Does the equivalent acceleration / deceleration required to reach whatever speed then come back and rest in the original frame of reference zero out the time dilation effects for each party?

So if we sent a rocket out which accelerated for 5 earth years to whatever speed we could achieve, then turned around and decelerated for another earth years and landed wouldn't both twins end up at actually the same age? However if you could fly by the earth without decelerating the space twin could observe the age difference on the other twin?


No. There is a unique (in flat spacetime, and often in curved spacetime as well) curve between any two timelike-separated events which maximises proper time. If you don't follow that curve you will experience less proper time. In any experiment like this, at most one of the twins can be on this curve and so the other will experience less proper time, and so be younger.

Note that it is possible to arrange life so that neither follow the geodesic, and further to arrange things so that they will end up experiencing equal proper times by so doing: but if one does follow the geodesic then other necessarily does not and will then be younger when they meet again.

  • $\begingroup$ So to clarify my understanding, because both objects are moving from the same point A to point B, and because space twin is covering more ground in the same time period, space twin will be younger. As a follow up question then, would earth twin be following actual proper time? Or would it just be much much closer to proper time because the speed is comparatively low? $\endgroup$ – tprox May 27 '16 at 21:06
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    $\begingroup$ @tprox 'proper time' is just the time as experienced by someone following a given path through spacetime, so each twin has their own proper time: it's just the length of the path they follow. It follows from Euclid (really!) that there is a single straight line between any two points: it follows from the nature of the metric (specifically that it has signature 2), that this line is the longest rather than the shortest curve between two points. In other words it's not about speed, it's about deviation from straightness (in fact, about acceleration). $\endgroup$ – tfb May 27 '16 at 22:01

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