Approximations 1928

Here we carefully slide over three years of fundamental advances in microphysics.  From 1925 to 1928, basic Quantum Mechanics was worked out and Dirac wrote out his first version of how fields could be quantized.  By 1928, even Bohr was willing to believe that, as a general rule, energy is conserved, and even, as Pauli wrote to Bohr, willing to “let the stars shine in peace” – which was to say without requiring that energy not be conserved in order to shine, as Pais notes on page 312 of Inward Bound.  Pais’ book is my main source for the three years that this blog is more-or-less skipping.

But another last look back at the World of Bohr and the BKS proposal, mostly to puzzle over what was so puzzling about tracking exact trajectories (ie in the Compton effect, the relation between the angle of the deflection of the photon and its energy, not to mention the exact detection of events with Geiger counters) in the world of 1925.  It is even more puzzling in retrospect and confusing in most accounts of quantum physics because Bohr’s ideas about complementarity and the Copenhagen Interpretation are injected at the level of particle interactions where they tend to obscure the basic readability of many kinds of quantum events.

Moreover, you would think that Rutherford’s use of particle trajectories (in 1911, preliminary and necessary to Bohr’s work on quantum energy levels) to work out the basic structure of atoms around the nucleus could have hinted at how single events could be tracked usefully at the subatomic level.  I guess the basic problem was imagining the photon (light-quantum) as having a single definite interaction with a single definite electron.  Even now that view of possible events (eg. an X-ray photon hits a relatively free electron) is seen as only one among many possible events – though at certain energies that is a reasonable description or approximation of the event.  The crucial object to picture is the single photon carrying a specific momentum (and therefore a trajectory and a wavelength) and in some ways the popular picture of quanta still makes this difficult to imagine, perhaps due explanations that rely on emphasizing some of the stranger verbiage of the Copenhagen interpretation such as the notion of an observer rather than the results of an interaction – interactions which at certain energies are more-or-less legible in terms of what happens with detectors over time. 

So, 1928, what have we got specifically for photons hitting electrons?  As noted, things seem to have been shaping up for not violating the conservation of energy as a general solution to problems with describing quantum fields.  Compton received the Nobel Prize in 1927 for working out the nature of the Compton Effect in 1922 and (also in 1927), Dirac produced a paper (Dirac 1927b) introducing the idea of quantum electrodynamics (QED) in terms of the interaction of the electromagnetic field with things like atoms or electrons.  The paper deals primarily with the interactions of the light-quantum and notes that a light-quantum in the state of zero momentum (required to be a possible state by absorption and the conservation of energy, Bose-Einstein statistics and Born’s rule of probability) essentially cease to exist but then can also be potentially created out of the fields involved in emission.  So, there is already a kind of proto-Dirac Sea, though it is a sea of photons and not yet a sea of electrons as well.  For the situation in 1928, it is important to keep in mind that the entire Dirac picture of QED was not yet available.

In early 1928, Dirac brought out his paper on the electron (featuring the famous Dirac Equation, though not interpreted as it is now).  So, by early 1928, a QED description of the photon and electron were available.  Some of the events that happen when photons interact with relatively free electrons were understood.  At low (visible light) energies you had Thomson Scattering.  At X-ray energies you had the Compton Effect.   

So, what does happen over the whole range of photon energies when you scatter photons at various energies off of relatively free electrons?  If we focus as much as possible only on what was known about that in 1928, we begin to see a lot of odd pathways and answers to that question.  First, there is a useful approximation, the Klein-Nishina and second, there is a set of theoretical descriptions of relativistic photons and electrons (more-or-less the first versions of Dirac’s theory), and third, a source of powerful particles, electrons and/or photos – “Cosmic Rays” – that is beginning to be investigated.  Even now, in 2022, the term astrophysicists use for non-nuclear processes more energetic than Thomson Scattering is “the Klein-Nishina Regime” – which – from the point of view of 1928 – includes a domain of events of completely unknown natures.  So next time: Cosmic Rays.

Clash of Cosmic Views

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