I mentioned before that there was something funny with Einstein's derivation of his famous equation. I'll now talk a little more about that. I mentioned that during the derivation, Einstein invokes something called a Taylor's Series to simplify his equation. The problem with a Taylor's Series is that unless you use all the terms (infinite) you don't exactly have the equation you started with. You have an approximation that works well for small deviations from a point on the graph that you decided to do that Taylor's series from. In Einstein's case he use v, velocity, = 0 as his point of simplification. So in other words, his equation works for cases where v is small (compared to c). Not a bad simplification, but nevertheless it's not exactly precise. In other words what Einstein really derived was the energy for a mass at rest or moving slowly.

Others have pointed out that the derivation in question is also faulty on some other levels. Unfortunately I cannot find a reference to either of the two papers that do this. There is even some discussion that Einstein knew a priori that he wanted to prove E=mc^2. How would he know that? Well Poincare for one almost stumbled onto the equation but didn't drive through to the end. And an Italian also seems to have stumbled upon the equation prior to Einstein's work and it is almost certain Einstein knew about it.

Nevertheless all 3 are approximations. If you want to generalize the energy for all bodies (moving and stationary) then you get,

E = m c^2 / (1 - v^2/c^2)^(1/2)

In other words there is a relativistic term (the denominator) that corrects the approximation. It's funny that of all people Einstein would be missing that correcting factor.

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