The theory of particles of spin half and the compton effect

It is shown that the original Dirac theory in which a particle of spin half h is described by the Dirac equation with all the negative energy states empty, and the hole theory in which all the negative energy states are filled each with one electron, donot in general lead to the same probabilities for second order processes, contrary to what is generally believed, due to the energy denominators in the quantum formula for a second order process being different in the two theories, although the matrix elements for each first order process are the same. The formula for the scattering of radiation by a free electron on the hole theory is calculated. This isnot the same as the Klein-Nishina formula which gives the scattering on the original Dirac theory. The new formula agrees with the Klein-Nishina formula only when the energy of the light quantum is small compared with the rest mass of the electron. For high energies it gives a greater scattered intensity at small angles and less at large angles than the Klein-Nishina formula and at extremely relativistic energies it gives a total scattering which is five times greater. The new formula at high energies is in definite disagreement with experiment, which agrees very well with the Klein-Nishina formula. Thus the hole theory is in definite disagreement with experiments on scattering although it is in at least qualitative agreement with nature in describing the existence of the positron and the process of pair creation, and is the only form in which the Dirac theory is logically tenable