How Time Passes Differently for Twins Traveling at Light Speed

[Prague]

I am trying to understand the twin paradox, so you have twin 1 and twin 2, both on planet earth. The twins are 23 years old and twin 2 leaves on a ship traveling close to the speed of light and then turns around (with or without a instantaneious turn around time?). On his return home twin 2 finds that twin 1 has aged far more than he has.

Now, why is this? Twin 2 travels away from Earth at the speed of light. Let's say 10 minutes (in a universal time) passes. Even though twin 2 is traveling at the speed of light, isn't he still traveling 10 mintues? And twin 1 would still be waiting for 10 mintues. Now let's say twin 2 turns around, and travels back to earth, this entire trip (from turnaround to landing) takes another 12 minutes. It still is 12 minutes for either twin 1 and 2 isn't it?

Just because he is traveling a distance why should he be younger? Is this just our notion of time (i understand if the times wasn't a 'universal time' it would make them much different in age) but isn't the notion of time false anyways? Our bodies don't slow for time, they always are dieing at an interval. So biologically wouldn't twin 1 and 2 be the same age, but theoretically (if we consider time as we concieve it, a real factor in our aging) there 'age' would be different.

 

[HallsofIvy]

"Twin 2 travels away from Earth at the speed of light. Let's say 10 minutes (in a universal time) passes. "

Right there you have two problems: you can't move at the speed of light (you are welcome to use "99% the speed of light). More importantly there is no such thing as "a universal time" so I don't know what you mean by this.

"It still is 12 minutes for either twin 1 and 2 isn't it?"

No, it isn't! That's the whole point of relativity. Again, there is no "universal time". There is no such thing as "time" except as measured in a particular frame of reference. There is no reason to think that the same amount of time will have passed for both.

And, no, the bodies of two people moving at very different speeds will age at different rates. While that hasn't be done with actual people (the difference in speeds would have to be much greater than anything we can achieve for it to show) it has been shown that elementary particles will have different "life spans" depending upon their speeds (measured relative to the laboratory, of course).

 

[Prague]

(sorry that was a typo, i meant close to the speed)

anyways, what is it that makes our bodies age less? How does speed affect this?

Perhaps my whole view on the times relative to each persons position/speed is wrong. The person moving at the speed of light is aging himself only let's say 10 minutes, but the person on Earth is aging more? I don't understand why this effects age, it's just distance.

Also, is the reason we can't have a universal time because time is distorted my certain objects, like the Earth for example? Time around the Earth is much different then the time around an object much larger than earth.

 

[JesseM]

Also, is the reason we can't have a universal time because time is distorted my certain objects, like the Earth for example?

Even in special relativity, where you ignore gravity, universal time doesn't make sense. For example, as long as two observers are moving at constant velocity (meaning unchanging speed and unchanging direction) relative to each other, there is no absolute truth about who is aging slower--in my reference frame you may be aging at half the speed as I am, but in your reference frame it is me who is aging at half the speed you are. Also, different reference frames disagree about "simultaneity", the question of whether two events at different locations happened "at the same time" or not--if I assign two events the same time-coordinate in my reference frame, then in your reference frame you will assign them two different time-coordinates, saying that one event happened after the other one.

 

[Prague]

Even in special relativity, where you ignore gravity, universal time doesn't make sense. For example, as long as two observers are moving at constant velocity (meaning unchanging speed and unchanging direction) relative to each other, there is no absolute truth about who is aging slower--in my reference frame you may be aging at half the speed as I am, but in your reference frame it is me who is aging at half the speed you are. Also, different reference frames disagree about "simultaneity", the question of whether two events at different locations happened "at the same time" or not--if I assign two events the same time-coordinate in my reference frame, then in your reference frame you will assign them two different time-coordinates, saying that one event happened after the other one.

Yes, but why is it that the observer see's the other aging slower. I am finding it hard to accept that speed and distance result in our aging. If you were to bring the two observers together again, who would be older. One observer saw the person aging slower than him, the other observer saw the same but in reverse. If you bring them together, who was correct?

 

[pervect]

Either one could be "correct". The observer that accelerates will be the younger observer when the re-unite. In order for them to re-unite, one observer has to accelerate.

 

[Prague]

Either one could be "correct". The observer that accelerates will be the younger observer when the re-unite. In order for them to re-unite, one observer has to accelerate.

ok, so why is it that acceleration decreases our age?

 

[robphy]

ok, so why is it that acceleration decreases our age?

It isn't the acceleration that decreases our age. Rather, it is a feature that distinguishes the motions of the two twins.
At the root of the matter, elapsed time is proportional to the arc-length in spacetime.

 

[JesseM]

ok, so why is it that acceleration decreases our age?

It's not that acceleration decreases your age, I'd say it's that the laws of physics have to work equally well in any non-accelerating reference frame, and in each frame a clock moving at velocity v must be ticking at $$\sqrt{1 - v^2/c^2}$$ times the rate of a clock at rest in that frame. So if you want to know how much time elapses on the clock of an observer who is changing velocities according to some function v(t), between times $$t_0$$ and $$t_1$$ (with velocity and time defined in terms of that frame) you'd evaluate the integral $$\int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt$$. The value always turns out to be less than the time elapsed on a clock that traveled inertially between the same two points in space in the same time interval. And since the laws of physics should work equally well in any inertial frame, you will get the same answer regardless of which frame you are using to define the time interval and the function v(t).

I don't think there's really an answer of what "causes" clocks to slow down, it's just sort of the nature of spacetime in relativity. But the way spacetime works in relativity does follow uniquely from two postulates, the first being that the laws of physics should work the same in every inertial frame, and the second being that the speed of light should be the same in every inertial frame.

 

[Prague]

It's not that acceleration decreases your age, I'd say it's that the laws of physics have to work equally well in any non-accelerating reference frame, and in each frame a clock moving at velocity v must be ticking at $$\sqrt{1 - v^2/c^2}$$ times the rate of a clock at rest in that frame. So if you want to know how much time elapses on the clock of an observer who is changing velocities according to some function v(t), between times $$t_0$$ and $$t_1$$ (with velocity and time defined in terms of that frame) you'd evaluate the integral $$\int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt$$. The value always turns out to be less than the time elapsed on a clock that traveled inertially between the same two points in space in the same time interval. And since the laws of physics should work equally well in any inertial frame, you will get the same answer regardless of which frame you are using to define the time interval and the function v(t).

I don't think there's really an answer of what "causes" clocks to slow down, it's just sort of the nature of spacetime in relativity. But the way spacetime works in relativity does follow uniquely from two postulates, the first being that the laws of physics should work the same in every inertial frame, and the second being that the speed of light should be the same in every inertial frame.

Ok, but we aren't mechanical clocks, we are biological clocks. Does biology agree with this? Sure if twin A was holding a clock and twin B was also holding a clock and they brought them together after B left, then sure I can kind of see now why the time would be different. But what about the twins, would twin B still be a little boy and twin A an old man.

 

[hypermorphism]

Ok, but we aren't mechanical clocks, we are biological clocks. Does biology agree with this?

The results of the postulates of special relativity have nothing to do with the specific construction of time-keeping devices. Simply something that measures position on a time axis from some initial time, or in more everyday language, change.

 

[Prague]

The results of the postulates of special relativity have nothing to do with the specific construction of time-keeping devices. Simply something that measures position on a time axis from some initial time, or in more everyday language, change.

Ok, I cleared up all my doubts, so what's the actual math/theory behind the issue this thread brought up? Specifically I mean.

 

[hypermorphism]

Hmm, I don't think it lends itself to a quick internet exhibition. The resulting equations come from considering two frames in relative motion of uniform velocity with respect to each other, and considering a light signal emitted in one of the frames. A layman's derivation is given in , where one can nowhere see any reference to physical clocks, just relative time and space variables obeying the postulates. There is a light-clock derivation in , but this refers to a specific construction of a clock only as an appeal to the student's geometric intuition. Their book is, however, one of the best introductions to the subject, as it is full of meaningful exercises (some are simplifications of results written in research papers) and intuitive illustrations.

 

[jdavel]

Prague,

Suppose the traveling twin goes to a planet that's 10 light years from Earth and travels at a speed that gets him there in 20 years (hardly close to light speed, but it will do). If each twin watches the other through a telescope throughout the twenty year trip, what will they each see happening? What will they each be seeing at the moment the traveller arrives at the distant planet?

 

[jtbell]

If each twin watches the other through a telescope throughout the twenty year trip, what will they each see happening?

I posted a detailed description of a similar scenario in this forum just a few days ago. See post #3 in this thread.

 

[Prague]

For a much more precise answer, look at this post by JesseM, which helped me understand the twin paradox "when I use it as a reference, I just learned it today afterall. Below is my attempt to explain without the math and without using JesseM's post as a reference.

Link: https://www.physicsforums.com/showpost.php?p=515872&postcount=18

Prague,

Suppose the traveling twin goes to a planet that's 10 light years from Earth and travels at a speed that gets him there in 20 years (hardly close to light speed, but it will do). If each twin watches the other through a telescope throughout the twenty year trip, what will they each see happening? What will they each be seeing at the moment the traveller arrives at the distant planet?

So you have twin A and twin B and Planet X. B departs for X which is 10 light years away. He travels at a speed somewhat near c, and it takes B 20 years to get to X. If B looks back at A during travel A will look as if he is aging slowly. If A looks at B the same affect happens. Now when B looks at a from X which I suppose is traveling relative to A's speed now making B traveling the same speed they would start to age the same speed again.

Now, when B lands on X he will be younger than A because his clock was traveling slower than A. (or perhaps I am wrong on this, I am not sure, because occording to the 'usual' twin paradox, B would have to travel back to A to be younger.)

I think that's correct.

 

[Ich]

Yep, B is younger in this frame. But there would still be people who think A is younger, namely those moving near c wrt this rest frame. That´s why they tell B to come back to have an unambigous solution.

 

[TheUnknown]

Yes, but why is it that the observer see's the other aging slower. I am finding it hard to accept that speed and distance result in our aging. If you were to bring the two observers together again, who would be older. One observer saw the person aging slower than him, the other observer saw the same but in reverse. If you bring them together, who was correct?

would they not be the same age when reunited? if observer A flies at close to the speed of light to point C (which will be farther than point D because of his speed compared to observer B) and observer B flies to point D at half the speed of light... and they both start at F and reunite at F at the same time, wouldn't their ages be the same? ah... i have edited this.. i have caught myself making a huge mistake... because the fact that observer B's travel distance is shorter than A's... he will also have to travel slower back to point F again... BUT... if you add a point G opposite of point F corresponding to points C and D... and they meet there, then they are the same age! because observer B now has to travel at A's initial speed... and A at b's initial speed! ah... time as we know it... it's so misleading. physics are great. :) i love this site, and all you guys are great for doing what you do.

 

[yogi]

Completed round trip journeys always result in the clock which made the trip having logged less time. But there are one way examples of clocks in motion also logging different times relative to the frame in which they were brought to rest - Einstein gives a clear statement of this reality in his 1905 paper - two clocks separated by a distance, both at rest in the same frame, and synchronized so that they run at the same rate. One clock is moved toward the other... when they meet they are found to be out of sync. Jesse doesn't like this experiment - he insists the two clocks can't really read differently - but as between Jesse and Einstein, I am leaning toward the latter.

 

[Ich]

Completed round trip journeys always result in the clock which made the trip having logged less time. But there are one way examples of clocks in motion also logging different times relative to the frame in which they were brought to rest - Einstein gives a clear statement of this reality in his 1905 paper - two clocks separated by a distance, both at rest in the same frame, and synchronized so that they run at the same rate. One clock is moved toward the other... when they meet they are found to be out of sync. Jesse doesn't like this experiment - he insists the two clocks can't really read differently - but as between Jesse and Einstein, I am leaning toward the latter.

Never heard about it - unless you mean "moved" as with a significant fraction of c.

 

[JesseM]

Completed round trip journeys always result in the clock which made the trip having logged less time. But there are one way examples of clocks in motion also logging different times relative to the frame in which they were brought to rest - Einstein gives a clear statement of this reality in his 1905 paper - two clocks separated by a distance, both at rest in the same frame, and synchronized so that they run at the same rate. One clock is moved toward the other... when they meet they are found to be out of sync. Jesse doesn't like this experiment - he insists the two clocks can't really read differently - but as between Jesse and Einstein, I am leaning toward the latter.

Einstein does not say that one has aged less in absolute terms, he just says that one is behind the other when they meet, which of course I agree with. Einstein also says that every reference frame is equally valid, and there is certainly a frame where the clock that accelerates is ticking faster then the one that doesn't as they approach each other (in this frame, they started out out-of-sync, so it will still be true that the clock that accelerated will be behind the other when they meet), so it's you who disagrees with Einstein if you're saying one clock ages less in an absolute sense, not me.

 

[Ich]

Einstein does not say that one has aged less in absolute terms, he just says that one is behind the other when they meet, which of course I agree with. Einstein also says that every reference frame is equally valid, and there is certainly a frame where the clock that accelerates is ticking faster then the one that doesn't as they approach each other (in this frame, they started out out-of-sync, so it will still be true that the clock that accelerated will be behind the other when they meet), so it's you who disagrees with Einstein if you're saying one clock ages less in an absolute sense, not me.

If you make a twin paradox out of this, you will end up with one twin being younger:
A anb B both start moving away from each other, very slowly. If they stop moving relative to another and compare clocks, they will find to be still in sync. Thats yogi´s starting point. When then B accelerates towards A and reaches him, he will have aged less.

 

[JesseM]

If you make a twin paradox out of this, you will end up with one twin being younger:
A anb B both start moving away from each other, very slowly. If they stop moving relative to another and compare clocks, they will find to be still in sync. Thats yogi´s starting point.

But in a frame where the Earth is moving at 0.99c or something, then if the second twin moves away from the Earth "very slowly" (ie if you take the limit as his velocity in the Earth's frame approaches zero), you still find that in this frame his clock gets significantly out-of-sync with the earth-twin's frame as they move a significant distance apart, so in this frame your "starting point" looks quite different, and is still compatible with the idea that the traveling twin's clock can be running faster after he accelerates and starts getting closer to Earth again.

 

[Ich]

But in a frame where the Earth is moving at 0.99c or something, then if the second twin moves away from the Earth "very slowly" (ie if you take the limit as his velocity in the Earth's frame approaches zero), you still find that in this frame his clock gets significantly out-of-sync with the earth-twin's frame as they move a significant distance apart, so in this frame your "starting point" looks quite different, and is still compatible with the idea that the traveling twin's clock can be running faster after he accelerates and starts getting closer to Earth again.

They will be out of sync as long as they are apart. When they rejoin, they will be in sync again except for this little difference one would calculate in the rest frame. Proper time is unambiguous.

 

[JesseM]

They will be out of sync as long as they are apart. When they rejoin, they will be in sync again except for this little difference one would calculate in the rest frame. Proper time is unambiguous.

Yes, if they moved slowly in both directions. But since we were talking about the twin paradox and age difference, I thought you meant that they would move apart very slowly, leading to the initial separation with their clocks still very close to synchronized in the Earth's frame, then reunite at some significant speed so the traveling twin would be noticeably younger when they met.

 

[Ich]

Yes, if they moved slowly in both directions. But since we were talking about the twin paradox and age difference, I thought you meant that they would move apart very slowly, leading to the initial separation with their clocks still very close to synchronized in the Earth's frame, then reunite at some significant speed so the traveling twin would be noticeably younger when they met.

That´s exactly what I meant, provided that they move VERY slowly wrt Earth in the beginning.
I´m afraid I´m starting missing something.

 

[JesseM]

That´s exactly what I meant, provided that they move VERY slowly wrt Earth in the beginning.
I´m afraid I´m starting missing something.

But then why did you say "When they rejoin, they will be in sync again except for this little difference one would calculate in the rest frame"? If they move together quickly, they will not be in sync again (or infinitesimally close to in sync, as they would if their relative motion was very slow in both directions), the clock of the twin who turned around will be significantly behind the clock of the twin who moved inertially.

Anyway, my point is that any inertial reference frame is equally valid, which means you cannot say that the traveling twin objectively "aged less" on just the inbound leg of the trip as yogi would, although you can say he aged less from the moment he departed the earth-twin to the moment they reunited. In a frame where the traveling twin was at rest during the inbound leg and the Earth was moving at high velocity towards him, it is the Earth that ages less during this leg of the trip. But in this frame, the traveling twin aged significantly less during the outbound leg, even though in the Earth's frame his velocity in the outbound leg was close to zero so his age stayed about the same as the earth-twin's. The result is that in this second frame, at the moment the traveling twin accelerates in the direction of the earth, he is already significantly younger than the earth-twin, so even though he ages faster than the earth-twin during the inbound leg in this frame, he will still be younger than the earth-twin when they reunite. But you cannot say that he "aged less" than the earth-twin during the inbound leg, in this frame he aged more during this period because the earth-twin's clock was ticking slower.

 

[Ich]

- that´s what i meant with "little" difference - I did not imagine B to accelerate to .99 c. Anyway - we agree here.
- I think I got your point. Still, the setup of yogi´s gedankenexperiment is such that you have three events:
1) A looks at his clock at time 0, position 0
2) B starts approaching A at time 0, position x
3) B passes A at time t, position 0
All times and position as measured in A´s frame.
It does not matter if B really accelerates or merely flies by - the interval between 2) and 3) is less than the interval between 1) and 3). So B aged less.
However, the situation is in no way symmetric, as yogi may conclude (would he?). If you change to a system which is in motion relative to A (eg B´s system), Events 1) and 2) would no longer be simultaneous. I think that´s what you want to say.

 

[JesseM]

- that´s what i meant with "little" difference - I did not imagine B to accelerate to .99 c. Anyway - we agree here.
- I think I got your point. Still, the setup of yogi´s gedankenexperiment is such that you have three events:
1) A looks at his clock at time 0, position 0
2) B starts approaching A at time 0, position x
3) B passes A at time t, position 0
All times and position as measured in A´s frame.
It does not matter if B really accelerates or merely flies by - the interval between 2) and 3) is less than the interval between 1) and 3). So B aged less.

But B only aged less in A's frame. If you look at things in the frame where A was at rest and B was moving towards him, in this frame A aged less between the time B accelerated and the time A and B passed each other. Yogi doesn't accept that either perspective is equally valid, and says there's some objective, frame-independent sense in which B really aged less between the time he accelerated and the time A and B passed, because B was the one who accelerated.

However, the situation is in no way symmetric, as yogi may conclude (would he?). If you change to a system which is in motion relative to A (eg B´s system), Events 1) and 2) would no longer be simultaneous. I think that´s what you want to say.

Yes, exactly.

 

[Rev Prez]

Just because he is traveling a distance why should he be younger?

Because, if we accept that the "stationary" observer is just that, the only one changing reference frames is the twin we expect would be younger. If you wouldn't describe two objects moving on two "different" paths relative to a stationary as being in the same reference frame, why would you try to do for a single object that moves along two "different" paths?

Rev Prez