In SR, pure relative velocity between two observers causes a time dilation between them. It seems that if the two observers were at rest w.r.t. each other at some point in time, then the one who accelerates to achieve the relative velocity is the one who gets time dilation (i.e. comparatively slower clock rate). The acceleration itself though is not the cause for the time dilation. The acceleration can be very brief anyway. - The velocity achieved by the accelerating observer is what causes the time dilation. - The longer he travels at that velocity, greater the total time dilation - When he decides to decelerate and stop (to breathe perhaps) w.r.t. the stationary observer, the time dilation between the two also stops - When the traveling observer decides to accelerate back to the other observer, his clock again starts ticking slower - So when the two get together again, the traveling observer's clock shows less time elapsed than the observer who never moved. If the above is correct, my questions is: - Is there a physical difference between the traveling observer and the stationary one, after the traveling observer has accelerated for a short period and then reached a steady inertial velocity w.r.t. the stationary observer? In other words, why is the asymmetric time dilation continuing for the traveling observer? Is this because his acceleration has made some fundamental change to his physical properties, which continues to exist even after the acceleration has stopped?