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lagerbaer t1_iuisayz wrote

Reply to comment by mumblerfish in When and how was special relativity integrated into QM/QFT? by YouSchee

I'm still amazed by the level of insight, inspiration and daring in going from Klein Gordon to Dirac.

"Hmmm. This naive way of introducing relativity into QM gives us an equation that doesn't appear to describe the electron. What if we made it four-dimension? Oh, and what if we interpret the negative energy solutions as particles, too? And what's this weird behavior of the thing under rotation? Let's call that spin".

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bapt_99 t1_iuixlnh wrote

It's even deeper than that. Dirac noticed that the Klein-Gordon equation didn't produce a positive-definite current density, ρ. There were thus issues with interpreting it as a probability. He postulated a new equation and required that is linear in ∂/∂t, unlike the K-G equation. This would result in the associated continuity equation (the one that would describe the continuous probability) describing an acceptable probability. This immediately lead to other conditions (namely, the equation has to be linear in ∇) due to Lorentz Covariance. He realized his equation had the form of:
i∂ψ/∂t = (-iα•∇+βm)ψ
What are α and β? The hisory goes as "he immediately understood those were 4×4 complex-entries hermitian spinors, with trace 0, determinant and eigenvalues ±1, and that they could be of higher dimension than 4×4 but then this dimension would need to be even"

He no joke deserved his Nobel Prize

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