Time dilation for clock thrown up and caught back

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Discussion Overview

This discussion revolves around the effects of gravitational time dilation and relative motion on two clocks: one that is thrown up in a gravitational field and then caught, and another that remains stationary at the surface. Participants explore whether the time recorded by both clocks will be the same, considering the interplay of gravitational potential and velocity.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants propose that the time dilation effects due to speed and gravitational potential may not balance each other out, leading to different time readings on the two clocks.
  • Others argue that the clock thrown up will record more time than the stationary clock, as it experiences maximum time between the toss and catch events.
  • One participant notes that time moves more slowly for objects in a lower gravitational potential, suggesting that the tossed clock, being higher up, runs more quickly, but its speed causes it to run more slowly.
  • Another participant mentions the need for corrections in GPS systems due to relativistic time effects, indicating practical implications of these theoretical discussions.
  • Some participants reference a related thread on tossing clocks for further insights and comparisons, indicating ongoing exploration of the topic.

Areas of Agreement / Disagreement

There is no consensus on whether the two clocks will show the same time. Multiple competing views remain regarding the effects of gravitational time dilation and relative motion.

Contextual Notes

Participants express uncertainty about the exact calculations and implications of the two different coordinate systems for understanding time in the universe, particularly in hypothetical scenarios like a Big Crunch.

  • #31
Frame Dragger said:
I feel your Edit... I mean pain. This to me is all the more reason to improve the terminology across physics so issues like "locality" are split into specific terms of art.

I'm on my way out with my family, so I can only make a brief comment. To add to the confusion, physicists and mathematicians often mean completely different things by "local"!
 
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  • #32
I just want to make a few comments about my earlier posts in this thread that sparked this current discussion. This is all according to my own limited knowledge:

A geodesic is a locally extremal path. The path itself may be very long, the word "local" in this context refers to the calculus of variations idea of entire functions that differ from one another by an infinitesimal amount. It in no way implies that the domain of those functions need be small. Specifically, this "local" is in no way related to the "local" of the equivalence principle. It is more closely related to the concept of "local" in optimization where a minimum may be a local minimum, but not a global minimum.

In the case of clocks A and B, they are both geodesics, so they are guaranteed to each be local maxima. The paths differ from each other by a finite amount, so there is no contradiction in one being longer than the other. Both are local maxima, but at most one could be the global maximum. If one is the global maximum then no non-geodesic clock can possibly record more proper time between the two events.
 

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