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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Confusion about How Dirac discovered Dirac's Equation

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