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## Main Question or Discussion Point

When I learned about Dirac's Equation, textbooks usually say that the earlier Klein-Gordon equation isn't linear in time derivative, contrary to what we expect from the time-dependent Schrodinger equation, therefore Dirac had to come up with a version that's linear. However, I think this doesn't really make sense. Klein-Gordon equation is perfectly acceptable if electrons were bosons. The only justification for Dirac's equation is the fermionic nature of electrons.

The "linear time derivative" argument just seems to be some irrelevant out-dated intuition from the structure of non-relativistic QM, and its only benefit is that we preserve the form of Schrodinger's equation and we can still talk about "Hamiltonian" and "energy levels" in a rather similar manner, e.g. in atomic physics, without going into quantum field theory. In contrast, for the Klein-Gordon equation you must treat it as a quantum field to recover the concept of Hamiltonian (now a field Hamiltonian) and a time-dependent Schrodinger equation which by definition is linear in time derivative. In short, the "linear time derivative" property just makes semi-classical treatment easy, and doesn't really have physical content.

Does what I say make sense? Or am I confused about something?

The "linear time derivative" argument just seems to be some irrelevant out-dated intuition from the structure of non-relativistic QM, and its only benefit is that we preserve the form of Schrodinger's equation and we can still talk about "Hamiltonian" and "energy levels" in a rather similar manner, e.g. in atomic physics, without going into quantum field theory. In contrast, for the Klein-Gordon equation you must treat it as a quantum field to recover the concept of Hamiltonian (now a field Hamiltonian) and a time-dependent Schrodinger equation which by definition is linear in time derivative. In short, the "linear time derivative" property just makes semi-classical treatment easy, and doesn't really have physical content.

Does what I say make sense? Or am I confused about something?