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Re: Questions you love/hate to have asked



A question for Leigh:
Seeing conservation of momentum and energy as consequences of the
basic symmetries of nature is the truly elegant way to regard
mechanics, but probably a bit sophisticated for young students? At
that level, I usually discuss energy and momentum as book-keeping
devices to keep track of work and impulse. How do you feel about
that approach, or do you think that the concept of force (see another
ongoing thread!) is too vague at this level to sustain this approach?
Margaret Mazzolini

If we can say that the electromagnetic field can carry
and transfer momentum as well as energy, why not bodies?

You can say it, but everything I said about the bodies
applies to fields as well. I will also point out that
energy is another quantity in the same category (it is
the fourth spacetime component of the momentum four-
vector). Surely thinking about the redshift will show
your students that the momentum and energy "inherent"
to a photon depend on frame of reference.

Think about the energy stored in a capacitor. Is it
stored in the charge as the formula

E = 1/2 QV

suggests? Or is it, perhaps, stored between the plates
as we calculate using the electric field energy density?
The answer is it is "stored" neither place. It is a
quantity which can be calculated in either of two ways,
neither of which says anything about its location.

You can say it, but you'd better recognize that it is
just an imprecise way of talking about an abstract
quantity. Once everyone understands that it is useful
to do so. Questions of the sort that started this thread
will arise, and they should be answered correctly. That
is easier to do if one makes clear at the outset what
the nature of physics is. It is an abstraction in
mathematics which is accurately isomorphic with Nature.

Leigh





Dr. Margaret Mazzolini
School of Biophysical Sciences and Electrical Engineering
Swinburne University of Technology
P.O. Box 218,
Hawthorn VIC 3122 Australia
email: mmazzolini@swin.edu.au
phone: (61 3) 9214 8084 fax: (61 3) 9819 0856