Inside the Centre: The Life of J. Robert Oppenheimer (21 page)

Though still a graduate student, Dirac was invited to give a course of lectures on quantum theory in the academic year 1925–6. Entitled ‘Quantum Theory (Recent Developments)’, it was the first course on quantum mechanics ever given at a British university. Among the few students who attended it was Oppenheimer, who, like the other attendees, was no doubt conscious of the privilege of being given access to Dirac’s latest thoughts on the subject before they were announced and published to the outside world. ‘Dirac gave us what he himself had recently done,’ remembers one member of this privileged group, adding: ‘We did not, it is true, form a very sociable group, but for anyone there it was impossible to forget the sense of excitement at the new work.’

Possibly through Dirac, or possibly through Blackett, Oppenheimer was introduced to the
²
V Club, usually referred to as the ‘Del Squared V Club’,
being a mathematical symbol and
²
being an operator (the ‘Laplacian operator’) frequently used in theoretical physics. Where the Kapitza Club consisted mainly of experimental physicists, the
²
V Club was for theorists. There Oppenheimer would have met all the leading theoretical physicists at Cambridge, including most notably Ralph Fowler, Dirac’s supervisor and Rutherford’s son-in-law. Fowler, who has been described as ‘a generous-spirited man with the build of Henry VIII and the voice of a drill sergeant’, was, until Dirac’s fame overshadowed him, the foremost theoretical physicist at Cambridge and, crucially for both Dirac and Oppenheimer, the one most fully abreast of developments on the continent.
^fn21

It was Fowler, for instance, who was first aware of the importance of the work of the French physicist Louis de Broglie, the man who took the initial steps towards the quantum-mechanics revolution. De Broglie, a member of one of the most ancient and distinguished French aristocratic families, had studied medieval history at the University of Paris before, under the influence of his elder brother, switching to physics. In the autumn of 1923, two years before Oppenheimer’s arrival at Cambridge, de Broglie had published a series of three short papers in the French journal
Comptes rendus
, putting forward the outlandish suggestion that electrons should be regarded as being
both
particles and waves.

The inspiration for this was Einstein’s Nobel Prize-winning suggestion in 1905 that light, previously thought of as consisting of waves, should be thought of as being made up of discrete ‘quanta’, or ‘photons’ as they are now called. Einstein had used this idea to account for the ‘photoelectric effect’ – that is, the fact that, when light is shone onto a metal surface, electrons are emitted, the energy of the electrons depending not on the intensity of the light, but on its frequency. This quantum theory of light (or, more generally, of electromagnetic radiation) was confirmed in 1922 in a series of experiments conducted by the American physicist Arthur Compton. De Broglie, in a flash of inspiration, saw that, if Einstein’s suggestion regarding light were extended to electrons, some of the difficulties faced by the Rutherford–Bohr–Sommerfeld model of the atom might be overcome. In particular, it would be possible to answer the question that Rutherford, with his unerring instinct for the heart of a problem, had raised about Bohr’s model of the atom: how do electrons ‘know’ which orbits to travel on? Or, to put it another way, why are electrons only ‘allowed’ certain orbits? De Broglie’s hypothesis of the wave-particle duality of electrons provided a brilliant answer to this: as
electrons are waves, they can only circle the nucleus in certain orbits, namely those that correspond to multiple whole units of their wavelengths.

To begin with, de Broglie’s brilliant idea aroused remarkably little interest among physicists. Fowler was one of the first to see any value in it, and it was he who in October 1923 submitted to the
Philosophical Magazine
an English version of de Broglie’s articles. Entitled ‘A Tentative Theory of Light Quanta’, this appeared in print in February 1924, and, though it made de Broglie’s revolutionary idea accessible to English-speaking physicists, it failed to attract very much attention. In fact, it required the advocacy of Einstein himself to make theorists take de Broglie seriously. In the spring of 1924, de Broglie wrote up his ideas and presented them as a PhD thesis, which was examined the following November. One of the examiners was Paul Langevin, who sent de Broglie’s thesis to Einstein, asking him what he thought. The reply was unequivocal: ‘He has lifted a corner of the great veil,’ wrote Einstein. De Broglie was duly awarded his doctorate and, five years later, after his hypothesis had been confirmed experimentally, was awarded the Nobel Prize.

Once it had been applauded by Einstein, de Broglie’s audacious idea of wave-particle duality caught the imagination of physicists everywhere. Patrick Blackett was reported to have returned from his year in Göttingen ‘brimful of talk and enthusiasm about de Broglie and wave mechanics’. In August 1925, a month before Oppenheimer arrived at Cambridge, Paul Dirac gave a paper to the Kapitza Club on de Broglie’s ideas.

By then, however, the attention of the few physicists keeping abreast of these developments had shifted to the work of the young German physicist Werner Heisenberg. Having received his doctorate (supervised by Arnold Sommerfeld) from the University of Munich in 1923, when he was still only twenty-one, Heisenberg moved to Göttingen to take up a position as Max Born’s assistant. During the first half of the academic year 1924–5, as Born was due to be in the United States on a lecture tour (which, in the event, he postponed until the following year), Heisenberg arranged to spend some months at Bohr’s institute in Copenhagen. There at the same time, taking sabbatical leave from Cambridge, was Ralph Fowler, who was thus able to add Heisenberg to his already impressive list of personal contacts among the leading and up-and-coming physicists in Europe. Meanwhile, Patrick Blackett was at Göttingen, discussing with Franck and Born (and then, when he returned to Göttingen in April 1925, with Heisenberg) the wave-particle duality of the electron posited by de Broglie.

Though de Broglie’s theory gave a convincing explanation of why electrons were confined to the orbits, or energy states, specified in Bohr’s model of the atom, it introduced an enormous problem of its own: how
could
an electron possibly be
both
a particle and a wave? We can picture
electrons as waves vibrating around the nucleus, or we can picture them as material objects orbiting the nucleus, but we cannot, surely, picture them as both at the same time. De Broglie’s initial attempt to solve this conundrum was to imagine electrons as particles moving along a wave-like path, but this stripped the theory of its power to explain Bohr’s orbits, since no good explanation could be given as to
why
electrons were tied to those wave-like paths. The beauty of de Broglie’s theory lay precisely in the thought that an electron
was
a wave, the wavelength of which explained the ‘static orbits’ of Bohr’s theory. And yet there were very good reasons for believing, and abundant experimental evidence to suggest, that electrons were particles.

Heisenberg’s novel response to this problem was to jettison all talk of orbits, particles and waves and refrain from picturing the electron
at all
. We must, he declared, confine ourselves to what can be observed. We cannot observe the orbiting of the nucleus by the electron; all we can observe is the energy given off by an electron when it ‘jumps’ from one state to another. The reason we can observe
this
is that the energy in question takes the form of visible light, thus enabling the technique of investigation known as spectroscopy: the study of the spectra of light emitted by electrons of various elements, which allows physicists to associate each element with its characteristic and unique spectrum of coloured light. It is upon the data provided by spectroscopy that Bohr’s theory of atomic structure was built (hence the title of Sommerfeld’s classic book on the subject:
Atombau und Spektrallinien
[
Atomic Structure and Spectral Lines
]), and when Heisenberg announced his intention of confining himself to what can be observed, he meant primarily: observed using the techniques of spectroscopy.

In June 1925, shortly after he returned to Göttingen from Copenhagen, Heisenberg, ill with hay fever, decided to recuperate on the North Sea island of Helgoland. There, thinking alone about the strictly observable properties of electrons, inspiration struck him and he formulated the basic ideas of the branch of physics that was to claim the attention of Oppenheimer and most of his contemporaries: quantum mechanics. The fundamental aim of this branch of physics is to provide quantum theory with a mechanics – that is, a mathematical model that would explain the apparently bizarre movements of electrons and of subatomic particles generally. What occurred to Heisenberg in Helgoland was (to him) a brand-new kind of mathematics, which one could use to model the behaviour of electrons.

At the heart of this mathematics was a numbering system that assigned to electrons a pair of numbers,
p
(representing the electron’s
momentum
– that is, its mass multiplied by its velocity) and
q
(representing the electron’s
position
), and a technique of multiplying these pairs of numbers.
The troubling aspect of this new mathematical model was that the multiplication rules for it were not commutative – that is,
p
x
q
was not, in general, equal to
q
x
p
. Heisenberg had no explanation for this departure from the basic rules of arithmetic, nor could he offer a picture of the physical processes that obeyed such odd rules. What he did have was a mathematical modelling of the behaviour of electrons, and this itself was exciting enough to ensure that he did not sleep very much in Helgoland; and enough, too, to ensure that, six years later, he won the Nobel Prize.

Returning to Göttingen in a state of excitement and optimism about his new work, Heisenberg hurriedly wrote up his new theory as a paper entitled ‘Quantum Theoretical Reinterpretation of Kinematic and Mechanical Relations’, which he gave to Born to submit for publication, while he himself left for Cambridge to fulfil a prior arrangement to deliver a talk to the Kapitza Club. The talk, delivered on 28 July 1925, was not on his revolutionary new ideas, but Heisenberg did mention his recently written paper to his host, Fowler, who asked to see it when Heisenberg had proof copies available. When, at the beginning of September, Fowler duly received a proof copy, he sent it to Dirac with a scribbled message on the front page: ‘What do you think of this? I shall be glad to hear.’