Inside the Centre: The Life of J. Robert Oppenheimer (47 page)

By 1938, it had all gone horribly wrong for everyone concerned. Landau was investigated during the Great Purge, arrested and imprisoned; and Beck, Schein, Placzek and Weisskopf were forced to flee, horrified at what
they had witnessed. As Oppenheimer put it, the description of the Soviet Union he received from these three very well-respected scientists was of ‘a land of purge and terror, of ludicrously bad management and of a long-suffering people’. ‘It’s worse than you can imagine,’ Weisskopf told him. ‘It’s a morass.’ As Weisskopf later remarked: ‘These conversations had a very deep influence on Robert. This was a decisive week in his life.’ This is confirmed by a letter written a few months later by Felix Bloch to Isidor Rabi. Oppenheimer, Bloch wrote, ‘is fine and sends you his greetings; honestly, I don’t think you wore him out but at least he does not praise Russia too loudly any more which is good progress.’

Oppenheimer might also have received a fairly clear-eyed picture of what was happening in the Soviet Union from one of his students. George Volkoff, who came to Berkeley to work with Oppenheimer in 1936, was born in Moscow, but brought up in Manchuria, where his father worked as a schoolteacher. Volkoff left Manchuria to study physics at the University of British Columbia in Canada, and never saw his parents again. His mother died in Manchuria, and in 1936 his father returned to Russia, where he was caught up in the purges and sent to Siberia, dying there in 1943. ‘Alone in North America,’ an obituary of Volkoff stated, ‘it did not help George emotionally that many of his associates continued to have rosy views of the Soviet Union.’

With Volkoff, Oppenheimer wrote one of his most interesting papers, one of a series of three, each written with a different co-author, on a subject with which Oppenheimer had not previously been associated: astrophysics. Though these papers received little attention at the time, they are now generally considered to be his greatest work, free of the mathematical errors that dogged his work on quantum electrodynamics and containing original and prescient insights that have been the basis of much subsequent important work. Many people think that, if he had lived a little longer, Oppenheimer would have received the Nobel Prize for these papers.

The particular subject of the paper Oppenheimer wrote with Volkoff at the end of 1938 was the physics of neutron stars. The concept of a neutron star had been introduced into physics just five years earlier at a meeting of the American Physical Society in 1933, only a year after the discovery of the neutron, by the Swiss physicist Fritz Zwicky and the German astronomer Walter Baade. Both were based in Pasadena, Zwicky at Caltech and Baade at the Mount Wilson Observatory. Zwicky, like many people at Caltech, was interested in cosmic rays, and, via Millikan’s view that these rays were the ‘birth cries’ of matter coming to us from outer space, this led him to a subject that Baade was already interested in: supernovae.

Supernovae are extraordinarily bright explosions in outer space, which have been observed and recorded at irregular intervals since the second
century
AD
. One of the most famous appeared in
AD
1054, when it was recorded by court astronomers in China, who described it as a ‘guest star’ and noted that it was brighter than Venus or any other star. It stayed visible, even in daylight, for twenty-three days, and at night could be seen for two years. In 1572 another supernova was observed by the Danish astronomer Tycho Brahe, who wrote a book about it,
De Nova Stella
, in which he showed that this ‘new star’ had to be further away from us than the moon and that therefore the view that the ‘starry heavens’ were immutable was wrong.

The word ‘supernova’ was introduced in the early 1930s by Baade and Zwicky. Even though their term incorporated from ancient descriptions the word ‘nova’, with its suggestions that these temporary bright stars were ‘new’, they were the first to develop a theory that explained supernovae as the
death
-throes of a star. A supernova, in their account, is a stellar explosion that marks the ‘cessation of its existence as an ordinary star’. They also ‘tentatively’ suggested what is now the accepted theory, that ‘the super-nova process represents the transition of an ordinary star into a neutron star’.

To understand what a neutron star is, it is helpful to consider the kind of dying star known as a ‘white dwarf’. In the nineteenth century, a mysterious star named Sirius B was discovered, which was much fainter than its partner, Sirius A. It was assumed that this was because it was cooler, but it was found to be, in fact, much hotter. This could only mean that it was, by comparison, extremely small. It was a star with the mass of our sun, but the volume of a mere planet; in other words, its density was extraordinary – much higher than anything encountered on earth. In the 1920s, these small, dense stars were given the name ‘white dwarfs’ and a theory was developed to explain them. The theory was that ordinary stars, such as our sun, are huge furnaces of hydrogen – the pressure and the heat at their core being sufficient to fuse hydrogen nuclei into helium (though how, exactly, that nuclear fusion worked was not clear until Hans Bethe’s work on the question was published in 1939). After a time, which will be several billions of years, the star runs out of hydrogen, and is no longer able to keep itself stable through thermonuclear reactions. At that stage, gravity takes over, and pulls all the particles that make up the star towards the centre. The star thus gets smaller and smaller and denser and denser. Eventually it gets so dense that there is no longer any room for the atomic electrons
^fn39
to move about as they do in normal conditions. At this point, the ‘white dwarf’ cannot get any smaller or denser and so achieves stability, the stability being attributable to what is called the
‘degeneracy pressure’ of the atomic electrons – namely, the fact that they are now all pressed together, unable to move.

In 1931 the Indian physicist Subrahmanyan Chandrasekhar showed that the process described above meant that white dwarfs had a maximum mass, which he calculated to be 1.4 solar masses (where a ‘solar mass’ is a mass equivalent to that of our sun). Anything with a mass greater than that, Chandrasekhar demonstrated, would exert a gravitational force too great for even degeneracy pressure to withstand. Most stars (something over 90 per cent) are estimated to fall below the ‘Chandrasekhar limit’, but that still means that a significant number of stars will not end up as white dwarfs. What happens to
them
is the problem solved by Baade and Zwicky and the notion of a ‘neutron star’.

A star with a core of more than 1.4 solar masses will exert enough gravitational pressure to overcome degeneracy pressure with really spectacular consequences. A massive star, in its dying phases, will consist of layers of matter, each layer getting more and more dense as one approaches the core. If the core is over the Chandrasekhar limit, the moment will arrive when it suddenly collapses under gravitational pressure. In one-tenth of a second, the material that makes up the core will explode and disintegrate into its basic constituent particles – protons, neutrons, electrons. At the fantastically high temperatures that are generated by this process, the velocities of the electrons approach that of light. But, being in such a dense, degenerate state, they have nowhere to go. And so, at terrifically high energies, they are pushed into the protons themselves, forming neutrons. This process, called ‘neutronisation’, results in an enormous increase in density; the core of the star is no longer made up of chemicals of any sort; it is rather one big nucleus. As this happens, the outer layers of the star, the non-neutronised sections, fall towards the centre, but are repelled by a shock wave of enormous energy that blows the star to smithereens. If the star originally had a mass twenty-five times the size of our sun, then what would be left is a neutron core with a mass equal to our sun and a volume the size not of a planet or even of a country, but of a city. The rest of the mass would be blown away. That explosion is a supernova, and the remaining core is a neutron star.

Ever since he arrived in California, Oppenheimer had taken an interest in the work being done at the Mount Wilson Observatory. In 1933, he gave a talk on ‘Stars and Nuclei’ to the Mount Wilson-Caltech Astronomy and Physics Club. His interest in astrophysics was evidently reawakened by Volkoff, who gave a talk at Berkeley in 1937 on ‘The Source of Stellar Energy’. This, as we have seen, is where astrophysics and nuclear physics meet, since the source of stellar energy is to be found in nuclear reactions. In 1938, Oppenheimer organised a symposium on ‘nuclear transformations
and their astrophysical significance’ for that year’s meeting of the American Physical Society, which was held in San Diego. Oppenheimer was to give a paper on stellar energy, but before the meeting he learned that whatever he had to say on that subject was about to be trumped by Hans Bethe’s Nobel Prize-winning work on the subject.

Soon after the meeting Oppenheimer published the first of his three papers on astrophysics, a letter to the editor of the
Physical Review
written jointly with Serber, called ‘On the Stability of Stellar Neutron Cores’. Acknowledging their debt to Bethe for ‘an interesting discussion of these questions’, Oppenheimer and Serber took up the question that had recently been discussed by Lev Landau: was there, for neutron stars, an equivalent to the ‘Chandrasekhar limit’? That is to say, does a neutron core have to be of some certain mass in order to remain stable? Like Landau, Oppenheimer and Serber considered a possible minimum limit, rather than a maximum, and came to the conclusion that Landau’s estimate of 0.001 solar masses was too low. The minimum limit was, they reckoned, more like 0.1 solar masses.

The second paper in the series, the one written with Volkoff and entitled ‘On Massive Neutron Cores’, was received by the
Physical Review
on 3 January 1939. An altogether more substantial piece of work than the Oppenheimer/Serber paper, it is often credited now with presenting the first serious theory of neutron stars. From it comes what has become known as the ‘Oppenheimer–Volkoff limit’, an upper limit for a stable neutron core, which they calculated to be 0.7 solar masses. The present estimate is between 3 and 5 solar masses. It was notoriously difficult to do the calculation for the reasons that Oppenheimer and Volkoff spelled out. First, the nuclear forces that operate between neutrons were not as well understood as the electromagnetic forces that operate between the electrons in a white dwarf. Second, when considering white dwarfs it is not necessary to take relativistic effects into account; the gravitational forces are weak enough for Newtonian theory to be sufficient. With the enormous gravitational forces at work in a neutron star, however, one needs to use general relativity, which introduces extremely complex and difficult equations.

Despite these difficulties, Oppenheimer and Volkoff laid out the basic theory of neutron stars – nearly thirty years before there were any empirical grounds for believing that such things really exist. The abstruse mathematics in the article, versions of which now appear in astrophysics textbooks under the name ‘Oppenheimer–Volkoff (O–V) equation of hydrostatic equilibrium’, was apparently the work of Volkoff alone. ‘I remember being greatly overawed by having to explain to Oppenheimer and Tolman what I had done,’ he later remembered. ‘We were sitting out on the lawn of the old faculty club at Berkeley. Amidst the nice green
grass and tall trees, here were these two venerated gentlemen and here I was, a graduate student just completing my PhD, explaining my calculations.’ What those calculations showed was extremely interesting: first, that neutron stars
could
indeed exist, so long as their mass was greater than 0.1 solar masses and less than 0.7 solar masses; second, that ‘the question of what happens, after energy sources are exhausted, to stars of mass greater than 1.5 solar masses still remains unanswered’;
^fn40
and most intriguingly of all: ‘There would seem to be only two answers possible to the question of the “final” behaviour of very massive stars: either the equation of state we have used so far fails to describe the behaviour of highly condensed matter . . . or the star will continue to contract indefinitely, never reaching equilibrium.’ According to their calculations, in other words, there is nothing, in stars with sufficient mass, to prevent the gravitational collapse from carrying on indefinitely, but how can something collapse, as it were, infinitely? The alternatives presented by their work, they concluded, ‘require serious consideration’.

Even to have raised the question of indefinite gravitational collapse required impressive boldness and imagination, but in his next paper Oppenheimer went one better: he answered it. The third and final paper in this series on astrophysics, though more or less completely ignored for nearly thirty years after its publication, has now become the most respected of them all. Jeremy Bernstein has called it ‘one of the great papers in twentieth-century physics’. Co-written with Hartland Snyder, who is remembered by Robert Serber as ‘the best mathematician of our Berkeley group’, it is entitled ‘On Continued Gravitational Contraction’ and was published in the September 1939 issue of the
Physical Review
.

The paper is celebrated for predicting the existence of what are now, and have been since the 1960s, called ‘black holes’, the next stage of a dying star of sufficient mass after it has passed through the white dwarf, supernova and neutron-star phases. ‘When all thermonuclear sources of energy are exhausted,’ runs the very first line of the paper, ‘a sufficiently heavy star will collapse.’ Furthermore, unless its mass is reduced in various ways (for example, by radiation) to that of our sun, ‘this contraction will continue indefinitely’.

The genius and the novelty of the paper lie in giving an account of what
‘indefinite contraction’ might mean. In the death of a massive star, we have imagined it going from many times bigger than our sun (its initial state as a glowing furnace of hydrogen) to something about the size of a planet (a white dwarf), then something about the size of, say, San Francisco (a neutron star). At each stage, its density gets greater and greater. Now we must imagine it contracting towards what is called a ‘singularity’, namely
zero
volume and
infinite
density. As Oppenheimer put it in a letter to George Uhlenbeck while he was working on this paper: ‘The results have been very odd.’ To describe this ‘oddness’, Oppenheimer and Snyder use the field equations of Einstein’s theory of relativity, the physical realities of which they illustrate from the points of view of two observers: one far away from the collapsing mass and the other inside it. It is a feature of relativity that, from the point of view of someone outside a gravitational field, time inside the field will run more and more slowly as the strength of the gravitation increases. Therefore, to an outside observer, the collapse of the mass will take an infinite amount of time; to the unfortunate observer inside the gravitational field, on the other hand, it is all over in an instant. Moreover,
nothing
can escape from the indefinitely collapsing mass, not even radiation; the blackness of a black star is absolute. ‘The star thus tends to close itself off from any communication with a distant observer,’ Oppenheimer and Snyder write; ‘only its gravitational field persists.’