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Re: energy, work, heat



Hi Dan-
You and John Denker are, of course, correct. I was thinking vectors,
not tensors.
You wrote:
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In reply to...

I think that the vanishing of a 4-divergence is to be interpreted
as the (in poetic terms) statement that the outward "flow" of the 3-vector
is equal to the time rate of change of the time component. I cannot make
sense of the statement (in this context) that "each component" of the
4-vector "is conserved".
Otherwise, keep up the good work!
Regards,
Jack

...I remind you that the stress-energy tensor has 16 components.
Roughly speaking, the first row is the densities of the four components
of the energy-momentum vector. The rest of the tensor gives the flows
of these four quantities in the three spatial directions. When we take
the divergence on only one index, we have not one equation but four.
These four equations say that each of the four components of the
energy-momentum vector is "conserved" in the same sense that charge
is conserved in electrodynamics. That is, for each of the four
components, the outward flow of the corresponding flux is equal to the
time rate of change of the local density. Make sense?

dan
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Regards,
Jack

"I scored the next great triumph for science myself,
to wit, how the milk gets into the cow. Both of us
had marveled over that mystery a long time. We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
Mark Twain, Extract from Eve's
Autobiography