Statistical Points: Stories of the Compton Effect and BKS (Bohr-Kramers-Slater Proposal) in 1924-5

The stories of the Compton Effect and the BKS proposal remain somewhat convoluted in the mid-1920s.  For example, in both Peter Galison’s account in Image and Logic and Stuewer’s account in The Compton Effect, the experimental results of Compton and Simon using cloud chamber photographs are described as less convincing than coincidences using Geiger Counters.  In both cases, the events surrounding the recoil of electrons in relation to the energies of the X-rays were shown (ironically perhaps) to be statistically more likely to be explained by simple conservation of energy than by the BKS proposal of an overall statistical scheme where virtual fields mediated the interactions.  The possible irony is that the BKS proposal that interactions were in themselves mediated by layers of virtual statistical virtual events was shown statistically not to work for events where the time dependence of the interactions could be tracked.

            In Mehra’s account in The Historical Development of Quantum Theory, the Bothe-Geiger experiment results not only become known sooner in Europe in early 1925, but the in the comparison of predicted rates, the results based on BKS predictions are given, in terms of the Bothe-Geiger framework, more or less a zero chance of being detected in a time-dependent observation and confirmed, while the Compton-Debye interpretation in terms of an interaction that instantaneously conserves energy can be detected in a time-dependent situation and confirmed in one out of 10 interactions, ie more or less with an infinitely greater probability of detection and confirmation (ie one tenth is a considerable greater probability than 0).  The key moment in most stories comes when Geiger writes a letter to Bohr on April 17, 1925, but Max Born wrote Bohr in January three months earlier with the same news – which was that sometimes it looked like Einstein’s quanta could be seen as colliding with electrons while conserving energy the whole time, that is in a context where the time dependence could be noted, and in the Bothe-Geiger case the time dependent observations took the form of many chronometric yards of film strips or “moving paper charts.” By April 21, Bohr was willing to set the BKS proposal aside, at least as an explanation of the Compton Effect.  Mehra goes on to quote Pauli in a letter to Kramers in July 1925 where Pauli gives equal emphasis to the results of Compton and Simon’s experiment as to the Bothe-Geiger experiment.  The interweaving of the stories can be seen as even stranger than that since R. N. Sen has recently pointed out that    Von Neuman, in formulating his mathematical axioms of quantum mechanics (published in 1932) seems to have confused the particular time dependent measurements of the Bothe-Geiger experiment with the trajectories involved in the Compton-Simon experiment (see R.N. Sen, “Von Neuman’s Book, the Compton-Simon Experiment and the Collapse Hypothesis” in, from January 4, 2022).

Of course, the thing about the Compton Effect is that it shows that at certain energies (ie the energy of an X-ray photon interacting with a relatively free electron), the interaction can be seen as (or approximated as) a simple collision which in turn implies the photon can be seen as (or approximated as) a single quantum particle.  This clarified the representation of radiation but perhaps just as importantly, it suggested that tracing the precise energies, trajectories and charges of particles could be very informative about the forces involved once time was assumed to be on hand rather than part of a virtual scheme.  So one might isolate two different sets of explanatory practices moving on from the Compton Effect (and ignoring at this early point, as perhaps Von Neuman did by accident, the difference between the tracks as images and the tracks as time dependent events in detectors): one that pursues approximations over the whole range of energies for events of a certain type and one that seeks to derive information from tracing the precise energies, trajectories, and charges of particles.

Next post, we will look at some of the implications of approximating quantum interactions over a range of energies.

Meanwhile, here we have the early “Turing Complete” ENIAC controls without any Von Neuman:

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