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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
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Some Twisted Quantum Chronologies

In some ways, Einstein invented the basics of quantum theory multiple times.  Special Relativity and the light-quantum in 1905, Specific Heats in 1906, electromagnetic emission and a generalized coordinate invariant version of the Bohr-Sommerfeld electron in 1917 and his insistence (along with Schroedinger, Debye and Compton) on the light-quantum in the mid-1920s during his first controversy with Bohr.  As usual, his biographer Pais is driven to remark that some of Einstein’s insights are so advanced that they don’t fit into the ordinary chronology of the logical development of particle physics.  That’s especially true of the whole batch of quantum papers from 1917.  Pais says he notes them where he does in his narrative for purely chronological reasons since they don’t fit in logically – the insights are so far ahead of where everyone else was at that time. 

But in the logical chronology of the theory of Specific Heats, Einstein, for once pretty much fits right in.  On page 394 of Subtle is the Lord, Pais writes “Until 1906, Planck’s quantum had played a role only in the rather isolated problem of blackbody radiation. Einstein’s work on specific heats is above all important because it made clear for the first time that quantum concepts have a far more general applicability.”  However, even though it seems Einstein was right in the chronological flow in terms of the development of theories, Einstein’s approach was not picked up right away by anyone else until around 1911 when, Nernst, Peter Debye and eventually Max Born and Theodore von Karman, worked out a more complete theoretical description.

But, as long as we are pretty much following Abraham Pais’ narrative of Einstein’s odd, but very bold, inventive, and fruitful work on quantum theory, just how twisted was the journey of the quantum in and out of Einstein’s work?  First, apparently people had a lot of trouble nailing down just which phenomena they wanted to associate with quanta. For example, Einstein pointed out the quantum nature of the photoelectric effect in 1905, but that description of the phenomena was not widely accepted until the early 1920s.  And for another example, X-rays were shown to have light-like qualities in 1912 by von Laue, but even Compton’s work showing that X-rays carried momentum like the postulated light-quantum was not conclusive evidence of the characteristics of light-quanta for Niels Bohr in 1924.

Finally, as Pais observes on page 197 of Subtle is the Lord, “it was Einstein’s style forever to avoid the quantum theory if he could help it.”  Possibly because he knew it was not widely accepted as he started to work on General Relativity in 1907, and perhaps partly to have the pleasure of demonstrating its effectiveness in many new ways.  As Pais continues his exposition, while Einstein started working out the gravitational red shift, Einstein skipped the easy method of showing that energy could be written as Planck’s constant times the light frequency, and “starts all over again” to derive the frequency shift.

But – to back up and go over all of this all over again and “start all over again” ourselves – what does the chronology of the theory of the light quantum look like?

1900 – Black body (heat) radiation is quantized (Planck’s  constant)

1905 – Photo-electric effect is shown to be quantized (Einstein)

1906—Specific Heats are shown to be quantized (Einstein)

1907 – Gravitational Redshift related to Planck’s constant (Einstein)

1913-1915 Bohr-Sommerfeld atom uses quantized values and works for describing the X-ray spectrum

1917 – quantized emission, absorption and stimulated emission all quantized with directional momentum (Einstein – the first step to quantum mechanics)

1922 – Schroedinger’s quantized molecular emission Doppler effect description

1923 – Compton Effect shows X-ray quanta with directional momenta

1925 – Bothe-Geiger and Compton-Simon experiments confirm quanta with directional momenta

1925 – Facing the BKS proposal of Bohr and company (Einstein and others save the quantum

{I’ll explain this more in the next post})

1926 – Lewis names the light-quantum the “Photon” and the name catches on very fast

So…next post, what was up with the BKS proposal? 

Bohr and Einstein around the time of the BKS proposal
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Back to the Journey to the Mesons

So before the detour to the Pyramid Texts, this blog had reached roughly 1923 in terms of particle physics.  At that point, the blog was tracing the light-quantum model of the Compton Effect (which involves the momenta of X-rays impacting electrons when the X-rays are viewed as electromagnetic light-quanta).

Or to repeat what I was saying last March (2021 and expanded slightly now):

As a growing acceptance of the Compton effect spread slowly across the experimental, phenomenological (approximations) and theoretical realms of the physicists’ concerns, five themes emerged related to how this blog is supposed to be approaching the world of the mesons.  First, we can say good-bye to the fading of the aether; it is pretty much as faded as it will ever be by 1923.  Second, we can say hello to the proto-photon as it emerges from the work of Einstein and Schroedinger and immediately runs into trouble with Bohr and the BKS theory which picture emission and absorption as acting in a virtual, statistically-governed region resembling a tiny patch of the old energy-storing aether that acted as a holding place for things that could not quite be accounted for without the use of quanta.  Third, as Schroedinger and Born get a handle on probability amplitudes, the amplitude approach immediately runs into trouble with Bohr and Heisenberg’s “Copenhagen Interpretation” much to the confusion of a century of quantum mechanists.  Fourth, new techniques for partially quantized situations emerge (such as the Born and Klein-Nishina approximations) just in time to deal with a steady rise in the energies that experiments can deal with.  And fifth, with the working out of field theories, new levels of theoretical approximations and refinements via perturbations and paths are developed – which gets us to the mid-1960s which is as far as this blog is going to go in terms of particle physics.

Speaking of partially quantized solutions, as Resnick and Halliday point out (on page 140 of Basic Concepts in Relativity and Early Quantum Theory), Planck’s quantum constant, as it was first discussed, could be seen as no more than a convenient way of tracking energy in cavity radiation, indeed as no more than a good approximation of a more complex situation that might not need a quantum explanation.  The first place that a more general quantum solution to a classical problem occurring for a wider range of situations was in Einstein’s explanation of specific heats in 1907.

At this point, I’d like to bring up two widely divergent topics that will later be seen to come together fairly well after we look into specific heats.  First a long note on two works of Einstein’s in 1917, just after he had introduced the basic theory of General Relativity.  The first work is his work on the first relativistic cosmological model, in which he introduced a cosmological constant to stabilize a relativistic universe that would otherwise expand.  This model was, of course, the first cosmological model based on General Relativity.  The second big Einsteinian idea of 1917 was one that seems to be even more inventive than a cosmological model and yet so totally basic to the quantum picture of reality that it is a bit hard to fit it into schemes of the development of quantum theory and the light quantum in particular.  And the second noted topic is about entropy and a trip to the zoo.

Back to the first note, second part:  Einstein’s 1917 paper on the details of the emission and absorption of light quanta as proved by thermodynamics – kind of a twist, but not for Einstein.  One of the many extraordinary things about this paper is that it is the real beginning of quantum mechanics – ie, there are mechanisms and they involve quanta.  No one doubts that this paper is the beginning of quantum mechanics and yet, at the same time, the work in this paper is so fundamental that – like the rapid use of special relativity to address all kinds of problems – this paper almost seems to disappear because its insights became “common knowledge” so quickly.  The fundamental work in this paper leads to an odd position for it in the physics tradition:  it is so basic that it appears logically very early in introductory texts ie along with Planck’s early work and special relativity and the photoelectric effect while chronologically it belongs in the strange gap between early theories of quantum events such as those of Bohr and Sommerfeld around 1915 and the later detailed work a decade later.  So there is a disjunction between the logically “early” or basic position of the paper and its (later) chronological location.  Abraham Pais notes a similar case for the details of the Compton effect when he says (page 413 Subtle is the Lord  ) “Why were these elementary equations not published five or ten years earlier?”  At any rate, by 1917, Einstein was able to demonstrate that quanta were emitted in discrete packets in totally random directions and not as spherical waves, though it took another decade or so for this view of the emission of light quanta to be generally accepted.   

We will look into that in more detail after a look at specific heats, but, for now, the story of Von Laue’s trip to the zoo ( from https://www.iucr.org/publ/50yearsofxraydiffraction/full-text/von-laue)

Von Laue says:

At this time (1905) I also began to do scientific work of my own. It is true I had already published in Göttingen an investigation of the propagation of natural radiation in dispersive media, based on Planck’s hypothesis concerning the nature of radiation. However, now, once more following Planck’s lead, I attacked the more profound problems of the reversibility of optical reflection and refraction.

Planck’s formula for the entropy of a pencil of light rays showed unequivocally that the division of energy from one ray into two geometrically equal rays, e.g. equally long ones, is accompanied by an increase of entropy if, as was then usual, one added their entropies. Then, according to the second law of thermodynamics, the separation of a beam into a reflected and a refracted part should be irreversible. However, a simple argument on optical interference showed that because of their coherence the two beams could be reunited into one, that differs in no way from the original one. This was a profound dilemma. Would one have to abandon the second law for optical processes?

The explanation lay with the already mentioned Boltzmann principle of entropy and probability. It showed clearly that while one could add the entropy of incoherent beams, this was not possible for coherent ones. The entropy of the two beams resulting from reflection and refraction is exactly equal to that of the entering beam.

An hour after leaving Planck’s home in the Grunewald following our decisive conversation on this subject, I found myself at the Zoological Gardens without knowing what I wanted there or how I had got there. So overwhelming was this experience.

And the Particle Zoo:

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Good-bye, Old Kingdom

Resurrection Sequence 214

So…what have we here with these lines of hieroglyphics?  These lines come from early in the Resurrection Sequence, texts or “utterances” or spells conventionally numbered 213-222 in the Pyramid Text corpus. As you can see, we are in six different versions of spell 214 as presented in http://ancientworldonline.blogspot.com/2013/07/a-new-concordance-of-pyramid-texts.html. 

The concordance was assembled by James Allen.  The labels at the top are the traditional ones since Sethe’s edition in 1908: W for the Pyramid of Wenis/Unis/Unas, T for Teti’s Pyramid,  N for Pepi II, Nt for the Pyramid of the first of Pepi II’s three queens, Queen Neith, Jp for Queen Iput and Wd for Queen Wedjedtni.  Pepi II is sometimes given credit for causing the ending of the Old Kingdom by reigning for 90 years.  Supposedly this long reign caused the administration of the kingdom to fail to respond well while the Nile floods lessened, agricultural production kept falling and provincial officials gained power.

Still, Old Kingdom or no, the texts of the Resurrection Sequence itself are a pretty stable set of spells all the way from the Pyramid of Unis – the first set of Pyramid Texts – in about 2350 BC clear down to the Middle Kingdom mastaba tomb of Senewosret-Ankh in 1900 BC. In “Reading a Pyramid” (https://www.pyramidtextsonline.com/), Allen notes that the Resurrection Sequence is placed on the SE wall, associated with the night sky.  The end of Spell 214 (which is in the hieroglyphics here) reads:

…become clean in the cool waters of the stars, and board the sunboat on ropes of metal…

You can see the sunboat at the bottom of the left columns for W, N and Wd and the stars and the ropes of metal as well.  (translation from Allen’s A Grammar of the Ancient Egyptian Pyramid Texts Vol I Unis – for other translations see Allen’s The Ancient Egyptian Pyramid Texts, which includes spells from later Old Kingdom pyramids)

I think, with Unis coming clean, hoisting himself into the skyboat and just generally getting resurrected and joining the gods, it is time to leave the Pyramid Texts and get back to early twentieth-century physics, particularly the quanta of light, which have been hanging suspended somewhere between Einstein’s notice of them in 1905 and Compton’s demonstration in 1922 that X-ray quanta carried momenta related to their wavelengths.

But first a few notes on departing from the Pyramid Texts and how they turned out to be (I think as most people will find these days on looking into them from James Allen’s work and the contexts provided by John Romer) quite different in many intriguing ways from what I expected.

First, I’d say, if you’ve seen a lot of later Middle and New Kingdom texts from Ancient Egypt, these late Old Kingdom texts will seem very different.  Although they are the core of all the later details about journeying through the underworld, the Pyramid Texts seem to be more about on reaching the doors of the Akhet (where the sun rises), unbolting them and rising into the sky by means of moderately technical gear – which I find intriguing compared to all the lakes of fire and poison and what-not that fill the massively expanded verbiage of the underworld by times of the New Kingdom.  At the same time, I feel there is an overall tone of intentionally (or even manipulative, but still fully evocative) primordiality to the spells of the Pyramid Texts.  The late Old Kingdom’s pyramids are smaller but are deliberately situated in a network of cosmic positions that suggests a cosmos with more working parts – a magical history that evades whatever it was that was going with the focus on the giant pyramids of the Fourth Dynasty but also evokes that power – whatever it was.

I guess also magical power itself in the Old Kingdom was different at least stylistically than what it became later.  For one thing, while there is a lot of liturgical repetition, there is not as much piling on of dreary detail as all the hours of the night voyage of the sun’s passage through the underworld.  Moreover, the ways of leaving the earth and journeying with the nightboats and the skyboats have a certain adventurous, rustic simplicity: the persons joining the gods appear mysteriously and sometimes keep their name secret.  The newly-dead are clever and agile, climbing into boats and evading many dangers.  The adventurous atmosphere even extends to the quasi-technical details such as the bolts of the doors of the Akhet or the metal ropes and metal hatchways in the sky.  In the Old Kingdom, it’s not the Bronze Age yet – metal is still experienced as the copper brought by royal power from far away to cut stone for huge monuments and meteoric iron that suggests the unearthly or celestial modes of operation of divine powers in the sky.

Anyway, farewell to the Old Kingdom.  The Pyramid Texts of Queen Neith in one of the very last Old Kingdom pyramids are the most complete and well-preserved of all the texts from the Old Kingdom, surpassed in completeness and preservation only by the very first Pyramid Texts in the Pyramid of Unis.  So we say good-bye to Queen Neith by noting some of the last stanzas of her Resurrection Sequence:

When this time comes tomorrow, prepare for a journey of three days, for a footpath will be set out for you walk to the sky and wander amid the Imperishable Stars.