## simple question regarding the twin paradox

Hi,

I am a little confused with this paradox. I asked my professor about it and he didnt really give a convincing answer. So the scenario basically seems to be some twins on earth(or anywhere) at rest, and then one leaves at relativistic speed for some time then comes back to see that his/her twin is much older than them.

My question is, how come you can tell which one would age more? Why couldn't it just as well be the one on the ship? From the twin on earths reference frame, they are at rest and then the rocket flies away from them, while in the rocket frame it is at rest and the earth flies away from them. From each of the twins perspective the other one moves and they are stationary in their own frames. How come the same thing wouldn't happen to the twin on earth and find the rocket twin older when the earth arrived back at the rocket?

I just took this paradox for granted for a long time but now I seem to be confused.

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 In order for twin on the rocket to return they must undergo acceleration, and therefore do not have an inertial frame of reference during the entire round trip.
 Recognitions: Gold Member You need to pick one inertial frame and stick with it from start to finish. And you need to understand that the faster you go in that frame, the slower your clock ticks. Now can you see that from the earth's frame, only the rocket twin's clock will run slow? And can you see that if you use the rocket's frame during the first half of the trip, only the earth's clock will run slow but during the last half of the trip, the rocket has to travel much faster than the earth in order to catch up with it and so its clock has to run even slower such that it ends up with less time on it when it gets back to earth?

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## simple question regarding the twin paradox

If you are at rest in a given inertial reference frame then you do not feel any proper acceleration. When the travelling twin turns around to head back he experiences proper acceleration and he can now be certain that he is not at rest in inertial reference frame. The stay at home twin does not feel proper acceleration during the turn around event, so the situation is not symmetrical.
 Recognitions: Science Advisor There is a simple way to understand it based on the Lorentz transformation. Say the traveler goes to a place ten light years away from earth. He quickly speeds up to almost the speed of light. The distance in his frame to his destination is now foreshortened and the time to get there is is greatly reduced. Once he gets there, stops and turns around to go back to earth, the same foreshortening of distance and time takes place. So in his frames the total time would be a lot less than twenty years, while the earth bound twin would age more than twenty years.
 Blog Entries: 9 Recognitions: Gold Member Science Advisor Visceral, you might want to read the Usenet Physics FAQ entry on the Twin Paradox: http://math.ucr.edu/home/baez/physic...n_paradox.html There are a number of different ways of understanding what's going on in this scenario (most of which have been mentioned in this thread), but the FAQ entry ties them all together. My personal preference is to look at everything using a spacetime diagram (the FAQ entry discusses this in some detail). Looking at it this way makes the solution obvious, in my view: you have two twins, each of which takes a different path through spacetime between the same pair of events (the event where they part, and the event where they come back together). The two paths they take have different lengths, so they experience different amounts of proper time passing between those two events (since the "length" of a worldline is just the proper time elapsed for someone following that worldline). Working out the actual math tells you that the stay-at-home twin's path is longer, so he ages more and is older when the two meet up again. It's no different in principle than the fact that two paths through Euclidean space that start and end at the same point can have different lengths; it's just geometry.

 Quote by Visceral ... My question is, how come you can tell which one would age more? Why couldn't it just as well be the one on the ship? ...
I think that's why it is called the twin paradox

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 Quote by gmax137 I think that's why it is called the twin paradox
Actually, no, it isn't. The term "paradox" is being used ironically- it is only a seeming paradox which can be resolved as others have said here.
 Recognitions: Gold Member Science Advisor Well, actually, the word "paradox" has multiple meanings including:a seemingly absurd or self-contradictory statement that is or may be true a self-contradictory proposition (my emphasis). Most of the paradoxes in physics and maths (including the twins paradox) turn out to be of the first type. Source: Collins Concise Dictionary, 4th Ed 1999
 Well, the OP said he suddenly thought to himself, why isn't this story symmetrical -- why is one twin different from the other?? But that's exactly the point of the story, isn't it? That's why it is the 'twin paradox' not the 'twin effect' or some such. As DrG points out, it seems contradictory, but it isn't.
 If the traveler twin, on both his outgoing trip and on his returning trip, says that his home twin is aging slower than he is, then how can he find the home twin to be older when he finally gets back? I think the answer is that the traveler twin says his home twin ages a lot during his turnaround.

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 Quote by Underwood If the traveler twin, on both his outgoing trip and on his returning trip, says that his home twin is aging slower than he is, then how can he find the home twin to be older when he finally gets back? I think the answer is that the traveler twin says his home twin ages a lot during his turnaround.
This is one way of looking at it, yes. Check out the Usenet Physics FAQ entry I linked to in post #6.

 Quote by PeterDonis This is one way of looking at it, yes. Check out the Usenet Physics FAQ entry I linked to in post #6.
Thanks. I read it, but it says that the gap is an accounting error. Seems like if the gap is an error, then it would also have to be an error for the traveler twin to say that the stay-home twin ages slower when the traveler's going away, and when he's coming back. Is that an error too? I hear lots of people talk like that's true.

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 Quote by Underwood Thanks. I read it, but it says that the gap is an accounting error.
I assume you're referring to the "Time Gap Objection" page...

http://math.ucr.edu/home/baez/physic.../twin_gap.html

...which says

 The apparent "gap" is just an accounting error, caused by switching from one frame to another.
The "accounting error" is basically changing the "zero point" of time; the outbound reference frame has a "zero" of time that is about 13 years and 8 months earlier than the "zero" point of time in the inbound reference frame. So when you switch frames, you have to switch zeros of time as well. That adds 13 years and 8 months to Terence's clock as seen by Stella.

 Quote by Underwood Seems like if the gap is an error, then it would also have to be an error for the traveler twin to say that the stay-home twin ages slower when the traveler's going away, and when he's coming back.
Why do you think the two have to be connected? "Ages slower" refers to the *rate* at which time "flows" in one frame compared to the other; it doesn't say anything about where the "zero point" of time is set. On the Time Gap Objection page, it says:

 During the Outbound Leg, Terence ages less than two months, according to Stella. (12 Stella-months / time dilation factor of 7.) During the Inbound Leg, Terence also ages less than two months, according to Stella, by the same computation.
So Terence does "age slower", according to Stella, on *both* legs, in this interpretation, even though he ends up older at the end (because of the change in "zero point" of time).

 Quote by Underwood I hear lots of people talk like that's true.
I suspect that's because they're trying to use a different interpretation than the "Time Gap" one. For example, check out the Doppler Shift Analysis page in the FAQ.

The key is that there is not a single unique "right answer" for most of these questions; how you answer them depends on how you interpret various observer-dependent quantities. The only question that has to have a unique answer is, how do the two twins' ages compare *when they meet again*. That answer is unique because both twins are at the same location at the same time, so none of the ambiguities in interpretation come into play.

 Quote by PeterDonis Why do you think the two have to be connected?
I'm just saying that if the traveling guy says that his home-staying twin's total aging while he is gone is the sum of 3 parts, then if one of the 3 parts is an error, the other 2 parts can't be right either. Because the sum is right.

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