Re: neophyte GR question

On Jul 28, 2:37=A0pm, leithaus <lgreg.mered...@xxxxxxxxx> wrote:
Something about the Hawking-Ellis presentation of GR has long bothered
me. In their presentation -- which i take to be more or less
definitive

That's not the "Hawking-Ellis" presentation of GR. It's the standard
treatment of manifolds and differential geometry that's been prevalent
since the turn of the 20th century. Hawking and Ellis have nothing,
per se, to do with any of that. In all likelihood, you're only pinning
their names to it, because it's the first place you saw it.

Now, what bugs me is that charts don't come for free. From meter rods
to GPS to atomic clocks, no physically useful coordinate machinery
comes without a footprint in the stress-energy tensor.

If you set everything up by echo-location signalling (with light) and
internal atomic clocks, you can subject the sources, themselves to the
equations governing the dynamics, express the solutions (e.g. the
number of send-receive echoes or the number of atomic oscillations) in
terms of whatever underlying coordinate system you wish to write out
the solutions in, and then invert to express the coordinate system in
terms of these. After inverting, you have the coordinates expressed in
terms of the material events, WITH the solutions already taken into
account.

But, in practice, tiny satellites in geosynchronous orbit are going to
have an utterly negligible back-reaction effect on the field that will
almost certainly be well beyond the ability of its technology (or any
other human-developed) technology to detect -- hence making the issue
of back-reaction effects irrelevant. Just think of all of the twisting
and contorsion that has to go into merely designing and constructing a
pendulum balance to detect the near-field for ordinary matter.

In any case, you can write it out as an iterative series: (1)
situation without back-reaction + invert to the material coordinates;
(2) include back-reaction as a minor modification (+ invert to
material coordinates and reverberate this onto everything else); (3)
include back-reaction of back-reaction; etc. It's a rapidly converging
series, since the back-reaction is much less than the field being
measured.

After all, you're not using giant celestial objects as clocks or
rulers.

.