- #141
timmdeeg
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So it seems rigorously applied the time dilation differs. Isn't this a reason to argue that if the time dilation for the rocket accelerating at constant proper acceleration and the gravitational time dilation for the rocket on Earth are unequal then the time dilation in the former case can't be named gravitational time dilation. It can't be named approximate gravitational time dilation either.stevendaryl said:For a rocket accelerating at constant proper acceleration:
- [itex]\tau_{rear}/\tau_{front} \approx 1 - \frac{gL}{c^2}[/itex], where [itex]g[/itex] is the acceleration of the rear of the rocket, and [itex]L[/itex] is the height of the rocket.
For a rocket at rest upright on the Earth:
These numbers are only approximately true, in the limit of small [itex]L[/itex], and where the time the clocks spend in transit is negligible.
- [itex]\tau_{rear}/\tau_{front} \approx 1 - \frac{gL}{c^2}[/itex], where [itex]g[/itex] is the acceleration of gravity at the rear rocket, and [itex]L[/itex] is the height of the rocket.
Please excuse should I've overlooked that this point was already clarified.