EHeller comments on How do you tell proto-science from pseudo-science? - Less Wrong Discussion
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Sadly, with lorentz invariance things get quite a bit more complicated. Adding in Lorentz invariance forces you to deal more directly with spin (and lets you prove spin-statisics), so you end up with the Klein-Gordon equation for spin 0, the Dirac equation for spin 1/2, and variants of the Maxwell equations for spin 1.
But you also get weird "paradoxical" effects trying to interpret the results of those equations along the lines of non-relativistic quantum, so you are forced to push towards full field theory.