# 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

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