On Thu, 31 Jul 2003 21:46:14 +0000 (UTC), "greywolf42"
wrote:

They are consistent with QM because moving into the quantum domain we
move from the category of continuous or even smooth fiber bundles
to the category of measurable functions and operator algebras.

I was under the impression we were discussing the physical universe, not
arbitrary mathematics.. Maxwell's equations are continuous approximations in
Maxwell's original derivation.

The mathematics here is not "arbitrary" - as you call it. The
mathematics here is the one that helps us to describe and predict
physical phenomena of interest.


In QM
dF=0 needs to hold only "almost everywhere", and this leads to the
possibility of having an infinite number of monopoles in the universe.

But there is no physical basis for dF0.

There may be one. We do not know. Quantum theory is not yet completely
understood. Let me quote from J. A. Wheeler: " No prediction lends
itself to a more critical test than this, that every law of physics,
pushed to the extreme, will be found to be statistical and approximate,
not mathematically perfect, precise."


Again, (as per the prior
statements and history that you snipped) your view was popular in the 60's
and 70's.

Popularity of some view is one thing, discussion of unpopular views can
also be revealing. Alpher and Herman predicted background radiation
already in 1948. As Herman wrote: " There was no doubt in our mind that
we had a very interesting result, but the reaction of the astronomical
community ranged from skeptical to hostile." So, perhaps, it is good to
be open-minded?

And a great deal of effort was spent looking for such things.
And nothing was found. To orders of magnitude lower incidences than
theorists expected.

Maybe people were looking at wrong places? Maybe the theory is not
ready? Maybe the theory needs a major re-thinking and re-writing? Or
maybe we will find something else - which will also be interesting. And,
we do not know that "nothing has been found". Perhaps something has
been found but the phenomenon is "elusive".

Certainly, absence of evidence is not evidence of
absence. However, when theorists have to keep "moving the goalposts" after
each "not found," one can infer a major flaw in the theory.


And yet theorists predicted antimatter. P.A.M. Dirac wrote:

"The pure mathematician who wants to set up all his work with absolute
accuracy is not likely to get very far in physics".

But he also wrote:

"There are, at present, fundamental problems in theoretical physics the
solution of which will presumably require a more drastic revision of our
fundamental concepts than any that have gone before. Quite likely, these
changes will be so great that it will be beyond the power of human
intelligence to get the necessary new ideas by direct attempts to
formulate the experimental data in mathematical terms. The theoretical
worker in the future will, therefore, have to proceed in a more direct
way. The more powerful method of advance that can be suggested at
present is to employ all resources of pure mathematics in attempts to
perfect and generalize the mathematical formalism that forms the
existing basis of theoretical physics, and after each success in this
direction, to try to interpret the new mathematical features in terms of
physical entities."

Of course we do not have to agree with all that Dirac wrote but, at
least, we should acknowledge that he may have had a point....

ark
--

Arkadiusz Jadczyk
http://www.cassiopaea.org/quantum_future/homepage.htm

--