This may seem like a stupid question, but i can't get my head around this so please bear with me. I just looked at the derivation of Dirac equation and my question is: do the solutions for a free particle obey special relativity? because if yes why? I mean I thought using E2=(mc2)2+(pc)2 would just give us more accurate energy levels. this energy momentum relation doesn't seem to include in itself the rules of special relativity, for example, where does it state that nothing goes faster than light? to state that don't we need the following relations: E=γmc2 and P=γmv? if this relation does in fact have SP rules encoded in it, then that means i can derive all the rules of SP from this simple relation right?