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

  • #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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Likes berkeman
  • #3
PeroK said:
Is there any reason you can't do the calculation yourself?
Getting too old, I guess... :confused:
 

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

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

Proper time is the time interval measured by a clock that is moving along with the object in question. For a vertically moving inertial clock, it is the time experienced by the clock itself as it moves through a gravitational field.

How does gravity affect the proper time of a vertically moving inertial clock?

Gravity affects the proper time of a vertically moving inertial clock through gravitational time dilation. Clocks closer to a massive object (lower gravitational potential) run slower compared to clocks further away (higher gravitational potential). Thus, the proper time will be affected by the clock's position and movement within the gravitational field.

Does the velocity of the clock impact its proper time?

Yes, the velocity of the clock does impact its proper time. According to special relativity, a clock moving at a high velocity relative to an observer will experience time dilation, meaning it will tick slower compared to a stationary clock. This effect combines with gravitational time dilation in a vertically moving inertial clock.

How can one calculate the proper time for a vertically moving inertial clock?

The proper time can be calculated using the metric of the spacetime in which the clock is moving. For a clock moving vertically in a gravitational field, the Schwarzschild metric is often used. The proper time \( \tau \) can be found by integrating the spacetime interval along the clock's worldline.

Is the proper time of a vertically moving inertial clock different from a horizontally moving one?

Yes, the proper time of a vertically moving inertial clock can be different from a horizontally moving one due to the influence of gravitational time dilation. In a gravitational field, vertical movement changes the gravitational potential, affecting the proper time, while horizontal movement primarily involves special relativistic time dilation without changing the gravitational potential significantly.

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