Photon-electron (Compton) scattering: a particle model of the photon

Let us analyze scattering of a high-energy photon from an electron. In previous blog posts we have stressed that we do not know the structure of the inner field of the electron, at a distance considerably less than the classical radius of the electron.

The wavelength of a 1 a MeV photon is 10^-12 m, much more than the classical radius of the electron. To probe the inner field, we should use 1 GeV photons. But then a collision produces a jet of particles. It is hard to deduce the structure of the inner field from a complicated jet.

Collision of a 511 keV photon and an electron: is this an analogue of pair production?

      e- ---------------------------------

                      /          \

          ~~~~              ~~~~

      511 keV photon

Suppose that a slow electron absorbs a 511 keV photon and subsequently emits a photon of roughly the same energy. If we switch the time axis t and a spatial axis x, the process somewhat resembles pair production or annihilation. A major difference is that after the switch, the electron/positron move superluminally.

In a Feynman diagram, one is allowed to rotate the diagram through 90 degrees. That suggests that there might be some connection between mundane Compton scattering and mysterious pair production/annihilation.

Compton scattering of a 511 keV photon produces a photon whose wavelength is 2.4 * 10^-12 m, while annihilation is a process where the electron and the positron come within 2.8 * 10^-15 m from each other. The length scales are very different, or are they? The uncertainty in the position of the electron and the positron is > 2.4 * 10^-12 m.

In our February 1, 2021 blog post we discussed the problem of different length scales.

A particle model of the photon

Let us introduce an alternative model for Compton scattering: the electron moves very sharply and abruptly when it absorbs a (pointlike?) particle photon. In the path integral of all histories, destructive interference wipes out sharp features of the wave produced by the abrupt movement. The remaining smooth emitted wave contains the emitted 511 keV photon.

Classically, we think of the electron as a particle and the photon as a wave. The new model may partially explain how the photon can be a particle and still appear as a wave.

Collisions of particles produce abrupt and sharp movements. Destructive interference in the path integral evens out sharp features in the produced waves.