Twin Paradox

Twin Paradox: There is a twin brother A & B. A takes space voyage and B remain in the earth. According to time dilation, the clock with B runs faster than clock with A.

 we know that,
                     

For example,   if B is measuring a span of 50 years, A would be measuring only 30 years.      

                   A would look 20 years younger than his twin B.

Let us study the problem from the point of view of A who is in space voyage. We know that if there is a relative motion between two observers, each one thinks that the other observer is moving. Here, A would see that his twin brother B and earth moves away from him with a velocity during his outward journey. So, A thinks that B's clock is running slower as per relativity and B is younger than A at the end of space voyage. Thus B thinks that A is younger and A thinks that B is younger and this creates a paradox.

The paradox comes from measurement made by A. According to him, he is in the inertial frame and earth moves with velocity away from him.  According to his calculation B's clock runs slower. This is not true because his frame is not perfectly inertial because he has to turn back his spaceship at one point of time to return back, so he would experience acceleration. So, all observers would agree that only A is in motion and his clock runs slower at the end of the space voyage. Actually A looks younger than B.

It has been proved that moving clock runs slower. The decay rate of fast moving radioactive materials is slower than the radioactive sample at rest.