[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 
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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