What is the proper time of a vertically moving inertial clock?

In summary, the proper time of a vertically moving inertial clock is the time measured by the clock itself, as it moves through a gravitational field. This proper time is affected by the effects of both gravitational time dilation and the relative motion of the clock, which can lead to differences when compared to clocks at rest in a different gravitational potential. The principles of general relativity explain how the clock's position and velocity influence the time experienced by the clock, ultimately leading to a nuanced understanding of time measurement in varying gravitational contexts.
  • #1
KDP
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What is the elapsed proper time of vertically moving inertial clock in Schwarzschild geometry?
Hi. I am looking for an equation for the round trip elapsed proper time of a clock that is initially moving vertically straight up with a given initial velocity, reaches apogee and then returns to the starting location under gravity. I would like to use the external Schwarzschild geometry of a non rotating black hole to keep things as simple as possible. At all times during the the experiment the clock is moving inertially, so no rockets or thrusters involved (and no horizontal motion allowed).
 
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  • #2
Is there any reason you can't do the calculation yourself?
 
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  • #3
PeroK said:
Is there any reason you can't do the calculation yourself?
Getting too old, I guess... :confused:
 

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