At 03:25 AM 8/8/99 -0400, David Bowman wrote about an Euler-Lagrange
formulation of the energy of a gravitational field.
1) Could you recommend a reference? This stuff is intriguing, but it's not
something people were born knowing, and it's hard to communicate it via email.
2) It looks your calculation applies to a *static* field. I see terms for
the scalar potential, but not the vector potential (or tensor potential).
I also don't see a Poynting vector. Right? How hard would it be to extend
the theory? Would that lead to full-blown general relativity, or something
else?
3) You critizice Leigh Palmer for arbitrarily excluding "rho phi" terms
from his calculation. But isn't your calculation, which includes them in a
particular form, equally arbitrary? In the Newtonian limit (i.e. excluding
dynamics and excluding nonlinearities) I don't see any experimental or
theoretical basis for favoring or disfavoring either version. Anybody care
to comment on this?
Note that arbitrary does not mean invalid, as long as the assumptions are
labelled as such, and not used to rule out other valid arbitrary assumptions.
4) Feynman (at the end of II-27-4) talks about rho phi terms, saying they
are optional for the static case and *not* correct for the dynamic case.
Any comments?