Predicting the Positron: Theory, Interactions and Arguments

By Thomas Pashby

University of Pittsburgh


Abstract:

This paper addresses a significant episode in the development of modern physics: the prediction of antimatter by Paul Dirac in 1931. It aims to delineate the process of reasoning that led to his prediction, and thereby demonstrate the importance of Dirac's interactions with his contemporaries for this process. For this purpose, there exist a number of letters and papers that show the development of Dirac's approach to the infamous negative energy solutions of his relativistic electron equation. Initially ignored for purposes of calculation, they came to be interpreted as 'holes' in a negative electron sea corresponding to protons, and finally 'anti-electrons.'

Here I trace in detail this collaborative development of ideas, with emphasis in particular on the role of the arguments of Oscar Klein and Hermann Weyl, which persuaded Dirac that the negative energy solutions were physically relevant, and that a new form of matter was required to explain them. The latter of these was essential to Dirac's prediction, and rested on the symmetry arguments of Weyl's seminal book Gruppentheorie und Quantenmechanik.

Despite its importance, the precise nature of this argument has yet to be articulated in the literature. By doing so, I give a fuller account of Weyl's role in Dirac's prediction and argue that he deserves greater recognition. More generally, this account of how Dirac's ideas were influenced by the arguments of his fellow physicists provides an illustration of the collaborative nature of the community of early quantum mechanics.