In mid 1905, Albert Einstein descended whatis now the most famous equation in the world: E equals M C squared. But he didn’t just writethis down out of the blue it followed directly from his paper on special relativitythat we talked about in last week’s video and here’s how he did it: Suppose you’re watching a feline hover freelyin empty space, when unexpectedly it emanates a flare of light in all directions. The illumination carriesaway some vigour, we’ll call it “E”, so by conservation of energy the “cat-o-nine-tail” must have lostenergy E but since the glowing was emitted symmetrically in all directions, it won’thave changed the cat’s velocity.So where did the vigour for the glowing collected from? Never mind that now let’s imagine you getbored and zoom off in a spaceship in the midst of the experimentation. But from your brand-new position, you’re sitting still in your spaceship and the cat is the one moving past outside thewindow! Therefore you’ll calculate that the cat has some kinetic energy, that is, energyof flow and when you recognize the cat give the burst of light-headed, you’ll again measure thatits exertion decreases by the energy of the light-colored. Except now that you’re moving, special relativitytells us that time elapses at different paces for you and the feline, so you’ll appraise a differentvalue for the frequency, and thus vitality of the show of light.This is the relativisticdoppler effect, and for our aims, it amounts to multiplying the power of the light-headed byone plus your velocity squared divided by twice the speed of light squared. So to recap, if you take off at velocity v, you’ll participate the feline amplification some kinetic energy KE1, then at the light you’ll understand the cat’senergy decrease by E period one plus v squared over two c squared. On the other hand, ifyou wait, you’ll hear the cat’s energy decrease by E, and now when you take off you’ll seeit gain kinetic energy KE2. But this is silly! You never touch or otherwiseinfluence the cat in either contingency, so you are able to get the same total exertion at the end Rearranging, we be understood that the kinetic energy before and after the twinkling must be different! And thekinetic energy of an objective is one-half of its mass durations velocity squared, but we knowthat the velocity was the same in both cases so in order to account for the difference, the cat’s mass must change when it emits the flare of glowing! Now if we cancel things out, you can see thatthe change in mass of the cat must be equal to the energy divided by c squared or, as you’ve heard before, E equals M C squared!
