Compton went to work in St. Louis and made
an important modification to his plans.
He used his Bragg spectrometer to select a single sector of X-ray
wavelengths, as Stuewer notes in his book on the Compton Effect (p.163). This meant that he was working with X-rays of
known energy and wavelength. To venture
again into explaining what was going on in terms of what we now know (a century
later), to get a clear view of what is happening with the Compton Effect and
the conservation of energy, you have to know the initial wavelength of the
light quantum (X-ray) that hits an electron and then the wavelengths and
out-going directions of the resulting quanta.
Of course, in 1921, Compton was still thinking in terms of waves or
pulses of X-rays, as was everyone else except Einstein (but we’ll get back to
Einstein on light quanta after following Compton’s elucidation of X-ray’s
hitting electrons).
As Stuewer describes things in 1921,
Compton agreed with some other experimentalists that the variations in X-ray
scattering were the result of multiple events with multiple electrons
(beta-rays) with Doppler-shifted
diffraction happening at relativistic speeds. The observed longer (less energetic)
wavelengths were due to secondary excitations in the target materials. On the other hand, Compton was able to
measure how a change in the direction of what he considered to be the
diffracted X-rays was related to the energy (wavelength) shift. He was driven to do this on October 10-12,
1921 in response to a paper by S. J. Plimpton that concluded that a mica
crystal bent into an equiangular spiral did not diffract X-rays differently at
different angles.
Compton set up his salt crystal (and
paraffin), dosed it with X-rays of a single wavelength, and found that
measurements at different angles of the resulting X-rays showed that the angle
of the exiting X-rays was related to the observed energy shift. Which meant (as Stuewer points out) to
Compton at that point, that his Doppler shifted secondary excitations were
happening as he thought they were even though he had actually just observed and
calculated something approximating what would eventually be known as the
Compton Effect.
Well…he’s getting closer and here he is about 10 years later working on Cosmic Rays:
We continue our detour into some of the
many branches of the Compton Effect, partly to show how fortunate it was that
Compton was looking at the interaction of X-rays and electrons and partly to
suggest how crucial it was to tease out a set of relatively simple observations
to clarify the interactions of light quanta and electrons because things can
get pretty complicated pretty fast with light quanta and electrons. These complications can be resolved with what
are called “QED corrections” – which is to say higher-order Quantum
Electro-Dynamic (QED) descriptions of interactions where the presence of fields
or higher energies are represented by additional particles (including light
quanta) that can be real or virtual ( virtual in the sense that they appear and
disappear within an interaction). One of
the nice things about the Compton Effect is that it is basically a purely QED
phenomenon, that is it generally involves only light quanta (photons) and
electrons (and positrons) which makes it useful for calibrating the effects of
other interactions and the expected range of things like polarization in high
energy interactions. Of course at really
high energies (eg above 2.5 gigaelectron volts (GeV)) processes involving initially only QED objects
(electrons, positrons, and light quanta) can produce quarks and those resolve
themselves into mesons and baryons, but I hope to keep this blog relatively
clear of quarks so we won’t go into that at the moment.
But, a digression within this digression
to clarify the meaning of “QED corrections.”
The assumption here – as usually illustrated and analyzed with Feynman
Diagrams – is that if you allow for the impact of every possible sequence of
interactions, sub-interactions and loops within an interaction, you have to put
that all into some kind of order.
Basically, the simplest sets of sequences are the events that contribute
most to what is observed as the results of an interaction, such as these two Feynman
diagrams of the Compton Effect:
But, especially at higher energies,
different kinds of events and sequences can contribute to what is seen as the
result of an interaction. The more
complex sequences are part of an ordered perturbative series of
sub-interactions that contribute less and less to the results as the complexity
increases — but their contributions can be analyzed and included in shifts
that can be observed. Here are a few
higher order Feynman diagrams from the perturbative series that describes the
Compton Effect:
As I noted in “Compton Two,” these are the
“higher order” effects in the quantum electrodynamic perturbation series that
involve branching and/or looping within the framework of the basic interaction.
So, to return to the main digression and
to hint at some of the other more complicated things that can happen, we want
to take a glance at two other aspects of the Compton Effect: higher order
perturbations at higher energies and the double Compton Effect in the early
universe with astrophysical plasmas.
I’ll be following three main sources:
“Complete
QED Corrections and Polarized Compton Scattering” – A. Denner and S. Dittmaier
– CERN-TH/98-142 May 1998 (the source of the Feynman diagrams in this post)
An
Introduction to Quantum Field Theory, Michael E. Preskin and
Daniel V. Schroeder, Addison Wesley, 1995
Examining the complete QED corrections to
characterize polarized Compton scattering noted in the first source has two
main motives – one to calibrate polarization in electron accelerators and two –
to define the effects of QED corrections at high energies. In the second of the two motives, we can see
why Compton was lucky to be working with the relatively low energies of X-rays
hitting electrons. At the energies he
was observing, QED corrections are very minor – only thousandths of a percent
in terms of their effects. In extremely high
energy situations, say 500 GeV (as with colliding electrons and positrons in an
accelerator), there can be as much as a 2% shift in measurements due to QED
corrections. Such shifts would have thrown Compton’s attempts at precise
measurement into turmoil, but, when he was working, only cosmic rays (not yet
even defined in those terms) would have provided such high energies to
experimenters.
In higher order corrections, you can have
loops in the interactions involved in the Compton Effect:
Intuitively a loop in an interaction does
sound like trouble, and, in fact, if you don’t correct these loops in the corrections,
integrating over all the possible momenta involved in a loop gives you infinite
momenta. We won’t be looking into how
correcting the corrections (or renormalization) works until this blog reaches
the early 1950s – still 30 years from where we are with Compton in about 1920.
And you can get “an extra real photon” in
the Double Compton (DC) Effect:
Because the DC Effect dominates
interactions for electrons at higher energies and photons are even more
relatively common than baryons in the early universe, the DC effect is crucial
in understanding the extreme situations in the early universe. Ravenni and Chluba
cite the 1952 paper of Mandl and Skyrme as the first detailed treatment of the
effect ( F. Mandl and T. H. R. Skyrme, “The Theory of the Double Compton
Effect,” Proceedings of the Royal Society of London, Dec 1952) It is a very cool paper and when the blog
gets to the early 1950s, we will look at it again. One interesting thing about it is that
Feynman diagrams are mentioned as part of the analysis but there are no Feynman
diagrams in the paper.
Anyway, enough of that. We will get back to Compton in 1920 in our
next post.
