1938/06/16 by Max Born · 2 citations
Physics and Astronomy · #Atomic and Molecular Physics #Nuclear physics research studies #Quantum Mechanics and Applications
paper · doi:10.1098/rspa.1938.0110
openalex publication_date 1938/06/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/05/21
Abstract 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 the x- and p-space simultaneously. But as x and p have different dimensions this can be done only by making all components dimensionless. One has to divide the x-line-element by an absolute length a, the p-line-element by an absolute momentum b = h / a. The latter part can be neglected for all processes involving only wave-lengths long compared with a, and vice versa, corresponding to the cases of pure x-metric (relativity) or pure p-metric. If one identifies b with the limiting momentum defined in (I), it follows from (I, 22) that a = πr0, where r0 = e2 / mc2 is the conventional radius of the electron. Instead of a and b one can consider as primary absolute constants h = ab and H = b / a = 0.0085 g./sec. (1) The constant H is characteristic for the idea of reciprocity in the same way as c is characteristic for relativity and h for quantum theory. This standpoint implies that the constant b is universal. This was also assumed in the numerical calculations of (I), but no deciding argument could be given for this hypothesis.