Bothe's 1925 heuristic assumption in the dawn of quantum field theory

摘要

In an unpublished manuscript filed at the Archive of the Max-Planck Society in Berlin, Walther Bothe (1891-1957) put, with one heuristic assumption, the spontaneous and induced transitions of light quanta, on an equal footing, probably as early as 1925. In modern terms, he assumed that the probability for the creation of a light quantum in a phase space cell already containing s light quanta is proportional to s + 1 and not, as assumed at that time, proportional to s; that is proportional to the fraction of the total radiation density which belongs to s light quanta. For Bothe, the added +1 somehow replaced the spontaneous decay and allowed him to treat empty phase space cells in a black body as thermodynamically consistent. We describe in some detail Bothe's route to this heuristic trick. Finally we discuss why, both Bose's and Bothe's heuristic assumptions lead to an identical distribution law for light quanta in a black body and thus to Planck's law and Einstein's fluctuation formula.