Post #3124445

Interesting bit in Sean Carroll's last AMA episode. The Dirac equation is *not* a replacement of the Schrödinger equation, something many times implied or explicitly alluded. The Dirac equation is a classical equation for particles of spin 1/2 with electric charge, like the Klein-Gordon equation is a classical equation for scalars. The Dirac equation is more like Maxwell's equations with spin 1/2. When quantized, the Dirac equation gives you quantum field theory, and that's what it's done nowadays. Indeed, Schrödinger tried an explicitly relativistic invariant equation and arrived to Klein-Gordon, but it didn't fit the experimental data for an electron in the atom. BTW, the Schrödinger equation with a relativistic hamiltonian is perfectly compatible with special relativity. (These are good news for MWI fans like Carroll himself, since they need an universally valid Schrödinger equation).