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Hans Bethe


The Lamb shift
Freeman Dyson Scientist
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One of the main reasons I came from England to America was because at the time when I made the decision all the good experiments were being done in America. I mean England was pretty barren as far as experimental physics was concerned, and then the main centre for the experimental work in America was Columbia. There was the physics department at Columbia; the leading spirit was Rabi who was a wonderful character and a great experimenter, and in Rabi's lab the decisive experiments were being done using the techniques of microwave spectroscopy that had been developed in World War II. So it was a spin-off essentially from the radar developments in World War II. All this microwave technology was available, and with microwaves you could observe very much finer details of atoms than you could before just with visible light. So, in particular, hydrogen, which is the thing that physicists love to play with, it is the simplest atom - you can do the spectrum of hydrogen with visible light, that had been done in the 1930s, and at that time they observed, there was a kind of suggestion, that things weren't quite right. The observed spectrum of hydrogen wasn't quite exactly what Dirac predicted it to be, but the difference was not quite clear because visible light isn't precise enough. But after the war when you had the microwave techniques you could measure the hydrogen spectrum really precisely, and that's what Lamb did. Willis Lamb, who was at Columbia working with Rabi, measured the hydrogen spectrum for the first time with really high precision with microwaves and he found this discrepancy between theory and experiment which is called the Lamb shift. Which was quite clear and definite with microwaves and you could measure it very accurately. So it became an outstanding problem for everybody to explain this. The hydrogen atom being the simplest and most deeply explored object in the whole universe, in a way - I mean if you don't understand the hydrogen atom, you don't understand anything, and to find that things were wrong even with a hydrogen atom was a big shock. So it became the ambition of every theoretical physicist to understand this. And basically that's why I came to America. I knew that's where the experiments were done, that's where I was likely to be able to really to get in touch with what was happening in the real world. And of course the people at Cornell were very closely in touch with the people in Columbia, and in particular Willis Lamb talked to Hans Bethe who was the professor at Cornell, and Bethe then sat down and gave the first more or less adequate theory of the Lamb shift, just from a physical point of view. He understood that the reason why you had the Lamb shift was that the electron in the hydrogen atom was interacting with the Maxwell electromagnetic field, in addition to interacting with the proton, so that the effect of the fluctuations in the Maxwell field were disturbing the electron while it was revolving around the proton, causing a slight change in the position of the orbits. And so it was the back reaction of the electromagnetic field on the electron that Lamb had been measuring. And so Bethe understood that from a physical point of view. The problem was then, could you actually calculate it? And with the quantum electrodynamics as it was then, it turned out you couldn't; that if you just applied the rules of the game as they were then understood and tried to calculate the Lamb shift, the answer came out infinity, not a number of megacycles but an infinite number of megacycles. So that wasn't very useful and so it was clearly a real defect of the theory that it couldn't grapple with this problem. And Hans Bethe in the spring of '47 succeeded in fudging it; by cutting off the Maxwell field at the high frequencies and considering only the low frequencies, he managed to get the right answer more or less.

[Q] By doing mass renormalisation?

Yes. He renormalised the mass, which means to say that he allowed for the fact that the measured mass of the electron already includes the back reaction of the Maxwell field, and so what you're comparing is not a bare electron and an interacting electron; you're comparing an interacting free electron with an interacting bound electron. So you have the interaction in both the bound and the free electron, so you're comparing the two states of an electron. So you can subtract away the infinite mass renormalisation, and with a little more fudging you do finally get a finite result, and that's how Hans got this thousand megacycles which agreed more or less with the experiment. So that was the situation when I came.

[Q] And you had heard of that result already in England?

In England we had heard of the result and I think we'd even seen Hans's calculation, but of course we felt frustrated being three thousand miles away and not knowing the latest gossip; you always feel very much left out if you're not in touch with the people directly. So it was a very strong reason to come over.

Born in England in 1923, Freeman Dyson moved to Cornell University after graduating from Cambridge University with a BA in Mathematics. He subsequently became a professor and worked on nuclear reactors, solid state physics, ferromagnetism, astrophysics and biology. He has published several books and, among other honours, has been awarded the Heineman Prize and the Royal Society's Hughes Medal.

Listeners: Sam Schweber

Silvan Sam Schweber is the Koret Professor of the History of Ideas and Professor of Physics at Brandeis University, and a Faculty Associate in the Department of the History of Science at Harvard University. He is the author of a history of the development of quantum electro mechanics, "QED and the men who made it", and has recently completed a biography of Hans Bethe and the history of nuclear weapons development, "In the Shadow of the Bomb: Oppenheimer, Bethe, and the Moral Responsibility of the Scientist" (Princeton University Press, 2000).

Tags: Lamb shift, UK, USA: Columbia University, WWII, Cornell University, 1947, Isidor Isaac Rabi, Paul Dirac, Willis Lamb, Hans Bethe

Duration: 5 minutes, 44 seconds

Date story recorded: June 1998

Date story went live: 24 January 2008