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Okay, I'm asking a question similar to this one here: Time Dilation - what happens when you bring the observers back together?. Specifically, I am curious about a specific angle on the second part of his question, regarding when two moving frames of reference (FoR) are brought back together, and how "it" knows which one should be still young.

The accepted answer on that question says that it is whichever FoR experienced the forces of acceleration/deceleration. But, isn't that the whole point of relativity, is that it's all ... well, relative; that it is not possible to say with a certainty that it was the traveler in the spaceship who was accelerating/decelerating?

Isn't it the case that it is just as legitimate to say that the universe and people on the planet accelerated/decelerated and the traveler in the spaceship was stationary? This would therefore then lead to that the universe and planet-side people should remain young and the spaceship occupant should be old, no?

Does dilation (temporal-spatial) just generally apply to the smaller of the two FoRs, or is there some other system or rule which "decides" which FoR gets dilated?

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up vote 15 down vote accepted

"Relativity" is actually a misleading word that Einstein didn't like. It doesn't mean "every vantage point is equivalent and it's all relative". It really means only inertial, non-accelerating vantage points are equivalent. You could think of it as, prior to relativity, people believed that there was an absolute position/speed to the universe. Special Relativity shows that there is not, but rather, there is an absolute acceleration to the universe.

This is illustrated by the famous rotating bucket thought experiment. You put a bucket out in the middle of empty space and spin it, and the water in it starts flowing towards the edges. But if all vantage points were the same, couldn't you also think of it as the universe spinning and the bucket stationary? But one vantage point is obviously more correct than the other, because only one involves the water flowing towards the edges. Thus there is a "universal" state of zero acceleration that is unambiguous.

It is interesting to note that Einstein's original idea for his theory of Special Relativity was a theory of Invariance (of the speed of light)

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That's not quite true: prior to STR, people thought that light has a special frame of a background "aether". Whether that also meant that there is a special inertial frame for mechanics is much stronger, and was not generally agreed upon. In reality, the principle of relativity goes all the way back to Galileo, and even Newton (who wanted absolute space) admitted that his theory is the same in every inertial frame. Einstein demonstrated that the transformation between frames in Lorentzian rather than Galilean by adding electrodynamics, but the core of the principle was much older. – Stan Liou Mar 2 '11 at 6:06
@Stan - I'm only an amateur, but doesn't aether imply that there is a special/desired velocity? (that is, zero with respect to the aether) – Justin L. Mar 2 '11 at 6:54
You're completely right in terms of EM: people did think that there was a single correct picture brought about by the reality of the aether. But this is a question of mechanics rather than EM, and in mechanics, the principle of relativity goes way back to Galileo, ca. 1630 (Einstein extended it to EM rather than make it from scratch). While Newton preferred absolute space, not everyone agreed with him (e.g., Leibniz). ... Though this is kind of nitpicky since the dispute is about history rather than physics. Feel free to ignore it on those grounds. (: – Stan Liou Mar 2 '11 at 7:18
@Stan Actually I see your point now; I was talking about history in the wrong context, heh. – Justin L. Mar 2 '11 at 7:22
@gwho Conceptually, inertial means nonaccelerating. Direction does not matter for time dilation between inertial frames. In spacetime, inertial worldlines (paths) are straight, and accelerated ones are bent, so not only is there an asymmetry, but since the length of the worldline is the time measured by a clock on it, having inertial and accelerated observers register different times is no more mysterious than the length of a line segment being different some other curved line connecting the endpoints. Beyond that, I suggest asking a separate question or looking for ones on twin paradox. – Stan Liou Oct 3 '14 at 0:06

Mentions of "acceleration", or lack of it, to establish the difference between the twins' careers, are confusing the issue. (This can be proved by concocting roadmaps for two travelers with identical acceleration or deceleration periods, only placed at different times of their respective journeys. This way, their watches don't show the same elapsed time when they are reunited.)

A better mental picture is obtained by considering paths in spacetime for each traveller. Both paths start from the same "event" (the event of the twins saying good bye to each other) and arrive at another event (their getting together again). Now, just as two different paths in space, with same beginning and same end, need not have the same length, two different paths in space-time need not have the same "four-dimensional length", so to speak. The quotes are meant to warn that this expression is not used by relativists: This "four-dimensional length" is actually what they call "proper time", and it happens to be (according to Special Relativity), what each twin's wristwatch is measuring.

So the main issue is this difference in spacetime trajectories, not gravitational effects per se. That the steady twin finds himself older than his sister at the end comes from the fact that his spacetime trajectory is rectilinear, whereas his twin's is curved. And contrary to three-dimensional length, "four-dimensional length", aka proper time, is maximal, not minimal, for straight (i.e., physically, inertial) spacetime trajectories.

Of course, one will suffer accelerations if one follows a curved 4-D path. But,

(1) Meaningful effects (in terms of age difference) can be obtained with small accelerations (of order 1 g) over a few years, so invoking GR is not necessary.

(2) Acceleration per se does not cause the proper-time discrepancy: Two traveling twins who suffer the same acceleration-deceleration events (the same in intensity and duration) can age differently if these events are not scheduled the same way. The real cause is this difference in scheduling, which is logically the same thing as a geometrical difference between the two 4-D paths.

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This discussion is way overkill for the basic twin paradox. All one needs is that one of the twins follows a geodesic while the other one does not (and therefore feels acceleration). So saying that accelerating twin is younger is equivalent to saying that geodesics maximize proper time. Hopefully, even strong opponents of acceleration explanation won't feel so disturbed by the purely geometrical observation on geodesics ;) – Marek Mar 1 '11 at 15:18
:D @Marek Did we just post the same answer simultaneously in the Earth's approximate inertial frame? – dbrane Mar 1 '11 at 16:19
I do agree it's overkill. But I want to make another point, for which it's not: That the issue is not "no acceleration, i.e. geodesic" versus "accelerations, i.e., non-geodetic worldline". One can schedule two trips with exactly the same episodes of acceleration-deceleration, only differently placed during the trips. The two worldlines are different, but both twins experiment the same total discomfort (or relief) due to acceleration (or lack of it). Yet, they age differently. This shows that differential aging is not (directly) caused by acceleration. – Bossavit Mar 1 '11 at 21:15

Isn't it the case that it is just as legitimate to say that the universe and people on the planet accelerated/decelerated

No, it's not. If you stay on the planet, you know you didn't accelerate (that is, not any more than usual due to the gravitation and rotation of Earth, etc.). But if you are in the spaceship and you turn your engine on, you'll definitely feel the acceleration (same way you feel it in your car). We call the former frames (those that don't feel the force) inertial and they play very special role in the theory of relativity (both special and general).

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The other answers all bring out the essential points but I'll try to rephrase things in a way that makes it clear how the two "twins" (of the twin paradox) are different without any reference to General Relativity.

The twin on earth is always on a geodesic of the spacetime (which is flat Minkowski) whereas the round-trip accelerating twin is on a worldine that clearly deviates from a geodesic. So in this picture, it is very clear that the situation is not symmetric with respect to the twins. And you can also calculate the proper time ("length" of the worldines) and see that it is shorter for the non-geodesic path. In fact, the Minkowski spacetime is such that the proper time is maximized for geodesics.

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Very good. This is the explanation I give when I know the person is familiar with underlying geometry. Otherwise I just talk about acceleration (which is equivalent). – Marek Mar 1 '11 at 15:46

In special relativity, acceleration breaks the symmetry between the two observers since SR is applicable only in the inertial frames. If you insists the relativity of all motions then you have to use GR. If you apply GR to the problem you will get the same answer. However, SR is sufficient to answer the twin paradox. Putting simply, just remember that although all motions are relative according to GR, the equivalence principle demands that acceleration is equivalent to gravitation for the observer accelerating. The symmetry between the two observers break there.

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