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Re: "quantization"

Thanks, Igal, I understand what you were saying a lot better now. It
seems to me, however, that this view is a lot more appealing if you
believe that "reality" is not mathematical, but that we are trying to
describe it with mathematical which may or may not fit very well.
Suppose reality (at least the part studied by the physical sciences) is
in fact itself mathematical, not necessarily the same mathematics as we
are currently using to approximate it. Does that make a difference in
what should be called non-uniqueness? If reality is mathematics, I
would tend to think of mathematically-equivalent descriptions as being
essentially the same. However, I would be interested in a
counter-argument on that one.


Igal Galili wrote:

Maurice,
Referring to your comment:

Do you know of any other examples of non-unique theories? In
particular, any in which the two theories are not mathematically
equivalent?

As always, it starts from terminology. If you agree that *theory* is
a
sort of theoretical representation, then QM provides a list of
complementary representations (x and p, and so on). In Classical
physics,
you may interpret as such alternative approaches (that is non-unique
theory) statistical physics and thermodynamics which may provide the
same
product either in macroscopic (phenomenological) approach or a
microscopic
one. In optics, you may account for particular physics phenomena
using the
theory rays behavior (geometrical optics) or waves (physical optics,
where,
of course, the smaller wavelength, the easier convergence to the same
result is reached). In mechanics, you may suggest an alternative
theory
which avoids the concept of force at all (Hertz, Kirchhoff?).

and:

Also, what makes the isomorphism of the Schrodinger and
Heisenberg formulations questionable? .... They certainly
always give the same answers, otherwise we would regard one as right
and
the other as wrong.

I did not mean they don't. I meant that the question about the nature
of
the correspondence to the *outside world* remains. But our community
(my
view) has an advantage (or disadvantage, depending on your view) not
to
touch on this philosophical issue in our PHYSICS instruction. This
subject
might be relevant to the classroom intellectual atmosphere, the image
of
the physics teacher, physics itself, etc., but all these are outside
of
physics subject matter, proper. Therefore we can carefully reduce
this
philosophical tension, focusing on our professional stuff which is
invariant in this respect.

Igal.

--
Maurice Barnhill, mvb@udel.edu
http://www.physics.udel.edu/~barnhill/
Physics Dept., University of Delaware, Newark, DE 19716