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

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: