Suppose in an empty space two rocketships exists with person A and B of same age inside each. Let A move with velocity c/2 away from B and return. They'll find out that B grew older while A didn't have that change in age due to relative passing of time. But this incident can also be interpreted in another way such that, we can assume B to be moving away while A stood still as there is no other frame to compare with. How will we define proper time and improper time in this case? Do we have to take the initial point of A in space into consideration? Doesn't this mean we're taking space as a universal reference frame?
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Hint: How does A return? – PM 2Ring Jun 22 '19 at 18:52
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2Hint 2: In order for A to start moving relative to B, it has to change reference frames, while B does not. – Dmitry Brant Jun 22 '19 at 19:01
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1The way you're using "event," "proper," and "improper" seems nonstandard. I think you mean "frame," "inertial," and "noninertial." – Jun 22 '19 at 23:18
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This problem was always a struggle for me, and the solution is that acceleration is measured with a scale; that is, acceleration is measured by measuring a force. Thus, the twin who in the rocket ship feels an acceleration as they speed up to their maximum velocity, and more importantly, they feel (and measure) an acceleration when turning around to come back. It is always the twin that feels the acceleration that ages more slowly, and it is clear from this definition of acceleration who that twin is.
Kraigolas
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but according to what we study we can't simply say there is acceleration only by feeling it. we always need a reference to judge the motion. how will we justify that? – Rahul Bhardwaj Jun 23 '19 at 06:20
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@rahulbhardwaj acceleration in relativity is defined through the measurement of a force. If had each twin stand on a scale, only one would read a force during the acceleration (ignore the surface gravity force for the twin who stays on earth, as this will be negligible compared to the other twins acceleration). This definition clears up the ambiguity which has you confused. – Kraigolas Jun 23 '19 at 12:58
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You just realized that constant speed is symmetrically relative. This means that there is a paradox called the twin paradox. Both twins could see the other speed away and age less.
Now the solution is in SR the change of reference frames, but the real solution is GR.
As per GR, and the equivalence principle, when the spaceship of A is returning, it needs to turn around.
Now turning around, needs deceleration and acceleration. Acceleration is the same as being in a gravitational field (equivalence principle). Acceleration is absolute.
Now when the spaceship of A turns around, it accelerates and during that acceleration, A is slowing down in the time dimension (relative to B), so he ages less during the turn around.
There is a age difference after the turn around, and that age difference is kept while A returns (with constant speed) to B.
Thus, when they meet again, A will seem to have aged less.
Árpád Szendrei
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SR is quite capable of dealing with acceleration in flat spacetime. You only need GR to handle curved spacetime. Please see John Rennie's answer to the linked question. But anyway, acceleration is a bit of a red herring. The core idea is the change of reference frame, acceleration is merely the means to achieve that change of frame. – PM 2Ring Jun 22 '19 at 21:06