This is an entirely different chapter of my life because it's... not talking about mathematics, but it's talking about my passion for details; that I just love all these peculiar things that one finds in the real world, like for example samarium 149. I mean, it just happens to be there, it has this enormous capture cross section for neutrons. That to me is beautiful. The world is full of things like that, just accidental coincidences which happen to be there, just like the birds outside flying around in the trees, these isotopes are just things that I've always fallen in love with; or the stars in the sky. The world is so rich in detail. Anyway, that's... that's why I found this subject so appealing. Anyhow, samarium has this enormous cross section for capturing neutrons. Well, why? And the answer is because there is a resonance, there is a bound state of the samarium 150 which is very, very close to zero energy, so when a free neutron comes in and is captured it can easily slide into this excited state which is actually one tenth of a volt above zero, but it's 8 million volts about the ground state of samarium 150. So it's just a remarkable coincidence that there is this excited state 8 million volts up which happens to be almost precisely equal to the zero energy of the incident neutron. Well what we've discovered then, by finding the depletion of the 149 in the fission... fossil fission reactors, is that that particular resonant capture level was there exactly in the same place 2 billion years ago as it is today. We see it today when we measure the cross sections, and it must have been there, or otherwise the isotope would not have been depleted. So that gives you an even more sensitive test for the variation of the levels. Again the... you have to do a rather careful calculation to see how the position of that resonance level would change if the fine-structure constant had changed between 2 billion years ago and today. It turns out to be immensely sensitive, much more so even than the rhenium. It's something... it's something like a tenth of a volt in 8 million volts, so it's roughly the 80 millionth power instead of 18,000. So if you change the fine-structure constant by one part in 80 million you'd have thrown the thing off by a tenth of a volt, which would have been enough to change the cross section by a factor 2, which is way over, way out of the experimental limits. So, that was Shlyakhter's idea and he published this in a little note in Nature about fifteen years ago and so that was the last word and... and the variation of the fine-structure constant then was limited, I mean it was still zero within the experimental errors. It was... it was bounded by something like 1 part in 10¹⁷ per year. And actually, just in the last two years, the last piece or serious honest physics I've done was a collaboration with Thibault Damour who is a French physicist who was here in Princeton. Two years ago Thibault Damour and I actually went over Shlyakhter's arguments and did a much more careful job, looking at the actual history of the fossil reactors and what the operating temperatures were, and finding more information about the neutron spectra and doing a more careful job with the mathematics also. So Thibault and I published this in Nuclear Physics just last year, and that's my last published work in physics, and we found, in fact, a slightly weaker but much more firmly based limit which agrees with Shlyakhter... apart from fine details, but it puts Shlyakhter's limit on a firmer basis, and it's still around a few parts in 10¹⁷ per year. So it's... the field is of course still open. The exciting thing, of course, which we all hope for, was we might find a real variation. That would open a real new chapter in science if we found a variation in the fine-structure constant, that would be a major revolution in science. Unfortunately we only found negative results, but there's always hope for the future. And it turns out that the progress in quantum optics is so fast that in fact even the Shlyakhter bound is likely to be - within a few years - superseded by actual laboratory experiments. Nowadays, because of quantum optics, one can measure optical frequencies to within one cycle and that... you can actually count vibrations of an atomic state in the optical range, and so you get... within a few years we'll have precisions probably even greater than 1 part in 10¹⁷. So the subject is still alive and there's always a hope that one day we'll find a real variation.

[Q] But the obverse side of that is that you know that the laws of quantum electrodynamics have been valid... the ones that we know at present, have been valid at least 4 billion years, if not longer, right?

Yes. And it's extraordinary... I mean, the precision with which one can do these experimental tests. I find the experimental tools are just as marvellous as the theory, and that's to me a... a great motivation for doing this kind of work.