Twin Paradox: Why Twin On Ship Ages Slower?

[patl]

The way the twin paradox is explained, the twin on the ship ages slower than the twin on Earth because he is moving at velocity with respect to the twin on earth. This makes sense from the twin on Earth's reference frame, but wouldn't the twin on the ship see it the opposite. From his viewpoint, the twin on Earth is aging slower? So from his viewpoint, he should be older than the twin on Earth upon returning because the Earth had been moving fast with respect to him.

Maybe the example is always just stated from the twin on Earth's perspective, but that's never explicitly stated. Sometimes it made to sounds like there is an absolute velocity in the universe and the twin on the ship IS moving fast with respect to the Earth and not the other way around. I know this is not true, but could someone clarify? Thanks.

 

[Mentz114]

Hi patl, welcome to the forum.

First, there are many threads in this forum that answer your questions. To summarize, there is no paradox because the situation is not symmetric. One twin blasts off in a rocket and accelerates on the outward journey, and decelerates on the return.

It is resolved in general relativity because the twins travel along different world lines which have different proper lengths.

 

[mathman]

A special relativity answer can be seen if you realize that the twin going off in the rocket is also going fast relative to the place he is traveling to. For example if he is going to a star ten light years away. By traveling near the speed of light, the distance gets foreshortened and the time taken becomes (to him) a lot less than ten years, even though it looks like more than ten years to the brother on earth. The same thing happens when he comes back. As a result the trip to the traveller appears to have taken a short time, while the Earth brother experiences an elapsed time of over twenty years.

 

[Dale]

It is resolved in general relativity because the twins travel along different world lines which have different proper lengths.

The different proper lengths of the world lines can be calculated in special relativity also. There is no need to invoke general relativity.

 

[patl]

Thanks for the responses guys. So, my last question is, from the perspective of the man on the shuttle, is the clock on Earth running faster or slower than his own clock. From his perspecitve, the rest of the universe is in motion so i would expect him to "see" the Earth clock running slower than his. If that were the case though, how could more time ellapse on Earth than on the shuttle?

Lets say the man left at noon and the trip took 10 hours based on his clock. If he could somehow watch the Earth clock the whole time, and it was running at say, half the speed, when he came back, wouldn't the Earth clock register 5PM while his clock registered 10PM? However, the way the example is stated, it seems that the Earth clock is running at twice the speed of his, meaning that it would register 8AM when he got back.

I realize i am probably thinking about this the wrong way, so i figured i'd just put the example as i see it currently so you can see where i am going wrong.

 

[robphy]

Have you seen the "Doppler"-based explanation of the Twin Paradox?
http://www.math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html#doppler

 

[mathman]

Thanks for the responses guys. So, my last question is, from the perspective of the man on the shuttle, is the clock on Earth running faster or slower than his own clock. From his perspecitve, the rest of the universe is in motion so i would expect him to "see" the Earth clock running slower than his. If that were the case though, how could more time ellapse on Earth than on the shuttle?

Lets say the man left at noon and the trip took 10 hours based on his clock. If he could somehow watch the Earth clock the whole time, and it was running at say, half the speed, when he came back, wouldn't the Earth clock register 5PM while his clock registered 10PM? However, the way the example is stated, it seems that the Earth clock is running at twice the speed of his, meaning that it would register 8AM when he got back.

I realize i am probably thinking about this the wrong way, so i figured i'd just put the example as i see it currently so you can see where i am going wrong.

I haven't done the analysis, but I suspect you have to see what he sees when he stops to turn around. I presume the clock issue would then be resolved.

 

[patl]

How about this:

If you are moving 0.7c in a spaceship, and pass a spaceship headed in the opposite direction at 0.7c, does that mean you view his clock as moving backwards because he is moving at 1.4c with respect to you? And when its said that you can't go faster than the speed of light, doesn't this scenario violate this. Like, speed of light with respect to what? With respect to the other ship, you are going faster than the speed of light. Or is there some 'absolute' speed in the universe -- something I've always thought not to be the case.

 

[Janus]

How abuot this:

If you are moving 0.7c in a spaceship, and pass a spaceship headed in the opposite direction at 0.7c, does that mean you view his clock as moving backwards because he is moving at 1.4c with respect to you? And when its said that you can't go faster than the speed of light, doesn't this scenario violate this. Like, speed of light with respect to what? With respect to the other ship, you are going faster than the speed of light. Or is there some 'absolute' speed in the universe -- something I've always thought not to be the case.

Velocities don't add by u+v=w but by

$$\frac{u+v}{1+\frac{uv}{c^2}}=w$$

So in this example, you would measure the others spaceship as having a relative velocity of 0.94c.

Notice that if v is very small in comparison to c, the answer comes out to almost the same as u+v

 

[patl]

ah, ok, gotcha. thanks Janus