Does Throwing a Clock in Free-Fall Affect Time Dilation Calculations?

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Discussion Overview

The discussion revolves around the effects of throwing a clock while in free-fall on time dilation calculations. Participants explore the implications of both special and general relativity, particularly focusing on whether gravitational time dilation needs to be considered alongside the effects of relative motion between the observer and the clock.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that while in free-fall, throwing a clock upwards does not change the rate at which time flows for the observer, as both remain in the same frame of reference.
  • Others argue that even in free-fall, the clock's motion away from the observer introduces time dilation effects due to relative motion.
  • A participant suggests that if the clock is thrown with a velocity v, time dilation can be calculated using the formula √(1-v^2/c^2), and gravitational time dilation can be ignored if the distance from the center of gravitational mass is sufficiently small.
  • Another participant mentions that in a free-fall frame near a massive body, the effects of gravitational time dilation can be approximated as negligible to the first order in (v/c), but second-order effects related to tidal forces may still be present.
  • There is a discussion about the validity of treating the situation as an inertial frame and the implications of the metric coefficient g_00 in the context of gravitational time dilation.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are competing views on whether gravitational time dilation should be considered alongside the effects of relative motion when analyzing the scenario of throwing a clock in free-fall.

Contextual Notes

Some participants note that the reasoning behind gravitational time dilation and its relationship to tidal forces may complicate the discussion, leading to a preference for simpler explanations unless further detail is requested.

cragar
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If I am in free-fall and then I throw a clock above me so that it is moving away from me
at a constant speed, can I just use regular time dilation to see how time is flowing in the clocks frame relative to my frame? Or do I need to worry about gravitational time dilation.
 
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You and the clock, even after you have thrown it away from you (ignoring the momentary acceleration) are still in the same frame of reference and you will not see any change in the rate of the clock. An observer, at rest with respect to the planet, will see both the clock and you slowing down as you go deeper into the gravity well.
 
ok so being in free-fall is the same as floating in free space. So when I throw the clock it moves away. Why is this considered the same reference frame. How could we release this clock so it appears to move away from me at a constant speed and be in a different frame of reference with me still in free fall ?
 
I was referring to the vertical motion only. You are correct that the clock has non zero horizontal speed with respect to you- that has nothing to do with the gravity.
 
cragar said:
If I am in free-fall and then I throw a clock above me so that it is moving away from me at a constant speed, can I just use regular time dilation to see how time is flowing in the clocks frame relative to my frame? Or do I need to worry about gravitational time dilation.
If you throw the clock upwards with velocity v, then it will time dilate by √(1-v^2/c^2). If the distance between you and the clock is Δr and the distance from the centre of gravitational mass is r, then if Δr/r is insignificant you can ignore gravitational time dilation. In other words, while you are in free fall the spacetime around you is aproximately flat Minkowskian in a small local region.
 
HallsofIvy said:
You and the clock, even after you have thrown it away from you (ignoring the momentary acceleration) are still in the same frame of reference and you will not see any change in the rate of the clock.
HallsofIvy said:
I was referring to the vertical motion only.
You are still wrong. When you are in free fall and throw the clock vertically upwards it will continue to move away from you. You and the clock stay in relative motion, so of course there is time dilation from motion.
 
cragar said:
If I am in free-fall and then I throw a clock above me so that it is moving away from me at a constant speed, can I just use regular time dilation to see how time is flowing in the clocks frame relative to my frame?
Short answer, yes. (In a local region.)
 
cragar said:
If I am in free-fall and then I throw a clock above me so that it is moving away from me
at a constant speed, can I just use regular time dilation to see how time is flowing in the clocks frame relative to my frame? Or do I need to worry about gravitational time dilation.

If you are in free fall near a massive body, such as the Earth, to the first order in (v/c), it will be as if you were in an inertial frame in which there was no gravitational time dilation.

You will see effects of second order in (v/c), which can be ascribed to tidal forces.

I have a feeling the detailed reasoning behind this would just confuse the thread, so I'll omit it unless asked. I will however state the results in a different way:

Gravitational time dilation can be thought of as the value of the metric coefficient g_00. In a free-fall frame, g_00 will be 1 and the first derivative of g_00 will be 0, but the second derivative of g_00 will be nonzero and proportional to the tidal forces in the free-falll frame.
 

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