Timeline for Two clocks in free fall
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 28, 2021 at 13:13 | comment | added | Carl Witthoft | Side question: does the delta time depend on the rocket being rigid, or at least compressed (due to acceleration force) to a constant length? And does this depend only on the direction of the virtual gravitational field, or if you mounted the thrust engines in nacelles off the nose would the situation change? | |
| Sep 28, 2021 at 6:46 | comment | added | PM 2Ring | Consider two 1 kg bodies in vacuum, freefalling towards the Earth. One body is at the initial distance $r$ from the centre of the Earth, the other is directly above the first, initially at $r+h$. The lower body is accelerating slightly faster, so the separation between them increases. If we do this experiment near a black hole, the differential acceleration can be quite large, as shown at physics.stackexchange.com/q/631414/123208 | |
| Sep 28, 2021 at 6:38 | comment | added | PM 2Ring | Gravitational time dilation is caused by differences in the gravitational potential, which in Newtonian mechanics is $-GM/r$, it has units of Joules/kg. The gravitational field strength is $GM/r^2$, it has units of Newtons/kg. | |
| Sep 28, 2021 at 5:03 | comment | added | Nitish Mandal | What causes a time difference between clocks in a rocket standing on earth? Isn't it the variation in the gravitational field? And, would the variation still matter if the rocket is in free fall? | |
| Sep 28, 2021 at 4:57 | comment | added | Vincent Thacker | @NitishMandal It depends on the size of the rocket compared to the scale of variation of the gravitational field. | |
| Sep 28, 2021 at 4:48 | comment | added | Nitish Mandal | So there would be a time difference because of the tidal forces? Or not? | |
| Sep 28, 2021 at 4:32 | comment | added | RC_23 | Actually, now that I think some more, I wonder if that is correct. If two clocks are falling on identical geodesics, one slightly behind the other, wouldn't the distance between them remain constant, and no forces would need manifest? | |
| Sep 28, 2021 at 4:25 | comment | added | RC_23 | Good point! I suppose I was implicitly assigning the rocket with opposing clocks to be an infinitesimal, so that locally in free fall it is a Mikowski space. | |
| Sep 28, 2021 at 4:22 | comment | added | John Rennie | Your last sentence would be true only in a uniform gravitational field. For a rocket falling towards Earth the two clocks would experience difference gravitational fields due to variation of gravity with distance, so they could not be both falling freely. One or both of them would have a force applied to them by their attachments to the rocket so their proper acceleration(s) would not be zero. | |
| Sep 28, 2021 at 4:17 | history | answered | RC_23 | CC BY-SA 4.0 |