by John Gribbin
The term at Cornell ended in June, and Dyson still hadn’t got Feynman’s new quantum theory straight. Thanks to Bethe, he had an opportunity to attend the summer school at the University of Michigan in Ann Arbor, the latest in a series of gatherings famous since 1930, where Schwinger would be giving a full account of his version of QED. He had two weeks to kill before the summer school started, and when Feynman invited Dyson to join him on a drive over to New Mexico, Dyson leapt at the chance.
The reason for the trip back to Albuquerque was a girl, a young woman that Feynman had dated after the death of Arline, and with whom, for a time, he imagined that he might settle down. In a letter home to his parents in England,25 Dyson mentioned the difficulties involved. ‘The girl is a Catholic. You can imagine all the troubles this raises, and if there is one thing Feynman could not do to save his soul it is to become a Catholic himself.’
As far as love was concerned, the trip was a waste of time. Feynman and the girl no longer felt the old attraction for one another, and the question of marriage never seriously arose. But on the way to Albuquerque Dyson had Feynman to himself (along with the occasional hitchhiker they picked up) for four whole days, discussing life and physics. In the middle of Oklahoma, they ran into torrential rain and flooding so bad that all progress was halted, and ended up in a place called Vinita looking for a room for the night. The town was packed with other stranded travellers, and all the hotels were full. Feynman, though, was unfazed. From his days seeking out the cheapest possible accommodation for his overnight visits to be near Arline, he knew what to do, and found them a room in a brothel that they could share for 50 cents apiece.
With the rain hammering down and the girls plying their trade in nearby rooms, there was no prospect of sleep that night, but the two travellers were happy simply to be warm and dry. They talked the night away – or rather, Feynman talked and Dyson mostly listened. He talked about Arline, and his work on the bomb. Then they talked about physics, and Dick’s way of visualizing quantum processes in spacetime. Dyson saw that Feynman’s sum over histories theory ‘was in the spirit of the young Einstein’. But ‘nobody but Dick could use his theory, because he was always invoking his intuition to make up the rules of the game as he went along. Until the rules were codified and made mathematically precise, I could not call it a theory.’26
The next day the rains had eased and the roads were passable. In Albuquerque, they made their farewells, and Dyson caught the Greyhound bus back east, travelling in easy stages to Ann Arbor and revelling in his first experiences of travelling alone across America. In five weeks at Ann Arbor, as well as attending lectures he made many new friends, and managed to talk at length with Schwinger about his theory. At the end, ‘I understood Schwinger’s theory as well as anybody could understand it, with the possible exception of Schwinger.’ From Ann Arbor, Dyson travelled back across the United States by Greyhound to holiday in San Francisco. At the beginning of September, it was time to head east once again, to Princeton. For three days and nights he travelled non-stop, as far as Chicago. He had nobody to talk to, the roads were too bumpy for sleep, and he:
looked out of the window and gradually fell into a comfortable stupor. As we were droning across Nebraska on the third day, something suddenly happened. For two weeks I had not thought about physics, and now it came bursting into my consciousness like an explosion. Feynman’s pictures and Schwinger’s equations began sorting themselves out in my head with a clarity they had never had before. For the first time I was able to put them all together. For an hour or two I arranged and rearranged the pieces. Then I knew that they all fitted. I had no pencil or paper, but everything was so clear I did not need to write it down. Feynman and Schwinger were just looking at the same set of ideas from two different sides.
So it was that Dyson wrote up a paper on ‘The Radiation Theories of Tomonaga, Schwinger and Feynman’, and sent it off to the Physical Review even before Oppenheimer returned from his own summer travels in Europe. The paper27 made the new quantum electrodynamics, at last, accessible to ordinary physicists, and made Dyson’s reputation, although Oppenheimer, as it turned out, needed a lot of convincing that it was all worthwhile. By now, Feynman was also pressing ahead with writing up his work for publication, and had sorted his ideas into a much more clear and accessible form than the messy failure of a lecture that he gave at the Pocono Conference. Because of Dyson’s comprehensive and influential review of the whole field, though, some people were initially confused about who had discovered (or invented) what, and for a time what are now known as ‘Feynman diagrams’ (which we discuss in the next chapter) were referred to in some quarters as ‘Dyson graphs’. It didn’t matter. Feynman and Schwinger were both happy to see their work receiving the attention that it deserved. As Steven Weinberg has observed, ‘with the publication of Dyson’s papers, there was at last a general and systematic formalism that physicists could easily learn to use, and that would provide a common language for the subsequent applications of quantum field theory to the problems of physics’. 28 Or as Dyson himself has put it, ‘my major contribution [was] to translate Feynman back into language that other people could understand … When Feynman’s tools first became available, it was a tremendous liberation – you could do all kinds of things with them you couldn’t have done before.’29
Almost immediately, Dyson was given a demonstration of the power of Feynman’s toolkit when wielded by Feynman himself. At the end of October, when Dyson had finished his paper, he visited Cornell with another physicist from the Institute, Cecile Morette, to discuss quantum electrodynamics and make sure there were no hard feelings about what he had done – that he had written an account of Feynman’s theory before Feynman had published it himself. Dyson had sent Feynman a copy of the paper, which Feynman had given to one of his students to read. He then asked the student if there was any need to read it himself, and the student said no, so he didn’t.30 Dyson and Morette arrived at Cornell on a Friday, and were entertained by Feynman with stories and drumming until 1am. The next day, he gave them a ‘masterly account’ of his theory. In the evening, Dyson mentioned that there were two outstanding problems that the theory had yet to tackle, and which had proved intractable for the old theories in spite of intensive efforts by many physicists. They were problems involving the scattering of light (photons) by an electric field, and the scattering of photons by other photons. ‘Feynman said “We’ll see about this,” and proceeded to sit down and in two hours, before our eyes, obtain finite and sensible answers to both problems. It was the most amazing piece of lightning calculation I have ever witnessed’, Dyson wrote to his parents, ‘and the results prove, apart from some unforeseen complications, the consistency of the whole theory.’ Years later, in a TV interview, Dyson described this as
just about the most dazzling display of Feynman’s powers I’ve ever seen. These were problems that had taken the greatest physicists months to fail to solve, and he knocked them off in a couple of hours … it was done in this extraordinary economical style, without heavy apparatus – just sort of stitching the answers before even writing down the equations, and deriving things directly from the diagrams. Well, after that there was nothing more to be done, but only to proclaim the triumph of the theory.31
This was Feynman at the height of his powers, delighting in applying his new theory to solving problems. This particular feat impressed Dyson; but Feynman managed to impress himself with his next tour de force, which took place at the January 1949 meeting of the American Physical Society. At the meeting, a physicist named Murray Slotnick presented some new results describing the way an electron bounces off a neutron. He had calculated these the old way, over a period of many months. Feynman missed the talk, but was told about it by a colleague. He asked Slotnick how he had approached the problem, and decided it would be ‘a welcome opportunity’ to test his theory by seeing if it gave the same answers. In his Nobel lecture, Feynman describes how he worked through the problem that evening, and next d
ay went up to Slotnick to compare notes. Slotnick said, ‘What do you mean, you worked it out last night, it took me six months!’ And when they checked, they found that not only had Feynman got the same answers as Slotnick, but that he had solved the problem in a much more general way, allowing for the momentum transferred by the electron to the neutron (the recoil of the neutron when hit by the electron); Slotnick had only solved the problem for zero momentum transfer (no recoil).
This, Feynman recalled in his Nobel lecture, was the moment when everything came together for him. ‘That convinced me, at last, that I did have some kind of method and technique and understood how to do something that other people did not know how to do. That was my moment of triumph.’
The work was published in a series of papers over the next three years, but by the beginning of 1949 everything was complete. Neatly rounding off this epic period in the development of quantum theory, the third, and last, of the postwar conferences organized by Oppenheimer and funded by the National Academy of Sciences took place from 11 to 14 April 1949, at Oldstone-on-the-Hudson in Peekskill, New York, 50 miles north of New York City. By now, Dyson was eminent enough to be included in the couple of dozen participants, and whereas Schwinger’s theory had formed the centrepiece of the Pocono Conference, while the Lamb shift had been the main talking point at Shelter Island, at the Oldstone Conference it was Feynman’s approach to QED that was at centre stage. A month before his thirty-first birthday, Feynman had become the leading physicist of his generation, pointing the way ahead with his new ideas.
Shortly after the Oldstone gathering, Dyson gave a talk in Washington to a meeting of the American Physical Society, at which he said:
We have the key to the Universe. Quantum electrodynamics works and does everything you wanted it to do. We understand how to calculate everything concerned with electrons and photons. Now all that remains is merely to apply the same [ideas] to understand weak interactions, to understand gravitation and to understand nuclear forces.32
These seemingly extravagant claims have largely been proved correct; although gravity has not yielded to the attack as easily as Dyson hoped in 1949, all of the rest of physics is now understood in the same terms as Feynman’s formulation of QED. Before we look at how Feynman’s life and career developed after 1949, it is worth taking stock of the breathtaking way in which QED, and especially Feynman’s formulation of QED, has played the central role in all of theoretical physics (except the investigation of gravity) throughout the second half of the 20th century.
Notes
1. Reprinted in Surely You’re Joking, from Reminiscences of Los Alamos, 1943–45, edited by Lawrence Badash, Joseph Hirschfelder and Herbert Broida (Reidel, Dordrecht, 1980). Unless otherwise indicated, anecdotes about Feynman’s time in Los Alamos come from this source.
2. Scientific American, June 1988.
3. Personal correspondence between Arline and Richard, transcribed and loaned by Michelle Feynman.
4. See Bethe’s contribution to Most of the Good Stuff.
5. See note 4.
6. What Do You Care.
7. What Do You Care.
8. See note 3.
9. What Do You Care.
10. See note 1.
11. Robert Oppenheimer: Letters and Recollections, edited by Alice Kimball Smith & Charles Weiner (Harvard University Press, 1980).
12. Mehra.
13. Interview with Silvan Schweber, reported in QED and the Men Who Made It.
14. See note 3.
15. Surely You’re Joking.
16. Nobel lecture.
17. Nobel lecture.
18. Mehra.
19. Quoted by Mehra.
20. Mehra.
21. Mehra.
22. Feynman, quoted by Mehra.
23. Freeman Dyson, Disturbing the Universe (Basic Books, New York, 1979).
24. See QED and the Men Who Made It.
25. Reprinted in Freeman Dyson, From Eros to Gaia (Pantheon, New York, 1992).
26. See note 23.
27. Physical Review, volume 75, page 486, 1949.
28. Steven Weinberg, The Quantum Theory of Fields (Cambridge University Press, 1995).
29. See Dyson’s contribution to No Ordinary Genius.
30. See note 25.
31. See No Ordinary Genius.
32. Quoted by Schweber.
* In Surely You’re Joking Feynman gave the ratio in the wrong way round, 2:1 for spin:wobble instead for wobble:spin, and the Cornell medallion on the plates may really have been blue, not red. Like all Feynman anecdotes, the precise details don’t matter, but the moral is clear.
6 The masterwork
Quantum electrodynamics is a theory that describes all interactions involving light (photons) and charged particles, and, in particular, all interactions involving photons and electrons. Because the interactions between atoms depend on the arrangement of electrons in the clouds around the nuclei, that means that, among other things, QED underpins all of chemistry. It explains how a spring stretches, and how dynamite explodes; the working of your eye, and how grass is green (it is also the explanation behind the intermolecular forces described in Feynman’s undergraduate thesis). In fact, as far as the everyday world is concerned, QED explains everything that isn’t explained by gravity. There are two other forces of nature, which only operate on a very small scale, essentially within the nucleus of an atom, and are responsible for holding those nuclei together and for radioactivity. But outside the nucleus, on the scale of atoms and above, all that matters is QED and gravity.
Both QED and gravity (in the form of Einstein’s General Theory of Relativity) are extremely accurate and well-understood theories. In terms of experiments actually carried out in laboratories here on Earth, though, QED is the outstanding example of a successful theory – that is, one which predicts with great precision the outcome of experiments. The property called the magnetic moment of the electron, which we mentioned in Chapter 5, is, along with the Lamb shift, a classic example of how the new theory achieved such success, and one which can be explained neatly using Feynman’s techniques. Using Dirac’s theory of the electron, you can choose to work in units in which the value of the magnetic moment of the electron is precisely1. QED, however, predicts a value of 1.00115965246, while experiments have measured the magnetic moment to be 1.00115965221. The uncertainty in the experimental measurement is about ±4 in the last number; the uncertainty in the theoretical calculation is about ±20 in the last two numbers. So theory and experiment agree to an accuracy of two parts in ten decimal places, or 0.00000002 per cent. In his book QED: The Strange Theory of Light and Matter,1 Feynman points out that this is equivalent to measuring the distance from Los Angeles to New York to the thickness of a human hair – and this is just one example of the many precise agreements between QED and experiment. Very recently, the General Theory of Relativity has been checked to a similar accuracy by studying the behaviour of an astronomical object known as the binary pulsar; but somehow, that isn’t quite the same as doing the experiments, for real, right here on Earth. In that sense, QED is the most successful and accurate of all scientific theories, although both kinds of observation are really equally valid.
Feynman’s approach to QED, using path integrals, can best be seen by starting out with the famous experiment with two holes, discussed in Chapter 2. The important thing about the experiment with two holes – thinking for the moment in terms of waves – is that waves that follow one path through the experiment to the detector screen can get out of step with waves that follow the other path through the experiment. Waves that march in step with one another are said to be in phase, and if both waves are of equal strength and in phase, they will add together to produce a wave that is twice as strong. But if two waves of equal size have opposite phase (that is, they are exactly out of phase), then they will cancel out. It is this addition and cancelling of waves that makes for the pattern of bright and dark bands on the screen in the experiment with two holes, even thoug
h all the waves have the same strength. It is also the difference in phase, not any difference in the strength of the waves, that makes the advanced and retarded waves in the absorber theory of radiation add up and cancel out in just the right way to explain how charged particles interact (see Figure 5). And, of course, as well as complete addition and cancellation it is possible to have intermediate cases, where two waves are out of phase but not perfectly opposed to one another, producing a partial cancellation.
All of this carries over to the alternative quantum mechanical description of what is going on, where the light is described in terms of entities (photons, electrons or anything else) that follow trajectories determined by quantum probabilities. These quantum probabilities are described by the Schrödinger equation, and behave exactly like waves, with phase all important in determining whether two probabilities add up to produce a strong likelihood of a photon (or whatever) following a particular path, or cancelling out to ensure that the photon never takes a second path. The only slight complication is that the actual probabilities are given in terms of the square of the wave property known as the amplitude – the probability amplitudes have to be combined first (putting the little arrows head to tail), and the answer you get then multiplied by itself to give the actual probability of a particular path being followed.
Figure 7. (a) A spacetime diagram can be used to show how an energetic photon (a gamma ray) can give up its energy to create an electron (e) and a positron (p). The positron later meets another electron and annihilates with it, to make a gamma ray. (b) But it is equally valid to say that there is only one electron (e), which starts out on the left moving into the future, then meets an energetic photon travelling backwards in time, which sends the electron moving backwards in time until it meets another gamma ray which bounces it back to the future. A positron is an electron going backwards in time.
