How do the effects of relativity cancel out in the twin paradox?

[CaptainN]

So I'm having a problem with relativity. If something is traveling at half the speed of light away from you (on Earth), the time on that object slows to half, is that correct?

If that is correct, then relatively, if you where on the object, the Earth would be moving away from you at half the speed of light and time on Earth would slow to half.

This obviously can't be right, because they cancel each other out.

What am I missing here?

 

[ahrkron]

The reduction would not be to half the time, but that is a minor detail.

The situation is analogous to two people looking at each other from some distance. Both of them experience a retinal projection of the other one that is smaller than his "normal" size. The effect does not cancel out, and it seems perfectly normal. We are just too used to it to give it much thought.

 

[HBar]

If that is correct, then relatively, if you where on the object, the Earth would be moving away from you at half the speed of light and time on Earth would slow to half.
This obviously can't be right, because they cancel each other out.

If I understand you correctly i believe you are having the same difficulty a lot of people have with the twin paradox. If you are not familiar with this paradox here it is:
Identicle twins are born and one is put on a spaceship traveling near light speed and the other is left on earth. Let's call the one on the spaceship twin B and the one on Earth twin A. After awhile twin B turns around and heads back to earth. When he arrives he brags to twin A that he is younger. But how can this be? You could say that twin A was the one really traveling at near light speed if you use the spaceship as the frame of reference. The answer is when twin B turns around and heads back toward earth. He experiences acceleration so no longer can he be thought of as the inertial frame of reference (the non changing frame of reference) so if must be concluded that time was progressing slower for twin B (and he will be younger).
In your example there is no acceleration so they are symmetrical, time is traveling slower for both depending on what you consider the stationary observer. A person on Earth can say time is slower for him and so can the person traveling away and they will both be right! I don't believe they would cancel each other out. If you consider the object traveling away from Earth as stationary than time will be normal for the pilot and slow for the earth, and vice versa if Earth was concidered stationary.
-HBar

 

[CaptainN]

So time is only different is during acceleration or deceleration? If both are just traveling at consistent speeds relative to each other (figuring in that you can reverse which is the stationary reference) no time difference is experienced?

 

[selfAdjoint]

No that's wrong.

First, in outer space you can never tell is you are at rest or traveling at a constant speed. The only reason you can ever do that here on Earth is because of gravity and friction.

So if you and a friend feel no forces and know from that that you are both either at rest or in constant motion, but see that there is a relative speed between the two of you then the following statements are true:

You will see your friend's lengths shortened and his time lengthened by a factor that depends on that speed. But he won't see any such thing; he is entitled to regard himself as being at rest.

And he will see your lengths shortened and your times lengthened by that same factor. But of course you also can regard yourself as being at rest, and you won't see anything funny with your length or time.

The situation is completely symmetrical. I want also to emphasize that just because I used the word "see" in this description I am not implying that the phenomena are just illusions. They are reality, as real as it gets. There is no reality more basic than this, there is no "preferred observer" who can tell you "what really happens" - it's truly all relative.

 

[CaptainN]

First, in outer space you can never tell is you are at rest or traveling at a constant speed.

But isn't it true that the according to the theory, there is no station point in space?

So if there is not a station point in space, with which to compare the speeds of the two objects with, to determine which is moving, then you have to pick one of the two moving objects to compare the other to, and you can pick either one, which leads to the paradox.

 

[HallsofIvy]

You are still going around in circles.


If person A is moving, relative to B, at a speed of 1/2 c, then the "factor" is sqrt(1- v^2/c^2)= sqrt(1- 1/4)= sqrt(3)/2.

That is, person A will see person B aging at sqrt(3)/4 his own rate as well as seeing objects or machines (clocks for example)operating at sqrt(3)/2 as compared with his own.

You are correct that since B is moving at 1/2 c relative to A, B will the same thing: to him it appears that A has slowed down.

That is not a paradox: things don't have to appear to one person as they do to another.

To have the "twin paradox", you have to have to processes (twins, say) that are in sychronization to start with, separate at some high speed (so that each appears to be slower than the other).
To have a "paradox" you have to have them back together again in order to compare their ages (the only way you can compare or synchronize two processes). You can imagine the two stopping at some point and then coming back together or moving in a huge circle: it doesn't matter because the time compression is not a vector quantity and doesn't "cancel" when you reverse direction.

The answer to the "paradox" is that you DO have to get the two twins together again and the only way to do that is to accelerate one or the other. As soon as you do that, special relativity no longer applies.