Understanding Time Dilation and Differential Aging in the Twin Paradox

[t_ras]

OK, I though I understand this one , yet something doesn't settle down...
If I had a tween flying in a rocket at a very high speed and he came back to earth, he would be younger then me. I understand the reason for that and it is fairly straight forward.
What strikes me is that velocity is relative, which would mean, if I got to a rocket and I "accelerated" to the same speed as my tween (compared to our triplet tween staying on earth), I would be the one younger then my tween. Since as far as he cares, I was traveling very fast until i got to him...Am I getting it right?
If so, how can we solve the following paradox:
I stayed on Earth and my tween got a rocket flying him at a hundredth of the speed of light. After a year in Earth I send him a message signing with a date and time. It gets to him and ,since the speed of light is absolute and the radio waves of the massage travels at the speed of light, he gets the message rather immediately. The date-time he would be seeing should be in his future, yet again, as far as he can tell, I'm the one traveling very fast and thus my time should run slower.
I'm obviously getting something wrong here...could some one explain?
Could it be that, somehow, the time dilation is always smaller than the time it would take for a wave of light to reach from the sender to the receiver?

 

[Khashishi]

OK, I though I understand this one , yet something doesn't settle down...
If I had a tween flying in a rocket at a very high speed and he came back to earth, he would be younger then me. I understand the reason for that and it is fairly straight forward.

So far, OK.

What strikes me is that velocity is relative, which would mean, if I got to a rocket and I "accelerated" to the same speed as my tween (compared to our triplet tween staying on earth), I would be the one younger then my tween. Since as far as he cares, I was traveling very fast until i got to him...Am I getting it right?

What do you mean by "until I got to him"? If you are going the same speed, you will never catch up to him. You have to go faster than him to catch up. If you do go faster to catch up, then you will be younger when you catch up. If you don't catch up, but instead maintain a fixed distance after matching speed, then who is younger depends on who is doing the calculation. According to the person on Earth, your twin who set out first is younger. According to both you and your twin who set out first, you are younger. You should do a world line drawing to increase your understanding and make sure you aren't missing anything.

I stayed on Earth and my tween got a rocket flying him at a hundredth of the speed of light. After a year in Earth I send him a message signing with a date and time. It gets to him and ,since the speed of light is absolute and the radio waves of the massage travels at the speed of light, he gets the message rather immediately.

Why do you say immediately? It takes time for light to travel to him. It should take close to a year/100 for the message to reach him. According to him, you sent the message before a year has past, but by the time the light reaches him, he will have been traveling for a little more than a year.

 

[t_ras]

Why do you say immediately? It takes time for light to travel to him. It should take close to a year/100 for the message to reach him. According to him, you sent the message before a year has past, but by the time the light reaches him, he will have been traveling for a little more than a year.

The issue is that, by his calculations, my clock goes slower. This means, somehow, for it to be right, the sum of the time he calculates has passed at my end + the time it takes the message to travel should be such that it shows my time is really going slower. Here is where I want to know how this is happening.
Could you point me to some time dilation formula maybe? Perhaps the mathematics will make it easier for me to understand it...

 

[PeroK]

The issue is that, by his calculations, my clock goes slower. This means, somehow, for it to be right, the sum of the time he calculates has passed at my end + the time it takes the message to travel should be such that it shows my time is really going slower. Here is where I want to know how this is happening.
Could you point me to some time dilation formula maybe? Perhaps the mathematics will make it easier for me to understand it...

In fact, neither clock is running slower than the other. Each clock measured in the other's reference frame is slower, but that is the same for both.

The differential ageing at the end of a trip depends on the spacetime paths and especially on changes in inertial reference frames.

 

[Janus]

OK, I though I understand this one , yet something doesn't settle down...
If I had a tween flying in a rocket at a very high speed and he came back to earth, he would be younger then me. I understand the reason for that and it is fairly straight forward.
What strikes me is that velocity is relative, which would mean, if I got to a rocket and I "accelerated" to the same speed as my tween (compared to our triplet tween staying on earth), I would be the one younger then my tween. Since as far as he cares, I was traveling very fast until i got to him...Am I getting it right?
If so, how can we solve the following paradox:
I stayed on Earth and my tween got a rocket flying him at a hundredth of the speed of light. After a year in Earth I send him a message signing with a date and time. It gets to him and ,since the speed of light is absolute and the radio waves of the massage travels at the speed of light, he gets the message rather immediately. The date-time he would be seeing should be in his future, yet again, as far as he can tell, I'm the one traveling very fast and thus my time should run slower.
I'm obviously getting something wrong here...could some one explain?
Could it be that, somehow, the time dilation is always smaller than the time it would take for a wave of light to reach from the sender to the receiver?

First off, the date time that he would see would not be "in his Future".
He is traveling at 0.01c, so after 1 year after he leaves and you send your message, he is 0.01 light years away. Your signal with a time-date mark of one year chases after him at c, but he is still moving at 0.01c away from you, so instead of taking 0.01 years to reach him, it will take 0.01010101 years by your clock for your signal to reach him. A total of 1.01010101 years passes between his leaving and his receiving your message between the time he left you until he gets the message. At 0.01 c, the time dilation factor is 0.999949999 so this is how fast his clock will tick relative to yours. Thus 1.01010101 x 0.999949999 = 1.0100505 years passing for him between the time he left you until the message arrive. He get a message with a date time mark of 1 year after he left , when his clock reads 1 year, 3 days 16 hrs and 6 min after he left. If he takes into account how far apart you are, and how fast you are moving apart, he can work out what time it was on his clock when you sent the message, come to the conclusion that you sent you 1 year date-time message after/i] his own clock read one year, and that your time is running slower than his. As long as he makes no changes to his velocity, he will always consider you clock as being behind him. It is only if he changes his velocity to come to a rest with respect to you or to reverse direction back to you, that this changes as far as he is concerned.

 

[Khashishi]

Could you point me to some time dilation formula maybe? Perhaps the mathematics will make it easier for me to understand it...

Try this one. If it doesn't make sense, then try starting from section 1.
http://www1.phys.vt.edu/~takeuchi/relativity/notes/section08.html

 

[pervect]

Since as far as he cares, I was traveling very fast until i got to him...Am I getting it right?
If so, how can we solve the following paradox:
I stayed on Earth and my tween got a rocket flying him at a hundredth of the speed of light. After a year in Earth I send him a message signing with a date and time. It gets to him and ,since the speed of light is absolute and the radio waves of the massage travels at the speed of light, he gets the message rather immediately.

You need to work out this part better.

The only answer you will get trying to ignore the propagation time of light is that at sufficiently low speeds, you can ignore relativistic effects. This won't help you understand relativity, or what happens at higher speeds.

Some numbers help illustrate. With a velocity v = $\beta \,c$, the expected time dilation is a factor of
$\frac{1}{\sqrt{1-\beta^2}}$ . In your example with $\beta=.01$, this works out to be a factor of 1.00005. But after one year, your twin has moved .01 light years, the propagation time is then .005 light years. So by ignoring the propagation time, yo' are ignoring things that are much larger than the relativistic effect you are trying to measure.

Working out the numbers is going to take some effort, and a book that explains relativity using actual math. Which will take some work on your part. It'll also be helpful to use higher velocities, so the relativistic effects are more obvious.

 

[t_ras]

Try this one. If it doesn't make sense, then try starting from section 1.
http://www1.phys.vt.edu/~takeuchi/relativity/notes/section08.html

I think this is what I was looking for. I vaguely remember this from my studies...

 

[sweet springs]

Hello. The twins separate and meet again. In order them to meet again, at least one of them have to change his course or more physically proper frame of inertia. This antisymmetry action explains which twin is younger and the other is older.
Best.

 

[vanhees71]

The twin paradox is very simply explained by just saying that aging is measured in terms of the proper time of the twins, moving along their world lines, i.e., for each twin the time relevant to measure their aging is
$$\Delta \tau =\int_{\lambda_1}^{\lambda_2} \mathrm{d} \lambda \sqrt{g_{\mu \nu} \dot{x}^{\mu} \dot{x}^{\nu}}.$$
As it stands, this holds for general (and thus of course also special) relativity.

 

[Alan McIntire]

Special Relativity does account for twin paradox. I get the following from a book by Paul Davies.

Assume Alpha Centari is exactly 4 light years away, and one twin is traveling there at 4/5 speed of light. (Using a 3,4,5 triangle I avoid
fractional and irrational numbers in my computations)
Traveling at 4/5 the speed of light, from the point of view of the stay at home twin, the trip will take 10 years, 5 years there, 5 years
back. Time for the traveller T' = T( sqrt( 1- (v^2/c^2))) = 3/5 T
Likewise, the distance for the traveler, D' = 3/5 D
The traveler on the spaceship sees himself traveling a distance of

4*3/5 = 2 2/5 light years in a time of 3 years, and likewise the 2 2/5
light years back in a time of 3 years, so the traveler will see the trip as lasting 6
years.

Suppose the twins have super telescopes and can see each other throughout
the trip. As long as they are traveling apart, the twins will see each other as
aging at 1/3 speed. As long as they are traveling towards each other,
the twins will see each other as aging at triple speed, thanks to the Doppler shift.

The difference is, the traveling twin will see the stay at home twin as aging at 1/3 speed for the 3 years to Alpha Centauri,
and at triple speed for the 3 year trip back to Earth for a total of 3* 1/3 + 3*3= 1 + 9= 10 years. The stay at home twin will see the travel age at 1/3 speed for 9 years, the 5 years it takes the traveler to get to Alpha Centauri,
plus the 4 years it takes the light to get back to earth. Since the total trip will take 10 years, the stay at home twin will see the
traveler age at triple speed during the one year he observes the traveler coming back to earth. The Earth observer sees the traveler
age at 1/3 speed for 9 years, and at triple speed for 1 year, for a total of 1/3*9 + 3*1 =3+3=6 years.

Both observers see each other aging at the same slow rate while moving apart, they see each other aging at the same fast rate while moving
together. The difference lies in one observer deliberately changes the relative motion of his rocket from moving away from Earth to
moving towards earth, and the other observer remaining passive, and not seeing the change until the light from the traveler reaches earth. If the Earth could be accelerated like a rocket ship, and the earthbound observer decided to change his frame so the rocket appeared to be moving towards him at 4/5 lightspeed
rather that away at 4/5 lightspeed, while the rocket remained in motion past Alpha Centauri, then it would have been the Earth twin who
appeared to age less.

Of course you could have some intermediate situation where BOTH observers decide to change their relative motion before they see the
other observer change his motion.

 

[Sveinbjoern]

I was going to make a post to ask about what I think the author of this post is asking.. Sorry t_ras if I am getting you wrong!

The question is who experiences the time dilation and why!?

When I first leaned about relativity (classic) it was liberating. Every speed was relative and no point or place was a true zero.
Special relativity came and took that away :) So sad and hard! But as soon as lightspeed came into the picture I was lost. If speed is relative then who experiences time dialation. If objects move relative only to each other then how can time move different in one then in comparisson to another.

So If you are aboard a beam of light traveling at the speed of light, experiencing no time. Why is not the rest of the world experiencing the time dialtion. They are from my viewpoint, of standing still.. moving really fast! In fact if my time is still but I am moving do they not seem to move eternally fast.

For the example of twins in space. Why does the twin traveling experience less time through his travels than me if from his viewpoint I am traveling really fast(not on a rocket but on a planet)? In a realtive world lightspeed restriction and time dilation does not seem to work. So is the world not realtive? Is there a null speed and do we know where no speed is?

I understand that there has to be an answer and that not everything can be moving at near the speed of light in every direction. Though in a total relativity it kind of does.. I can see that the lorentz transformation changes the relative experiences but not who experiences effects. The only thing you plot in it is speed but if speed is realtive the same effect must be added to another object relative to that object!

Is there a factor of acceleration? Is there a factor of gravity(another form of acceleration)? Mass? How Is special relativity relativ?!

 

[Ibix]

The question is who experiences the time dilation and why!?

No one experiences time dilation. Your own clock always runs at one second per second.

So If you are aboard a beam of light traveling at the speed of light, experiencing no time

You can't travel at the speed of light; trying to do so is self-contradictory. Don't try to make sense of it - it cannot be done.

For the example of twins in space.

You appear to be mixing two different phenomena. The relevant effect in the twin paradox is differential ageing; this is similar to time dilation in some senses, but is very different in others.

Let's start with time dilation. This is an effect that happens when you compare two clocks that are moving inertially - i.e., in a straight line at constant speed. The thing to realize is that there is no absolute sense of "at the same time" in relativity. And inertial clocks can only meet once - so "what does his clock read at the same time as my clock reads one hour after we met up" can mean different things. That's ultimately what time dilation is. It's closely analogous to cars moving at the same speed along straight roads that diverge at angle $\theta$. Each car will see the other car falling behind, because its speed is reduced by $\cos\theta$. The two cars don't agree on what forwards is, so they don't agree which one is behind. Similarly (remembering that time is a dimension), the two clocks don't agree on which direction time is.

The other effect is differential ageing. It turns out that what your wrist-watch measures is a "distance" you have traveled through spacetime, in much the same way that your car's odometer measures distance through space. Once you look at it like that, it's hopefully not particularly surprising that you get different elapsed times for different routes through spacetime, even if the start and end points are the same. The funny thing about these "distances" through spacetime (called the interval) is that the straight line path is the longest. That's why the stay at home twin ends up the oldest.

I strongly recommend looking up Minkowski diagrams. They are a simple way of visualising spacetime, and were the thing that made special relativity make sense for me.