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

**Solution**: **Method 1**

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

u = (u’ + v)/ (1 + u’(v/c^{2}))

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 – v^{2}/c^{2})

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 the light.

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