Re: energy, work, heat

[Leigh Palmer <palmer@SFU.CA>]

> Dear Leigh and anyone else who thinks he might be right:
>
> > The discussion in Chapter 5 [in MTW] seems to be about 4-momentum, one
> > component of which is the energy. While Taylor and Wheeler do speak
> > (somewhat inelegantly) of the flow of 4-momentum in a fluid-like way:
> >
> >          Total flux of 4-momentum outward across a closed
> >          three-dimensional surface must vanish.
> >
> > They make no such claim for energy *per se*.
>
> Can you construct a syllogism?  Energy is one component of the
> four-momentum.  Each component of the four-momentum is locally
> conserved.  Therefore energy is locally conserved.

Note that your second premise is not one advanced by MTW. The
syllogism is fallacious.

> (Are you bothered by the fact that energy is frame-dependent?
> That's true for any component of a vector, and has no effect
> on conservation, so long as the other components are also
> conserved so the conservation law will be true in all (inertial)
> frames.)

Who said anything about inertial frames? I thought we were
discussing the general case here! Energy either is or is not
locally conserved. Charge is locally conserved. Atoms are
locally conserved. They don't care about inertial frames. They
are substantial; energy is not. That is the important point
you seem to be missing (or, more probably, resisting).

We seem to have an irreconcilable difference here, Dan, and
rather than goad you into more gratuitous patronization I will
stop here.

Leigh