From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>
Date: Fri, 3 Sep 1999 23:44:03 -0500
Hi Dan-
You write, in part:
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On the other hand, I don't understand all your nitpicking about
local conservation of nongravitational energy-momentum. This is
an extremely important physical principle, whatever one wants to
call it. In tensor notation it's written D_mu T^munu = 0.
In a locally inertial frame with cartesian coordinates this
says d_mu T^munu = 0 (ordinary rather than covariant derivative),
and I would interpret this as saying that each component of the
energy-momentum vector is locally conserved. Would you like to
restate it in some other way?
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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 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