The Physicists Page 5

  With Chadwick, Rutherford spent the next five years breaking up the nuclei of another ten elements, using alpha-particle projectiles. These experiments didn’t leave much room for argument. And as well as the philosophical implication of changing elements, the Rutherford–Chadwick experiments showed that the nuclei of atoms could be probed. They were not just positively charged, dense balls of matter: they must have some kind of internal structure.

  That was an experimental conquest. Meanwhile, the understanding of the arrangement of electrons in the outer part of the atom hadn’t made much progress. Einstein took a hand. He calculated just how bright the different spectral lines from Bohr’s atom should be (producing a formula which later led to the development of the laser). He was also developing a new kind of statistics to deal with sub-atomic particles, following a proposal by the Indian physicist, Satyendra Bose. On the philosophical front, Einstein was gently insisting on the classical axiom – that if you knew everything about a present physical situation, you could predict everything about its future. At their first meeting, Bohr was already, though polite and deferential, in his brooding, inexplicit fashion feeling dubious. That interchange cast its shadow before it.

  The fact was, there was no satisfactory theory of the atom. Bohr’s model explained the simplest atom, hydrogen, brilliantly, but it totally failed when confronted by the spectra of other elements. Clearly the situation was much more complicated when atoms had more than one electron. And even in the case of hydrogen, Bohr had simply made two assumptions without any theoretical backing. There was no kind of logical rigour. There was, however, plenty of opportunity for experiment, enough to keep ‘particle physics’ – as the science of probing the ever-smaller was becoming known – bounding along. Rutherford moved from Manchester to succeed Thomson in the Cavendish Chair at Cambridge in 1919, and immediately collected many of the future galaxy. That was when Kapitsa began studying the professor’s temperament and when Chadwick clinched Rutherford’s experiments on the first human-directed nuclear disintegration. In Copenhagen Bohr was, with his customary thoroughness, supervising all details of his new institute. He didn’t leave architecture, any more than his verbal statements, to chance.

  Cambridge and Copenhagen were set to lead the new atomic physics, bound by the personal ties of Rutherford and Bohr, and by the functional ties of Copenhagen theory and Cambridge experiment. But there still wasn’t a fundamental solution to the problem of the atom’s structure, certainly not one which would satisfy any kind of mathematical inspection. A third plinth was needed. It came in what still seems a fantastically short time. It came from Germany.

  At this time, physicists wanted to know how the electrons in an atom were arranged, what governed their energies and motions. Although Rutherford and Chadwick had begun to probe the central nucleus, most scientists were content to let its problems rest until the structure of the orbiting electrons was worked out. It needed someone to look at the observable facts with a fresh eye.

  There was no way of directly ‘seeing’ an atom. But as Bohr had pointed out, the spectrum of light from an element was speaking of energy changes within the atom as electrons moved from one permissible state (orbits in Bohr’s model) to another. Every element produces its own characteristic set of distinct wavelengths of light, forming ‘lines’ in the spectrum. And most are far more complex than the spectrum of hydrogen.

  Experimentalists could probe atomic structure further, by perturbing the electrons with magnetic fields and electric fields. When atoms of an element were put between the poles of a powerful magnet, or between electrically charged plates, the spectrum altered slightly. Each spectral line split up into a number of closely spaced lines, each of slightly different wavelength.

  As if all this wealth of unexplained detail from spectra wasn’t enough, the energy needed to knock electrons out of atoms could be measured by shooting at them with fast electrons in a nearly evacuated tube. It was a sophisticated version of the old cathode ray experiments. Except that now the experimenters were not interested in the cathode rays themselves: these electrons were just bullets to attack the atoms of gas left in the tube.

  The experiments had gathered a tremendous harvest of observable facts – too tremendous for comfort. Bohr’s simple intuitive model for hydrogen just could not cope; all rough and ready constructions had to be swept away before a complete theory of the atom could emerge. Was a physical picture of the atom even necessary? Perhaps one could write down a purely mathematical representation of the atom, without thinking of individual electrons moving in orbits at all.

  On this view, each type of atom would have a particular set of numbers associated with it. Then there would be rules to calculate its observable properties. For example, you want to know the wavelengths of sodium’s spectral lines? Apply the ‘spectral lines’ rule to a set of numbers corresponding to sodium, and the wavelengths will drop out. You can apply this same rule to the mathematical representation of sulphur, and out will come its spectral line wavelengths. To work out how sodium’s spectral lines are split up by a magnetic field, apply another rule – the ‘Zeeman effect’ rule – to the set of numbers describing sodium. And so on.

  There’s no point in talking about things you can’t measure directly – like electron orbits. Write down mathematical formulations that relate directly to the observable facts. That was the thought of a very young man of genius, Werner Heisenberg, who had both physical and mathematical insight ready to burst out to the highest degree. The trouble was, he didn’t know enough of the curiosities of nineteenth-century mathematics, when all kinds of mathematical arts had been developed. Not for use, but for the sheer beauty of the game.

  Fortunately there was a slightly older theoretician at Göttingen who was not only gifted but had had the most thorough of German mathematical educations. This was Max Born. He told Heisenberg, like someone pointing to a paragraph in a newspaper, that there was no problem. The old subject of matrix algebra, half forgotten but completely available, would give them precisely what they needed. A ‘matrix’ is a two dimensional table of numbers, and in 1859 the English mathematician Arthur Cayley had devised rules by which two matrices can be ‘multiplied’ together to give another matrix. In Heisenberg’s scheme, each atom would be represented by a matrix; each ‘rule’ by another matrix. If one multiplied the ‘sodium’ matrix by the ‘spectral lines’ matrix this should give the matrix of wavelengths of sodium’s spectral lines. And it did. Heisenberg was a natural mathematician, and it took him only a few days to assimilate matrix algebra. Born knew as much mathematics as any physicist alive. They co-opted another clever young man, Pascual Jordan, and completed a paper on matrix mechanics, the foundation of the new atomic theory, in less than a month.

  Thus Göttingen took the lead in the new theory. It became known as quantum mechanics. For the first time, atomic structure had a genuine, though very surprising, mathematical base. The climate of Göttingen was in the highest tradition of German scientific thinking. This was then familiar to the whole of academic Europe. Only ten years or so earlier, that is before the 1914–18 war, Englishmen regularly went to Germany for their graduate work. Germany had been, in many fields including mathematics, the centre of the academic world. The English had been amateurs, sometimes gifted amateurs, playing with professionals. Born and Heisenberg came straight from the elite of German academic life. Remarkably like Bohr in Denmark, both came from talented families. Their fathers had occupied distinguished Professorial Chairs before them. They were steeped in the culture, wide and deep, which had somehow escaped their English counterparts. Literature and music were part of the air they had always breathed. Born was Jewish on both sides; he was also a splendid example of German liberal civilization at its most refined.

  There was one singularity. The general atmosphere of the three plinths of atomic physics in 1925 was vaguely liberal, strongly international, pacific, often apolitical. That last was specially true of the Cavendish. The young Heisenberg, thoug
h he didn’t obtrude his opinions, was an odd man out. He was an active man, a good games player, fond of the physical life; not a bit like the stereotype of an asthenic conceptual thinker. He was pure German, not Jewish. He was, quietly, a German nationalist. As a student, he had belonged to one of the nationalist organizations – not the Nazis, who would have been too crude at that period for a young man of his calibre. All this had consequences twenty years later. The level of intellectual excitement in 1925, however, was so high that interest in others’ opinions outside science was correspondingly low. And anyway, that kind of personal perception wasn’t a necessary quality among high class scientists.

  The level of intellectual excitement ran even higher, when another theory arrived out of the blue. On the face of it, this theory appeared to have nothing in common with quantum mechanics. The maddening thing was, it also worked. It also happened in 1925, the cardinal year of atomic physics. In Paris, Louis de Broglie (who was a member of a suitably Proustian ducal family), working entirely on his own account, proposed that if atomic particles were regarded simultaneously as waves, some pleasant simplification and explanation would follow.

  The idea was completely novel. Like nearly all the best ideas, it wasn’t elaborate. It simply hadn’t occurred to others. Planck and Einstein had shown that light – always regarded as a kind of wave – could sometimes act as if it was ‘solid’ particle carrying a certain amount of energy (a quantum). Now de Broglie was saying that particles – like electrons, or even whole atoms – could sometimes behave like waves. Experiments quickly proved he was right. The wave-particle duality of matter is not easy to grasp intuitively, though. Exact interpretations varied from scientist to scientist, but it’s easiest to think of an electron (for example) being a particle with a ‘guiding wave’. Classical wave phenomena happen to these guiding waves, like interference where the troughs and crests of two waves can cancel out. The intensity of the wave at any point indicates how likely you are to find the electron there.

  Despite its apparent oddness, the idea of de Broglie waves immediately caught on. Erwin Schrödinger, an Austrian of much intellectual power, set to work to give meaning, and mathematical articulation, to the de Broglie waves. He applied them to the electrons in atoms, and found that they explained as much as the quantum mechanical descriptions. The mathematics was more commonplace, and easier to handle.

  Take the hydrogen atom for example. Schrödinger thought of the electron in its orbit not as a miniature planet, but as a wave – like the wiggles in a rope when you jerk the end up and down. But the electron rope is tied right round the nucleus. It has no end. To think of it another way, the two ends are tied together, so as it vibrates the two ‘ends’ must move with one another. This means there must be a whole number of ‘wiggles’ (electron wavelengths) in the rope. There could be one, two, ten – but not 2½, 3¾, etc. – because then one ‘end’ would not be moving with the other. So the Schrödinger atom has electrons only at certain distances from the nucleus, where the circumference of their path is a whole number of electron wavelengths. And using de Broglie’s formula for the wavelength, Schrödinger found his permissible electron paths were exactly those that Bohr had found from his assumptions. The reason for Bohr’s permissible orbits turned out to lie in the wave-nature of matter. But the Schrödinger theory not only explained Bohr’s hydrogen atom; it successfully predicted the properties of other atoms.

  The Schrödinger-de Broglie method was utterly different both in spirit and form from quantum mechanics. Yet both arrived at the same result; both could explain the observed facts equally well. Impasse. Confusion. The best conceptual minds in physics argued away: which was right? Then, to the general relief, there was anticlimax. Schrödinger demonstrated that the two formulations were equivalent. Although matter waves and matrices seem so different, they were only different mathematical ways of saying the same thing. You could use whichever you wanted, and change from one to the other. The physicists were happy that they had the explanation, at last a mathematically sound atomic theory, in their hands.

  Heisenberg then produced one of the most dramatic of all physical concepts. It became known as the Uncertainty Principle – meaning that the exact position and precise velocity of an electron could not be determined at the same time. Which meant something more disturbing – that, in the sub-atomic world, causality broke down. It would never (literally never) be possible to predict exactly where an individual electron would be. The only statements that could be made, and this was as far as human minds could reach, were statistical. For an individual electron, one could only say where it was likely to be. Detailed predictions were valid for assemblies of large numbers of particles, not for one. This became the final ground of the Einstein–Bohr debate a few years later, a debate which continued until the end of Einstein’s life.

  In the late 1920s, the masters of theoretical physics had reached a peak of achievement and confidence (Einstein dissenting). It was possible to say – it was said by some with the most critical minds – that the fundamental laws of physics and chemistry were now laid down for ever. That wasn’t a boast. Though there have been qualifications since, those laws are now part of the scientific edifice – the most successful of the collective works of the human intellect.

  It is true some of the laws when first enunciated appeared bizarre. But wise men said that, within a generation, those laws would become familiar, part of the common scientific language, as taken for granted as those of Maxwell or Newton. That has been demonstrated, now that time has passed. Any competent student today accepts the Uncertainty Principle as a matter of course; and knows about the most beautiful creation of that extraordinary epoch in scientific history. Here I refer to the culmination of wave mechanics, quantum mechanics and atomic structure, in the work of Dirac.

  Dirac crowned the achievement of that marvellous decade by combining all the ideas of de Broglie, Schrödinger, Heisenberg and Born with the relativity theory of Einstein. Physicists had been totally preoccupied with sorting out atomic structure. Though they knew that relativity had to be included somehow, it wasn’t obvious how. Dirac pulled all the strings together in 1928, and showed that incorporating relativity removed the last of the atom’s puzzles. It explained quite naturally the rather odd fact that individual electrons spin around on their own axes, like miniature tops, as they orbit within the atom.

  In the judgement of the most accomplished pure mathematicians, Dirac, of all the theoretical physicists, was the one who had, in mathematics itself, the greatest elegance and power. He also had intense physical insight, but that pure mathematicians were not concerned with. He ought to have been a real mathematician, they said, rather as English soldiers regretted that Joan of Arc had the bad luck not to be one of them.

  Dirac was English by birth, the only representative of his nationality to play a major part in this explosion of theoretical physics. As a matter of biographical history, his father was a Swiss, who had migrated to England and become a language teacher at a Bristol grammar school. Paul Dirac was brought up bilingually in French and English: with the curious consequence that he turned out abnormally taciturn in both languages. When he did express himself, however, it was with the absolute precision that distinguished all his thinking.

  Symbols were Dirac’s natural medium, and from a very early age – before he was three, which is about par for future mathematicians of the highest conceptual gifts – he was playing with mathematical ideas, such as the singular properties of infinite numbers. By what seems to have been sheer chance, he took his first degree in engineering. This didn’t frustrate him unduly, since like Einstein in the Swiss patent office he showed a clear-eyed practical streak. But his ultimate gift was too remarkable to escape notice, quiet as he was. So he was duly propelled to Cambridge, and in his early twenties was publishing work which had clarity, originality and certitude. At that time there was only one Chair at Cambridge tenable by a mathematical physicist, and possible candidates were saying, witho
ut rancour, since genius of this order would have made rancour ridiculous, ‘Oh well, there is no chance for us now.’

  It was an illusion, commonly held, that all the greatest theoretical physicists were supreme mathematicians. That wasn’t so. Physical insight was the necessary gift. Of course, they had no trouble with mathematical concepts. Dirac could have been any sort of mathematician, by the highest standards. Heisenberg had great natural ability, Bohr profound mathematical scholarship. But Einstein, who had been bored with mathematics as a student, had to pick up the techniques as he went along. Bohr hadn’t anything like the mathematical facility of dozens of talented but lesser men – that may have been one reason why he chose his Socratic or conversational methods; and it may have inhibited him from producing the final formulation of the ideas of which, in the opinion of all round him, he was the originator.

  Justice is hard to reach in any estimate of a collective enterprise. As well as the great names, there were many other men of talent milling round in those dazzling days of modern physics. It was a bit like the Elizabethan-Jacobean theatre. Then, anyone who could write at all could add something. The climate was right, the language was right, the conditions were all in favour. The major genius of Shakespeare, and perhaps the genius of another – Christopher Marlowe – would have triumphed in any period. Others were lucky just to be borne along on the collective wave. That was so among the theoreticians of Göttingen and Copenhagen. One or two were slightly unlucky to be overshadowed by the Heisenbergs and Diracs.

  An interesting character was Wolfgang Pauli, often invoked because of the edge of his critical intelligence. He was responsible for creative work of decisive significance. It is likely that in other times he would have stood out as a dominating figure. His major contribution was the Exclusion Principle, which explained why the electrons in an atom don’t all drop down to the orbit (or energy level) closest to the nucleus: once an electron is in an orbit, it excludes any other from occupying the same orbit. As it is Pauli stands out in scientific legend, respected for the Exclusion Principle, but remembered for his viperish tongue. In the midst of so much gentleness and human acceptance, he was capable of savage sarcasm, very funny to those not on the receiving end. In literary terms, the Pauli comments were vastly preferable to the amiable strains of scientists’ facetiousness.