bapt_99

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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