Chapter 15, Problem 26A

To determine

To Explain: Whether a person gets younger by travelling at speed near the speed of light or not.

Explanation of Solution

Introduction:

Twin paradox is the famous example in special theory of relativity. According Einstein’s Special Theory of Relativity, the time observed by the different observer depends on observer’s velocity. Time is not absolute according to Einstein’s theory of relativity. One of the best outcomes of special theory of relativity is the time dilation and length contraction. According to the time dilation, when body moves with speed comparable to the speed of light, time runs slowly in that frame. Mathematically it can be written as,

  $T=\frac{T_0}{\sqrt{1-\frac{v^2}{c^2}}}$

Where,

  $T_o$ = Time measured when person is stationary in inertial frame of reference.

T = Time measured when person is in motion seen by the observer.

v = Velocity of the person with respect to ground observer.

c = Speed of the light.

Two synchronized clocks put together, one clock is sent with person to travel through space with speed comparable to the speed of the light and another clock is placed on the earth which is stationary. When the person returns from the space journey and time is measured in both the clocks, time measured by the person in spaceship and that of the stationary observer on the earth is different. The time shown by the clock travelled in the space is small as compared to the time shown by the clock which is stationary on the earth. By the same analogy, if a person measures his age before and after the space journey, he finds his age is less as compared to the age measured by the stationary observer on the earth.

Conclusion:

Therefore, relative to stationary person on the earth, person seems younger if he/she travels at the speed near the speed of light.