In 1917, with his idea of the diffraction of X-rays through very large electrons, Arthur Compton started on his own personal way to working out what would become known as the Compton Effect. We now think of the effect as being what happens when a single, relatively powerful photon hits a relatively free electron. I suppose in some respects this interaction of a photon and an electron doesn’t look the way people are sometimes supposed to imagine quantum events – perhaps it’s not all that obvious from the various mysterious wisdoms hidden in the quantum realm tend to be portrayed that there are some relatively simple events involving quanta, but the Compton effect can be seen as just that: a relatively simple event involving quanta or even just one quantum hitting one electron.
Even a quantum event this clear, simple, definite, and well-defined was almost impossible to imagine in 1917 or even in 1925 or even now if one wants to stay on the “spooky” side of the quantum realm. As we will see, Einstein was generally able to stay on the side of some sort of quantum clarity at least until the late 1920s – a realm of clarity that he alone inhabited from around 1905 to around 1925. All of his work on various kinds of relativity was acceptable physics well before the light quantum was imaginable. This is, of course, mostly because of the interpretation of Maxwell’s equations and their effects as requiring diffuse, but precisely fixed in terms of energy, fields and wave pulses – very useful concepts, but not always applicable to interactions such what happens between a light quantum (an X-ray in Compton’s experiments) and an electron.
Compton knew he was dealing with a scattering problem of X-rays off of electrons with some range of resulting energies in the scattered X-rays and by 1917 those were well-defined types of problems in many ways. Thomson scattering, for example, involves light with longer wavelengths being diverted by electrons without a change in wavelength. At lower energy levels the interaction of light quanta and electrons can be adequately described in classical terms since the accelerated electron emits a light quantum of the same wavelength as the light quantum that accelerated it, though polarized and redirected. The very large electrons that Compton proposed were supposed to explain the shift in frequency that occurred when X-rays hit electrons by proposing that the size of the electrons was close to the size of the X-ray (or in later experiments) gamma-ray wavelengths, thus explaining the wavelength changes as diffraction due to the size electron (Roger H. Stuewer The Compton Effect, page 99).
It was a strange idea, but it made sense at the time sort of since it avoided the quantum explanation that everybody (except Einstein) worked hard to avoid from 1905 to 1925. And, as Kragh notes in his book on Bohr (on page 59), there were plenty of adjustable sizes in circulation at the time – notably Thomson’s blob of positive atomic charge in his only-recently discarded model of the atom – but including aspects of Rutherford scattering and the giant “Ryberg” atoms that were possible in Bohr’s atomic model (and which turned out to be observable astronomically in reality as well). Compton had himself accepted the Bohr model without much fuss in his PH.D. work at Princeton in 1916.
So when 1917 came along, Compton was ready with 3 different versions of possible giant electrons (here is the most abstract representation of their diffactive virtues):
