Who Ages Faster in the Twin Paradox?

[Visceral]

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 Earth's 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.

Thanks for reading.

 

[TheEtherWind]

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.

 

[ghwellsjr]

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?

 

[yuiop]

If you are at rest in a given inertial reference frame then you do not feel any proper acceleration. When the traveling 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.

 

[mathman]

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.

 

[PeterDonis]

Visceral, you might want to read the Usenet Physics FAQ entry on the Twin Paradox:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_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.

 

[gmax137]

...
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

 

[HallsofIvy]

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.

 

[DrGreg]

Well, actually, the word "paradox" has multiple meanings including:

1. a seemingly absurd or self-contradictory statement that is or may be true
2. 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

 

[gmax137]

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.

 

[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.

 

[PeterDonis]

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.

 

[Underwood]

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.

 

[PeterDonis]

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/physics/Relativity/SR/TwinParadox/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.

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).

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.

 

[Underwood]

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.

 

[PeterDonis]

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.

Ah, I see. You are interpreting "error" as "wrong" ; but the FAQ really means "error" as in "something that has to be compensated for by adding in an additional term". In this case, what has to be compensated for is the difference in the zero of time between the two frames, i.e., the "error" is a "correction" you have to apply to convert one frame's time into the other's. The term "accounting error" is an unfortunate choice of words; the FAQ is not trying to say that the 13 year 8 month difference is an incorrect value; all 3 parts, as given in the FAQ, are correct values, and are added together correctly to give the correct final answer. It's just that one of them, the 13 years 8 months, doesn't correspond (in the Time Gap version, where the turnaround is instantaneous) to anything "observed" by Stella; it's just a change in zero of time that she has to apply when she changes inertial frames.

 

[whiskybob]

so has anyone actually flown a clock in space at relativistic speeds(or really fast speeds at least - I know clocks can be very accurate tools nowadays) and then collected it to see if it's fast or slow?

 

[Nugatory]

Yes, many times. Look at the FAQ on experimental support, a stcky thread at the top of this sub forum.

 

[Underwood]

all 3 parts, as given in the FAQ, are correct values, and are added together correctly to give the correct final answer.

OK, so it's right for the traveler guy to say that the homey girl gets a lot older when he turns around. It all comes out right. Thanks.

 

[Underwood]

For the problem we've been talking about, we can figure out how much older the homey girl got while the traveling guy was turning around by figuring out how much extra she had to age so that she would be the right age when he gets back. But is there any way to figure it out before he gets back? Can he figure it out right after he finishes turning around?

 

[indirachap]

With reference to the twin paradox: in order for one twin to end up younger than the twin on the ground the astronaught twin would have had to have spent his time in space in "slow motion" to account for difference in time between the clocks on the ground and on the spaceship.

Is this correct?

 

[Darwin123]

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 Earth's 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.

Thanks for reading.

What breaks the symmetry is the external force on the observer. The twin on Earth never has an external force applied to him. In order for the twin in the rocket ship to turn around, a large external force has to be applied to him.
Other people on this forum claim that the acceleration of the rocket breaks the symmetry. They are talking about a dynamic acceleration, not the kinematic acceleration. The kinematic acceleration is defined in terms of geometry, and so is symmetric to both observers. The dynamic acceleration is roughly the external force divided by the mass of the observer.
The magnitude of kinematic acceleration is the same for both twins, since the geometry is quite symmetric. This is probably what you are talking about. However, the dynamic acceleration is quite different. The twin in the spaceship, when turning around, is going to experience a large external force.
The twin who turns around is going to experience a "speed up" of his Earth twins aging no matter how long the turn around time is. The asymmetry of the time dilation increases with the linear impulse and distance between observers. Contrary to some critics, there is no way an observer that turns around won't be aware of his twins "extra age".
There is a little confusion due to the following misunderstanding. Some scientists have written that there is "no such thing as force in relativity". This is technically true only in a very narrow sense. Actually, the nature of the forces is critical to understanding relativity. In the case of special relativity, it is important to understand that the external impulse on the observer that breaks the symmetry.
So long as both observers do not experience an impulse, their observations will be symmetric. The impulse necessary to turn the spaceship around "causes" the Earth twin to age relative to the spaceship twin. Understand this is not a "cause" in the classical sense. Nothing happens to the Earth twin due to the impulse. However, the timing of the internal forces in the space rocket twin are changed by the impulse in a way that is inconsistent with Principia.

 

[Darwin123]

With reference to the twin paradox: in order for one twin to end up younger than the twin on the ground the astronaught twin would have had to have spent his time in space in "slow motion" to account for difference in time between the clocks on the ground and on the spaceship.

Is this correct?

Not for the entire trip. For example, the twin on Earth can "jump" ahead as seen by the rocket ship twin during the external impulse that turns him around.
This description of the Earth twin "jumping ahead" in age is a little oversimplified. Of course, there is Doppler effect and signal propagation issues. I am also ignoring the basic issue of how the rocket ship twin avoids getting squashed during the impulse. However, the experiences of the rocket twin during the turn around impulse are significantly different from any twin in an inertial frame.
If the rocket engines never fire, the twin in the rocket ship is going to go in a straight line and never meet his twin. Then, there is no paradox. However, the rocket engines cause the rocket to turn around. Contact forces in the floor or ceiling then apply an external impulse to the rocket twin. It is the external impulse, caused by the rockets, that cause the asymmetry.
There are several ways to say it. Some say acceleration, some say external forces, some say impulse, others talk about equivalent gravitational fields and some talk about space-time. However, the bottom line is that the external force on an observer distorts the measurements of time and distance.
An observer experiencing an impulse is not in an inertial frame. Therefore, special relativity without modifications doesn't work while the observer is undergoing dynamic acceleration. General relativity is the topic which describes precisely what the rocket twin sees.

 

[Nugatory]

An observer experiencing an impulse is not in an inertial frame.

Yes

Therefore, special relativity without modifications doesn't work while the observer is undergoing dynamic acceleration. General relativity is the topic which describes precisely what the rocket twin sees.

No. SR works just fine even for accelerations as long as you're in a flat space-time, one not curved by gravitational effects.

At a hand-wavy level... Even when accelerations are involved, at any given instant the speeds have definite values so SR will accurately describe the effects of those speeds at that instant. Google "Rindler coordinates" and "Bell spaceship paradox" for examples of how the math works out.

 

[Nugatory]

With reference to the twin paradox: in order for one twin to end up younger than the twin on the ground the astronaut twin would have had to have spent his time in space in "slow motion" to account for difference in time between the clocks on the ground and on the spaceship.

Is this correct?

No.

Consider that you could just as easily have said that the at-home twin would have had to spend his time in "fast motion" to account for the difference in time. What's to make the one description better than the other?

You're going wrong when you start thinking in terms of one twin being in slow (or fast) motion. When you're thinking that way, you're implicitly assuming that there's some true correct time out there so that you can compare the two twins's travel time against that time to see which one is "really" fast or slow.

 

[indirachap]

No.

Consider that you could just as easily have said that the at-home twin would have had to spend his time in "fast motion" to account for the difference in time. What's to make the one description better than the other?

You're going wrong when you start thinking in terms of one twin being in slow (or fast) motion. When you're thinking that way, you're implicitly assuming that there's some true correct time out there so that you can compare the two twins's travel time against that time to see which one is "really" fast or slow.

For me this is absolutely huge - I don't have a problem with anything else but this. I can't get my mind to accept the fact that "the books of time do not have to be balanced" like in accountancy.

From my Earthly point of view, it is essential to explain the discrepancy in the time of the two clocks - this is cardinal for my sanity! And the only explanation I can fnd is the fact
that the astronaught twin spent most of his time in space "in slow motion". This supplies the answer for the "missing time" between the two clocks.

The answer given to me by the scientists, on the face of it, sound just too metaphysical!
I suppose I will just have to accept it! Thanks

 

[ghwellsjr]

For me this is absolutely huge - I don't have a problem with anything else but this. I can't get my mind to accept the fact that "the books of time do not have to be balanced" like in accountancy.

From my Earthly point of view, it is essential to explain the discrepancy in the time of the two clocks - this is cardinal for my sanity! And the only explanation I can fnd is the fact
that the astronaught twin spent most of his time in space "in slow motion". This supplies the answer for the "missing time" between the two clocks.

The answer given to me by the scientists, on the face of it, sound just too metaphysical!
I suppose I will just have to accept it! Thanks

You are correct in saying that the astronaut twin spends most of his time "in slow motion" from an Earthly point of view, if by that you mean from an inertial Frame of Reference in which the Earth is at rest, the Earth twin and his clocks run at normal speed while the astronaut twin and his clocks run slower. However, you should not think that the astronaut twin can be aware that he and his clocks are running slower, in fact, as far as he is concerned, everything is normal because when he measures his heart rate using his clock, he still gets around 1 beat per second.

Also, you should be aware that there is nothing sacrosanct about the Earth's inertial rest frame, you can analyze the situation from any other inertial frame, including the ones in which the astronaut is at rest during either the first half or during the last half of his trip. This is what I pointed out in post #3. There is no "missing time" or "time gap" to be concerned about if you use just one inertial Frame of Reference. Please read it and see if it makes sense to you. If not, ask.

 

[phyti]

What breaks the symmetry is the external force on the observer.

What if the Earth twin decides to accelerate into space to hasten their reunion?

 

[Mentz114]

What if the Earth twin decides to accelerate into space to hasten their reunion?

Who ages most depends on the proper time ( also called proper length) of their journeys through spacetime. See here for an explanation of proper time

http://en.wikipedia.org/wiki/Proper_time

 

[Mark M]

It only seems metaphysical to you because you aren't working out the specific calculation. See 'specific example' here:

http://en.wikipedia.org/wiki/Twin_paradox

Even though two observers moving relative to each other should both say the other's clock is ticking slower, this doesn't account for other relativistic effects. When you work out the calculation as in the article, it works out fine. The real problem behind the twin paradox is the fact that it seems that one inertial observer is singled out as *really* moving, although this seems to violate the principle of relativity. The solution is that the observer isn't an inertial frame, since he had to accelerate up to his speed. So, he is distinguishable from the observer on earth.