In sci.physics Gordon D. Pusch wrote:
"Old Man" writes:
Gordon D. Pusch wrote in message
...
(Starblade Darksquall) writes:
[snip]
A beam of light only exerts
"no gravitational force" on _another beam of light traveling in
the same direction_. On a massive particle, it exerts =TWICE=
the "gravitational force" one would naively calculate by Newton,
just as it experiences =TWICE= the gravitational deflection that
one would naively calculate by Newton --- and two light beams
traveling in opposite directions each experience _FOUR TIMES_
the "gravitational force" and gravitational deflection one would
naively calculate using Newton.
Wrong.
I'm sorry, but it is YOU who are wrong. This is a =VERY= well-established
general relativistic result, first derived by Tolman, Ehrenfest, and
Podolsky in 1931 [Phys. Rev. v.37, p.602; see also Tolman "Relativity,
Thermodynamics and Cosmology" (Oxford 1934), and "The gravitational
interaction of light: from weak to strong fields," by V. Faraoni and
R.M. Dumse, http://arxiv.org/abs/gr-qc/9811052]. John Wheeler
makes use of this important result in his theory of "geons" --- objects
composed entirely of electromagnetic or gravitational waves that are
quasi-bound by their own self-gravitation.
This is a bit tricky -- you're both right (or both wrong), depending on
the details of the system you're talking about.
For pure disordered electromagnetic radiation, it is definitely true that
the effective gravitational mass is twice the energy. On the other hand,
if you look at ``light in a box of mirrors,'' and assume that the matter
that makes up the mirrors is electromagnetically bound, there is some
cancellation between the energy of the light and the binding energy
needed to keep the walls of the box from being pushed apart. If you
use the virial theorem, you'll find that the total electromagnetic
contribution to the mass is now just the energy, not twice the energy.
I discuss this issue in section IV of gr-qc/9909014.
Steve Carlip