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Re: "quantization"




Well, ANY physical concept is not more than a mental construct

Hmm. Is electrical charge a mental construct? Conservation of
charge is also a counterpart of a symmetry of Nature. Charge is,
somehow, a different sort of physical quantity than energy. For
example, the quantity of charge is independent of the frame from
which it is observed; the quantity of energy observed depends
upon the observer's frame. Charge is quantized; energy is not.
Charge is locally conserved; energy is not even localizable.

There are large qualitative differences between the concepts of
charge and energy. Charge is substantial; energy is insubstantial.

Whatever charge you mean, electrical or others, their conservation can be
interpreted as following a symmetry of some additional dimension (which may
be closed, to provide quantization?). Leigh, let me explain myself. I
mentioned my reservation putting ("within the known limits"). Conservation
of charge is the first question which can be raised (and is discussed in
the supersymetry theory, I believe), but AFTER a great success of our
understanding of the origin for energy, momentum and angular momentum (in
classical theory) and parity (in quantum theory) to conserve. The open
questions regarding all other charges remain, meanwhile, out of a regular
curriculum, and occupy the minds of theoreticians. All this does not (for
me and I am quite sure, for the students) spoil the beauty of the emerging
picture. Just the opposite, it inspires an appetite for further search
for this elucidating connection: symmetry - conservation.

I believe that if your claim above is not trivial then it is not
correct, either.

I am sorry, Leigh, I do not follow your logic. I said that
symmetry-conservation law connection is a discovery of the twenties century
physics, which has not yet sufficiently used in introductory physics
courses. Not more than this. I did not intend to say anything more.

(see Dewey's aftermail quote of Einstein).

I'm told Einstein spoke German. I don't recall a German quote
following Dewey's signature.

No problem:

"Physical concepts are the free creations of the human mind and
are not, however it may seem, uniquely determined by the external
world."--A. Einstein in The Evolution of Physics with L. Infeld,
1938.

I know that if time invariance
then energy conservation; I ask if it also works the other way.
Is this an "if and only if"? I believe that it is.

I can not claim what I do not remember or checked. We need to check it.
However, my major claim about not used great pedagogical potential of this
issue in physics course remains. Newton did not prove back and forth
validity of the relation "elliptic trajectory - the law of gravitation", it
was done much later (there was a paper in the AJP). Do we use to check
this critical (in view of any mathematician) point in our lectures? Never.
We even do not prove it in one direction restricting ourselves to the
circular trajectory. This is physics. We proceed practicing it relying
more on our beleif and intuition (not observing any reason why not) until
we fail. Please, do not get me wrong: it IS the issue which should and
must bother physicists. Meanwhile, it does not reduce, however, the
importance of the law of the universal gravitation as a subject presented
on physics lectures.

You should look at the textbook by Eugene Hecht. There are many
gratuitous bows made to Noether's theorem, for no reason other
than Noether's sex, so far as I can tell. There is a big graphic
each time the subject arises. It is most distracting from the
physical thread!

OK, I will, and may be, you will see Landau's text. We then can proceed.
Unless, somebody else could do it better than I.

Igal.