Re: "quantization"

[Leigh Palmer <palmer@sfu.ca>]

> > > Let me ask, without making no powerful reference (which is almost never a
> > > problem), what is wrong in saying that energy is a physical entity which
> > > conservation follows the time invariance of physics laws?
> >
> > I think Noether's theorem's consequence is usually stated a bit
> > differently, but I understand that energy conservation is a
> > necessary counterpart (not a consequence) of the time invariance
> > of physical law. Let me also point out that energy conservation,
> > like energy itself, is a mathematical abstraction. The time
> > invariance of physical law is a quantitative statement as well.
> >
> > Leigh
>
> 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.

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

> (see Dewey's aftermail quote of Einstein).

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

> It does not prevent us from using them.  As far as I know, the
> energy conservation follows the explicit demand of time
> invariance expressed in math terms.

That's the answer I was seeking. 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.

> But in any case (that is whether you
> are going to derive it or restrict yourself to a claim, which is sufficient
> to the great majority of students), I am convinced (because I have enough
> supporting experience) that to provide some theoretical ecology,  almost
> regardless the level of physics instruction, is essential and contributes a
> lot to people's understanding.  A mere joking on the subject is a play
> which is good only for the great performers (e.g., Feynman) who can
> compensate listeners later on with a plenty of other brilliant pieces.  In
> a regular case (e.g. myself) it might not help: " What is good for Jupiter
> is not for an ox."  I feel much better (and it guarantees the similar to my
> students), when I do relate energy conservation with the time invariance (a
> causal connection) and generalize this approach to other conservation laws
> (within the known limits).  Let me make a reference to Landau & Lifshits
> Vol. I (Mechanics)  and express a pity that this point is not widely
> adopted in INTRODUCTORY physics courses.

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!

Leigh