In Praise of 1948

An important year in quantum history

Me speaking at the APS March Meeting; photo from Steven Thomson’s Twitter feed.

Some months back, I got an invitation to speak in a session on the history of physics at the APS March Meeting. The session title was “…And It Was a Very Good Year!” with a hook of marking important anniversaries. My initial reaction was thus “This year isn’t the anniversary of anything important…”

Of course, in a very narrow technical sense, that’s not true, since anniversaries are, by definition, annual occurrences. (It’s right there in the name.) The eventual talk was given on March 9, 2023, which was the 227th wedding anniversary of Napoléon Bonaparte’s and Joséphine de Beauharnais, the 161st anniversary of the Battle of Hampton Roads, and the 64th anniversary of the Barbie doll making its debut. Those are all real; I looked them up.

Of course, none of those anniversaries were particularly hyped up in the year of our Lord 2023, because they’re weird numbers of years. When we’re talking about the sorts of historical anniversaries that people celebrate in splashy ways, we’re talking about integer multiples of 25 years. And those quarter-century intervals mostly don’t line up with anything important in the development of quantum mechanics.

If we start at the present and work backwards, 25 and 50 years ago both fall within my lifetime (admittedly, 1973 not by much), so I refuse to hear them discussed in a session about history. A century back is 1923, which is kind of the peak of the “Old Quantum Theory” era, where people were thinking in terms of electrons in Keplerian orbits around nuclei, using the Bohr-Sommerfeld model to determine energies. That… doesn’t really work. Within a couple of years, that picture was discarded entirely in favor of modern quantum mechanics, and basically nobody looked back. (Except this guy, whose explanation was enormously helpful when I needed to write about this.)

Go back another quarter-century, to 1898, and there’s no quantum theory at all. The first use of the quantum hypothesis of light energy coming in integer multiples of some characteristic frequency is from Max Planck in 1900, so we’ve still got two years to go for the Quantum Century-and-a-Quarter.

But the quarter-century year I skipped over, 1948, is actually a sneaky important one for quantum physics. It marks the 75th anniversary of the birth of modern Quantum Electrodynamics (efficiently and affectionately shortened to QED), and the culmination of the shockingly rapid development of the theory. And that’s the thing I agreed to talk about at the March Meeting.

The capsule history of quantum physics is pretty well known, and I won’t belabor it too much, here. It starts in desperation with Planck’s invocation of the quantum hypothesis to derive the black-body radiation formula, but then gets taken up more seriously by Einstein in 1905 as a “heuristic model” for the photoelectric effect. People tinker around with this in a bunch of different ways— there’s a parallel path here through thermal properties of materials that I don’t understand all that well— eventually leading to Niels Bohr and his quantum model of the atom in 1913, patching up Rutherford’s solar-system model by introducing the idea of special allowed orbits in which an electron will not radiate energy away.

Bohr’s model with circular orbits works great as a way to explain the hydrogen spectrum, and qualitatively explains some X-ray emission, but isn’t all that great. Arnold Sommerfeld works out an alternative form of the quantization condition in 1919 that allows for elliptical orbits, and that’s much better, forming the centerpiece of the “Old Quantum Theory.” By the mid-1920’s, though, this has serious cracks in it— it’s conceptually very useful, but attempts to apply it to multi-electron atoms and molecules keep ending in disaster.

The key breakthroughs come on vacation. Werner Heisenberg has a bad attack of hay fever in 1925 and retreats to Heligoland to contemplate physics in a place with less plant life, where he hits on the idea of abandoning unmeasurable orbits in favor of only calculating observable quantities, and thereby invents matrix mechanics. Then Erwin Schrödinger shacks up with an old girlfriend over the Christmas holidays, and comes up with an alternative model based on solving a wave equation (picking up a suggestion from Louis de Broglie), which also abandons well-defined orbits in favor of a fuzzier “wavefunction.” Both of these work great at explaining the things that the Bohr-Sommerfeld model did, but also have success in places where it failed, and they’re quickly shown to be mathematically equivalent, allowing physicists to switch between them as needed.

Then in 1928, P. A. M. Dirac leverages his weird dude energy to triumphant success: a fully relativistic matrix equation that explains all the known physics of the electron, including the intrinsic spin that otherwise had to be added by hand to the Schrödinger or Heisenberg versions. Dirac’s triumph is not complete, though, because when you attempt to use the Dirac equation to account for the electron’s self-energy, its interaction with its own electric field, you get an infinite answer. If you just ignore that element, though, the theory works really well, certainly well enough to match the best experimental measurements available in the early 1930’s. Which is a really odd situation, and it pops up again with the “vacuum polarization,” an interaction between a single electron and the negative-energy electron states that Dirac’s original model has as an explanation for antimatter.

So, quantum mechanics circa 1930 is in a weird and awkward place. If you try to do comprehensive and really careful calculations, you get nonsensical answers, but if you just ignore the problems by leaving those terms out, it works just fine. This is a major headache for the smallish community of theorists who really care about it, but everybody else kind of rolls with the Dirac equation through the 1930’s, arbitrarily setting the infinite terms to zero by fiat.

World War II kind of puts a hold on everything for several years, but after the war people get back to doing basic physics. During the war, though, the intensive research into improving radar systems has led to the development of vastly better technology for generating and detecting microwaves. These new tools are brought to bear on the spectroscopy of atoms, which immediately reveal problems: Lamb and Retherford show that two states in hydrogen that the Dirac equation says should have identical energies in a world without self-energy or vacuum polarization terms are, in fact, separated by a small amount. And Karp and Foley show a similar problem with the relationship between the spin of an electron and its magnetic properties: a constant that the Dirac theory without the problem terms says is exactly 2 is, in fact, slightly larger than 2.

These convince everybody that the solution to the infinities coming from the Dirac equation is not, in fact, to just throw them away. They are clearly neither infinite nor exactly zero, but make a very small contribution to the energy of the electron, and a method needs to be found to calculate what that is.

Which brings us to 1948, when four critically important events happen that bring modern QED into existence:

1. Schwinger’s presentation at the Pocono Conference: The Lamb shift and the anomalous magnetic moment of the electron were announced at the Shelter Island conference on the foundations of quantum mechanics in 1947. The follow-up meeting in 1948 was held in Pennsylvania, and almost an entire day of the four-day workshop was devoted to a presentation by Julian Schwinger laying out his solution to the problem of QED with a kind of mathematical virtuosity. The details were extremely difficult to follow, but everybody agreed that it was a brilliant piece of work, and he had found a method to calculate finite results for the problems of QED.

2. Feynman’s presentation at the Pocono Conference: Schwinger was a hard act to follow, and the poor sap who had to go next was Richard Feynman, who had also developed a method for doing QED calculations, using a series of approximations that he shorthanded with little diagrams. Feynman took a very ill-advised approach to his presentation, though, and managed to confuse and/or annoy everyone there; he knew how to calculate the same things Schwinger could, but couldn’t convince anyone else that his method was valid. This was actually a good thing, though, because the humiliation of bombing at Pocono actually got him motivated to write up his method in a clear and convincing fashion, which he was otherwise not really inclined to do.

3. Tomonaga’s letter to Oppenheimer: When Robert Oppenheimer got back to Berkeley after the Pocono Conference, he found a package from Japan waiting for him. This contained papers and calculations from Sin-Itiro Tomonaga, who had managed to sustain his group through the absolutely appalling conditions of wartime and post-war Japan. In the process, he had independently found a formulation of QED that worked. They learned about the Lamb shift from a news squib, and quickly calculated its value, which Tomonaga sent to Oppenheimer. Recognizing this as something very similar to what Schwinger had presented, Oppenheimer circulated Tomonaga’s papers to the Pocono attendees, and helped arrange publication in the Physical Review so they would get proper credit.

4. Dyson’s summer vacation: Freeman Dyson had recently arrived in the US to work with Hans Bethe at Cornell, which was also where Feynman was at the time. Being young and curious about the US, he jumped at the chance to drive from Ithaca to Los Alamos with Feynman (who was trekking across the country for personal reasons). On the way, they talked at length about physics, and Feynman’s methods of QED. After arriving in New Mexico, Dyson hopped on a bus to Michigan, where he attended a summer school Schwinger was putting on in Ann Arbor to explain his method. The combination of those two extended sessions and Dyson’s formidable mathematical talents put him in the unique position of being able to understand all three versions of QED (Tomonaga’s approach being similar to Schwinger’s). Which he did, well enough to show that they were mathematically equivalent. This played a key role in convincing people that the problems of QED were, in fact, solved in a consistent way, and opened the door for people to adopt Feynman’s more user-friendly approach to calculations, which is now ubiquitous (to the point that when you read about Schwinger’s method in modern books, the discussion is almost always illustrated with Feynman diagrams…).

Those four events make 1948 a remarkably significant year in the history of quantum physics, whose 75th anniversary is well worth celebrating. It’s the culmination of a process spanning a bit under 50 years from Planck’s introduction of the idea of connecting energy to frequency to the fully relativistic theory of electrons interacting with light. There are some lessons to be drawn from this about physics more broadly— in good parallel-construction form, I identified four of those, too— but I have some other work that needs to get done today, so I’ll stop here and do that as a separate post tomorrow.

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That’s my quick case for QED as the second-most-significant thing that happened in 1948 (top of the list is my mom being born…). If you want to read the take-away points from this that I promised (threatened?) for tomorrow, here’s a button to get them sent directly to your inbox:

If you’d like to quibble with any of my potted history above, the comments will be open: