by John Gribbin
In order to represent this on a Feynman diagram, you can use one of Feynman’s neat tricks. An antiparticle leaving the neutron and heading into the future is the same as a particle arriving at the neutron from the past. In Feynman’s world, the prefix ‘anti’ on a particle’s name means ‘going backwards in time’. So the fundamental example of the weak interaction at work is represented by a diagram like Figure 14. The key point is that this description of the weak interaction is exactly the same as QED, once allowance is made for the extra particles and their properties. It even includes the same kind of infinities as QED, which are removed in the same way, by renormalization. Among other things, this means that all the arrows on the diagram (on any Feynman diagram) can be reversed to describe an equally valid fundamental interaction – in this case, a proton and an electron can interact, with the exchange of a W– particle, to make a neutron and a neutrino.
The match between the rules of the weak interaction and the rules of QED is so exact, in fact, that there is no point in trying to pretend that they are different theories. Today, physicists speak of the ‘electroweak’ theory of particle physics, one set of equations that describes all interactions involving either electromagnetism or the weak interaction, or both (including, remember, all of classical mechanics, in Feynman’s formulation of QED). That set of equations (and diagrams) is essentially the QED template itself. As well as explaining everything there is to explain about interactions involving electrons and photons, the QED template explains everything there is to explain about weak interactions, to almost the same high precision as QED itself.
Figure 14. Using QED as its template, the electroweak theory describes an interaction in which a neutron (N) interacts with a neutrino (Ve) by the exchange of a W– particle to produce a proton (p+) and an electron (e–) (compare with Figure 11). Such a Feynman diagram can be read equally validly ‘down the page’, with (in this case) an electron and a proton interacting to produce a neutron and a neutrino.
The situation isn’t quite so rosy when it comes to the strong interaction, but great progress has been made towards unifying the description of this fundamental force with the electroweak theory. By the 1980s, when the basic quark model of protons and neutrons was well established (once again, Feynman was involved in this; see Chapter 10), physicists had been so impressed by the success of QED and the electroweak theory that they deliberately set out to explain the strong force in similar terms. The picture that emerges is that protons and neutrons are each composed of three fundamental particles, called quarks, bound together by the exchange of particles which do the same work as photons do in QED and intermediate vector bosons do in weak interactions. This makes quarks and leptons the truly fundamental building blocks of everyday matter. The strong force, as we see it operating between protons and neutrons, is then explained as a residue of the real strong force operating between quarks, the truly fundamental fourth interaction, alongside gravity, electromagnetism and the weak nuclear force.
Quarks come in several varieties, revealed by high-energy events in particle accelerators like those at Fermilab and at CERN. But happily for us only two varieties are needed to make protons and neutrons. These have been whimsically given the names ‘up’ and ‘down’. Among their other properties, each up quark carries an electrical charge of +⅔, while each down quark carries an electrical charge of –⅓. A neutron consists of two down quarks and one up quark bound together by the strong interaction, and a proton consists of two up quarks and one down quark bound together by the strong interaction. On this picture, neutron decay actually involves the transformation of a down quark into an up quark, with the aid of an intermediate vector boson (a W particle) linking the transforming quark to an electron-antineutrino pair.
The particles which are exchanged between quarks and bind them tightly together are also given a whimsical but this time descriptive name – gluons. Gluons carry the strong force, in the same way that photons carry electromagnetic forces. They can do this because the quarks themselves have another kind of charge, as well as, and distinct from, their electrical charge. In order to distinguish this charge from electrical charge, and for want of a better name, it is called ‘colour’. Unlike electrical charge, colour charge comes in three varieties, not two. Instead of just plus and minus charge, we have ‘red’, ‘blue’ and ‘green’ charge. This doesn’t mean that quarks are ‘really’ coloured; it is just a type of label. Remember that the names plus and minus for electrical charge are themselves arbitrary conventions, and only pass without comment because we are so used to them. The two kinds of electrical charge could themselves have been dubbed ‘red’ and ‘blue’, or (more plausibly) ‘up’ and ‘down’ when they were discovered. The property represented by the ‘redness’, ‘greenness’ or ‘blueness’ of a quark could itself just as easily have been dubbed eeny, meeny and miny, or anything else you like. But calling this property colour charge does have one neat side benefit; it means that the theory of how the strong force works, by exchanging colour charge between quarks with the aid of ‘coloured’ gluons, can be called quantum chromodynamics, or QCD for short.
QCD is an extremely successful theory in its own right. But it is a more complicated and mathematically hairy theory because more kinds of particles and varieties of ‘charge’ are involved. A major problem is that the higher-order terms in the calculation of things like the magnetic moment of, in this case, the proton are much more important in QCD than in QED. In QED, allowing for just three virtual photons being emitted and reabsorbed gets you close to the experimental number, but in QCD terms with six junctions involving gluons would have to be calculated to get anything like the same accuracy. The experiments are pretty accurate, they tell you that the magnetic moment of the proton is 2.79275. But the best calculations yet carried out with QCD ‘only’ give a value of 2.7, with an error of ±0.3.
In QED, Feynman dismissed this as pretty poor – an error of 10 per cent, 10,000 times less accurate than experiment. In fact, the result is pretty impressive, as long as we don’t use the yardstick of the superb accuracy of QED itself, and shows just how good QCD really is.
Nevertheless, partly because of these problems, it has proved very difficult to make QCD exactly fit the QED template, and it has not yet proved possible to unite QCD and electroweak theory into one single mathematical package, a so-called ‘Grand Unified Theory’, or GUT. Even if that can be achieved, there will still be the problem of bringing in gravity as well, to make a unified ‘Theory of Everything’, or TOE (more of this in Chapter 14). But in spite of its imperfections, QCD is a pretty good theory; it just isn’t quite as good as QED itself. And all of the success of QCD in explaining the workings of the world at the level of quarks and gluons depends directly and explicitly on the applications of the QED template to this deeper level of the structure of matter – not just QED, but specifically Feynman’s formulation of QED and the use of Feynman diagrams. The tools that Feynman developed half a century ago are still the tools being used by theoretical physicists at the cutting edge of research today.
This is not without its little irony, because Feynman himself was never convinced that he really had said the last word in quantum electrodynamics. In particular, like Dirac, he was never entirely happy with renormalization, which he described in his Nobel lecture as ‘a way to sweep the difficulties of the divergences of electrodynamics under the mg’. In QED, he used more typical Feynman language to describe renormalization: ‘It is what I would call a dippy process!’
Dippy or not, it worked. Feynman’s version of QED was the last word on quantum theory in 1949, and it is still the last word today. Feynman’s last two great papers on quantum theory were published in 1951, but everything had been worked out by the end of 1948. As Feynman said later, he had
disgorged myself of all the things I had thought about in the context of quantum electrodynamics … I had completed the project on quantum electrodynamics. I didn’t have anything else remaining that required publish
ing. In these two papers, I put everything that I had done and thought should be published on the subject. And that was the end of my published work in this field.5
By the middle of 1951, Feynman was 33 years old. He could have rested on his laurels, led a quiet life as a professor at Cornell, never done any more research, and still he would have won the Nobel Prize and gone down in history as one of the greatest physicists of the 20th century, ‘another Dirac’. But that wasn’t Feynman’s way. By now, he was becoming restless, finding Cornell not as congenial a working environment as he had hoped, and finding new fields of physics to conquer. It was time to move on, both physically and as a physicist.
Notes
1. See Bibliography. This book is a masterpiece of clarity, in the authentic Feynman voice, transcribed and edited by Ralph Leighton from a series of lectures by Feynman. We follow it closely in our description of Feynman’s masterwork.
2. Mehra.
3. Quoted by Gleick.
4. If you want to know more about how this works, see John Gribbin, In Search of Schrödinger’s Cat.
5. Mehra.
7 The legend of Richard Feynman
By the end of the 1940s, there were many reasons for Feynman to feel restless. Professionally, although he was in the process of achieving his greatest triumph, he was also just passing his thirtieth birthday, and must have been aware that very few great physicists have made major contributions to their craft after passing that landmark. Dirac himself, Feynman’s hero, was a good example of a physicist who achieved much in his twenties, and very little of any real importance thereafter. Indeed, there is a piece of doggerel, sometimes ascribed to Dirac, which makes the point forcefully:
Age is, of course, a fever chill
that every physicist must fear.
He’s better dead than living still
when once he’s past his thirtieth year.1
There have been very few exceptions to this rule. Erwin Schrödinger was 39 when he made his greatest contribution to science, the wave version of quantum mechanics. But that was very much a special case, since Schrödinger was deliberately harking back to old ideas about waves, trying to rescue quantum mechanics from the mess it seemed to have got into and return it to the comfortable physics he had learned in his youth. In that sense, it was very much the work of a (relatively) old man, looking backward rather than forward. A more relevant exception was Einstein, who continued to make significant and forward-looking contributions to quantum theory until well into his forties – but even the 30-year-old Dick Feynman might have stopped short of regarding himself as another Einstein.
There was also a problem with his social life. As a young, good-looking, charming and extrovert professor at Cornell, Feynman had achieved considerable success with women. By the standards of the late 1940s, he had achieved (if that is the right word) a reputation as a ladykiller which, with hindsight, can be seen as overcompensation for the loss of Arline. One of his most successful ploys was to hang out in the student union (Willard Straight Hall), drinking coffee and offering to help pretty girls who were having difficulty with their physics homework. In a typical Feynman anecdote, where the truth (or at least, part of the truth) is made palatable with layers of humour, he later told a colleague that he had decided to leave Cornell ‘when he tried that routine on a coed and she said, “I know who you are. You’re not a student, you’re Dick Feynman.”’2 Fame, it seemed, did have its drawbacks.
More seriously, by hanging out with the students Feynman came to appreciate that a lot of what was being taught at Cornell was what he regarded as dopey stuff. This might not have been the sort of thing you would notice when working flat out on a theory like QED, but once the pressure eased and he had more time to take stock, it became a major nuisance. To someone who regarded English literature and philosophy as distinctly dippy subjects, it was utterly bizarre to find that a student could spend four years studying home economics or hotel management (he had first-hand experience of the hotel business, after all) and end up with a degree that was, on the face of it, as good as a degree in physics. There were exceptions – the physics school itself, of course, and some of the other scientific work being done at Cornell. But it was rare for Feynman to find anyone outside his own field with whom he could enjoy an intellectual conversation about their work. He met with what he described to Mehra as a general ‘dopiness’ among the students and faculty, a ‘low-level baloney’, quite different from his recollections of his own student days at MIT and Princeton. Not that he was against dopiness per se – just that ‘It’s not all right if you are talking to students and professors. That bothered me enormously.’3
And then there was the weather. Cornell is in upstate New York, in the small town of Ithaca, and it gets cold there in winter. In Surely You’re Joking, Feynman graphically describes the hassle of driving in snow, stopping and fitting snow chains to the wheels with frozen fingers, ‘and your hand’s hurting, and the damn thing’s not going down – well, I remember that that was the moment when I decided that this is insane; there must be a part of the world that doesn’t have this problem’.
One option was a move to South America. Feynman had been intrigued by the possibility after picking up a hitchhiker who told him how interesting it was, and suggested that he might go there.4 It wasn’t just the weather that appealed. This was in the early years of the Cold War, when many of Feynman’s former Los Alamos colleagues were, he knew, involved in work on the hydrogen bomb, and he still felt that nuclear war was inevitable (which was perhaps also a factor in his wilder adventures). It is hard to appreciate today just how seriously the threat was taken in those days, right through the 1950s and into the 1960s, and Feynman was by no means alone in thinking that South America might be a safer place to settle down than the United States. He even went so far as to learn Spanish, in preparation for a trip south, because it was the most widely spoken language in South America. But that turned out to be a mistake.
Early in 1949, Feynman met a Brazilian physicist, Jaime Tiomno, who was visiting Princeton. When Tiomno heard of Feynman’s vague plans to visit South America, he offered to arrange for Feynman to spend part of the summer at the Brazilian Centre for Research in Physics, in Rio de Janeiro. The offer was irresistible, but it meant Feynman had to take a crash course converting his Spanish into Portuguese in time for the trip.
The six-week visit to Rio, in July and August 1949, was a huge success. Feynman’s first encounter with the relaxed lifestyle came when he landed at Recife to change planes, and was met by representatives of the Centre. His onward flight was cancelled, and the next scheduled flight, 48 hours later, would not get him to Rio until the following Tuesday, a day after he was supposed to take up his summer post.
I got all upset. ‘Maybe there’s a cargo plane. I’ll travel in a cargo plane,’ I said.
‘Professor!’ they said. ‘It’s really quite nice here in Recife. We’ll show you around. Why don’t you relax – you’re in Brazil!’5
In Rio, Feynman taught physics in the mornings (lecturing in what he called ‘“Feynman’s Portuguese,” which I knew couldn’t be the same as real Portuguese, because I could understand what I was saying, while I couldn’t understand what the people in the street were saying’) and relaxed on the beach in the afternoons. There were other physicists to talk to, including Cecile Morette who was visiting the Centre from France, and lots of pretty girls (one of whom actually came back to Ithaca with him, but stayed for only a short time). Rio was definitely Dick Feynman’s kind of place.
Returning from there to Cornell in the autumn of 1949, with the prospect of another New York winter ahead, may have helped to focus Feynman’s mind on a more permanent move to warmer climes. By now Robert Bacher, another member of the old Los Alamos team, was head of the Division of Physical Sciences at the California Institute of Technology, and he invited Feynman to give a series of lectures at Caltech between January and March 1950. Feynman leapt at the opportunity to escape from the New York
winter, and while he was in Caltech Bacher sounded him out about making the move on a permanent basis. Caltech had everything going for it – the climate in Pasadena was a distinct improvement, but most of all the place lacked dopiness. There were no home economics students there, but there were plenty of good scientists, everything from astronomers to zoologists. Caltech, too, was Dick Feynman’s kind of place.
The only thing that made the prospect of the move difficult was that it would mean leaving Bethe, Feynman’s mentor both at Los Alamos and in the difficult years at Cornell getting his theory of quantum electrodynamics established. Once again, Feynman was in demand, and when Cornell learned he was thinking of moving they made him a better offer, only for Caltech to increase their offer. Feynman really was undecided (around this time, he also asked the Centre in Rio if there was any chance of a permanent post there), until in the spring of 1950 Caltech found the ultimate sweetener. If Feynman stayed at Cornell, he would be entitled to a sabbatical year, which would give him a chance to go back to Brazil for an extended stay. Caltech said, OK, come here and you can still have the year off to go to Brazil, at our expense instead of Cornell’s. That clinched it. Feynman agreed that he would take up the appointment at Caltech in the autumn of 1950, with the promise that he could spend the academic year of 1951–2 in Rio.
Before that, he made his first trip to Europe, in April 1950, to attend an international scientific gathering in Paris, and went on briefly to Zurich, where he lectured at Einstein’s old school, the ETH (Federal Institute of Technology). Paris, also, turned out to be Dick Feynman’s kind of place: ‘I had met several of the girls who were dancing at the Lido in Paris, at Las Vegas. I watched rehearsals at the Lido, went backstage, and had all kinds of fun.’6