Inside the Centre: The Life of J. Robert Oppenheimer
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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.’
In four pages, mostly filled with the imposing equations of relativistic gravitational theory, Oppenheimer and Snyder provided a way of understanding the collapse of a neutron star into a black hole, the implications of which are still being explored today. Pick up a popular book on black holes now and the chances are that what you will see is a description extending over several pages, even several chapters, of the physical realities that correspond to the equations of Oppenheimer and Snyder. Almost certainly, the book will also attempt to convey the nature of black holes using the device adopted by Oppenheimer and Snyder of imagining two observers.
And yet, during Oppenheimer’s lifetime, this remarkable paper – and the ones preceding it written with Serber and Volkoff – were greeted with silence from both astronomers and physicists. This silence ended with the discovery in 1967 of ‘pulsars’, which, it was realised, are rotating neutron stars; the following year it was discovered that what had been known for a long time as the Crab Nebula was in fact the remnant of the 1064 supernova and that in the middle of it was a neutron star. Since then, neutron stars have even been photographed. As for black holes, though they have not been (and could not be) photographed, there is now abundant evidence that they exist and they are the subject of intensive theorising and observational work.
One of the leading figures in the study of black holes, John Archibald Wheeler, was also one of the first people to revive interest in Oppenheimer’s work on the subject, and is credited with having introduced the term ‘black hole’. In the 1960s, shortly before Oppenheimer’s death, Wheeler tried to talk to him about his work on gravitational collapse, but Oppenheimer was not interested. Had he lived just a few years longer, Oppenheimer would have seen the empirical evidence which confirmed that the theory developed by him and his students in the late 1930s was not just a piece of mathematics, but was a description of physical reality.
One reason for the initial lack of interest in these great papers of Oppenheimer and his students has to do with the timing of two very different events. Oppenheimer’s paper with Volkoff was written in the very month that it was announced that scientists in Germany had discovered nuclear fission; his paper with Snyder, meanwhile, was published on the very day that the Second World War began. For the time being, the question of what happened inside a massive stellar core was of far less interest, and far less import, than the questions of what might be made to happen inside a uranium nucleus and what might become of Europe.
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fn37 Chevalier was evidently a little hazy on the exact years, as these do not match the dates he gave in his letter to Oppenheimer.
fn38 It has worried some people that Griffiths mentions three members of the unit, while Chevalier mentions seven. However, Griffiths does not say it only had three members. He says rather: ‘Of the several hundred members of the faculty at Berkeley three were members of the communist group.’ As neither Addis nor Radin was at Berkeley during the period in question and the other two were not university people at all, this is perfectly consistent with Chevalier’s description of the group having seven members.
fn39 ‘Atomic electrons’ are those outside the nucleus, as opposed to those that are emitted from the nucleus in beta decay.
fn40 The figures here are perhaps confusing. The Chandrasekhar limit of 1.4 solar masses given previously is a calculation of how much mass a white dwarf can have without collapsing into a neutron star. The Oppenheimer–Volkoff limit of 0.7 solar masses is a calculation of how much mass a neutron star can have and still be stable – that is, without collapsing further. What happens to a neutron star that continues to collapse is an unanswered question, which is why Oppenheimer says the question of what happens to large stars (those more massive than 1.5 suns) still remains unsolved. The full story about the gravitational collapse of large stars, he is indicating, has yet to be told.
10
Fission
THE RESPONSE OF scientists to the news of nuclear fission in the New Year of 1939 was in itself a remarkable chain reaction, with Oppenheimer and his colleagues on the West Coast of America somewhat at the end of the chain.
It began with two chemists in Berlin, the eminent Otto Hahn and his young assistant Fritz Strassmann. They had been bombarding uranium with fairly slow, low-energy neutrons, trying to repeat the experiments conducted in Paris by Irène Curie and her assistant, which had produced some puzzling results. On 19 December 1938, Hahn wrote to his friend and former colleague Lise Meitner, who, because she was Jewish, had recently fled Germany and was now in Sweden. Meitner was a very able physicist to whom Hahn had often appealed in the past to explain his results. Now he asked her to explain something that had utterly perplexed him and Strassmann: when their slow neutrons hit uranium, the result seemed to be the emission of barium.
To understand why this was so puzzling, one has to take a step back and survey what had been achieved up to that point in the way of changing one element into another. Rutherford, back in 1919, had been the first modern alchemist, changing nitrogen into oxygen by bombarding it with alpha particles. What, exactly, was happening in this process was made clear by the photographs Blackett took in 1924: nitrogen, with atomic mass 14, was absorbing the alpha particle (mass 4), producing oxygen (mass 17) and emitting a proton (mass 1), or, in symbols: N14 +α4 → O17 + p1. Then, in 1932, Cockcroft and Walton had split a lithium atom by bombarding it with protons, and again there was no mystery about what was happening: lithium (mass 7) was absorbing a proton (mass 1) and then splitting into two helium nuclei, each with a mass of 4: Li7 + p1 → α4 + α4.
At the heart of these processes is not only some fairly basic arithmetic (14 + 4 = 17 + 1 and 7 + 1 = 4 + 4), but also some fairly basic chipping away at atomic nuclei, with nothing more dramatic than the absorption and emission here and there of an alpha particle and/or a proton. But it is impossible to understand how barium could be emitted from uranium by such means. Uranium is a very heavy element. In fact, it is the heaviest naturally occurring element. It has ninety-two protons and, in its most common and stable form, 146 neutrons, giving it an atomic mass of 238. Barium has fifty-six protons and, in its most common and stable form, eighty-two neutrons, giving it a mass of 138. You cannot, therefore, get barium from uranium by either adding or subtracting a proton or an alpha particle; you need to lose about 100 nucleons (protons and/or neutrons)! Whatever that is, it is not ‘chipping’.
Hahn and Strassmann had already strained credulity by suggesting earlier that what they had witnessed was the emission of an isotope of radium (atomic number 88, atomic mass 223–8), but it was just about conceivable how this might happen by, as they said, ‘the emission of two successive alpha particles’ (together with a couple of neutrons or protons). But no amount of juggling with the figures could explain how barium could be emitted from uranium on the assumption that transmutation was due to the emission or absorption of protons, neutrons or alpha particles. Something else was going on, something not previously encountered.
In Sweden, Meitner was joined by her nephew Otto Frisch, a young physicist who had lately been working in Copenhagen with Niels Bohr. On Christmas Eve 1938, Frisch and Meitner discussed the results obtained by Hahn and Strassmann. ‘But it’s impossible,’ Frisch remembers them thinking. ‘You couldn’t chip a hundred particles off a nucleus in one blow.’
Following a suggestion by George Gamow, Bohr had recently put forward the idea that an atomic nucleus is more like a liquid drop than a billiard ball; not a hard, stable object, but something continually moving, wobbling, with the forces acting not only on it but in it, pulling it in
different directions. Among those forces in an atomic nucleus is the electrostatic repulsion that protons exert on one another. Seen like this, the heavier the nucleus is, the less stable it should be, because it will have more protons, all trying to pull away from the others. That is, in fact, why no elements heavier than uranium exist in nature; as soon as they are created, they pull themselves apart.
This fact was not well understood in 1938. Up to then, scientists thought that by bombarding uranium with neutrons they would create heavier, ‘transuranic’ elements. They thought that the uranium would absorb a neutron, which would then, through beta decay, transform into a proton, thus creating a new, heavier element. Thinking about the results Hahn and Strassmann had obtained in terms of Bohr’s image of the nucleus as a drop of water, Frisch and Meitner realised that the opposite had happened: instead of the uranium absorbing a neutron, the neutron had hit a wobbling nucleus (which they pictured like a balloon full of water, pinched at the middle), making it wobble a bit more until it split in half. Frisch and Meitner also realised that this splitting – to which Frisch gave the name ‘fission’ – would release enormous amounts of energy, namely the binding energy holding the nucleons of the uranium nuclei together. They were able to be fairly precise about how much energy would be released, since they knew that the separated pieces of the split uranium nucleus – one of barium, the other (therefore) of kryptonfn41 – would have a slightly smaller combined mass than that of the original nucleus, and were able to calculate what that difference would be. The answer is: a mass equal to one-fifth of a proton. Then, using the famous formula E = mc2, they could convert that mass into energy and thus work out that the amount of energy released by the fission of uranium is 200 million electron volts, which, not coincidently, is exactly the amount of energy Frisch and Meitner had calculated would be needed to pull the protons apart.