Deriving the E=mc²

The Equation of special relativity

This is a little complicated though not that difficult if you are curious to know about the theories of Einstein. So this all started of an imaginary clock known as the light clock. This consists of two mirrors placed parallel mirrors.

 A beam of light is shined and keeps on going up and down as shown in scenario 1. Now for example your friend 'a' is holding the light clock in the dark in front of you 'b'. Lets take the legnth between the two mirrors as 1 m. Thus the time take for the light to go from the 1st mirror to the 2nd is = 1/300000000=3.3 nanoseconds. Let us draw this in the form of a triangle. So side b is 3.3cm(.now it is going to become a little complicated)

But if 'b' starts moving with the light clock at half the speed of light. the light forms a zig-zag pattern as shown in scenario 2. Now 'b' is running at half the speed of light so his path will also be half the time taken by light while moving (represented by line a). Thus by the pythagoras theorem, we find that the length of line c,time taken by light when the clock moves, is 3.8cm which is nothing but 3.8 nano seconds. Thus we find that motion slows time down. With this Einstein got the equation: (which works , try it)