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Benjamin Thompson's experiment



Bottom line, folks: energy is not locally conserved. It is not
locally conserved precisely because it cannot be localized*.
Energy is an abstract quantity which depends upon the parameters
which describe the state of a system. Do not imbue energy with
a reality of its own. That way lies utter confusion. It would
be ironic indeed to teach such things in a "conceptual" physics
course.

Charge is locally conserved; baryons, leptons, etc. are locally
conserved. Milk is locally conserved in the absence of cows or
consumers.

Energy is *different*. Charge and milk flow; energy doesn't.

No one has explained Benjamin Thompson's observation in terms
of a "flow of energy" because it can't be done! Why is it that,
more than two centuries after his discovery, with the progress
made since then (especially relativity), and with all the
exposure his discovery has had in textbooks at all levels (my
text for next semester even has a racy personal profile of him
in it) the important lesson hasn't been learned? Energy doesn't
flow. Caloric flows, but it doesn't explain Nature.

Consider once more Thompson's observation:

We have a motor doing work with power P at one end of a shaft.
At the other end we have a dull bit in a bath of lubricant in a
cannon bore. The internal energy of the bath and the cannon is
increasing at a rate P. For the purposes of this discussion we
will assume that its temperature remains constant, a condition
that could be realized, for example, by putting ice cubes in
the lubricant and running it at 0 degrees C.

It is important to note that the intervening shaft is not
"transmitting energy". Its energy is constant; no part of it
exhibits any time evolution whatever. It simply rotates at
constant speed and at a constant level of stress. It is in a
state of mechanical equilibrium. If the upper end of the shaft
it maintained at the temperature of the lubricant bath it can
even be kept in a state of thermodynamic equilibrium, though
that is not necessary for this argument. It is only important
that the physical state of the shaft does not vary in time.
Suggesting that the shaft is "transmitting energy" can only be
done as a figure of speech. It makes no physical sense on a
microscopic or macroscopic scale.

It is as though energy is disappearing at one end of the shaft
and instantaneously reappearing at the other end of the shaft
at exactly the same rate, P! Of course one could "explain" it
in this way, but doing so would violate all sorts of physical
laws. It is important to amintain the integrity of the world
view. We cannot suspend the laws of Nature at our whim, and we
should not ignore them when they come into conflict.

(Observe this from any frame of reference which moves with a
constant speed in a direction parallel with the shaft and you
will observe something interesting, since "instantaneously" is
a word we do not employ lightly when speaking of spatially
separated events.)

Bottom line: energy is not locally conserved.

Leigh

*One cannot uniquely determine the amount of this quantity
contained within an arbitrarily small volume.