Re: Newtonian gravitational field energy (long)

["JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>]

Hi David Bowman-
        Would you remind me where your u_g term comes from?  The conventional
derivation, I just looked it up in Slater & Frank,<E & M>, would have just
1/2 of your first term which, after subtraction of a surface term that recedes
to, and vanishes, infinity:
***************************************************************
U_tot = Integral{all space; (dr^3)*([rho]*[phi] + u_g)}
**********************************

        This leaves one with the usual 1/2 E^2 term.  In gravity, E would
be the force on a mass per unit mass.  S&F finish the derivation with the
remark: "This is the expression for the electrostatic energy in terms of
the field.  It's interpretation is that we may imagine the energy to be
localized throughout the field."
        To which I say, "Hurrah!".  That's because when we quantize the
EM field, we, to wax poetic, quantize the field quantities at a point.
We then ascribe energy to the quanta, thereby bestowing upon nature the
possibility of giving us the photelectric effect.

                                        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