‘Why is it that nobody understands me and everybody likes me?’ Albert Einstein’s question, quoted in the New York Times in 1944, acknowledges the great mystery of his celebrity. He was a popular, instantly recognisable figure during his lifetime, and has remained so more than seventy years after his death. Yet the theory of relativity, the work for which he is best known, is still, more than a hundred years after its formulation, beyond the grasp of all but a tiny minority.
Many attempts have been made to explain relativity to non-scientists, among them several by Einstein himself, beginning with Relativity: The Special and General Theory (1916, first published in English in 1920). It is still in print today, though despite having had so many readers it has not succeeded in persuading the general public to abandon fundamental intuitions about space, time, mass, motion and gravity in favour of the deeply counterintuitive view of the physical world put forward by Einstein. Our minds and imaginations remain stubbornly Newtonian. Most of us find it hard to shake the instinctual belief that an apple falls to the ground because it is pulled there by the force of gravity, the same force that keeps the planets in their orbits.
Einstein himself we find both fascinating and endearing. ‘[His] personality, for no clear reason, triggers outbursts of a kind of mass hysteria,’ a German consul wrote to his superiors in Berlin during Einstein’s visit to America in 1930. Wherever he appeared, the consul reported ruefully, he attracted huge, worshipful audiences. Overwrought admirers crowded around him, wanting to kiss his hand, touch his clothes or gaze into his eyes. After his death in 1955, his body was cremated, but not before various bits of it had been removed and preserved. His brain became the prized possession of Thomas Harvey, the pathologist who conducted the autopsy. For decades, Harvey kept his treasure in two glass jars, one containing pieces of the cerebral cortex encased in transparent blocks, and the other the cerebellum, floating in formaldehyde. After Harvey’s death in 2007, the brain was transferred to the National Museum of Health and Medicine in Maryland. Einstein’s eyes, meanwhile, were given to his optician Henry Abrams, who kept them in a safe deposit box in New Jersey.
People want to get to know Einstein, to see the world through his eyes. Several biographies have appeared over the years. The most scientifically detailed is Subtle Is the Lord by the physicist Abraham Pais, which, though enormously valuable to the mathematically competent, contains far too many difficult equations to be readily comprehensible to most. Much more accessible (though more than six hundred pages long) is Einstein: His Life and Universe by Walter Isaacson, published in 2007. Free Creations of the Human Mind: The Worlds of Albert Einstein is not a serious rival to either Pais or Isaacson. It is much too short for that. However, it serves as a pretty good introduction to Einstein’s life and mind. One of its co-authors, Diana Kormos Buchwald, is the director of the Einstein Papers Project at Caltech, which has so far produced seventeen volumes of the Collected Papers of Albert Einstein, several of which were co-edited by Buchwald herself. She has also co-edited both volumes of The Essential Einstein, which aims to select from the Collected Papers ‘a central core of materials that captures the essentials of his thinking’.
Einstein had a deep interest in philosophy. ‘Science without epistemology,’ he wrote, ‘is – in so far as it is thinkable at all – primitive and muddled.’ In explaining his own philosophy of science, he used the phrase ‘free creations of the human mind’ on several occasions. The first seems to have been in ‘Geometry and Experience’, a public lecture he delivered in 1921 at the Prussian Academy of Sciences. In it, he addresses the question of whether mathematics, whose truths are absolutely certain and indisputable, can furnish us with knowledge about the world. His answer, in brief, is that ‘in so far as the laws of mathematics refer to reality, they are not certain, and in so far as they are certain, they do not refer to reality.’ In this spirit, he distinguishes ‘axiomatic geometry’, such as the system outlined in Euclid’s Elements, from ‘practical geometry’, which supplements such systems with ‘real objects of experience’. The axioms are free creations of the human mind, and in axiomatic geometry the words ‘point’, ‘straight line’ and so on stand only for empty conceptual schemata; what gives them substance lies outside mathematics. When these conceptual schemata are supplemented by objects of experience, the geometry that results, ‘practical geometry’, is ‘evidently a natural science; we may, in fact, regard it as the most ancient branch of physics.’ That the theorems of Euclidean geometry follow from its axioms is certain and indisputable, but the question of whether the practical geometry of the universe is Euclidean or not can only be answered by experience. Without this view of geometry, Einstein told his audience in Berlin, ‘I would have been unable to formulate the theory of relativity.’ If we are to understand the world of experience, he added, ‘we must abandon Euclidean geometry,’ and being able to do so depends on its axioms’ being ‘free creations of the human mind’.
The alternative view, the one adopted by Newton and his contemporaries, is discussed by Einstein in the Herbert Spencer Lecture which he delivered, in English, at Oxford in 1933. The title he chose was ‘On the Method of Theoretical Physics’. The scientists of Newton’s time, Einstein said, were for the most part convinced that the basic concepts and laws of physics were not free creations of the human mind but were instead logically derivable from experiments and sensory experience. It was ‘the general theory of relativity which showed in a convincing manner the incorrectness of this view’. Experience can guide us in our choice of mathematical concepts, but it can’t possibly be the source from which they are derived. The source, rather, lies in our minds, our imaginations, and ‘the truly creative principle resides in mathematics.’
In the essays collected in The Essential Einstein: Public Writings, Einstein has much to say not only about his philosophy of physics but also about his own style of thinking and what he several times refers to as his ‘religion’. At the root of this weren’t any supernatural beliefs, but rather reverence and wonder. ‘The most beautiful thing we can experience,’ he writes in ‘What I Believe’, from 1930, ‘is the mysterious. It is the source of all true art and science. He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe, is as good as dead: his eyes are closed.’ In ‘Religion and Science’, written around the same time, he speaks of the ‘cosmic religious sense’, which he characterises as a feeling of ‘the vanity of human desires and aims, and the nobility and marvellous order which are revealed in nature and in the world of thought’. It is, he insists, the most important function of both art and science to arouse and keep alive this feeling. It is the cosmic religious sense, he believes, that inspired the devotion, the sheer hard work and the deep faith in the rationality of the structure of the world that enabled Kepler, Newton and (it is surely implied) himself to turn away from immediate practical life in order to ‘unravel the mechanism of the heavens in long years of lonely work’.
In the ‘Autobiographical Notes’ that Einstein wrote in 1949, he recalls that in his youth he was vividly conscious of the ‘nothingness of the hopes and strivings’ which most men pursue restlessly throughout their lives, and of the fact that participating in that pursuit could satisfy the stomach but not ‘man in so far as he is a thinking and feeling being’. After looking to organised religion to fill that gap and finding it wanting, he set out instead to attempt to grasp ‘this huge world, which exists independently of us human beings and which stands before us like a great, eternal riddle’. But what does this effort to grasp the world consist in?
What, precisely, is ‘thinking’? When, at the reception of sense-impressions, memory-pictures emerge, this is not yet ‘thinking’. And when such pictures form a series, each member of which calls forth another, this too is not yet ‘thinking’. When, however, a certain picture turns up in many such series, then – precisely through such return – it becomes an ordering element for such series, in that it connects series which in themselves are unconnected. Such an element becomes an instrument, a concept. I think that the transition from free association or ‘dreaming’ to thinking is characterised by the more or less dominating role which the ‘concept’ plays in it. It is by no means necessary that a concept must be connected with a sensorially cognisable and reproducible sign (word); but when this is the case, thinking becomes by means of that fact communicable.
So, for Einstein, the attempt to grasp the world consists in the search not for the right words but for the right picture, a picture that would order other pictures, thereby becoming a dominant ‘concept’ capable of providing shape and structure to what would otherwise be idle daydreaming.
Here Einstein echoes Wittgenstein, who emphasised in his later work that his aim was to provide ‘the understanding that consists in seeing connections’ – literally, a new way of looking. In tracing philosophical confusion to its origin, Wittgenstein says, ‘a picture held us captive,’ and what he sought to achieve was the dismantling of that picture and its replacement by another. The peculiar depth of Einstein’s thinking is, it seems to me, similarly linked to his determination to burrow beneath conscious thoughts, typically expressed in words, to the images that lie behind them and shape them, images of which we are often unaware.
Einstein’s attempts to ‘unravel the mechanism of the heavens in long years of lonely work’ began at a young age, though there is remarkably little to be learned about his earliest thoughts in Free Creations of the Human Mind, which glosses over his childhood with indecent haste, moving from his birth in Ulm on 14 March 1879 to his move to Bern at the age of 22 in a single page. Einstein’s own recollections of his intellectual development were less rushed. He often dwelled, for example, on the fascination he’d had at the age of four or five with a compass his father had given him. He remembered being so excited by this mysterious object that he trembled and grew cold. The needle fascinated him because he didn’t understand it. Nothing was touching it and yet it moved, apparently under the influence of an invisible force. ‘Something deeply hidden had to be behind things,’ he concluded. Of the three scientific idols whose portraits Einstein liked to hang on the walls of his study wherever he lived, two of them – Michael Faraday and James Clerk Maxwell – had devoted themselves to understanding electromagnetism (the third portrait was of Newton).
Einstein’s childhood was spent in Munich, where his parents moved a year after he was born, and where in 1881 his sister, Maria (always called Maja), was born. ‘Of all the women who were to play a role in Einstein’s life,’ Pais writes, ‘Maja was the one to whom he always felt closest.’ He was slow in learning to talk, and, Maja recalls, even after he had mastered speech, he would, before he uttered a sentence, repeat it softly to himself before saying it out loud. He later told a psychologist that, even in adulthood, he rarely thought in words: ‘A thought comes, and I may try to express it in words afterwards.’
Nevertheless, he did well at school, both at the Volksschule and at the Gymnasium. In 1894, when his father’s electrical engineering company began to struggle, the family moved to Milan. Initially, Einstein lived with relatives in Munich, but he hated it so much that he bought himself a train ticket to Milan and refused to return to Germany. He finished his high school education in Switzerland (which he always loved) and in 1895 was admitted to Zurich Polytechnic to study physics. There, he renounced his German nationality and became officially stateless.
At the age of sixteen, Einstein came up with a thought experiment that would have a formative influence on the development of physics in the 20th century. He imagined a single light beam and a man running alongside it at the speed of light. How would the light look to the runner? The answer seems to be that it would appear to be frozen. But then, how is the runner able to determine whether he is at rest or moving? In this paradox, Einstein later remarked, ‘the germ of the special relativity theory is already contained.’
At Zurich Polytechnic, Einstein met Mileva Marić, a fellow physics student three years older than him. In the summer of 1901 they took a holiday together in the mountains of Italy and Switzerland, from which Marić returned to find that she was pregnant. Their daughter, Lieserl, was born at the end of January 1902 in Marić’s hometown of Novi Sad in Serbia. Einstein, meanwhile, was in Bern. In June, he learned that he had been accepted for the post of ‘technical expert III class’ in the Swiss Patent Office. When Marić joined him in Bern she didn’t bring the baby. In August the following year, Lieserl came down with scarlet fever. What happened to her after that, nobody knows. All traces of her existence were erased, and Einstein, who probably never saw her, didn’t speak of her again.
Einstein and Marić were married in January 1903, and their first son, Hans Albert, was born the following spring. Thus Einstein began 1905, often called his ‘miracle year’, as a married man with a young child, a demanding job and a small flat in Bern. He had no academic position, but somehow managed during that year to write 21 reviews for an academic journal and to publish four major scientific papers. One of them would win him the Nobel Prize in Physics; another contained the special theory of relativity, the biggest advance in physics since the time of Newton. He also wrote a paper that was submitted and accepted as his doctoral thesis.
All four of the major scientific papers are contained in The Essential Einstein: Scientific Writings, and are interesting to look at even if you find the equations they contain unintelligible. The first, ‘On a Heuristic Point of View Concerning the Production and Transformation of Light’, is the one for which Einstein was given the Nobel Prize, in 1922. He submitted it in March 1905 to Annalen der Physik, the leading German-language journal of physics, whose editor was Max Planck. It is a remarkably self-assured piece of work, and Einstein was fully conscious of its importance. ‘The paper deals with radiation and the energy properties of light,’ he wrote to a friend, ‘and is very revolutionary.’ In it he attempts to explain certain experimental results that were baffling scientists at the time, among which was the ‘photoelectric effect’. It was discovered that sometimes when light is shone onto a metal plate it causes electrons to be emitted. What was puzzling was that the energy of the emitted electrons didn’t depend on the intensity of the light, but on its frequency, its colour. Einstein’s suggestion was that this can be understood if instead of – or as well as – regarding light as continuous waves, we regard it as being made up of, so to speak, ‘projectiles’, whose energy depends only on the frequency of the light, not its intensity. Any such projectile, or ‘quantum’, that has energy above a certain threshold will be able to eject an electron from the target, thereby causing the photoelectric effect. ‘In the propagation of a light ray emitted from a point source,’ he writes, ‘the energy is not distributed continuously over ever-increasing volumes of space, but consists of a finite number of energy quanta localised at points in space that move without dividing and can be absorbed or generated only as complete units.’ What is characteristically brilliant here is that Einstein begins with a puzzle and ends with a radical new conception of a fundamental notion or phenomenon, in this case light.
A month later, Einstein submitted his remarkably short PhD dissertation to the University of Zurich. ‘A New Determination of Molecular Dimensions’ was an attempt to calculate what is known as ‘Avogadro’s number’. Amedeo Avogadro was an Italian scientist who, in the early 19th century, hypothesised that equal volumes of gases, whatever the gas, will contain equal numbers of molecules. A ‘mole’ of a gas is an amount equal to its atomic or molecular weight in grams: hydrogen has an atomic mass of 1, so a mole of hydrogen would be 1 gram; helium has an atomic mass of 4, so a mole of helium would be 4 grams, etc. Each of these would have the same number of atoms. Einstein’s estimate of that number, based on his calculations, was 2.1 x 1023. The Annalen der Physik, which published the dissertation in 1906, supplied him with better data than he’d had previously, which he used to recalculate the number to 4.15 x 1023. The figure currently accepted is 6.02214 x 1023. The thesis is generally regarded as one of Einstein’s less groundbreaking works – it isn’t included in Scientific Writings – though Pais considers it ‘one of his most fundamental papers’.
The thesis also led to his third paper of this extraordinary year, ‘On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat’, which explained something else that had been puzzling scientists for a long time, namely ‘Brownian motion’, the apparently random movement of tiny particles (such as pollen) in water. Einstein showed that these movements were caused by the jostling of the particles by water molecules, and supplied a mathematical model of these movements that could be used to determine Avogadro’s number, as well as the size of water molecules, experimentally. This had an importance far beyond the explanation of Brownian motion. ‘At the time atoms and molecules were still far from regarded as real,’ the physicist Max Born said. Einstein’s investigations had ‘done more than any other work’ to convince physicists of that reality.
Einstein’s greatest achievement that year, and one of the greatest achievements of 20th-century science, was yet to come. In June 1905, he submitted to Annalen der Physik a paper called ‘On the Electrodynamics of Moving Bodies’, which put forward what is now known as the special theory of relativity. Buchwald and Gordin, in common with many other expositors, begin their account of Einstein’s theory with Galileo’s description of the notion of relativity from The Dialogue Concerning the Two Chief World Systems (1632). ‘Shut yourself up with some friend in the main cabin below decks on some large ship,’ Galileo writes, ‘and have with you there some flies, butterflies and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it.’ When the ship is standing still, he continues, observe carefully and notice that the animals will fly to all sides of the cabin with equal speed, the fish will swim in all directions, the drops will fall into the vessel beneath, and, if you throw something to your friend, you will need to throw it no more strongly in one direction than another. Now compare what happens when the ship moves. So long as the ship’s motion is uniform – that is, moving at a constant speed and not accelerating – everything will be exactly the same. ‘You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still.’ Galileo’s reasoning had a special significance in the 17th century, since it answered detractors of the Copernican view of the solar system, who argued that if the Earth were spinning on its axis and orbiting around the sun, we would surely feel the motion.
This was Einstein’s starting point in developing the special theory of relativity: you can’t tell from looking at the way things behave around you whether you are at rest or moving at a constant speed. Leaving acceleration aside, motion is relative. If you are in a train going past another, stationary train at ten miles an hour, everything will be just the same as if your train is standing still and the other is going past you at ten miles an hour. Nothing inside your carriage will tell you whether it is your train or the other one that is moving. In the jargon of physics, a point of view from a stationary position or one in uniform motion is called an ‘inertial frame of reference’, and Galileo’s principle can be expressed in the form in which it became the first postulate of Einstein’s special theory of relativity: the laws of physics are the same in all inertial frames of reference. The second postulate says that the speed of light is constant for all observers. Following discoveries made in the 19th century by Faraday and Maxwell, among others, ‘light’ here means all electromagnetic radiation, not just the visible spectrum but also infrared and ultraviolet and, as we now know, radio waves, X-rays, gamma rays and so on. The speed of light has been calculated to be roughly 300,000 kilometres per second.
It would be natural to ask: light travels at that constant speed relative to what? The answer seems to be: everything. What bothered Einstein was that this appeared to be inconsistent with the principle of relativity, a consequence of which is that velocities are additive. If I am walking at four miles per hour relative to someone standing still, and a car is travelling at 60 mph relative to me, then relative to the person at rest the car is going at 64 mph. So you might think that if I am sitting on a light wave travelling along at 300,000 km/s relative to someone standing still, and I shine a torch, then the light from the torch should be travelling at 600,000 km/s relative to that person. But then the speed of light would not be, as we know that it is, the same for all observers.
At the time Einstein was wrestling with this problem, the accepted answer to the question ‘what is the speed of light relative to?’ was ‘the ether’. The work of Faraday and Maxwell had convinced physicists that light travelled in waves, but waves in what? Sound is a wave in air, surfers ride waves in water. No one had discovered what medium light waves travelled in, so something was postulated and named ‘the ether’. Since light travels to Earth from distant stars, the ether must be pervasive throughout space. Therefore, just as a boat moving through water creates a disturbance, so too must the Earth moving through the ether. Yet again and again, experiments designed to register the effects of the Earth’s movement in the ether had failed to detect it.
Einstein was convinced that there was no such thing as the ether. He wanted to think through the problem afresh. One striking thing about ‘On the Electrodynamics of Moving Bodies’ is that it contains no citations at all to previously published work. Its only acknowledgment comes right at the end, where Einstein notes that ‘my friend and colleague, M. Besso, steadfastly stood by me in my work on the problem discussed here.’ Michele Besso was a fellow physics student at Zurich Polytechnic, who became one of Einstein’s closest friends and followed him into a job at the Swiss Patent Office. One day early in the summer of 1905, the two of them discussed the question of how to reconcile the principle of relativity with the fact that the speed of light seemed the same to all observers. ‘I’m going to give it up,’ Einstein said. But, he later recalled, as they discussed it ‘I suddenly saw the key to the problem.’ The next day, he visited Besso again and told him: ‘Thank you. I’ve completely solved my problem.’
The key was what Einstein called ‘the relativity of simultaneity’. ‘It turns out,’ Einstein wrote, ‘that two events simultaneous with respect to one observer are, in general, not simultaneous with respect to a second observer moving relative to the first one.’ ‘This signifies,’ he added, ‘a fundamental change in our concept of time.’ As he once rather charmingly put it, ‘there is no audible tick-tock everywhere in the world.’ Every frame of reference has its own time and, relative to us, time goes more slowly in a frame of reference that is moving very quickly in relation to us. This phenomenon, known as ‘time dilation’, is no longer just a matter of theory. The satellites used by GPS systems orbit the Earth at 14,000 km/h, which is fast enough to cause relativistic effects large enough that they must be taken into account if the accuracy of the systems is to be maintained.*
In the final paper he published in his ‘miracle year’, ‘Does the Inertia of a Body Depend upon its Energy Content?’, Einstein drew out another implication of special relativity, and along the way introduced the most famous equation in all of science: E = mc2, or, as it appears on this occasion, m = L/V2, where L, not E, is the symbol for energy, and V is the constant for the speed of light. Two years later, Einstein was describing this as ‘the equivalence of mass and energy’.
Buchwald and Gordin have a neat way of explaining how this equivalence follows from special relativity. Imagine a lab in a space station in which scientists are measuring the velocities of particles in a vessel. You glimpse the set-up from a spaceship passing by at a very fast speed, and make your own measurements of the particles’ behaviour. The two sets of measurements will not agree because you and the space station are moving in relation to each other. The only way to account for the difference in velocities while respecting the law of the conservation of energy is to recognise a difference in the mass of the particles. You measure ‘particles moving (very fast) with respect to you as being more massive by a small amount; that amount is the energy that has been transmogrified into mass because of the inability of any particle to accelerate beyond the speed of light.’
Since the laws of physics are the same in all inertial frames of reference, the equivalence of mass and energy also applies to particles that are stationary relative to us. For example, radioactive atoms generate heat when they decay because some of their mass transforms into energy. The equation E = mc2 tells us precisely how much. In particular, it tells us that a tiny amount of mass will be converted into a lot of energy, because c2 is a big number. This was shown to devastating effect by the use of the atomic bomb in 1945. The following year, Einstein published a piece in Science Illustrated, ‘E = MC2: The Most Urgent Problem of Our Time’, in which he said that the conversion of mass to energy ‘brings with it a great threat of evil’.
The papers that Einstein published in 1905 did not by any means go unnoticed. Planck lectured on the theory of relativity as soon as it was published, and it also attracted the attention of the eminent mathematician Hermann Minkowski, who remembered Einstein as one of his students at Zurich Polytechnic. (‘Always missing lectures,’ Minkowski is said to have remarked. ‘I really would not have believed him capable of it.’) Yet Einstein’s efforts weren’t sufficient to secure him an academic position. His application to teach at the University of Bern in 1907 was rejected on the grounds that he had not yet submitted a Habilitation, a second dissertation. He remedied that in January 1908 and the following month gained the relatively humble position of Privatdozent, which was so badly paid that he carried on working at the Patent Office too. But his admirers were growing in number and influence. In the spring of 1909 he was appointed as an untenured professor of theoretical physics at the University of Zurich, and in 1911 made a full professor at the University of Prague. That year he was also nominated for the Nobel Prize in Physics, and in October was one of the eighteen leading physicists invited to gather at the first Solvay Conference. After a brief spell back in Zurich, he was lured to Berlin, where he was made the youngest current member of the Prussian Academy of Sciences.
During these years, Einstein focused his thinking on the extension of the special theory of relativity to include not just bodies in inertial frames of reference but also those that are accelerating. In particular, the general theory of relativity would deal with gravity (objects in gravitational freefall close to the Earth’s surface are accelerating at the rate of about 9.8 m/s2). It is here that we see just how profound and original a thinker he was, and the way his peculiarly visual way of thinking enabled him to free himself from conventional ideas.
The foundational thought of the general theory came to Einstein in November 1907. ‘I was sitting in a chair in the patent office in Bern,’ he recalled, ‘when all of a sudden a thought occurred to me: “If a person falls freely he will not feel his own weight.” I was startled. This simple thought … impelled me towards a theory of gravitation.’ On another occasion, he spelled out the significance of this thought at greater length. What it suggested was that gravity and accelerated motion are equivalent. ‘For an observer falling freely from the roof of a house there exists – at least in his immediate surroundings – no gravitational field.’ Imagine that while falling this person lets go of something that he is holding – a book, say. The book will then fall at exactly the same rate as he is falling. In other words, relative to him, it will be at rest. He ‘therefore has the right to interpret his state as “at rest”’. That is to say, just as in Galileo’s example of the person in a ship moving at a uniform rate, there is nothing to tell him whether he is moving or at rest, so in this case there is nothing that would enable the falling man to decide whether he is accelerating towards the ground or the ground is accelerating towards him.
This is Einstein’s ‘equivalence principle’: that gravity and acceleration are equivalent to each other. To explain, he devised another thought experiment. Imagine that you are in a box in deep space, away from any sun or planet and so not subject to gravity. Now imagine that someone attaches a rope to the top of the box and pulls it ‘upwards’. Your feet would become pressed against the floor. Moreover, if you dropped something, a book say, it would fall to the floor. There would be nothing to tell you whether you were in such a box or on the Earth’s surface. The acceleration through space caused by the pull on the rope and the effect of gravity on Earth would be exactly equivalent.
One notable consequence of the equivalence principle is that gravity bends light. To see this, imagine there is a pinhole in the wall of the box as it accelerates through space, and that a beam of light is shining through it. The light takes some time to reach the far side of the box and will, given the acceleration of the box, hit that side closer to the floor than the hole through which it entered. If you traced the path of the light, it would curve downwards. But light, by definition, travels in a straight line. So, Einstein concluded, in a gravitational field, a straight line must follow a curved path. This brings us back to Einstein’s remark that ‘we must abandon Euclidean geometry.’ In a non-Euclidean ‘elliptic’ geometry, parallel lines can meet one another, and the angles of a triangle add up to more than 180 degrees. This is, in other words, the geometry of curved space. Think, for example, of the surface of a sphere, like the Earth. If you were to plot the shortest distance between two points on the globe, say from London to Sydney, that line – by definition a straight line – would trace the curvature of the sphere.
This led Einstein to a bold new imagining of gravity. Instead of conceiving it as a force exerted by large objects on smaller ones – pulling the Earth towards the Sun, for example, or the Moon towards the Earth – he pictured it as geometry, as the curvature of space (or, more correctly, of spacetime). The Earth is not pulled towards the Sun by an invisible force; it is moving in a straight line through space that has been curved by the Sun.
It wasn’t until 1915 that Einstein arrived at a fully worked-out version of his ‘simple thought’ from eight years earlier, by which time he had achieved significant status as a professor at the University of Berlin. The mathematics he needed for the theory was extremely difficult and he sought the help of his old friend from Zurich Polytechnic Marcel Grossmann, who had become the head of the mathematics department there. In 1916 Einstein published ‘The Foundations of the General Theory of Relativity’, the first comprehensive account of the new theory. It is an extremely long paper, most of it incomprehensible to a layperson, but at the end he makes a very specific prediction in terms that anyone can grasp. If his theory is right, he says, then ‘a ray of light going past the sun undergoes a deflection of 1.7 arcseconds.’†
One way to test this prediction would be to measure the deflection of light reaching us from stars behind the sun. The problem is that under normal conditions such observations are impossible: the light from the stars is undetectable in the Sun’s glare. Except, that is, during a total solar eclipse, when the Moon passes in front of the Sun, greatly reducing the glare. Such an eclipse was due in the summer of 1919. In May, the English astronomer Arthur Eddington led an expedition to the island of Principe in the Gulf of Guinea to take pictures of the eclipse. Once developed, printed and analysed, the photographs confirmed Einstein’s prediction that starlight would be deflected 1.7 arcseconds by the Sun. The result was announced in November 1919 at a joint meeting of the Royal Society and the Royal Astronomical Society in London. J.J. Thomson, discoverer of the electron and president of the Royal Society, chaired the meeting. He declared Einstein’s theory, now confirmed, to be ‘one of the greatest achievements of human thought’. ‘Revolution in Science’, the Times declared on its front page the next day, ‘New Theory of the Universe, Newtonian Ideas Overthrown’. Other papers, on both sides of the Atlantic, were just as unrestrained. No longer simply an eminent scientist, Einstein was suddenly an international celebrity.
Earlier that year he had divorced Mileva and was now married to his cousin Elsa, with whose daughters from her first marriage, Margot and Ilse, he had formed a close bond. Free Creations of the Human Mind contains very little about Elsa, or about Einstein’s emotional life in general. A fuller, more satisfying account can be found in Isaacson’s biography. Einstein’s move to Berlin in 1914 was pivotal. It was a city Mileva strongly disliked and in which Elsa was already happily established. The two cousins had played together as children and were reacquainted in 1912, when Einstein visited Berlin alone, soon after which they began exchanging affectionate letters. Meanwhile, Einstein’s marriage was coming under strain. As he became more and more successful, Mileva felt increasingly neglected, and resented the fact that he lavished more attention on his work than he did on her and their two sons, Hans-Albert, who in 1912 was eight, and Eduard, who at the age of two was already showing signs of the physical and mental illnesses he suffered throughout his life (he died in a psychiatric clinic in Zurich at the age of 55). ‘I must confess with a bit of shame,’ Mileva wrote to a friend, ‘that we are unimportant to him and take second place.’ To Elsa, Einstein spoke of Mileva with a shocking coldness: ‘I treat my wife as an employee whom I cannot fire. I have my own bedroom and avoid being alone with her.’
This state of affairs couldn’t go on for long, and by the beginning of 1918 Einstein was pressing Mileva for a divorce, offering her an unusual financial inducement. If he won the Nobel Prize, he told her, he would hand the prize money over to her in full. In 1918, that was 135,000 Swedish kronor, the equivalent of 225,000 German marks, or 37 times Mileva’s annual income at the time. She accepted. A deal was struck whereby she kept the boys and continued to live in Switzerland, leaving him free to marry Elsa and live with her and her two girls in Berlin. Unlike Mileva, Elsa was gregarious and positively enjoyed the limelight. When she accompanied Einstein on his first trip to the United States in 1921, their boat, arriving in New York, was met by crowds of reporters and press photographers. One of them asked Elsa if she understood relativity. ‘Oh, no,’ she answered with a smile, ‘but it is not necessary to my happiness.’
The following year, Einstein was awarded the delayed 1921 Nobel Prize in physics. At the ceremony – which Einstein didn’t attend; the award was accepted in his absence by the German ambassador – the committee made it clear that he had been honoured not for relativity but for his work on the photoelectric effect. The chair of the committee was the Swedish chemist Svante Arrhenius, now best known as a founder of climate science and for being an ancestral cousin of Greta Thunberg. In his presentation speech he dismissed relativity as something that ‘pertains essentially to epistemology’. Einstein, in his official acceptance speech a year later, pointedly did not mention the photoelectric effect but spoke exclusively about relativity. (Giving the speech was a prerequisite of receiving the money, and thus he was able to fulfil his promise to Mileva, who used it to buy three apartment buildings in Zurich.)
One irony of Einstein’s receiving the Nobel Prize for his paper on the photoelectric effect is that it is widely credited with providing the foundation for a branch of physics about which he had great misgivings: quantum theory. The quantum mechanics developed in the 1920s, especially the so-called ‘Copenhagen Interpretation’ of it associated with the Danish physicist Niels Bohr, was something Einstein could never accept. He found its abandonment of causal determinacy, in particular, deeply troubling. ‘I myself accord to this interpretation no more than a transitory significance,’ he said in his Herbert Spencer Lecture at Oxford in 1933. ‘I still believe in the possibility of giving a model of reality, a theory, that is to say, which shall represent events themselves and not merely the probability of their occurrence.’ Or, as he memorably put it, ‘God does not play dice.’
Buchwald and Gordin address Einstein’s views on this matter with the aim of defending him, as far as possible, from the consensus view among physicists that he was simply wrong. The locus classicus of Einstein’s objections to quantum mechanics is a paper from 1935, included in the Scientific Writings, which he wrote with two younger physicists, Boris Podolsky and Nathan Rosen, titled ‘Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?’ The authors make clear at the outset that their criticisms of quantum mechanics are based on general philosophical principles, namely that it must be possible to predict physical reality with certainty, that it must be possible to separate objective reality from our theories of it, and that the nature of physical reality can’t be determined a priori but has to be ascertained by observation and experiment. Quantum mechanics, according to Einstein, Podolsky and Rosen, fails to satisfy these principles. Their argument makes use of what today would be called ‘quantum entanglement’. In quantum mechanics, two particles – two electrons, say – can become ‘entangled’ in such a way that their properties are complementary. For example, the property that physicists call ‘spin’ can be of two kinds, either ‘up’ or ‘down’. When two particles become entangled, if one has ‘spin up’ then the other must have ‘spin down’. Now, it is a feature of quantum mechanics that a particle is in a state of ‘superposition’ until it is measured. With regard to spin, this means that it has both ‘up’ and ‘down’ spin until it is measured, at which point it must have one or the other but not both.
This issues in what Einstein, Podolsky and Rosen consider an unacceptable consequence, now widely known as the ‘EPR Paradox’: when we determine the spin of one particle in an entangled pair, we instantaneously determine the spin of the other, no matter how far apart they are. Imagine that these particles are more than 300 million metres apart. How can it be that our measurement immediately determines the property not only of the particle we are measuring but also of its twin, which is so far away? This effect, which Einstein described as ‘spooky action at a distance’, must be operating faster than the speed of light, which, according to the theory of relativity, is impossible. Quantum mechanics must, Einstein, Podolsky and Rosen reason, be an incomplete description; there must be some ‘hidden variables’ as yet undiscovered.
Although Buchwald and Gordin seek to present Einstein’s objections to quantum mechanics as sympathetically as they can, they are compelled to point out that subsequent developments in physics have shown that what Einstein, Podolsky and Rosen describe as a ‘paradox’ is just how the world is. Experiment after experiment has shown that quantum entanglement and its associated ‘spooky action at a distance’ are detectable aspects of reality. ‘Even the great Einstein,’ they conclude, ‘could be wrong about important questions in physics.’
In a different context, but also concerning the relation between physical theory and unexpected empirical evidence, Einstein once remarked: ‘Subtle is the Lord, but He is not malicious.’ For someone with no religious belief in the usual sense, Einstein invoked the name of God with surprising frequency. Public Writings includes a piece published in the New York Times in which he is asked directly: ‘Do you believe in God?’ ‘I believe in Spinoza’s God,’ he replied, ‘who reveals himself in the orderly harmony of what exists, not in a God who concerns himself with fates and actions of human beings.’ Rabbi Herbert Goldstein of the Orthodox Institutional Synagogue of New York is quoted as enthusiastically endorsing Einstein’s remark and claiming Einstein, if not specifically for the Jewish faith, then at least for monotheism.
Actually, as Buchwald and Gordin make clear, Einstein was throughout his life happy to be regarded as, in some sense, a Jew. His sense of being Jewish, they say, was ‘an emotional, tribal, familial and historical affinity’. He didn’t formally join any Zionist organisations, but did lend his support to many Zionist causes, especially the establishment of the Hebrew University of Jerusalem. When the first president of Israel, Chaim Weizmann, died in 1952, David Ben-Gurion is reported to have said: ‘There is only one man whom we should ask to become the president of the State of Israel. He is the greatest Jew on Earth. Maybe the greatest human being on Earth: Einstein.’ Einstein demurred. ‘My relationship to the Jewish people has become my strongest human bond,’ he said, but having devoted his life to the understanding of objective matters, ‘I lack both the natural aptitude and the experience to deal properly with people and to exercise official functions.’
Yet as Public Writings shows, Einstein occupied himself with political matters throughout his life. His public identification with his Jewish heritage, indeed, was at least in part a response to the antisemitism that he saw take hold of Germany in the 1920s and 1930s. And when, after the rise of Hitler, he settled in the US, he involved himself in particular with the struggle for justice and equality for Black people. ‘The more I feel an American,’ he wrote in ‘A Message to My Adopted Country’ (1946) with regard to racial prejudice, ‘the more this situation pains me. I can escape the feeling of complicity in it only by speaking out.’
Einstein’s most abiding political passion, however, was his lifelong opposition to nationalism, militarism and war. He was horrified by the madness of the First World War (‘At such times,’ he wrote to his friend Paul Ehrenfest, ‘one sees to what deplorable breed of animalistic brutes we belong’), and in the early 1920s was an active supporter of the League of Nations. His horror of the Nazis prompted him to urge Roosevelt to accelerate the programme to develop an atomic bomb before the Germans did, but, when he learned of the destruction of Hiroshima his reaction was to mobilise his scientific colleagues and political contacts to lobby for the international control of nuclear weapons. His last public statement, which he signed in April 1955 a week before he died, was issued jointly with Bertrand Russell. The ‘Einstein-Russell Manifesto’ called for ‘the abolition of war’, while conceding that such an end would require ‘distasteful limitations of national sovereignty’.
In some ways, a more fitting epitaph is provided by something Einstein said to his student Esther Polianowski in 1925, as they walked together through the streets of Berlin. ‘I want to go to France,’ Polianowski said. ‘I would like to find myself in new surroundings.’ ‘I never look for that,’ Einstein replied.
I like Paris, but I don’t want to go there or anywhere. I should not like to learn a new language. I don’t like new food or new clothes. I’m not much with people, and I’m not a family man. I want my peace. I want to know how God created the world. I’m not interested in this or that phenomenon, in the spectrum of this or that element. I want to know His thoughts, the rest are details.