by John Gribbin
But this approach never caught on. In universities around the world, even today, half a century after Feynman’s insight, students are still taught classical mechanics the old-fashioned way, and then forced to train themselves into a new way of thinking in order to study quantum mechanics using the Hamiltonian approach and the Schrödinger equation. By the time most people learn about Feynman’s approach (if they ever do), their brains have been battered by so much mechanics of one kind or another that it is hard to appreciate its simplicity, and galling to realize that they could have saved time and effort by learning quantum theory (and classical theory!) Feynman’s way in the first place. Feynman’s approach is not the standard way to teach physics for the same reason that the Betamax system is not the standard format for home video, and the Apple Macintosh is not the standard for personal computers, because an inferior system got established in the marketplace first, and continues to dominate as much through inertia and resistance to change as anything else. Such considerations, though, were hardly at the forefront of any physicist’s mind in 1942, when Feynman finished his PhD, left Princeton and set off to work on the Manhattan Project in Los Alamos.
Notes
1. Told by Feynman to Mehra.
2. Richard Feynman, Science, volume 153, pp. 699–708, 1966. This is the published version of the Nobel lecture delivered in Stockholm on 11 December 1965. Hereafter referred to as ‘Nobel lecture’.
3. Silvan Schweber mentions these earlier investigations of action at a distance in electrodynamics in QED and the Men Who Made It (see Bibliography).
4. Nobel lecture.
5. Nobel lecture.
6. Surely You’re Joking.
7. Mehra.
8. Nobel lecture.
9. See Mehra. This conversation, the first between Dirac and Feynman, may seem a little terse. In fact, by Dirac’s standards it was positively voluble. In 1929, just 27 years old but already an acclaimed genius who had made a major contribution to the development of quantum theory, he visited the University of Wisconsin. The Wisconsin State Journal published an interview with the young genius in which his part of the conversation consisted almost entirely of monosyllables. In a typical exchange, the reporter asks if Dirac ever goes to the movies. ‘Yes’, he replies. ‘When?’, the interviewer asks. ‘In 1920.’
10. Nobel lecture.
11. Richard Feynman, The Principle of Least Action in Quantum Mechanics, PhD thesis, Princeton University, May 1942.
12. See, for example, John Gribbin, In Search of Schrödinger’s Cat.
13. Most of the Good Stuff.
* Unfortunately, the word ‘action’ is used in two different ways by physicists. This ‘action at a distance’ has nothing to do with the ‘action’ that appears in the Principle of Least Action, but is shorthand for ‘interaction at a distance’.
5 From Los Alamos to Cornell
Once a decision had been made to build an atomic bomb, the first problem that had to be tackled was getting enough radioactive material of the right – potentially explosive – kind to do the job. The runaway process of nuclear fission that powers such a bomb happens when nuclei of a certain kind of heavy element split into two or more lighter nuclei, with energy being released. The key to an explosive chain reaction is that when one nucleus splits it also releases two or more neutrons, which collide with other nuclei and make them split in turn, in a growing cascade. Calculations showed that an explosive chain reaction ought to occur if a sufficiently large quantity of either of two radioactive elements, uranium-235 or plutonium-239, could be brought together in the right way in a bomb.
Plutonium could only be manufactured artificially, by the bombardment of another, more stable form of uranium, uranium-238, with subatomic particles. The difference between uranium-235 and uranium-238 is simply that each nucleus of uranium-238 contains three more neutrons than each nucleus of uranium-235, but that is enough to make the nucleus relatively stable – it is radioactive, but has a very long lifetime. Uranium-235 is much more radioactive and potentially explosive, but occurs naturally mixed with uranium-238 in trace quantities, with only seven atoms of uranium-235 for every 1,000 atoms of uranium-238. Both routes to a nuclear bomb were taken by the Manhattan Project: the manufacture of plutonium-239, and the separation of uranium-235 from naturally occurring uranium.
The Princeton project that Feynman joined under Robert Wilson, before completing his thesis, was one of several attempts to find a way of separating out uranium-235 in the quantities required. Progress was slow, which was partly why Feynman was, after all, able to take time off in the spring and early summer of 1942 to complete his PhD and get married. Late in 1942, the Princeton approach to the uranium separation problem was abandoned, in favour of a technique being developed at Berkeley, in California, which was making more rapid progress. But the entire Princeton team, along with other researchers involved in the atomic bomb project, was invited to move to Los Alamos, where a new, secret research centre was being built to solve the problem of actually building the bomb and making it work. They all signed up, but then had to sit around, twiddling their thumbs for several months while the Los Alamos lab was actually being built.
In order to make good use of the time, Wilson found several minor problems for the team to tackle. He also sent Feynman off to visit the Metallurgical Laboratory in Chicago, at that time the heart of the Manhattan Project, where Enrico Fermi’s team was building the world’s first nuclear reactor, then called an atomic pile. Wilson wanted as much information as Feynman could get about the whole Top Secret project. Feynman’s reminiscence about his war work can be found in an article called ‘Los Alamos from Below’;1 in that article, he recounts how Wilson instructed Feynman to go to each group of researchers in Chicago, say that he was going to be working with them, and ask for enough information about the project to enable him to start work. His conscience troubled him, because he expected to go away from Chicago without having given anything back in return. But, as Wilson may well have expected when choosing Feynman for the job, it didn’t work out like that. He not only obtained all the information that Wilson wanted, but everywhere he went he made valuable suggestions, helping the work in Chicago along. In an obituary of Feynman published in 1988,2 Philip Morrison, a member of Fermi’s Chicago team, recalled how ‘we all came to meet this brash champion’, who ‘did not disappoint us; he explained on the spot how to gain a quick result that had evaded one of our clever calculators for a month’. The way Feynman told the story, it was just luck that he happened to know a mathematical trick that would work on that problem; to everybody else, it was an example not only of his mathematical genius, but his ability to see to the heart of a problem as soon as it was suggested to him. Both abilities would shortly be exercised to the fullest.
The scientific head of the Manhattan Project was Robert Oppenheimer, a renowned physicist whose work before the war included investigations involving the Dirac equation and theoretical studies of what are now known as neutron stars and black holes, three decades before such objects were discovered. Like Feynman, Oppenheimer would eventually (in 1967) die of cancer. Suggestions that this was possibly related to his wartime work with radioactive materials should be taken with a pinch of salt; Oppenheimer’s cancer of the throat was more probably a result of his chain-smoking of cigarettes.
Oppenheimer was the ideal man to head the scientific side of the Manhattan Project, providing an interface between the scientists and the military, having a thorough understanding of the science involved in the project and, not least, taking a close personal interest in the wellbeing of everyone at Los Alamos. In Feynman’s case, this extended to finding a sanatorium for Arline to stay at in Albuquerque, as close as possible to Los Alamos itself. Feynman was deeply touched by this personal attention, and like the rest of the team would do anything for ‘Oppie’.
The nearest railway station to Los Alamos was at Lamy, New Mexico, and when the Princeton group were finally given the OK to move out to New Mexico,
that was where they were headed. But Princeton was a small town, and the authorities were worried that curiosity might be aroused if all the physicists suddenly upped and left for Lamy. So they were told to buy their train tickets elsewhere, in order not to cause gossip locally. Feynman, as ever, had his own way of looking at things. If everybody else was buying their tickets in other towns, it would do no harm if one person – Feynman – bought a ticket to Lamy at Princeton station. So he did. ‘Oh,’ said the man at the ticket office, ‘so all this stuff is for you!’ The team had been shipping out crates of material for weeks, all going from Princeton to Lamy by rail. At least, by buying his ticket in Princeton, Feynman had explained who all the stuff was for.
Feynman was one of the first scientists to set out for Los Alamos, leaving Princeton, with Arline, on 28 March 1943. They paid extra for a private suite on the train, treating the long cross-country ride as a holiday. Arline had hoped that it might also be something of a honeymoon – as yet, the marriage had not been consummated, partly through lack of opportunity, partly through fear of the effect on Arline’s health, and the possibility of Richard’s becoming infected with TB. But it seems that nothing came of these hopes.3
Feynman’s own accounts of his time at Los Alamos focus on the fun and games – his safecracking exploits, and the battles with the censor, being classic examples. The censorship problems arose because both Arline and Melville used to write to Richard in code, using systems they had invented, and which he didn’t have a key to. The game – light relief in the midst of his serious work on the project – was for him to crack the code in order to read the letters. But the censors wouldn’t allow coded messages to go in or out of Los Alamos! The situation was eventually resolved when the censor agreed to allow this, provided a key was included in each letter so that the censor could read it before passing it on, without the key, to Feynman. Feynman milked the deliciously bureaucratic problem for all it was worth. The very fact that the mail was being censored was officially a secret, so when Feynman was told to tell Arline not to mention censorship in her letters, he promptly wrote her a letter beginning, ‘I have been instructed to inform you not to mention censorship in your letters.’ The censor, of course, censored the letter; Richard had to go and tell Arline what was going on in person.
The fun and games may seem childish, but they were an important safety valve for Feynman and his colleagues – more so for him than for most. He was not quite 25 when he arrived in Los Alamos, where he had another piece of what he called luck. It happened that most of the big shots were away at the time, and Hans Bethe, who was the head of the Theory Division on the project, needed someone to bounce some ideas off. He came into Feynman’s office, and started talking physics. As always, when talking physics Feynman forgot who he was talking with, and was unimpressed by their status. He told Bethe his ideas were crazy, Bethe argued his case, Feynman responded by pointing out the flaws in it, and the arguing went on until the problem was solved, just as in the debates with Wheeler back in Princeton. Bethe, who already knew of Feynman’s reputation, was impressed, and made him a group leader in the Division, in charge of a team of four other researchers. He was the youngest group leader by about ten years (Bethe himself was 37 in 1943), and showed a real flair for getting the best out of his team.
Feynman became something of a troubleshooter, a Mr Fixit, for the whole Theory Division. Always fascinated by mechanical things, he spent a lot of time repairing mechanical calculators (glorified adding machines) and typewriters, until Bethe decided that this was a waste of his talents and ordered him to stop.4 But then the project took delivery of a new kind of calculating machine, delivered from IBM in many boxes. Feynman and a colleague took the parts out of the boxes and put them together to assemble the machines. A week later, the official IBM engineer, drafted for the duration, arrived to assemble and look after the machines; he told Bethe that he had never seen such machines put together by non-experts before, but that they were all working properly.
When the machines were first put to use, however, there were problems. The leaders of the group using the calculators were fascinated by their abilities, and loved to play with them, but the real work, calculating important numbers needed for the construction of the bomb, simply wasn’t getting done. Bethe’s answer was to put Feynman in charge of the IBM machines, as head of the Theoretical Computations Group – by then, the most important group in the Theory Division. ‘Soon the group was working efficiently, and we got our answers promptly and steadily.’5
Feynman’s ability was also noticed by outsiders. When Niels Bohr, one of the greatest physicists and a founding father of quantum theory, visited the project, he noticed the way Feynman spoke up in meetings, cutting to the heart of the problem in question. The next time Bohr came to Los Alamos, Feynman received a call from Bohr’s son, also a physicist, asking him to meet the great man early, at 8am, before the big meeting. For a couple of hours Bohr went over his ideas, with Feynman, as usual, interrupting to point out what was wrong with them, shouting, ‘you’re crazy’, treating Bohr the way he would treat any physicist. At last everything was sorted out. ‘Well,’ said Bohr, ‘I guess we can call in the big shots now.’ The younger Bohr explained – after the previous visit, Bohr senior had commented on Feynman’s contributions to the discussion: ‘He’s the only guy who’s not afraid of me, and will say when I’ve got a crazy idea. So next time when we want to discuss ideas, we’re not going to be able to do it with these guys who say everything is yes, yes, Dr Bohr. Get that guy and we’ll talk to him first.’
With all this going on, Richard still had Arline to consider. Every week, he would hitchhike (or if he was lucky, borrow a car) to travel almost 100 miles to see her in Albuquerque on the Saturday afternoon. He would stay in a cheap hotel overnight, visit her again on Sunday morning, and make his way back to Los Alamos in the afternoon. He used the long trips to think about quantum mechanics, developing the ideas in his thesis further. Given the pressures he was under, it’s hardly surprising that when the opportunity presented itself he couldn’t resist winding up the censors, or having fun in whatever other way he could.
Much of that fun was provided by Arline, sometimes to Richard’s embarrassment. In What Do You Care, he tells how she reminded him of his own dictum, to take no notice of what other people thought. The sanatorium was right on Route 66, the main road across the United States, with trucks rolling by what passed for the lawn in front of the building. As part of her attempt to lead a normal life, Arline bought, by mail order, a little barbecue grill, and made Dick go out on the lawn and cook her steaks, most weekends, dressed in a chef’s hat and apron. At first he protested. But – ‘What do you care what other people think?’, she responded. The first Christmas in New Mexico, Arline ordered a batch of printed cards for the couple to send out, nice cards with the message inside ‘Merry Christmas, from Rich & Putsy’. Feynman protested that they were too informal to send to important people like Oppenheimer and Bethe, but out they went anyway. The next year, by which time Feynman was on familiar terms even with the senior scientists like Bethe, she showed him another batch of cards, with the message ‘Merry Christmas and a Happy New Year from Richard and Arline Feynman’. As soon as he expressed his relief at their suitability, she produced another box of cards, especially for the important people, signed ‘From Dr & Mrs R. P. Feynman’. Out they went, resulting in Feynman being ribbed by his colleagues about the stuffy formality of his Christmas greetings.6
Of course, his friends knew it was a joke. Many of them visited Arline in the sanatorium – even Wheeler, on a visit to Los Alamos, found time to call in on her – and they were pleased with anything that made her happy. Always busy, she taught herself Chinese calligraphy, and made many plans for a future in which Dick would be a real professor and they would raise a son called Donald. In What Do You Care, Feynman explained that neither of them felt overwhelmed by her condition, that they had ‘a hell of a good time together’. After all, he points out, ever
ybody knows that they will die eventually. The only difference for them was that they had five years together instead of 50 years:
Why make yourself miserable saying things like, ‘Why do we have such bad luck? What has God done to us? What have we done to deserve this?’ – all of which, if you understand reality and take it completely into your heart, are irrelevant and unsolvable. They are just things that nobody can know. Your situation is just an accident of life.7
Back at Los Alamos, Feynman was making another reputation for himself, as a teacher. Part of the reason for his success in getting the Theoretical Computations Group working so well was because he explained to them what was going on. The people operating the machines were essentially kids fresh out of high school, called up and dumped in barracks, told to operate these machines using punch cards, without any clue as to what the work was all about. It needed Oppenheimer to arrange a special security clearance, but then Feynman told them all about the project and how important their work was, firing them with enthusiasm. In the nine months before he took over the group, it had solved three problems. In the three months after he took over, it solved nine problems – the same people, using the same machines, but under new leadership.