Question

show that no signal can travel faster than the velocity of light

Answer 1

Method 1  

As relativistic addition of velocity relation is already derived and from Addition of velocity relation  

u = (u’ + v)/ (1 + u’(v/c2))  

Suppose there is a signal which travels equal to the speed of light that is put u’ = c and then try to solve, the answer will be  

u = c  

If we put u’ = c and v = c then solve, we get  

u = c  

It proves that no signal can travel faster than the speed of the light.  

Method 2:  

Suppose there is a signal which travels faster than the speed of light, that is  

v > c  

By relation of length contraction in relativity  

l = l’(√1 – v2/c2)  

if we put v > c, then l become imaginary but length can not be imaginary. Therefore it prove that no signal can travel faster than the speed of light.

thnx