Comment by jesuslop
8 hours ago
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.
It’s worth mentioning that, brilliant as Dirac’s “sea of filled negative energy states” picture was, no one believes that interpretation now. The Dirac equation is better seen as the classical equation of motion for the Grassmann-valued electron field (just as Maxwell’s equations are the classical eom for photon field). There are only positive-energy states (=quantized excitations of the field). I do think popular accounts should begin mentioning this in order not to keep reinforcing the old Dirac sea interpretation.