Application of “reciprocity” to nuclei

This paper is a continuation of a recent publication (Born 1938) under the title “A suggestion for unifying quantum theory and relativity”, which I shall quote here as (I). The central question which arises from the idea of “reciprocity” is the generalization of the conception of a metric in such a way that it comprises thex - andp -space simultaneously. But asx andp have different dimensions this can be done only by making all components dimensionless. One has to divide thex -line-element by an absolute lengtha , thep -line-element by an absolute momentumb =h /a . The latter part can be neglected for all processes involving only wave-lengths long compared witha , and vice versa, corresponding to the cases of purex -metric (relativity) or purep -metric. If one identifiesb with the limiting momentum defined in (I), it follows from (I, 22) thata =πr 0 , wherer 0 =e 2 /mc 2 is the conventional radius of the electron. Instead ofa andb one can consider as primary absolute constantsh =ab andH =b /a = 0.0085 g./sec. (1) The constantH is characteristic for the idea of reciprocity in the same way asc is characteristic for relativity andh for quantum theory. This standpoint implies that the constantb is universal. This was also assumed in the numerical calculations of (I), but no deciding argument could be given for this hypothesis.