise way, that
one does not know what one is talking about.

> Are you saying that probabilistic theories in physics are inherently
> dubious?

Only those that take probability as an innate aspect of the theory.
There is no problem with probabilistic theories that are based on
incomplete information or an incomplete model.

> It is not clear that there even exists such a notion of "random
> sequence" as you seem to think would be required. (There are, of
> course, definitions of "random sequence", just not of the sort meant
> in this context.) People can perfectly well formalize probability
> theory, however.

I have no problems with probability theory. It is the notion of an
inherently random process that cannot be formalized.

> Probabilistic models, on one interpretation, tell us how thoroughly to
> expect certain events to occur, how much confidence to place in events
> occurring.  It is not clear that one ought somehow to be able to
> convert such a theory into one which gives a black-and-white criterion
> for when a sequence of events does or does not conform to
> expectations- for whether the sequence is "a random sequence" or
> isn't. Confirmation is a matter of degrees.

One can develop an algebra of probabilities and apply this to any model.
This is completely different than formalizing the model itself. The latter
is the problem with quantum mechanics.

> Yet I don't think it has persuaded any of us to abandon probabilistic
> models.

It should give you food for thought if you advocate a physical model
in which probability is an innate property.

Paul Budnik