Comment by elashri
10 hours ago
Dirac was not working in vaccum . Klein-Jordan equation was the simplest and the most obvious extension of Schrodinger equation in relativistic manner.
So historically, Dirac was focused on correcting the Klein-Gordon equation, which had issues with negative probabilities and describing electron behavior. His goal was to find a relativistic equation that resolved these problems while maintaining consistency with his own matrix mechanics formulation of quantum mechanics.
By extending his matrix mechanics formalism, Dirac derived an equation that not only addressed the issues with the Klein-Gordon equation but also predicted the existence of antimatter. I would argue that Dirac's approach was consistent with his established framework, and while he found renormalization mathematically unsatisfactory, it does not diminish the validity of his method in deriving the Dirac equation. I doubt he focused on any elegant solutions, he was actually quite happy working with matrix mechanics framework.
Bohr was a big shot, Nobel prized establishment authority. In Weimberg QFT book he recalls a fragment of Dirac's memoirs:
"I remember once when I was in Copenhagen, that Bohr asked me what I was working on and I told him I was trying to get a satisfactory relativistic theory of the electron, and Bohr said 'But Klein and Gordon have already done that!' That answer first rather disturbed me. Bohr seemed quite satisfied by Klein's solution, but I was not because of the negative probabilities that it led to. I just kept on with it, worrying about getting a theory which would have only positive probabilities."
Is there a relationship between the negative probabilities of Klein and the negative energy of Dirac? Did his formulation just move the problem? If so, does it imply anything? Like are probability and energy related?
Klein-Jordan equation does have both problems, negative probabilities and energies. Dirac equation solved negative probabilities and now predicts positive probabilities for both positive and negative energy states. But the negative energies problem still exists and Dirac used different interpenetration to explain them and did not get rid of them (which we knew later that this was the correct things to do). So he came with the famous negative energy solutions interpreted as antiparticles.