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I've obviously seen that $E=mc^2$. But I've also seen that the equation $E^2=(mc^2)^2+(pc)^2$ (where $p$ = momentum) is true.
If you square $E=mc^2$, and subtract the result from the other equation, you get $0=(pc)^2$. In other words, momentum doesn't exist!
I assume combining these equations is a mistake. Is $E=mc^2$ only something that holds in certain circumstances? Is $E^2=(mc^2)^2+(pc)^2$ the more complete, correct version of $E=mc^2$?
I know I'm wrong -- where, exactly, is my mistake?