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Re: energy, work, heat



Leigh,

Local conservation of energy and momentum is discussed at length
in Chapter 5 of Misner, Thorne, and Wheeler. It is dynamically
guaranteed by the Einstein field equations. However, the
energy and momentum referred to here does not include gravitational
contributions; in GR it's most natural to give gravity special
treatment and, if possible, not even think about gravitational
energy.

When we switch to a Newtonian viewpoint and treat gravity as a
force, it is often possible (and convenient) to talk about gravitational
energy and treat it like other forms of energy. So we can talk about
a binary pulsar losing gravitational energy in the form of gravitational
waves. We're in the weak-field limit here and everything is consistent,
to a very good approximation. At a more fundamental level, of course,
the Newtonian viewpoint breaks down and we shouldn't treat gravitational
energy in this way. In that case, please see the previous paragraph.

To suggest that we should *never* talk about local conservation of
energy just because the concept can't be applied to gravitational
energy in all situations is most certainly throwing the baby out
with the bathwater. Again, GR *requires* local conservation of
all (nongravitational) energy.

dan