Re: heat is a form of energy, & Re: Time conservation

[Leigh Palmer <palmer@SFU.CA>]

> If a nucleus absorbs a photon it gains energy and has a measurably greater
> rest mass.  I always felt that the energy was now localized in the
> nucleus, where it wasn't before the absorption.  Although I agree with
> everything Leigh says, I still find it hard to let go of this feeling. If
> the nucleus is replaced by a star, its mass can be measured by the
> curvature of space on a bounding surface.  Absorbing the photon changes
> its mass and therefore the local curvature of space.  It sort of seems
> the energy is now "inside the bounding surface"?
>
> Enlightenment, anyone?              Crawford

I did not mean to suggest that the energy of an isolated system is not
localized to the extent that it is contained within the boundary of the
system. Though a truly isolated nontrivial system does not exist because
gravity exists, I certainly use the concept myself. Please see my two
automobile system example.

> I would assert that the statement that "energy is not localizable" is too
> restrictive.  I would, rather, support the statement that energy is not
> always UNIQUELY localizable.  For example, electrostatic energy may be
> assigned using an energy density which is a function only of E ( and
> non-zero only where E is non-zero), or the same total energy may be
> assigned using an energy density which is a function of charge density
> (and non-zero only where charge density is non-zero).  These two different
> (and physically equivalent) allocations of "how much energy is where"
> distribute the same total energy differently in space;  and both are
> correct.  Either  (not neither) may be used - energy is localizable, but
> not uniquely so.
>
> Bob

You might add "neither is its quantity uniquely determined". Consider
my two automobile example. The kinetic energy in the center of mass
frame is half what it is in either of the drivers' frames. Otherwise
I have no objection to Bob's statement, but even without this
qualification is it strong enough to be useful? After all, in one of
the examples I gave, the energy is localized to all of the universe
outside a spherical shell of charge! My statement is that one cannot
justify saying that half the energy is in the upper half-space in
that case. One can certainly say it, and justify it by saying that it
comes out right, or "by symmetry", or some other hand-wave, but if
the region of space about which this claim is made is not isolated,
then the law of conservation of energy is silent regarding it.

Finally,

> God knows I learn a lot from PHYS-L, but I am at a complete loss to
> understand the prodigal fecundity of these writers. I just spent two
> hours reading and digesting today's mail, so I must ask, "How long does
> it take you chaps to write all that stuff, and where in hell do you get
> the time?"

Beats me. I had three contact hours today, 335 students in a lecture,
then 120 in another, then a calculus tutorial for a half dozen students
in my introductory class who have had *no* claculus before this semester.
I saw many students one-on-one. I'm tired, but no lectures tomorrow, and
my turn to cook dinner. I did watch part of Miami Denver. This is how I
unwind.

Leigh
> poj