The interaction of electric charges

1. The present investigation is a sequel to two earlier papers in these 'Proceedings.' In II a theory of the electron was proposed which led to a prediction of the value of the constant 2πe 2 /hc . The theory involved an appeal to the analogies of classical dynamics, which frequently prove useful though precarious; it has been my purpose to substitute a more satisfactory geometrical basis. In a problem of this kind, concerned with the whole question of the significance of the methods of quantum theory, it is unlikely that finality can have been reached even at the second attempt; but I think that the progress is now sufficient to justify publication. According to II the value ofhc /2πe 2 was 136. I remarked that, as it represented the number of degrees of freedom of a system, small mistakes were unlikely; nevertheless I appear to have made such a mistake, and the new prediction is 137 (16). The 136 symmetrical degrees of freedom are a generalisation of rotations and translations in space; but it is characteristic of a pair of electrons that they possess one special degree of freedom unlike the others which has no analogue in the theory of a single electron, viz., an alteration of the proper distance between them; and whereas the 136 rotations are relative to the frame of reference employed, the odd degree of freedom represents alteration of an absolute quantity (the interval). The mistake in the earlier theory was not so much in overlooking this degree of freedom (for it there appeared as the rotation which "interchanges the identity of the two electrons") as in not recognising its distinctness from the others. No one of the 136 relativity transformations can play the part of this non-relativity or gauge transformation.