Compton Effect and BKS (Bohr-Kramers-Slater Proposal) : Puzzles of Electromagnetic Quanta in 1923

First a quick chronological note:  according to all sources (especially Mehra – see the source note), the BKS proposal was a direct response to the interpretation of the Compton Effect put forward by Compton and Debye in 1922-23.  News of the experimental findings and their interpretation by Compton came out quickly.  Sommerfeld heard about the interpretation while in California in January 1923 and wrote Bohr immediately (Stuewer, The Compton Effect, page 241).

Source note for the Compton Effect and the BKS Proposal:

  1. Mehra and Rechenberg, The Historical Development of Quantum Theory Vol 1, part2
  2. Roger L. Stuewer, The Compton Effect
  3. Abraham Pais, Subtle is the Lord
  4. Helge Kragh, Niels Bohr and the Quantum Atom
  5. Peter Galison Image and Logic

So the context in 1923, Einstein had shown (in 1917) from thermodynamic arguments that radiated quanta had to have directional/linear momenta, ie there was no spherical emission involved in single radiative events.  Schroedinger had also demonstrated that the kinetic reverse was true (so to speak) in that emissions could show optical Doppler effects, ie the motion of the emitter, even in relativistic terms, had an effect on the wavelength of the emitted quantum – that is if one assumes that quanta existed.  Millikan’s work on the photoelectric effect (for which Einstein had won the Nobel Prize in 1921) had shown that the energies and frequencies involved were exactly what Einstein had predicted in 1905.  And yet no one but Schroedinger, Einstein, Compton, Debye, and possibly Sommerfeld thought that the complete light-quantum in terms of  imagery, implications and energy structures was particularly plausible overall, however useful it might be as a picture for certain situations.  The problem with accepting electromagnetic quanta as particles was that light and x-rays could be shown to have wave-like properties.  Of course, we now find that to be a matter of how particles get distributed, but at the time it was very hard to picture how particles could produce wave-like effects.  So hard, in fact, that it was easier to assume that energy was not conserved exactly in interactions involving electromagnetic quanta.  The mechanisms and logic of this non-conservation were the topics that the BKS proposal addressed.

But first, in early 1923, what was Compton’s interpretation of the Compton Effect?  Based on the post-interactive angles that X-rays of known energies (=wavelength) had and the wavelengths of the X-rays entering and exiting the interaction, he interpreted the events as being single interactions between one X-ray quantum and one electron.  He showed that X-ray scattered by a particular angle was related to its wavelength resulting from the scattering. The greater the scattered angle, the greater the lengthening of the wavelength and that lengthening would be due to the loss of energy/momentum caused by the collision with the free or loosely bound electron involved.  So one X-ray quantum hits one electron and the energies and momenta of the interaction are precisely and directly related in terms of the conservation of energy.  The interactions can be seen as elastic collisions in terms of conservation of momenta and energy analogous to billiard balls – context of the effect – X-rays hitting loosely bound electrons.

(As another side note: by 1923, physicists had accepted Rutherford scattering (ie using alpha particles to detect atomic forces and the nucleus of the atom) and Thomson Scattering (the deflection of electromagnetic radiation less energetic than X-rays).  It seems odd now that the idea of a single X-ray quantum interacting with a single electron was so hard to picture in 1923.)

So how did the BKS proposal suggest getting around the problem of the Compton Effect?  It is important to note that the experimental data for the effect was all in terms of angles and frequencies: specific X-ray frequencies going in were observed leaving the interaction with frequencies/wavelengths that were greater (ie less energetic) the greater the scattered angle.  There was no data related to the exact tracks of electrons being hit or single X-rays being counted.  So the essence of the BKS proposal was that these supposed “interactions” were really statistical summations of overall probabilities in terms of “spherical wavelets set up by each of the illuminated atoms” (page 550 Mehra, quoting the BKS proposal paper) and “a (virtual) radiation field which through probability laws again induce changes in the motion of the electron that may be regarded as continuous.” (Mehra 551 quoting the BKS proposal).  So, according to the BKS proposal the effects of the Compton Effect were not to be described in terms of the causal relations of a single collision where energy was demonstrably exactly conserved, but, instead, in terms of a series of virtual fields in and between atoms where energy was generally conserved overall, but not necessarily in any particular set of virtual events.  In effect, for the effect in BKS in terms of electromagnetic radiation, there were no “real” events and no “real” collisions, only virtual sets of virtual events, or to put it another way (as Mehra explains on page 548-9), there were no instantaneous interactions, only virtual accumulations of virtual energies that were eventually actually really emitted somehow.  This allowed electromagnetic radiation to retain all its wave-like characteristics while excluding anything suggesting actual electromagnetic quanta really colliding with anything.

            At the time (1924, when the BKS proposal came out) almost everyone (Heisenberg, Pauli, Born, Schroedinger etc.) thought this was a good solution to the problems of relating the observed quanta and the observed emissions.  Naturally, Einstein did not believe any of that BKS stuff, and neither did Compton, while, just as naturally, Bohr and his associates were perfectly happy with not conserving energy as long as electromagnetic radiation remained more-or-less wave-like.  In fact, not conserving energy was a kind of obsession of Bohr’s, and well into the early 1930s, he was intrigued by his idea of powering stellar/solar energy with some kind of “reverse radioactive process” that produced nuclear energy from the void (Kragh, Cosmology and Controversy page 86-87).  However, by early 1925, Compton’s interpretation of the Compton Effect (as a single, energy-conserving interaction between one X-ray and one electron) was accepted by everyone, including, for example, Bohr and Pauli.  In the next post,we will look into that quick change of perspective.

Einstein amused by Bohr