Take the tour ×  What is each mathematical step (in detail) that
one would take to get from:  $E^2 - p^2c^2 = m^2c^4$   $E =
\gamma mc^2$,  where $\gamma$ is the relativistic dilation
factor.  This is for an object in motion.  NOTE: in the answer,
I would like full explanation. E.g. when explaining how to
derive $x$ from $\frac{x+2}{2}=4$, rather than giving an answer
of "$\frac{x+2}{2}=4$, $x+2 = 8$, $x = 6$" give one where you
describe each step, like "times 2 both sides, -2 both sides" but
of course still with the numbers on display. (You'd be surprised
at how people would assume not to describe in this detail).
share|improve this question I've changed $m$ to $m_0$ to make it
clear it's the rest mass. If you didn't mean this please revert
my edit. –  John Rennie May 18 '12 at 15:46 I forgot about that,
thanks –  Olly Price May 18 '12 at 15:48 Oh wait, I think this
is for when it's moving, because this equation $E=\gamma mc^2$
goes to show how if an object reached the speed of light it
would have used infi