# If acceleration causes relative time dilation does the eventual deceleration reverse it?

If acceleration causes relative time dilation does the eventual deceleration reverse it?

For example: traveling to Alpha Centauri

Based on me reading this site: http://www.convertalot.com/relativistic_star_ship_calculator.html

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It's velocity that causes time dilation, not acceleration. – David Z Nov 29 '12 at 0:08

You don't say how much you know about special relativity, and the calculations involved in handling acceleration are a bit involved unless you are already fairly familiar with the subject. The calculation is described in chapter 6 of Gravitation by Misner, Thorne and Wheeler, or if you just want the results see John Baez's article on the relativistic rocket. The simple answer is that no, the deceleration does not reverse the effects of acceleration.

You can see why this is because as dmckee and cb3 have said, it is the velocity that causes the time dilation not the acceleration. The acceleration is symmetric about zero because the positive is balanced out by the negative so you'd expect it's effects to cancel, and indeed they do because you start at rest and end at rest. However the velocity is not symmetric about zero because it starts at zero, rises to a maximum and falls back to zero. So there's no reason to expect the effects of the velocity to cancel. This means that the time dilation caused by the velocity wouldn't cancel either.

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John, I was voting this up and accedentally clicked on the wrong one. I now cannot change this. I apologise and will upvote if you make an edit... – Killercam Nov 29 '12 at 11:23
@Killercam - go on then, anything for an upvote :-) – John Rennie Nov 29 '12 at 14:59

As was pointed out it is relative velocity, not acceleration, which results in time dilation. Acceleration does, however, play a role in the perceived amount of time elapsed between events. So, special relativity can give insight into your question about "reversing" the effects of acceleration. Have a look at the Twin Paradox and you will see

${\Delta}{\tau}={\int}_{t_1}^{t_2}\sqrt{1-\frac{v^2(t)}{c^2}}dt$

where $t_2-t_1$ is the apparent elapsed time for the twin who stayed on Earth, ${\Delta}{\tau}$ is the apparent elapsed time for the twin on the rocket, and $v(t)$ is the velocity of the rocket relative to the earth which can change in time (acceleration). In general, $t_2-t_1>{\Delta}{\tau}$, so even though $v(t)$ may go from zero at $t_1$, to nonzero, then back to zero at $t_2$, the effect of the acceleration does not vanish. The twin who experienced acceleration will have aged less than his Earthbound sibling. A similar question was posed in terms of gravity wells.

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