Big things come in little packages: How Willis Lamb's tiny measurement revolutionized 20th century physics

It's the end of World War 2. Scientists and especially physicists have spent the last four years working on military hardware, culminating in radar and the atomic bomb. Many of these talented men and women are eager to go back to their university campuses and resume normal civilian life; some of them are distraught at their role in engineering such horrific weapons and want to return to the carefree life of fundamental physics research which they knew before the war.

To reconnect the country's leading physicists with each other and with the great research problems which they left behind, the National Academy of Sciences decides to organize a series of conferences on the frontiers of physics. It's not hard to decide who should lead these conferences. Robert Oppenheimer has just led the wartime Los Alamos laboratory which produced the first nuclear weapons to high fame and glory. At Los Alamos and before at Berkeley, Oppenheimer has been widely acknowledged as the founder of the modern school of American theoretical physics and a man whose intellectual mastery of a wide array of disciplines is unmatched. It seems natural to have Oppenheimer be in charge of this post-war re-organization of physics in the country.

Oppenheimer and the National Academy of Sciences put together a list of the scientists they want to invite. Except for the famous Solvay Conferences organized in Europe during a more peaceful time, it's hard to think of another scientific gathering that attracted such an unprecedented constellation of talent. A dozen or more of the attendees have already won Nobel Prizes or would go on to win them; some for work which they would present during the conferences. The list of names is an all-star list in every respect: Hans Bethe, Enrico Fermi, Isidor Rabi, Robert Serber, Victor Weisskopf, Edward Teller, Abraham Pais, John Wheeler, Richard Feynman, Julian Schwinger and Hendrik Kramers. The meeting brings together both the new stars and the old guard (I mentioned Bohr and Dirac earlier, but as M Tucker points out in the comments section, they were present at a later conference: more on this equally interesting meeting in a future post).

Some of the participants at the Shelter Island conference:
Lamb (far left), Oppenheimer, (on arm rest) Feynman (seated
and writing) and Schwinger (second from right)

The first conference takes place in June 1947 at a tiny island called Shelter Island, situated in the jaws of the Long Island crocodile. The exclusive list of attendees gets escorted by a special police escort through major towns during their bus ride. Their selection as attendees, the cutting edge topics at the conference and Oppenheimer's leadership all make it clear that the center of physics has decidedly shifted from Europe to the United States. Shelter Island would go down in history as one of the most important conferences in the history of 20th century physics, but the participants don't quite know it yet.

One attendee in particular, a young protege of Oppenheimer's from Columbia University, is perhaps not as well known as the others: Willis Lamb. Lamb comes from a robust working class household and has obtained both his undergraduate and graduate degrees at Berkeley. Right before the war he got married to a German emigre, and as the story goes, for some time the authorities forbade him from walking on the beach and confiscated his shortwave radio for fear that he might be sympathetic with his wife's German compatriots and might try to communicate with German submarines. During the war he has worked on microwave radar with Rabi and others at Columbia. What is also perhaps not as well known is Lamb's versatility as a physicist. He is an experimental physicist now, but he got his PhD with Oppenheimer at Berkeley in the 1930s. This makes him one of the few scientists around to excel in both theoretical and experimental physics. Lamb's presence is already consequential since the participants at Shelter Island are pondering a discovery he made right after the war: a discovery important enough to be enshrined with his name - the Lamb Shift. The Lamb Shift will herald a new age in physics.

To understand the Lamb Shift, let's descend deep into the world of the atom with its electrons, protons and neutrons. Let's look at the simplest atom, hydrogen. As most of us have learnt in high school and college, electrons exist in energy levels defined by atomic orbitals. Each electron is defined by four so-called quantum numbers. In hydrogen, for the principal quantum number 2, the lone electron can exist in two orbitals defined by the secondary or angular quantum number: 2S and 2P. During the 1930s, in the heyday of quantum mechanics, the great English physicist Paul Dirac had worked out that the energy of the electron in these levels should be the same. Dirac's theory which also achieved the feat of marrying Einstein's special theory of relativity to the new quantum mechanics was the spectacular culmination of a decade of revolution in physics, a revolution led by men like Heisenberg, Bohr and Born, going back all the way to Einstein and Planck at the beginning of the century. The Dirac theory promises to be the icing on the cake of quantum mechanics, and its prediction of equivalent energies for the 2S and 2P orbitals of the hydrogen atom seems solid and indisputable.

But now, Willis Lamb has found that the two levels are different in energy by a tiny amount. It's an amount tiny enough to be undetectable except by the most sophisticated techniques and experimenters, but it causes shock waves in the world of physics and cries for an explanation. The Lamb Shift would be to quantum mechanics what the perihelion of Mercury was to astrophysics. Lamb with his background in both experimental and theoretical physics is in a unique position to measure this difference. He knows enough quantum mechanics to understand Dirac's theory of the electron. He knows enough atomic spectroscopy to understand the experimental underpinnings of the two energy levels. And, thanks to his work with microwave radar during the war, he knows enough microwave spectroscopy in particular to use microwaves to delicately probe the energies of the two levels. Microwave radiation may seem intense - it can sear your food to a crisp after all - but microwaves are actually pretty low in frequency compared to ultraviolet or visible light. By wielding them the way a surgeon wields a fine scalpel, Lamb and his graduate student Robert Retherford have probed the 2S and 2P levels of the hydrogen atom without injecting enough energetic radiation to cause other spectroscopic transitions and contaminate the experimental output. The number he gets is 1000 megahertz, a number which is a fraction of the kinds of frequencies emitted in spectroscopy and which could only have been determined by an experimenter of the first rank.

The Lamb Shift causes ripples in physics because it seems to point at physics beyond the Dirac equation. It's one of those rare, precious measurements in science which seem to inaugurate an entire field of study, a tiny, elusive number that points to great truths. In fact even during the 1930s some prescient physicists, Oppenheimer and Heisenberg among them, had suspected that the two energy levels might be different. But when they tried to calculate the actual number they started getting an absurd value for it: infinity. Nobody has bettered that result, partly because there was no experimental number to compare it with, but now at last, there is a solid reference number which the theoreticians can calibrate their calculations against. It's a rudder which they can finally use to guide the ship of their collective imagination.

The participants at the Shelter Island conference take the Lamb Shift to heart. The discussions continue into the twilight hours. Suggestions are thrown around without definite follow ups. One can sense the fomenting of a movement, but the destination is unclear. It's also clear from the conference that it's going to be the young breed of physicists who's going to crack the puzzle. First comes Julian Schwinger whose hours-long talk is like a prodigious performance by a violin virtuoso. His dazzling equations leave the attendees breathless. Then comes Richard Feynman, irreverent and colloquial with a wholly new way of looking at quantum mechanics, a language of wiggles and pictures which leaves the participants befuddled. It would take some time for his way of thinking to sink in. The proceedings of the conference are now legendary, with someone asking "What the hell should I calculate next?", Isidor Rabi asking "Who ordered that?" in response to the announcement of the muon, and Oppenheimer holding the gathering mesmerized with his splendid command over language, lightning fast mind and propensity to instantly summarize all agreements and disagreements into a concise package. And yet the Lamb Shift beckons.

It takes the resources of Hans Bethe with his unmatched ability to pound calculations into workable numbers to make the first great move; it's no wonder that years later after Bethe's death, his then promising protege Freeman Dyson called him "the supreme problem solver of the twentieth century". After the conference, Bethe astounds everyone by calculating the Lamb shift from scratch. One of his strokes of insight is to realize that even a non-relativistic calculation which ignores the effects of special relativity can give a number which is pretty damn close to the experimental value: 1040 megahertz. This requires a shift of a reference frame, so to speak, since everyone seems to have assumed that a non-relativistic calculation would be too inaccurate and unrealistic. And, as part of a Bethe story that has passed into lore, he does the calculation on the train ride home to upstate New York.

By his own account, Hans Bethe did the first calculation of
the Lamb Shift on a train ride to Schenectady in New York

Bethe's calculation energizes the physics community. It breathes life into a new technique called renormalization which gets rid of the ugly infinities plaguing pre-war calculations. It propels Feynman, Schwinger and Dyson along with Japanese physicist Sin-Itiro Tomonaga to put the finishing touches on their theory of quantum electrodynamics which is presented in the rest of the series of the conferences. Quantum electrodynamics reveals a magical world of so-called virtual particles such as photons that can flit in and out of existence in an eye-blink as the electron transitions between the 2S and 2P energy levels. These particles may seem to violate the conservation of energy because of their sudden appearance and disappearance, but Heisenberg's uncertainty principle as applied to energy and time ensures that one can have virtual particles existing for a definite amount of time as long as there is a finite uncertainty in the value of their energies. That uncertainty manifests itself as a difference in energy which is precisely equivalent in terms of frequency to the Lamb Shift.

The Lamb Shift achieves a flowering of theoretical physics that has not been seen since the heyday of quantum mechanics in the 1930s. Quantum electrodynamics becomes the most accurate theory of physics. It calculates the magnetic moment of the electron correctly to sixteen decimal places; later Richard Feynman famously compared this to measuring the distance between New York and New Orleans to within the width of a human hair. It uncovers a universe that is alive with virtual particles and fields; these particles even permeate an absolute vacuum and give rise to so-called vacuum energy. It gives voice to a new generation of American physicists whose descendants are still housed in the country's leading physics departments. These men and women not only develop quantum electrodynamics, but the techniques they pioneer - Feynman diagrams, renormalization, scattering matrices - are used in the development of all of particle physics in the future, culminating first in the Standard Model and finally in the discovery of the Higgs Boson seven decades later. Feynman, Schwinger and Sin-Itiro Tomonaga deservedly win Nobel Prizes. The Lamb Shift and its implications of a vacuum energy even helps Stephen Hawking postulate the presence of energetic radiation from black holes.

But none of this would have been possible without Willis Lamb, the perfect incarnation of theorist and experimentalist who was present at the right place at the right time. Lamb received the Nobel Prize in physics in 1955, and spent the rest of his career at Oxford, Yale and Arizona (where he moved so that his wife could find a faculty position). He mentored other successful students and developed another highly productive career in laser physics; ironically, one of his papers in this field is cited even more extensively than the one on the Lamb Shift. He lived a long and productive life and died in 2008. But it's the Lamb Shift that will go down in history as the opening shot which inaugurated a golden age of physics. As Freeman Dyson who was one of the prime participants in that saga complimented Lamb on his 65th birthday, 

"Those years, when the Lamb shift was the central theme of physics, were golden years for all the physicists of my generation. You were the first to see that this tiny shift, so elusive and hard to measure, would clarify our thinking about particles and fields."

And that's all we are, really, particles and fields. Happy 103rd birthday, Willis Lamb.