Hi!

I am studying special relativity and I still don't understand completely the relativity of time dilation:
each twin sees that the time of the other twin is dilated, so how can exist the asimmetry in the measurements (only one twin at the end has really dilated his time)?

I'll make an example:
two objects (A and B) are in the same reference frame. B object accelerates to a very small speed (near to 0) and continues with costant speed for a very long time, so that the difference between time intervals of the two object becomes arbitrarily big. The object B thinks that A time is dilated but if he decelerates back to 0 speed, he must discover that he was wrong, and B time is dilated instead. I.E. if he measures that A time is retarding by 100s, when he decelerates, the time difference must switch from 100s to -100s.
Can a very small deceleration do this? (time difference can be arbitrarily high.)

P.S. I hadn't study yet general relativity, so maybe I'm saying lots of bull****s ... :D

Thanks.
KKnull.

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A.T.
each twin sees that the time of the other twin is dilated, so how can exist the asimmetry in the measurements (only one twin at the end has really dilated his time)?
If they have a spatial separation if have to distinguish between what they see and what they measure. Here you can see how they see each other on the right side:

I.E. if he measures that A time is retarding by 100s, when he decelerates, the time difference must switch from 100s to -100s.
Can a very small deceleration do this?

You can look at this in two ways:

1) Twin B turns around instantaneously to fly back to A. During that turn B switches between two inertial frames. And in the new frame (moving to A) the twin A is already much older than in the first frame (moving away from A). This is called relativity of simultaneity.

2) Twin B experiences an acceleration phase when turning around. If you observe that phase from B's perspective you find yourself in an non-inertial reference frame. In such an accelerated frame time runs at different speeds along the direction of acceleration, and so B measures the clock of A run much faster than the own clock. The stronger the acceleration and the larger the distance between A and B, the bigger the difference of clock rates.

So basically B measures the time of A to run slower when it's own accelerometer shows zero. But when B measures an acceleration towards A, it also measures A's clock to run much faster that the own clock, catching up and overtaking it.

The main thing to keep in mind when analyzing this paradox (what has helped me the most, at least) is that although in uniformly moving frames one cannot be prefered over the other, this does not happen in accelerated frames: uniform motion is relative, acceleration is not.

Imagine the classical depiction of the twin paradox: one twin stays on earth and the other travels back and forth in a spaceship. Now, when one just read a bunch of theory saying that motion is relative and that a reference frame can't be favored over another, one is tempted to think that this would be equivalent to the earth moving away from the spaceship and then coming back, however, this is not so.

Imagine you are in the spaceship in rest relative to the earth, you accelerate moving away from the earth to 10 mph and then stop. Intuitively, you know that when the spaceship starts moving you will feel as if you were being pushed to the back of the ship, and when it stops you will feel a push forward. If the earth starts moving away from you, reaches 10 mph and then stops, you can also intuitively see that you will not feel the pushes you felt in your body in the first experiment. This difference clarifies that the experiments are not equivalent, in the first one you can tell by the pushes you feel that it is you who is accelerating relative to the earth, while in the second one you can see the earth move and know that it is the earth that's accelerating relative to you because you don't feel the pushes.

I hope this thought experiment gives you some insight on why there is indeed a difference between one twin's experience and the other's.

One can observe the accelerating twin from a nonaccelerating reference frame. The well-known result is that the frequency of events seen by the accelerating twin changes (see the Feynman lectures). Those events towards which the twin is accelerating seem to happen faster. Those to which the twin is accelerating away seem to be happening more slowly. The difficulty is in figuring out how the accelerating twin interprets what it sees. Since the frequencies of events change to the twin, speeds change. It is possible to say that everything works out sensibly if the speed of light is allowed to change, since the v/c will be the same value as in a non-accelerating frame (all speeds, including the speed of light change by the same factor). All interactions of momentum and energy will work out the same as in a nonaccelerating frame.

Once you dilated, u can't go back and un dilated man. The dilation equation don't care about your acceleration. I know u aware of this. It only care about your speed. Put the dilation equation as T/To = Lorentz transformation. Now u can see that with a certain speed, there is a time factor T/To. Let say the one running go with speed where it gives T/To=2. It means that "if your clock tick 2 sec(still guy), mine tick 1 sec(the speed guy)"

The reason for the change in frequency is the time dilation factor between the accelerating twin and signals traveling at light speed coming from events seperated in space. This results in an effective time dilation factor between spatially seperated events which is different from the instantaneous one.

well,
thanks to all, but I can't understand yet.
I'll make a pratical example:
A space ship dists from Earth 1x10^10 lightyears.
The ship accelerates ,reach the speed of 1km/h and travels toward the Earth with that constant speed.
After many many years (:D), the ship reaches the Earth.
In the ship reference, the clock is showing 1000000000000000 years from the beginning, and (according to Lorentz trasmformations), a man in the ship sees that a clock on Earth is showing 999999999999990 years.
At this point, the ship decelerates (from 1km/h to 0) and immediately the Earth clock turns from 999999999999990 years to 1000000000000010 years (a difference of 20 years!).
A didn't care of initial acceleration, but it is clear that it is the same of the final deceleration.
Is that possible? Am I missing something?
thanks.

The acceleration only has an effect when there is a spatial seperation. So when the distant twin accelerates towards the other, due to the acceleration in combination with the spatial seperation, the twin gains time.