In the Dirac tradition The late Richard Feynman - 'a way of looking at things so they appear not so mysterious'. It was Paul Dirac who cast quantum mechanics into the form we now use, and many generations of theo­ reticians openly acknowledge his in­ fluence on their thinking. When Dirac died in 1984, St. John's College, Cambridge, his base for most of his lifetime, institu­ ted an annual lecture in his memory at Cambridge. The first lecture, in 1986, attracted two heavyweights - Richard Feynman (see page 1) and Steven Weinberg. Far from using the lectures as a platform for their own work, in the Dirac tradition they pre­ sented stimulating material on deep underlying questions. (The lectures - 'Elementary Parti­ cles and the Laws of Physics' by Richard P. Feynman and Steven Weinberg - are published by Cam­ bridge University Press.) Richard Feynman When I was a young man, Dirac was my hero. He made a break­ through, a new method of doing tic quantum mechanics. However, cles, then to get the new wave- physics. He had the courage to the puzzle of negative energies that function from the old you must put simply guess at the form of an the equation presented, when it in a minus sign. It is easy to de­ equation, the equation we now call was solved, eventually showed monstrate that if Nature was non- the Dirac equation, and to try to in­ that the crucial idea necessary to relativistic, if things started out that terpret it afterwards. Maxwell in his wed quantum mechanics and relati­ way then it would be that way for day got his equations, but only in vity together was the existence of all time, and so the problem would an enormous mass of 'gear antiparticles. Once you have that be pushed back to Creation itself, wheels' and so forth. idea, you can do it for any spin, as and God only knows how that was I feel very honoured to be here. Pauli and Weisskopf proved, and done. With the existence of anti­ I had to accept the invitation, after therefore I want to start the other particles, though, pair production all he was my hero all the time, and way about, and try to explain why of a particle with its antiparticle be­ it is kind of wonderful to find my­ there must be antiparticles if you comes possible, for example with self giving a lecture in his honour. try to put quantum mechanics with electrons and positrons. The mys­ Dirac with his relativistic equa­ relativity. tery now is, if we pair produce an tion for the electron was the first Working along these lines will electron and a positron, why does to, as he put it, wed quantum me­ permit us to explain another of the the new electron that has just been chanics and relativity together. At grand mysteries of the world, na­ made have to be antisymmetric first he thought that the spin, or mely the Pauli exclusion principle. with respect to the electrons which the intrinsic angular momentum The Pauli exclusion principle says were already around ? That is, why that the equation demanded, was that if you take the wavefunction can't it get into the same state as the key, and that spin was the fun­ for a pair of spin one-half particles one of the others that were already damental consequence of relativis­ and then interchange the two parti­ there ? 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All these things have been sol­ ved long ago, in a beautiful way which is simplest in the spirit of Di- rac with lots of symbols and opera­ tors. I am going to go further back to Maxwell's 'gear wheels' and try to tell you as best I can a way of looking at these things so that they appear not so mysterious.' Steven Weinberg 'I am very grateful to St. John's College and to the Cambridge Ma­ thematics Faculty for inviting me here to speak in honour of Paul Di- rac. I was much in awe of him when as a student I learned of his great achievements. Later I had the privilege of meeting Dirac a few times, and I still am very much in awe of him. It's really quite a chal­ lenge to give a talk in honour of so great a man, and in planning it I felt we will discover some day in the movement toward greater simplici­ that it would not be appropriate to future ?' ty. It's not that the mathematics speak about anything less than a First of all, let me say what I gets easier as time passes, or that great subject. I am going to jump mean by a final underlying theory. the number of supposed elementa­ over all details, and speak about Over the last few hundred years ry particles necessarily decreases what is for people working in my scientists have forged chains of ex­ every year, but rather that the prin­ own area of physics the greatest planation leading downward from ciples become more logically cohe­ question of all: 'What are the final the scale of ordinary life to the in­ rent ; they have a greater sense of laws of physics ?' creasingly microscopic. So many of inevitability about them. My collea­ Well, not quite. Much as I would the old questions - Why is the sky gue at Texas, John Wheeler, has like to honour Dirac by presenting a blue ? Why is water wet ? and so predicted that, when we eventually transparency on which I have writ­ on - have been answered in terms know the final laws of physics, it ten the final laws of physics, in fact of the properties of atoms and of will surprise us that they weren't I am not going to be able to do light. In turn, those properties have obvious from the beginning. that. My real topic must necessarily been explained in terms of the pro­ I don't know if we will ever get be more modest. It will have to be perties of what we call the elemen­ there; in fact I am not even sure 'What clues can we find in today's tary particles : quarks, leptons, that there is such a thing as a set physics that tell us about the shape gauge bosons and a few others. At of simple, final, underlying laws of of the final underlying theory, that the same time there has been a physics. 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