After Oct 18, 1921, Compton started a new series of measurements of X-ray scattering angles and wavelengths using some new equipment in new arrangements.

For his book on the Compton effect, published in 1975, Roger H. Stuewer reconstructed these experiments and their results from Compton’s notebooks. In explaining what he is observing, Compton uses some quantum elements, but decides that oscillations of the electrons are causing the shifts in wavelength due to optical Doppler Effects.

Meanwhile, Schroedinger was also wondering about the optical Doppler effect. Or at least those examples shown in the case of emission line broadening in molecules – which he linked to a translational term ie, in Schroedinger’s case, a simple change in the speed of a molecule, intending to show that “the resulting ‘velocity jump’ , according to Bohr’s frequency condition (for light emission), yields the Doppler shift precisely…as demanded by the theory of relativity.” As Stuewer notes (p. 222), “The key point is that Schroedinger’s entire analysis was possible only because he assigned momentum hv/c (ie Planck’s constant times wavelength/frequency over the speed of light) to the emitted quantum… — an assumption which he knew was completely in accord with Einstein’s 1917 conclusion.” We will look at Einstein’s 1917 conclusion in a later post.

Also meanwhile, In March 1922, Compton was
briefly diverted by a controversy about the refraction of X-Rays. Compton spent part of March 23^{rd} wondering how to observe such a refraction and by March 25 he had observed the
refraction he expected. He reported his
results and as Stuewer points out on page 192,
these results alone would be enough to establish Compton in the first
rank of experimental physicists. It was
the first experimental determination of the index of refraction of X-rays and
the first confirmation of the Drude-Lorentz dispersion formula, which all
tended to confirm that no quantum theory was needed to explain what was
happening with X-rays.

But maybe some satisfactory non-quantum descriptions of X-rays lent some clarity to the central issues that interested Compton. He spent most of the rest of the year working on a bulletin for the National Research Council on “secondary radiations produced by X-rays” and things weren’t quite adding up. The problem was with the momentum of the electrons and how the electrons re-radiated the X-rays. Compton described these events in quantum terms but, in effect, only for the momentum of the electron. When the bulletin came out in October 1922, he pointed out that, while the electrons and the final emission of X-ray from an electron were best described in quantum terms, he concluded that the quantum of radiant energy “cannot always retain its integrity.” This fractionation of the quantum is used to explain how the longer wavelength radiation is produced when X-rays interact with electrons.

Jumping ahead as usual – this time to give us a little more “context from the future” (to sort of twist a bit of probably mis-attributed Karl Popperian wisdom) – in 2002 the historian of science, physicist, student of Richard Feynman, and early explorer of the full elaboration of the QED aspects of the Compton Effect, Laurie M. Brown, published an article on the history of the Compton Effect. It was fifty years after his work with Feynman on the topic and an intriguing “historical” moment for looking at the effect as it was understood in the 1920s and the Effect’s place in the development of QED. More on L. M. Brown’s paper later.

And so, meanwhile, on Dec 13, 1922, Compton wrote a comprehensive paper describing the Effect as a quantum event. When the paper came out in May 1923, for its first diagram, the paper featured a clear image of the momentum interaction as a classical vector diagram – like the classic “billiard balls colliding” image that is often claimed doesn’t characterize quantum interactions – which, in fact, works perfectly well for the simplest case of the Compton Effect (luckily for the understanding of X-rays and light as quanta). There are no fractional quanta and no Doppler effects – just the simple case of an X-ray quantum colliding with an electron resulting in the departure of an X-ray with a lower wavelength at an angle with the scattered electron such that all the momenta involved are exactly conserved.

Stuewer suggests that Compton’s shift to a completely quantum-based interpretation of the results of X-rays hitting electrons was motivated by considering how fast an electron would have to be moving to produce the scattered rays via a Doppler effect: half-the speed of light. Well, clearly only a few electrons would be doing that since X-rays were not blasting the target materials to bits. So, as Compton says, “The idea thus presented itself that an electron, if it scatters at all, scatters a complete quantum…” This reduces the complexity of the description of the interaction, at least for X-rays hitting single electrons. The great advantage of the new description was that it was easy to visualize and calculate; it did not leap out of the thousands of points of experimental data. On the other hand, the new quantum description did suggest new types of observational work to do and, over the next few years, Compton would work on many experimental methods to demonstrate the aptness of his basic insight.

The image below resembles Compton’s image 1922 image. Of course he wrote “incident quantum” and “scattered quantum” rather than “photon” and his incident quantum did not have a squiggly appearance. His image had thick, simple lines, heavily labeled with angles and momenta and a kind of auxiliary joiner’s try square for calculating the angles that conservation of energy required in the resulting motions.