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LoginNotice that this applies, to a single electron, your universe consists of a single electron in isolation (no measurement). Not a realistic condition.

So to make it more realistic, we can start with a single electron moving in an EM field (Quantum Electrodynamics). To apply it further, to the EM field itself we get Relativistic Quantum Field Theory. One comeuppance is that an election in a EM field, moving relativistically, can't have a single trajectory, because of QM or because of Relativity, but the combination means that it can't even be a single electron, but an infinity of them (many worlds theory). The problem with quantum gravity, is that the Pythagorean equation ain't exact anymore, but approximate (because of space-time curvature).

The Dirac equation by assumptions, only works in a flat space-time, so without gravity. But Einstein showed that Special Relativity wasn't consistent, without General Relativity. This means that the Dirac Equation in some subtle way, isn't self consistent (in all circumstances). It works plenty well in many circumstances (but has to be solved numerically, not in closed form) ... remember in this first video, that the energy of the election has become an infinite series.

The whole series for the Dirac Equation is in 3 parts.