Question

Consider a situation where immediately after birth, twins are separated. One continues to live on earth, while the other is whisked away in a space ship at 90% of the speed of light. After 65 years they are reunited. Will they look the same? Show proof of your answer through mathematics.

Answer 1

The twin who is "whisked away" at high speed and then returns (presumably at the same speed) will have aged less, by a factor of sqrt[1-(0.9)^2] = 0.436 

He will have aged 28.3 Earth years.

Hope this helps.

Answer 2

Answer:

Age of the one who lived on Earth is 65 years

Age of other who moved out at speed 0.90c is 28.33 years

Explanation:

As per the Einstein's time dilation relation we know that the time will be different in frame in which we are moving with speed comparable to speed of light.

The relation of the time is given as

$\Delta t' = \Delta t \sqrt{1 - \frac{v^2}{c^2}}$

here we know that

$v = 0.90 c$

so here we have

$\Delta t' = (65 years)\sqrt{1 - 0.90^2}$

$\Delta t' = 28.33 years$

So here we can say that the age of two will not be same when they unite after 65 years

Age of the one who lived on Earth is 65 years

Age of other who moved out at speed 0.90c is 28.33 years