[time-nuts] Pendulums and Atomic Clocks and Gravity :probably more than you want to know...
mike c
mcrescim at cc.ysu.edu
Fri Jun 1 11:36:29 EDT 2007
Dear Dr. Bruce and Bill B and all timenuts in this thread. My two cents
about the
conundrums and how physicists think about atomic clocks in geodesy
around the earth.
For each mass in space, whatever its orbit, if there are no other
fields (ex: electric/magnetic or drag forces) acting on it, then it
sees space and time locally as if it
were an inertial observer in an intertial
frame. There is no gravitational field in that frame...technically the
metric is exactly that of flat
space locally and one of the curvature quantities, the so-called Ricci
tensor, vanishes identically
(and not just locally!) The point is, that all that is left of gravity
when you are falling is the tides...that is test masses released from
rest in your local inertial frame BUT at a distance from you will not
remain stationary, but will start to move relative to you -even though
there
are no other forces than gravity present-. Technically this is due to
the fact that there
is another curvature quantity that is non-zero in the space around a
massive body, it is the so called Riemann tensor. This is just how GR
talks about tidal forces, which is (almost) all that remains of gravity.
Now, releasing those masses, atleast for a few orbits the masses
will appear to kindof orbit around each other and the mass that defined
the original frame. If you are very far from the parent body (and
neglecting effects from other bodies outside the system and between the
masses themselves) then they will continue to stay close and orbit for a
long time. Classically, if the orbits had different major axes they will
eventually walk off because - like two precision clocks- they will
dephase. As this happens, no SV will be large enough. If however the
masses are released
so that their major axis is the same, then even in full GR and being
close to the parent body,
they will stay close to one another, 'orbiting' each other as it were,
forever. (We are
neglecting some truly minute effects here) So a very small SV would -in
principle- do.
Hope that wasn't too long/confusing...this is all in the framework
of GR, but, hey,
maybe there is more to gravity and time and space than that...
- Mike
clock and gravity guy
\\
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