This was Heisenberg’s central insight, but in a hectic three weeks he went further, developing a method of mathematics, known as matrix math, originating from an idea by David Hilbert, in which the measurements obtained are grouped in a two-dimensional table of numbers where two matrices can be multiplied together to give another matrix.18 In Heisenberg’s scheme, each atom would be represented by one matrix, each ‘rule’ by another. If one multiplied the ‘sodium matrix’ by the ‘spectral line matrix,’ the result should give the matrix of wavelengths of sodium’s spectral lines. To Heisenberg’s, and Bohr’s, great satisfaction, it did; ‘For the first time, atomic structure had a genuine, though very surprising, mathematical base.’19 Heisenberg called his creation/discovery quantum mechanics.
The acceptance of Heisenberg’s idea was made easier by a new theory of Louis de Broglie in Paris, also published in 1925. Both Planck and Einstein had argued that light, hitherto regarded as a wave, could sometimes behave as a particle. De Broglie reversed this idea, arguing that particles could sometimes behave like waves. No sooner had de Broglie broached this theory than experimentation proved him right.20 The wave-particle duality of matter was the second weird notion of physics, but it caught on quickly. One reason was the work of yet another genius, the Austrian Erwin Schrödinger, who was disturbed by Heisenberg’s idea and fascinated by de Broglie’s. Schrödinger, who at thirty-nine was quite ‘old’ for a physicist, added the notion that the electron, in its orbit around the nucleus, is not like a planet but like a wave.21 Moreover, this wave pattern determines the size of the orbit, because to form a complete circle the wave must conform to a whole number, not fractions (otherwise the wave would descend into chaos). In turn this determined the distance of the orbit from the nucleus. Schrödinger’s work, set out in four long papers in Annalen der Physik in spring and summer 1926, was elegant and explained the position of Bohr’s orbits. The mathematics that underlay his theory also proved to be much the same as Heisenberg’s matrices, only simpler. Again knowledge was coming together.22
The final layer of weirdness came in 1927, again from Heisenberg. It was late February, and Bohr had gone off to Norway to ski. Heisenberg paced the streets of Copenhagen on his own. Late one evening, in his room high up in Bohr’s institute, a remark of Einstein’s stirred something deep in Heisenberg’s brain: ‘It is the theory which decides what we can observe.’23 It was well after midnight, but he decided he needed some air, so he went out and trudged across the muddy soccer fields. As he walked, an idea began to germinate in his brain. Unlike the immensity of the heavens above, the world the quantum physicists dealt with was unimaginably small. Could it be, Heisenberg asked himself, that at the level of the atom there was a limit to what could be known? To identify the position of a particle, it must impact on a zinc-sulphide screen. But this alters its velocity, which means that it cannot be measured at the crucial moment. Conversely, when the velocity of a particle is measured by scattering gamma rays from it, say, it is knocked into a different path, and its exact position at the point of measurement is changed. Heisenberg’s uncertainty principle, as it came to be called, posited that the exact position and precise velocity of an electron could not be determined at the same time.24 This was disturbing both practically and philosophically, because it implied that in the subatomic world cause and effect could never be measured. The only way to understand electron behaviour was statistical, using the rules of probability. ‘Even in principle,’ Heisenberg said, ‘we cannot know the present in all detail. For that reason everything observed is a selection from a plenitude of possibilities and a limitation on what is possible in the future.’25
Einstein, no less, was never very happy with the basic notion of quantum theory, that the subatomic world could only be understood statistically. It remained a bone of contention between him and Bohr until the end of his life. In 1926 he wrote a famous letter to the physicist Max Born in Göttingen. ‘Quantum mechanics demands serious attention,’ he wrote. ‘But an inner voice tells me that this is not the true Jacob. The theory accomplishes a lot, but it does not bring us closer to the secrets of the Old One. In any case, I am convinced that He does not play dice.’26
For close on a decade, quantum mechanics had been making news. At the height of the golden age, German preeminence was shown by the fact that more papers on the subject were published in that language than in all others put together.27 During that time, experimental particle physics had been stalled. It is difficult at this distance to say why, for in 1920 Ernest Rutherford had made an extraordinary prediction. Delivering the Bakerian lecture before the Royal Society of London, Rutherford gave an insider’s account of his nitrogen experiment of the year before; but he also went on to speculate about future work.28 He broached the possibility of a third major constituent of atoms in addition to electrons and protons. He even described some of the properties of this constituent, which, he said, would have ‘zero nucleus charge.’ ‘Such an atom,’ he argued, ‘would have very novel properties. Its external [electrical] field would be practically zero, except very close to the nucleus, and in consequence it should be able to move freely through matter.’ Though difficult to discover, he said, it would be well worth finding: ‘it should readily enter the structure of atoms, and may either unite with the nucleus or be disintegrated by its intense field.’ If this constituent did indeed exist, he said, he proposed calling it the neutron.29
Just as James Chadwick had been present in 1911, in Manchester, when Rutherford had revealed the structure of the atom, so he was in the audience for the Bakerian lecture. After ad, he was Rutherford’s right-hand man now. At the time, however, he did not ready share his boss’s enthusiasm for the neutron. The symmetry of the electron and the proton, negative and positive, seemed perfect, complete. Other physicists may never have read the Bakerian lecture – it was a stuffy affair – and so never have had their minds stimulated. Throughout the late 1920s, however, anomalies built up. One of the more intriguing was the relationship between atomic weight and atomic number. The atomic number was derived from the nucleus’s electrical charge and a count of the protons. Thus helium’s atomic number was 2, but its atomic weight was 4. For silver the equivalent numbers were 47 and 107, for uranium 92 and 235 or 238.30 One popular theory was that there were additional protons in the nucleus, linked with electrons that neutralised them. But this only created another, theoretical anomaly: particles as small and as light as electrons could only be kept within the nucleus by enormous quantities of energy. That energy should show itself when the nucleus was bombarded and had its structure changed – and that never happened.31 Much of the early 1920s was taken up by repeating the nitrogen transmutation experiment with other light elements, so Chadwick scarcely had time on his hands. However, when the anomalies showed no sign of being satisfactorily resolved, he came round to Rutherford’s view. Something like a neutron must exist.