It is less than three decades since Albert Einstein died, yet many different personae have been supposed behind the familiar mild exterior. Nobody would impute any lack of psychic integrity in the man himself. True enough, he was a peculiarly self-contained person whose inner life was always opaque, even to his most intimate companions. But there was no harsh discontinuity or irreconcilable inconsistency in his temperament, and we have no reason to suppose that he was nervously guarding some guilty secret like Newton’s heretical Unitarianism. His private and public activities are amply documented, and are seldom inexplicable to an intelligent and imaginative observer. Yet even in his scientific work, Einstein can be represented as playing several different roles, in several quite different dramas.
Abraham Pais is a distinguished theoretical physicist who knew Einstein well in his later years at Princeton. The personal and political aspects of his life are dealt with at length in a sympathetic spirit, but this is an intellectual biography, and will long hold its place as the authoritative account of his scientific achievements. It is extraordinarily well done. For anyone who can read the standard language of physics, this is a fascinating book. Here are the famous formulae that we have had to learn or to teach, here are the subtle concepts and profound arguments that we have all had to master, seen in their moments of discovery, when all is glory. It is all familiar, and yet it is a pleasure to be told it all again.
Consider him, first, in the role of iconoclast, or revolutionary. The theory of relativity upset everybody’s settled notions of the uniqueness and universality of space and time. Not, of course, that people took an entirely conservative attitude towards their everyday co-ordinates. Even in 1905, the passengers on a steamship to Australia did not try to carry with them, all the way from Britain, the exact moment of twelve noon, or the direction of Nor’Nor’East. In the end, that would have meant lunching at midnight, standing on their heads. Life on a rotating planet is more conveniently ordered according to local space-time conventions, which vary systematically from place to place. But the ship’s navigator had his chronometer set to Greenwich time, and knew how to orient the ship in relation to the celestial sphere of the fixed stars. For what had always seemed convincing philosophical reasons, these were considered unambiguous, absolute co-ordinates. Any event, anywhere in the universe, could in principle be located at a particular point, at a particular moment, in this complete, unique framework.
It was very shocking, then, to have young Einstein point out that this was not a very convenient scheme for talking physics when one is dealing with objects that are travelling at very high speeds. Even as a schoolboy he had tried to imagine what an electromagnetic wave – that is, a beam of light – would seem like if one tried to catch up with it and observe it as if it were nearly at rest. This almost unthinkable conception was somehow unphysical: the observer on the high-speed space-ship would be seeing something that was not permitted by the laws of physics. The only way to make scientific sense of such a situation was to conjecture that the observer would automatically carry around with him his own personal framework of space and time, in which the light would still appear to be travelling at its usual enormous speed. Every scientist, on every moving space-ship or planet, would naturally prefer to plot the events of the universe on a slightly different map, according to a slightly different calendar. Every world-view was thus, in some degree, relative to the situation of the viewer.
At first this sounds reasonable enough; the perspective from Sydney is not by any means the same as it is from London. But when Einstein insisted that clocks on fast-moving vehicles would appear to be running fast or slow, depending on the point of view, this was clearly prejudicial to good scientific order and discipline. In fact, he was lucky in his radicalism. Other theoretical physicists, older and better-established, had been having similar dangerous thoughts. Einstein brought this revolution to a head, but he did not make it quite alone. Nor was it quite as anarchical as many people seem to think. Different observers certainly prefer to use different maps and clocks, but these are not arbitrary or idiosyncratic. They are all related to one another by strict mathematical formulae, just as a map on Mercator’s projection is precisely related to a map of the same region on a stereographic projection. All that Einstein was saying was that there is no special, no unique point of view, corresponding, say, to a point at rest in the ether. Strange physical phenomena might be observed on bodies moving nearly at the speed of light, but most of the ordinary laws of physics remain unchanged. As in all the best revolutions, the classical achievements of the past were preserved and enhanced.
See Einstein as iconoclast if you like – but see him also as a creative artist. The General Theory of Relativity that he called into being in 1916 is a daring product of pure thought. It was built upon the Special Theory with the aid of only one further fact of nature – the familiar equivalence of inertial mass and gravitational weight. Accelerate away in your space-shuttle, and everyone in the cabin will become heavier by exactly the same factor: get into orbit, where acceleration and gravity are balanced, and you will find yourself as weightless as the cup of coffee in your hand. Every physicist since Galileo has known this principle as an ‘accidental’ law of physics: Einstein reformulated it as a logical necessity, derived from the curved geometry of the space-time continuum. As Professor Pais shows in detail, this amazing idea was not the product of a moment of artistic inspiration. First there had to be some concentrated physical thinking. What sort of physics would you expect to find in the cabin of the space-shuttle, up there in orbit? How do you measure lengths and intervals of time, electric and magnetic fields, energy and momentum, paths of light rays and of charged particles, in a weightless environment? Can you do all the usual experiments, and get all the usual answers, as if the only effect of the motion were to reduce the force of gravity to zero? Or (here is the inspiration) can you now go back to Earth, and calculate the tiny effect of gravity on, say, the propagation of light as if this were due to an unsuspected acceleration of your whole laboratory? The principle of equivalence, alone, is a powerful tool in the hands of a supreme artist of physical theory.
But now you need a systematic way of thinking about all the different representations of space, time, matter, motion and electricity that might be used by different observers moving on the most complicated curved and accelerated trajectories relative to one another. This is like asking for a general mathematical formalism for mapping all possible lines and surfaces in a space of many dimensions. Einstein was fortunate to find a mathematician who knew about the progress that had been made on this daunting problem, and taught himself the language and concepts of the tensor calculus and differential geometry. However complicated your path through space and time, at each point it has well-defined local values of curvature and torsion. The surface of the sea, on a calm day, exhibits its intrinsic sphericity whenever a ship is seen to sink below the horizon. Out of more sophisticated generalisations of spatial curvature and sphericity, Einstein constructed a formalism for the laws of physics as they might appear locally to any particular observer, and showed how these formulae were transformed as one took on the point of view of any other.
In this formalism, the generalised ‘curvature’ of the local space-time framework can equally well be described as an unsuspected acceleration – in other words, it will look exactly like a local gravitational field. But what puts this warp into the space-time framework? Surely this must come from the well-known source of all gravity – the presence of matter itself. There is nothing in physics more beautiful and perfect than Einstein’s formula equating a highly abstracted measure of the local density of mass and energy to an equally abstracted measure of the ‘curvature of space and time’ in that neighbourhood.
But what does this formula tell us? Whole treatises have been written on the subject. For a start, take the Sun as your local concentration of matter, and calculate the path of a particle, step by step, curving gently as it follows the dictates of the warped geometry. You will find the orbit of a planet, almost exactly as Newton described it, apparently attracted by the ‘gravitational force’ of the Sun. Carry this calculation to a higher order of accuracy, and you can predict an anomaly in the behaviour of the orbit of Mercury which has long been observed and never explained. That was one of the most exciting moments in Einstein’s life. Work out that a ray of light will be bent as it passes very close to the Sun, and an expedition will be sent out to Africa to observe the stars at the next eclipse. No wonder Einstein became world-famous, in 1919, when this prediction was precisely confirmed.
The products of creative scientific artistry are not purely idiosyncratic, however. Other theoretical physicists and mathematicians were snuffling round in the neighbourhood of this theory, and would probably have unearthed the same formula some time in the next fifty years, even if Einstein had never lived. It was the outcome of profound thought. In its final abstract form, it is extraordinarily simple and compelling. It has been the inspiration of astrophysics and cosmology for half a century. We still think it is perfectly correct. And yet we know that it could still prove to be wrong. The role of the scientific genius is more narrowly defined than that of the creative artist, although no easier to emulate.
To the present generation, Einstein’s name is inseparable from the formula that allows nuclear mass to be transformed into nuclear energy. The lifelong pacifist is cast incongruously in the role of the magician whose incantations unleash demonic powers. This formula does, in fact, come out of relativity theory – but it is only one example of the immense technological consequences of Einstein’s theoretical research. The hypothesis that light itself is quantised, which he put forward in that same miraculous year, 1905, is the basis of all our understanding of the interaction of light and matter, and thus of every sort of photo-electric or electro-optical device. He can be blamed for the pretty picture on our TV screens, or for the optical fibres that will soon be replacing telephone cables, as much as for the Bomb.
The light-quantum hypothesis itself smelt of magic to most physicists of the time. The triumph of 19th-century physics had been to prove that light was a moving wave of linked electric and magnetic fields, spreading out continuously in space. It seemed quite nonsensical, if not downright reactionary, to go back to Newton’s way of talking about a beam of light as if it were a stream of discrete particles. Yet Einstein sensed that there were some subtle inconsistencies in Max Planck’s analysis of the emission of light from a red-hot or white-hot object. If the light could only be emitted in ‘quanta’, then surely it must be absorbed in the same way. Let us look more closely at the photo-electric effect, he suggested. How is it that each electron that is ejected from a metal surface can pick up such a lot of energy from the light that is played on it? It is as if the waves breaking on an ocean beach occasionally picked up one-ton rocks, and hurled them a thousand feet into the air. Think of the light as a hail of ‘photons’, dislodging the electrons by the sheer force of their separate impacts, and everything fits.
It is a very simple, direct hypothesis. It can be tested in a variety of ways, by very elementary apparatus. It works for the light entering the eye, for telescopes, for X-rays, and for the interactions of strange particles in billion-volt accelerators. Every physicist knows it, and uses it without a second thought. Yet it retains its magical quality. Allow me some advanced mathematical formalisms, and give me time to work it all through, and I am confident that I could show you that the wave and particle properties of light are complementary aspects of a logically coherent, self-consistent conceptual scheme. I know for sure that this scheme gets the right answers for all the experiments that have ever been devised to test it. But I am not sure that I could make you believe in it as the true nature of light.
Never a professional philosopher, Einstein cast himself into a more and more philosophical role in relation to the later developments of quantum physics. This is a paradoxical story, told by Professor Pais with great clarity and understanding. Until 1925, Einstein had been at the forefront of the scientific enterprise to make sense of atomic and nuclear phenomena. Then, when Heisenberg and Schrödinger produced the new quantum theory which cleared up almost all the old confusions, Einstein held back, and seemed to take a very negative, critical position. In a famous correspondence and series of debates, he argued and argued against the doctrines he had laboured so long to bring to birth.
Einstein’s critique of the new quantum theory was not directed against its technical achievements. He did not, himself, make use of the new formalisms to explain atomic and nuclear phenomena, but he had no objections to those who did so, and was perfectly sensible of their successes. It was just that he could not make himself believe that this was, indeed, the true nature of things. He was particularly concerned about the probabilistic interpretation of physical phenomena. He knew, of course, that many sub-microscopic events, such as the emission of a photon by an atom or the radioactive decay of a nucleus, occur as if at random. Was it sufficient to describe such events as if this randomness were fundamental and intrinsic to the situation? ‘God does not play at dice,’ he insisted, and asked for an even better theory which did not suffer from this defect. It is proper to call this a philosophical stance, because it did not result in any new physics. All that he could do was to suggest some very cunning ‘thought experiments’ which might have overthrown the new orthodoxy. But these experiments could not be carried out with the apparatus then available, and most physicists brushed his objections aside. In recent years, the issue of ‘causality’ in quantum phenomena has been reopened, in the very spirit that Einstein affirmed, but it has still not been resolved. An experiment along the lines he proposed has recently given results that are consistent with the standard quantum formalism – but what does that prove against a metaphysical dissenter?
Einstein as philosopher still fascinates. Heinz Pagels, another thoughtful physicist, travels for many chapters along ‘the road to quantum reality’, insisting that for the general public this must be the most exciting question in physics. For a reader drawn along the same road, he can be recommended as a guide. But Jonathan Powers is a genuine philosopher. As his elegant little book makes plain, almost everything that physicists have ever told us about ‘the true nature of things’ is worthy of sceptical philosophical analysis. This is the deeper source of Einstein’s lifelong interest in philosophy, and of his profound grasp of the intellectual strategies of scientific theorising.
Einstein’s personal life was not without its strains and tragedies. Neither of his marriages seems to have been very happy, and he was a driven into exile by the advent of Hitler when he was already over 50. At the age of 40, he suddenly became one of the most celebrated people in the world, and was irresistibly plunged into public affairs. As the Centennial Symposium shows, much symbolic responsibility was loaded on him, to add to his own concern about the state of the world. He did his duty as a supporter of Zionism and of pacifism with beguiling modesty and simplicity. Yet it was only in his physics that he finally came to play a heroic role – not in his triumph, but in his patience and persistence.
He could never be satisfied with a general theory of space, time and matter that did not include the classical laws of electricity and magnetism. Gravity had been transformed into a geometrical convolution of the continuum. Relativity theory showed that magnetic forces were merely the effects produced by electricity in motion: was it possible to represent the electric field itself in the language of space-time geometry? This was the goal of almost all his scientific work for the last thirty years of his life. He searched for a ‘unified field’ theory with all his physical understanding, with all his mathematical skills, with all his imagination, and with all his will. He worked with a number of gifted collaborators. He would go into the fifth dimension, if necessary. There were times when he thought he had the creature in his grasp, but it would twist and turn and get away.
The world of physics did not share his confidence that this was an attainable goal, and passed over his work in silence. The world of physics was probably right. The equations that he was studying were just too simple to represent all the phenomena that had been discovered since he began his quest. Experiments with elementary particles were finding several other fields of force that would have to be geometrised in the same way. There were quantum effects that he was ignoring. He was proving himself the last of the classical physicists, rather than the first, and foremost, of the 20th-century breed. Nevertheless, in his cheerful persistence he provides a model for any scientist. It is unjust to say that he was already so famous that his final failure cost him little. The message is, rather, that the scientific hero embarks upon whatever research enterprise he believes to be worthy of his steel, regardless of the risks of defeat.
These are some of the faces that Albert Einstein presents to us now. But for his contemporaries he must also have played a more immediate role – the fellow-citizen of the republic of learning. Consider the third of those marvellous 1905 papers, the one on the Brownian motion. It takes a little knowledge of the earlier history of physics to appreciate its importance. For a hundred years the question was: were atoms and molecules real? There was strong circumstantial evidence for them from chemistry, but could one actually detect them as distinct particles? How big are they anyway? If you look down a microscope, you certainly cannot observe atoms directly, but you can see some signs of the granularity of matter. Watch a tiny speck, such as a pollen grain, floating in a liquid: it seems to move irregularly, as if under the impact of tiny hammer blows in random directions. Is it being knocked hither and thither by the molecules of the liquid, in their eternal, restless motion? Not precisely: each molecule is much too small to move the grain perceptibly on its own. But Einstein calculated the statistical fluctuations in the forces produced by the impacts of myriads of molecules, and linked the suspected properties of the sub-microscopic world to the observed phenomenon. That young man from the Patent Office had not only solved this famous problem: he had demonstrated an uncanny mastery of the tradition of statistical physics. Here was a new member to be welcomed into the guild, a brilliant craftsman in physical intuition and mathematical analysis. The outstanding virtue of Professor Pais’s book is that it places Albert Einstein in the milieu that he himself had chosen for his life work, and judges him by the most demanding standards of that most rigorous profession, as the greatest of them all, since Newton.
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