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

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Discussion Overview

The discussion revolves around the calculation of the round trip elapsed proper time of a clock that moves vertically under the influence of gravity, specifically using the Schwarzschild geometry of a non-rotating black hole. The focus is on deriving an equation for this scenario while ensuring the clock remains in inertial motion throughout the experiment.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant seeks an equation for the proper time of a clock moving vertically under gravity, emphasizing that the clock remains inertial and does not use propulsion.
  • Another participant questions the initial request, suggesting that the original poster might be able to perform the calculation independently.
  • A later reply expresses a sense of frustration or resignation regarding the ability to perform the calculation, indicating a personal struggle with the task.
  • Participants share links to external resources that may assist in understanding the calculations related to freefall and proper time in the context of general relativity.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as there are differing views on whether the original poster should conduct the calculation themselves, and the responses indicate a mix of support and challenge regarding the request for assistance.

Contextual Notes

Participants reference external papers and resources that may contain relevant mathematical frameworks or examples, but the applicability of these resources to the specific problem posed remains unverified within the discussion.

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TL;DR
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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Is there any reason you can't do the calculation yourself?
 
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Likes   Reactions: berkeman
PeroK said:
Is there any reason you can't do the calculation yourself?
Getting too old, I guess... :confused:
 

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