Since then, the "secret" of making the bomb has also been mastered by the UK, the USSR (as was), France, China and India. Other countries are regarded as "threshold" states: they have built the bomb but held back from setting off a nuclear test explosion. The most notable of these threshold states is Israel, which is rumoured to have more than 100 bombs stored, partly assembled, in the Negev desert. The old South Africa, too, had nuclear pretensions, and the aftermath of the Gulf war revealed that Saddam Hussein had been desperate to acquire nuclear weapons (although he had not got as far as producing enough nuclear material for even one bomb).
Given this dismal roll-call of nuclear or near-nuclear states, the belief has grownthat "you can't uninvent the bomb". Nuclear disarmament is impossible, it is alleged, because the knowledge of how to make nuclear weapons will always be there. This deeply entrenched piece of conventional wisdom is hardly ever challenged. Yet it is largely wrong.
Short of social catastrophe, the kind of knowledge found in textbooks of nuclear physics will not vanish. Designing and building nuclear weapons, however, also calls for "tacit knowledge", the kind of knowledge that cannot be written down. Many everyday activities, such as riding a bicycle, depend on tacit knowledge. Most of us can ride perfectly well, but few of us could even begin to say exactly how we do it. We certainly don't teach children to ride by giving them long lists of instructions.
We usually think of science and technology as areas where explicit knowledge holds sway. Yet tacit knowledge is important there too. Take someone off the street - even someone who has extensive "book knowledge" of science - and ask them to perform a delicate scientific experiment on the basis of written instructions alone. They will fail at first and will learn, if at all, only slowly and painfully. Sometimes, the tacit knowledge involved in scientific procedures is so specific that even an experienced laboratory scientist requires either face-to-face instruction or protracted trial and error.
To the extent that nuclear weapons depend on highly specific tacit knowledge, they can be uninvented. Tacit knowledge is, quite literally, embodied in the people who possess it. If these people die without a new generation of nuclear-weapons designers to pass it on to, their knowledge dies with them. It could be recreated only by going through a process of learning akin to the original invention of nuclear weapons. Nuclear weapons could be reinvented after a period of nuclear disarmament, but the task would be much harder than commonly thought.
In an article in last month's American Journal of Science, we explored the role of tacit knowledge in designing and building nuclear weapons. The physicists involved in the original Manhattan Project thought at first that the difficulties lay in producing enough plutonium or enriched uranium, not in turning that fissile material into a bomb. Physicist Edward Teller recalls being advised by future Nobel laureate Eugene Wigner not to join the new laboratory at Los Alamos, in New Mexico, because its task - designing the atomic bomb - would be too easy.
Los Alamos ended up needing several thousand staff, many of whom were engaged in a multitude of engineering design tasks that the physicists had underestimated. Technological skill turned out to be just as important as a knowledge of nuclear physics.
The explicit knowledge generated by the Manhattan Project spread quickly. Soviet intelligence learnt of the West's atomic-bomb research as early as September 1941. In June 1945, the Los Alamos physicist Klaus Fuchs gave the Soviets a sketch, measurements and a detailed description of the bomb design to be tested at Trinity Site on 16 July and to devastate Nagasaki on 9 August.
Soviet bomb designers then set out simply to copy the Trinity bomb. Despite the fact that Soviet physicists were among the most sophisticated in Europe, and despite the top priority Stalin gave their work, it took them four years, slightly longer than the Americans had taken to make the original. Producing plutonium in the war-devastated Soviet Union required a massive effort, but also important was the fact that explicit knowledge of the sort passed on by Fuchs did not solve all the problems of bomb design. The required technological skills had to be created afresh.
Britain, too, began by trying to copy the Trinity bomb, on which several British scientists had worked. The task again took longer than the original Manhattan Project, led to a design that differed significantly from the original, and involved a multitude of practical problems. More recent nuclear states have had the advantage of sometimes being able to buy key equipment rather than needing to make it. But even those whose purchases were most successful, notably Iraq, found that they also needed time to develop the skills to operate the equipment successfully. By the time of its Gulf war defeat, Iraq had still not solved all the problems of producing fissile materials and of designing a nuclear weapon.
Understanding of nuclear explosions is most fully explicit at the weapons laboratories of the nuclear powers, which have developed large computer programs, called codes, to assist nuclear-weapons design. A modern American code can consist of up to a million lines of program, and runs on the world's most powerful supercomputer. Yet when we interviewed weapons designers at Los Alamos and at its sister laboratory, the Lawrence Livermore in California, they were emphatic that the codes did not eliminate the need for human judgement. The pool of fully experienced designers in the US is surprisingly small - no greater than a few dozen - and has been shrinking fast as key staff retire and leave.
None of this means that we should be complacent about the spread of fissile materials. Nothing that we found in our research rules out the possibility that a crude nuclear device could be put together reasonably quickly by those prepared to take short cuts. Indeed, the South African bomb programme to some extent did this. However, even the relatively small, covert South African programme was well-known to US intelligence, which was able to monitor it in reasonable detail.
Achieving nuclear disarmament, and making it permanent and verifiable, are ultimately political, rather than technical, problems. The obstacles remain daunting. Yet the late Nineties are potentially a period of unique opportunity. The main global nuclear rivalry, the Cold War, has ended. Other potential nuclear arms races, such India versus Pakistan, or Israel versus its Arab neighbours, have yet to become fully fledged. If we do not act now to shut the nuclear genie back in its bottle, will our descendants forgive us?
Donald MacKenzie holds a personal chair in sociology, and Graham Spinardi is a senior research fellow at the Research Centre for Social Science, both at the University of Edinburgh.