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Re: "quantization"



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.