Chapter 1

[B]efore Maxwell, people conceived of physical reality . . . as material points, whose changes consist exclusively of motions. . . . After Maxwell, they conceived of physical reality as represented by continuous fields, not mechanically explicable. . . . This change in the conception of reality is the most profound and fruitful one that has come to physics since Newton; but it has at the same time to be admitted that the programme has by no means been completely carried out yet.

Essay written by Einstein for the centennial celebration of the
birth of James Clerk Maxwell, published by
Cambridge University Press, 1931

On the walls of his apartment in 1920s Berlin, and later in his Princeton house, Einstein hung portraits of three British natural philosophers: the physicists Isaac Newton, Michael Faraday and James Clerk Maxwell – and no other scientists. Each of this trio he unquestionably revered. ‘England has always produced the best physicists,’ Einstein said in 1925 to a young Ukrainian-Jewish woman, Esther Salaman, attending his lectures on relativity in Berlin. He advised her to study physics at the University of Cambridge: the home of Newton in the second half of the seventeenth century and later the scientific base of Maxwell, founder of Cambridge’s Cavendish Laboratory in the 1870s. As Einstein explained to Salaman: ‘I’m not thinking only of Newton. There would be no modern physics without Maxwell’s electromagnetic equations: I owe more to Maxwell than to anyone. But remember,’ he warned her, ‘in England everything is judged by achievement.’

While visiting England in 1930, immediately after stopping at Newton’s birthplace in Woolsthorpe to pay tribute, Einstein remarked simply, before giving a lecture at the University of Nottingham: ‘It is a pleasure and an honour to speak in the country in which my science, theoretical physics, was born.’ In his last ever interview, two weeks before his death in Princeton, much of his conversation revolved around Newton’s fascinating writings, scientific and theological, published and unpublished, without overlooking Newton’s misanthropic personality – so different from Einstein’s own. (‘Newton is the Old Testament god; it is Einstein who is the New Testament figure . . . full of humanity, pity, a sense of enormous sympathy,’ the Polish-born British mathematician Jacob Bronowski remarked in his 1970s BBC television series The Ascent of Man.)

EARLY YEARS IN GERMANY

Although England played little role in Einstein’s childhood and adolescence in 1880s–90s Germany, some understanding of his early years is essential to appreciate his first receptive encounters with English physics, which he studied as a teenage autodidact in Germany from the early 1890s and then, more attentively, as a university student in Switzerland. Einstein’s unconventional upbringing was what set him on the path not only to his theory of relativity and his quantum theory but also to his later, ultimately unfulfilled, pursuit of a unified field theory of gravity and electromagnetism.

There was no hint of any intellectual distinction in Einstein’s family tree. His father, Hermann, was an easy-going businessman who was not very successful in electrical engineering and his paternal grandfather a merchant, while his mother, Pauline, a fine piano player but otherwise not gifted, also came from a business family which ran a profitable grain concern and was wealthy. Though both sides of the family were Jewish, neither was orthodox. Hermann and Pauline Einstein were thoroughly assimilated and non-observant Jews (‘entirely irreligious’, according to their son), who conversed in German, not Yiddish/Hebrew.

Nor was there much sign of distinction in Einstein as a child. Albert Abraham – the first name a common one among the ruling Hohenzollern dynasty, the second from Einstein’s paternal grandfather – was born on 14 March 1879 in Ulm, in southern Germany, in the semi-rural province of the Swabians. Their ‘speculative brooding’, ‘often roguish and occasionally coarse humour’ and ‘pronounced, individualistic obstinacy’ Einstein would share, according to his biographer Albrecht Fölsing. He was a quiet baby, so quiet that his parents became seriously concerned and consulted a doctor about his not learning to talk. But when a daughter, Maja, was born in November 1881, Albert apparently asked promptly: Where are the wheels of my new toy? It turned out that his ambition was to speak in complete sentences: first he would try out a sentence in his head, while moving his lips, and only then repeat it aloud. The habit lasted until his seventh year or even later. The family maidservant dubbed him ‘stupid’.

His first school was a Catholic one in Munich, where the Einstein family had relocated in 1880. Albert was the only Jew in a class of about seventy students. But he seems to have felt anti-Semitism among the teachers only in the religious education classes, not in the rest of the school curriculum. Among the students, however, anti-Semitism was commonplace, and though it was not vicious, it encouraged Einstein’s early sense of being an outsider, a feeling that would intensify throughout adulthood.

Academically he was good yet by no means a prodigy, both at this school and at his high school, the Luitpold Gymnasium. However, Einstein showed hardly any affection for his schooling and in later life excoriated the system of formal education current in Germany. He referred to his teachers as ‘sergeants’ and ‘lieutenants’, disliked physical training and competitive games – even intellectual games such as chess – and detested anything that smacked of the military discipline typical of the Prussian ethos of northern Germany. ‘Constraint has always been his personal enemy. His whole youth was a battle against it,’ wrote a friend and Einstein biographer, Antonina Vallentin, in 1954. ‘When he uttered the German word for it, an abrupt word, with a particular sinister sound, Zwang, everything tolerant, humorous or resigned in his expression vanished.’ In 1920, he even told a Berlin interviewer that the school matriculation exam should be abolished. ‘Let us return to Nature, which upholds the principle of getting the maximum amount of effect from the minimum of effort, whereas the matriculation test does exactly the opposite.’ As he astutely remarked in 1930 after he had become world famous: ‘To punish me for my contempt of authority, Fate has made me an authority myself.’

Part of Einstein’s problem lay in the heavy emphasis in the German Gymnasiums – as in British public schools of the period – on the humanities; that is, on classical studies and, to a lesser extent, German history and literature, to the detriment of modern foreign languages, such as French and English. Science and mathematics were regarded as the subjects with the lowest status.

But the main problem with school was probably that Albert was a confirmed autodidact, who preferred his own company to that of his teachers and fellow students. ‘Private study’ is a phrase frequent in his early letters and adult writings on education. It was clearly his chief means of becoming educated. His sister Maja recalled that even in noisy company her brother could ‘withdraw to the sofa, take pen and paper in hand, set the inkstand precariously on the armrest, and lose himself so completely in a problem that the conversation of many voices stimulated rather than disturbed him’.

At a relatively early age, he began reading mathematics and science books simply out of curiosity; at college in Zurich he ranged very widely in his reading, including the latest scientific journals; and as an adult he never read books simply because they were said to be classics, only if they appealed to him. ‘Einstein was more of an artist than a scholar; in other words, he did not clutter up his mind too much with other people’s ideas,’ according to the British mathematician and cosmologist Gerald Whitrow. Maybe there is a parallel here with Newton, an eclectic reader who nevertheless does not seem to have read many of the great scientific names of his own or earlier times.

His first scientific experience occurred as a child of four or five, according to Einstein, when his father showed him a magnetic compass. ‘I can still remember,’ he wrote half a century later, ‘– or at least believe I can remember – that this experience made a deep and lasting impression upon me. Something deeply hidden had to be behind things.’

Then, aged twelve, he experienced ‘a second wonder of a totally different nature’ while working through a book of Euclidian plane geometry. The ‘lucidity and certainty’ of the geometrical proofs, based on Euclid’s ten simple axioms, made another deep impression, and set Einstein thinking for the rest of his life on the true relationship between purely mathematical forms and the same forms found in the physical world. Hence the strong appeal to him of Johannes Kepler’s discovery that the planetary orbits are ellipses. The very word geometry, Einstein noted, was from the Greek for ‘earth-measuring’, which implied that mathematics ‘owes its existence to the need which was felt of learning something about the behaviour of real objects’.

At the same time, Albert began reading two popular science books in German brought for him by a poor medical student, Max Talmud, who was given a weekly lunch by his parents – among the few Jewish customs the Einsteins did observe. These introduced him to the work of Newton and set him on course to be a scientist. They also convinced him – although they did not attack religion as such – that much of the Bible was untrue, and induced a ‘suspicion against every kind of authority’ which would last until his dying day.

At school, things came to a head in 1894. A new class teacher informed Einstein that ‘he would never get anywhere in life’. When Einstein replied that surely he ‘had not committed any offence’, he was told: ‘Your mere presence here undermines the class’s respect for me.’ For the rest of his life, Einstein would be known for a mocking (and self-mocking) way with words that was sometimes biting and always at odds with his later gentle image. When as an adult he chanced upon a German psychiatrist’s book, Physique and Character, he was shaken by it and wrote down the following words in his diary, which he apparently thought applied to himself: ‘Hypersensitivity transformed into indifference. During adolescence, inwardly inhibited and unworldly. Glass pane between subject and other people. Unmotivated mistrust. Substitute paper world. Ascetic impulses.’

At home, too, all was not going well. In 1893, after a battle with larger companies, the Einstein company had failed to get a contract for lighting an important part of Munich. The following year the company was liquidated and a new one set up in Italy, with a new factory. Maja moved there with her parents, but Albert was left alone in Munich with some distant relatives in order to take his matriculation exam. Meanwhile the beloved Einstein home in Munich was sold and quickly demolished by developers under his eyes.

The combination of disruptions at school and at home seems to have been too much for Albert, who would never refer to this unhappy period. Without consulting his parents, he got a doctor (Talmud’s elder brother) to state that he was suffering from exhaustion and needed time off school, and convinced a teacher to give him a certificate of excellence in mathematics. The school authorities willingly released him. Then he headed south to Milan to face his surprised parents.

EDUCATION AND EMPLOYMENT IN SWITZERLAND

Einstein did not return to graduate, and a year later rejected his German nationality, presumably to avoid military service, becoming stateless until he was accepted as a Swiss citizen in 1901. Instead, after much private study at home in Italy in 1895, he sat the exam early for the Swiss Polytechnic in Zurich, probably the leading centre for the study of science in central Europe outside of Germany. He failed. However his brilliance in mathematics and physics was recognised, and he was encouraged to try again the following year after further schooling. On the advice of a Polytechnic professor, he went to a Swiss cantonal school in Aarau, which enjoyed a much less authoritarian atmosphere than the school in Munich. When he passed its final exam, which qualified him to begin study in Zurich in 1896, he wrote a revealing essay in (execrable) French on ‘My plans for the future’. It announced his desire to study the theoretical part of physics because of ‘my individual inclination for abstract and mathematical thinking, lack of imagination and of practical sense’, and concluded significantly: ‘Besides, I am also much attracted by a certain independence offered by the scientific profession.’

Switzerland now became integral to Einstein’s life, during this formative intellectual period, which was also the time of his first love affair, with his fellow physics student Mileva Maric´, whom he married in 1903. ‘So far as he was ever at home, at any time in his life, it was in Bern and Zurich, before the First World War,’ wrote the British novelist C. P. Snow after discussions with Einstein in the late 1930s. Judging from his youthful letters, his love of the soaring, solitary splendour of the alpine peaks influenced his scientific theorising. After he eventually became a professor in Zurich, Einstein’s students remembered him standing in the middle of a snowstorm under a street lamp at the foot of the Zurichberg, handing his unfurled umbrella to a companion and jotting down formulae for ten minutes while snowflakes fell on his notebook. Much later, in The Evolution of Physics, he wrote:

creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting-point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up.

Thus, in the mid-1890s, Einstein would start from Newton’s laws of force and motion and Maxwell’s equations of electromagnetism and ascend to the heights of the field equations of general relativity twenty years later, not by overturning Newton or Maxwell but rather by subsuming them into a more comprehensive theory, somewhat as the map of a continent subsumes a map of an individual country.

The main source for Einstein’s thinking in his early Zurich years are his love letters to Mileva. They were peppered with references to his wide scientific reading. But there is not much technical detail, probably because Mileva avoided science in her replies. So it is hard to penetrate the evolution of Einstein’s ideas. Perhaps the most revealing glimpse came in 1899, when he wrote to her of Maxwell’s theories about how electromagnetic light waves move through space – the hypothetical medium then known as the ‘luminiferous ether’ – as follows: ‘I’m convinced more and more that the electrodynamics of moving bodies as it is presented today doesn’t correspond to reality, and that it will be possible to present it in a simpler way.’ According to the novice Einstein, ‘The introduction of the term “ether” into theories of electricity has led to the conception of a medium whose motion can be described, without, I believe, being able to ascribe physical meaning to it.’ Soon, his scepticism about the ether would turn to outright rejection of Maxwell’s concept as a physical entity.

What is clear, however, is Einstein’s dissatisfaction with some of the science teaching at the Swiss Polytechnic. He paid tribute to his professors of mathematics, particularly Hermann Minkowski, although he failed to apply himself to mathematics assiduously. (Minkowski remembered his student Einstein as a ‘lazy dog’ in a letter to Max Born, while himself developing special relativity mathematically after 1905, as we shall see.) But he regarded his physics professors as behind the times and unable to cope with challenges to their authority. Even allowing for the fact that Einstein was extremely precocious in theoretical physics for a student of the late 1890s, it is astonishing that no course was offered to him and his fellow Zurich students on Maxwell’s equations, which had been published as long ago as the 1860s. Despite the experimental physicist Heinrich Hertz’s justification of Maxwell’s electromagnetic theory in 1888, the electromagnetic field was still considered too recent and controversial for students.

After four years of study, most of it ‘private’, Einstein graduated in 1900 with a diploma entitling him to teach mathematics in Swiss schools. His aim was to become an assistant to a professor at the Polytechnic, write a doctoral thesis and enter the academic world. But now his ‘impudence’, ‘my guardian angel’ (to quote another letter to Mileva), of which Einstein had made little secret at university, told against him.

The next two years would be very tough indeed for Albert and Mileva (who had failed to acquire a diploma). He was not offered an assistantship, unlike some other students. Nevertheless he thought continually about physics and began to publish theoretical papers in a well-known physics journal; he also completed a thesis, but it was not accepted by the University of Zurich. When he wrote letters to notable professors offering his services, they were ignored. (One of the professors, the chemist Wilhelm Ostwald, ironically would be the first scientist to nominate Einstein for a Nobel prize, a mere nine years later!) Soon Albert was virtually starving, dependent on casual school teaching, and at risk of malnutrition. Then Mileva became pregnant, failed the Polytechnic exam again, and gave birth to a daughter, which had to be hushed up. Einstein’s parents had always hotly opposed his proposed marriage and refused their consent; it was not given until his father lay dying in 1902, his business in bankruptcy, although his mother would never accept the marriage. Only Einstein’s unshakeable confidence in his own scientific prowess, encouraged by Mileva’s single-minded devotion, could have carried him through these desperate two years.

Rescue came in 1902 from a fellow student at Zurich, Marcel Grossmann, who would also play a significant role in the mathematics of general relativity. ‘He a model student; I untidy and a daydreamer. He on excellent terms with the teachers and grasping everything easily; I aloof and discontented, not very popular,’ Einstein later confessed in a condolence letter to Grossmann’s widow.

Grossmann’s father secured Einstein a job at the Federal Swiss Office for Intellectual Property – the Patent Office – in Bern. He was a friend of the office’s long-standing director, who was looking for a patent examiner with the ability to understand inventions in the burgeoning electrical industry. Einstein’s knowledge of electromagnetic theory, and his considerable practical exposure to electrical devices through his family’s engineering business, were deemed sufficient. On 23 June 1902, he reported for duty as a ‘technical expert, third class’ – the most junior post of its kind. The Swiss Patent Office would become the somewhat unlikely setting that would allow Einstein to make his name as a physicist with his quantum, relativity and atomic theories during his ‘miraculous year’, 1905. ‘It gave me the opportunity to think about physics,’ he later reflected. ‘Moreover, a practical profession is a salvation for a man of my type; an academic career compels a young man to scientific production, and only strong characters can resist the temptation of superficial analysis.’

Part of the reason for Einstein’s profound success was surely his wide and precocious reading in science, fuelled by his voracious curiosity allied to his unusual power of concentration, as already noted. In addition, he had an analytical ability worthy of Sherlock Holmes. John Rigden, a physicist, remarked in Einstein 1905: The Standard of Greatness that Einstein ‘was intrigued rather than dismayed by apparent contradictions, whether they consisted of experimental results that conflicted with theoretical predictions’ – as shown in his paper on quantum theory – ‘or theories with formal inconsistencies’ – as demonstrated in his paper on relativity.

A third clue to Einstein’s success is that he relished debate, even if his ideas got torn apart. About a year after arriving in Bern, he formed a small club with two friends of his own age, Conrad Habicht and Maurice Solovine. As a joke they gave it a high-sounding name, the Olympia Academy, with Einstein as president, and arranged to meet in the cafés of the city, at music recitals, on long walks at the weekend or in the Einsteins’ small apartment. Besides reading Mach together, the ‘three intellectual musketeers’ argued in detail about a recently published book, Science and Hypothesis, by the mathematician Henri Poincaré, and debated the thoughts of David Hume, Baruch de Spinoza and other philosophers, while also tackling some classic literary works. Sometimes Einstein would play his violin. They also stuffed themselves with as much good food as they could afford, and generally horsed around. Once, Habicht had a tin plate engraved by a tradesman and fixed it to the Einsteins’ door. It proclaimed: ‘Albert Ritter von Steissbein, President of the Olympia Academy’ – meaning roughly ‘Albert Knight of the Backside’ or maybe something worse (since the rhyming word Scheissbein means ‘shit-leg’!). Albert and Mileva ‘laughed so much they thought they would die,’ according to Solovine. Decades later, Einstein remembered the Olympia Academy in a letter to Solovine as being ‘far less childish than those respectable ones which I later got to know’. Its discussions, and Einstein’s talks with a few other close friends in Bern, were unquestionably a key stimulus to him in 1902–5.

The most important of all these friends was probably Michele Besso (who was not an ‘Olympian’), six years older than Einstein, a well-read, quick-witted and affectionate man whose career as a mechanical engineer did not prosper because of a natural indecisiveness. Einstein got to know him at a musical gathering in his first year in Zurich and would remain in touch for six decades until Besso’s death just a month before Einstein’s own. In 1904, at Einstein’s suggestion, Besso joined the Patent Office too, and soon the two friends were walking back and forth from the office discussing physics. Earlier, Besso had been the person who had interested the student Einstein in Mach. Now he became the catalyst in the solving of the relativity problem.

Sometime in the middle of May 1905, Einstein tells us that he went to see Besso for a chat about every aspect of relativity. After a searching discussion, Einstein returned to his apartment, and during that evening and night he saw the solution to his difficulties. The following day he went back to Besso and straightaway told him, without even saying hello: ‘Thank you. I’ve completely solved the problem. An analysis of the concept of time was my solution. Time cannot be absolutely defined, and there is an inseparable relation between time and signal velocity.’ Einstein’s sincere gratitude can be felt in his published acknowledgement to Besso for his ‘steadfastness’ and for ‘many a valuable suggestion’ in his 1905 paper on relativity – especially given the astonishing fact that this paper contains not a single bibliographical reference to established scientists!

SPECIAL RELATIVITY

So how did Einstein come up with special relativity? The physicist Stephen Hawking, in his millennial essay ‘A Brief History of Relativity’, observed that Einstein ‘started from the postulate that the laws of science should appear the same to all freely moving observers. In particular, they should all measure the same speed for light, no matter how fast they were moving.’ Let us try to unpack these tricky ideas a little.

Near the beginning of Einstein’s 1916 introduction to relativity for the general reader, published in English translation in 1920, he described a simple but profound observation. You stand at the window of a railway carriage which is travelling uniformly, in other words at constant velocity, not accelerating or decelerating – and let fall a stone on to the embankment, without throwing it. If air resistance is disregarded, you, though you are moving, see the stone descend in a straight line. But a stationary pedestrian, that is someone ‘at rest’, who sees your action (‘misdeed’ says Einstein) from the footpath, sees the stone fall in a parabolic curve. Which of the observed paths, the straight line or the parabola, is true ‘in reality’, asked Einstein? The answer is – both paths. ‘Reality’ here depends on which frame of reference – which system of coordinates in geometrical terms – the observer is attached to: the train’s or the embankment’s. One can rephrase what happens in relative terms as follows, said Einstein:

The stone traverses a straight line relative to a system of coordinates rigidly attached to the carriage, but relative to a system of coordinates rigidly attached to the ground (embankment) it describes a parabola. With the aid of this example it is clearly seen that there is no such thing as an independently existing trajectory (lit. ‘path-curve’), but only a trajectory relative to a particular body of reference.

Another, somewhat less familiar, situation involving relativity that bothered Einstein concerned electrodynamics. An electric charge at rest produces no magnetic field, while a moving charge – an electric current – generates a magnetic field (circular lines of magnetic force around a current-carrying wire), as first described by Faraday. Imagine a stationary electrically charged object with an observer A, also at rest relative to the object; the observer will measure no magnetic field using a compass needle. Now add an observer B moving uniformly to the east. Relative to B’s reference system, the charged object (and observer A) will appear to be moving west uniformly; B, using a sensitive compass, will detect a magnetic field around the moving charged object. So, from A’s point of view, there is no magnetic field around the charged object, while from B’s uniformly moving point of view there is a magnetic field.

Anomalies of this kind intrigued Einstein. He was determined to resolve them. It was his deeply held view that throughout the physical world the laws of mechanics, and indeed the laws of science as a whole, must be the same – ‘invariant’ in scientific language – for all observers, whether they are ‘at rest’ or moving uniformly. For Einstein believed that it made no physical sense to postulate such a thing as Newton’s absolute space or Maxwell’s ether: a universal frame of reference to which the movement of all bodies could be tacitly referred. Instead, he argued, the position in space of a body must always be specified relative to a given system of coordinates. We may choose to describe our car as moving down a motorway at a velocity of 110 kilometres per hour, but this figure has no absolute significance; it defines our position and speed relative only to the ground and takes no account of the Earth’s rotational position and velocity around its axis or Earth’s orbital position and velocity around the Sun.

But if this new postulate about the invariance of the laws of nature was actually correct, it must apply not only to moving bodies but also to electricity, magnetism and light, the electromagnetic wave of Maxwell and Hertz, which was known from experiment to move at a constant velocity in a vacuum of about 300,000 kilometres per second, supposedly relative to the ether. This posed a severe problem. While Einstein was contented enough to relinquish the ether, which had never satisfied him as a concept, the constancy of the speed of light was another matter altogether.

In 1895 (maybe while preparing at home in Milan to take the entry exam for the Swiss Polytechnic), Einstein had reflected on what would happen if one chased light and caught up with it. Contra Newton, he now concluded: ‘If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing, whether on the basis of experience or according to Maxwell’s equations.’ To catch up with light would be as impossible as trying to see a chase scene in a movie in freeze-frame: light exists only when it moves, the chase exists only when the film’s frames move through the projector. Were we to travel faster than light, Einstein imagined a situation in which we should be able to run away from a light signal and catch up with previously sent light signals. The most recently sent light signal would be detected first by our eyes, then we would see progressively older light signals. ‘We should catch them in a reverse order to that in which they were sent, and the train of happenings on our Earth would appear like a film shown backwards, beginning with a happy ending.’ The idea of catching or overtaking light was clearly absurd.

Einstein therefore formulated a radical second postulate: the speed of light is always the same in all coordinate systems, independent of how the emitting source or the detector moves. However fast his hypothetical vehicle might travel in chasing a beam of light, it could never catch it: relative to him the beam would always appear to travel away from him at the speed of light.

This could be true, he eventually realised, only if time, as well as space, was relative and not absolute. In order to make his first postulate about relativity compatible with his second about the speed of light, two ‘unjustifiable hypotheses’ from Newtonian mechanics had therefore to be abandoned. The first – absolute time – was that ‘the time-interval (time) between two events is independent of the condition of motion of the body of reference’. The second – absolute space – was that ‘the space-interval (distance) between two points of a rigid body is independent of the condition of motion of the body of reference’.

Thus the time of the person chasing the light wave and the time of the wave itself are not the same. Time flows for the person at a rate different from that of the wave. The faster the person goes, the slower his time flows, and therefore the less distance he covers (since distance travelled equals speed multiplied by duration of travel). As he approaches the speed of light, his watch gets slower and slower until it almost stops. In Hawking’s words, relativity ‘required abandoning the idea that there is a universal quantity called time that all clocks would measure. Instead, everyone would have his or her own personal time.’ For space there is a difference, too, between the person and the light wave. The faster the person goes, the more his space contracts, and therefore the less distance he covers. As he approaches the speed of light, he shrinks to almost nothing. Depending on how close the person’s speed is to the speed of light, he experiences a mixture of time slowing and space contracting, according to Einstein’s equations of relativity.

These ideas seem extremely alien because we never travel at speeds of even a tiny fraction of the speed of light, so we never observe any ‘relativistic’ slowing of time or contraction of space – though we are familiar with the effect of perspective when two people walk away from each other and each sees the other person as diminished in height. Our human motions seem to be governed entirely by Newton’s laws of motion (in which the speed of light, c, is a quantity that does not even appear). Einstein himself had to struggle hard in 1905 – hence his need for an intense discussion with Besso – to accept these relativistic concepts so remote from everyday experience.

With space contraction, he at least had the knowledge of a comparable earlier proposal by the physicists Hendrik Lorentz and George FitzGerald, though this had a different theoretical basis from his own and relied on the existence of the ether, a concept which Einstein had of course rejected. But the abandonment of absolute time, too, required a still greater leap of the imagination. Poincaré had questioned the concept of simultaneity in 1902 in Science and Hypothesis: ‘Not only do we have no direct experience of the equality of two times, but we do not even have one of the simultaneity of two events occurring in different places.’ Indeed, Poincaré seems to have come very close to a theory of relativity just before Einstein, but apparently drew back because its implications were too disturbing to the foundations of physics. Simultaneity is a very persistent illusion for us on Earth because we so easily neglect the time of propagation of light; we think of light as ‘instantaneous’ relative to other familiar phenomena like sound. ‘We are accustomed on this account to fail to differentiate between “simultaneously seen” and “simultaneously happening”; and, as a result, the difference between time and local time is blurred,’ wrote Einstein.

QUANTUM THEORY

Yet, despite the strangeness of its predictions, relativity was built on the mechanics of Newton modified by the electrodynamics of Maxwell, as Einstein was at pains to emphasise. Most modern physicists regard relativity theory as revolutionary, but Einstein himself did not, and reserved ‘revolutionary’ to describe his paper on the quantum theory. Ironically, although the quantum paper was published in April 1905 before his relativity paper in June 1905, his relativity paper does not refer to the quantum theory; the relativity paper treats electromagnetic radiation purely as a wave and never so much as hints that it might consist of particles or quanta of energy. Presumably Einstein recognised that one big new idea per paper would be indigestible enough for most physicists. Perhaps, too, his isolating of the two ideas in two separate papers reflected his own doubts about the quantum concept. Nevertheless, with these two papers he became the first physicist to accept what is today the orthodoxy in physics: light can behave both like a wave (in relativity theory) and like a particle (in quantum theory).

Newton had been divided about the relative merits of waves and particles, on the whole favouring the latter in his ‘corpuscular’ theory of light, which dominated physics until convincing new evidence for the wave theory was discovered by Thomas Young (yet another English physicist admired by Einstein) soon after 1800. As for gravity, Newton had no idea at all as to how such a continuous influence might arise from discrete (in other words discontinuous) masses. Indeed, the debate about whether nature is fundamentally continuous or discontinuous runs through science – from the atomic theory of ancient Greece right up to the present day with its opposing concepts of analogue and digital, and the wave/particle ‘duality’ of subatomic entities like the electron. Russell is supposed to have asked: Is the world a bucket of molasses or a pail of sand? In mathematical terms, asked the physicist Rigden, ‘Is the world to be described geometrically as endless unbroken lines, or is it to be counted with the algebra of discrete numbers? Which best describes Nature – geometry or algebra?’

Quantum theory, the modern corpuscular theory, was born with the new century, in 1900, as a result of the work of the physicist Max Planck, although it would remain in limbo until 1905, when Einstein’s paper would endow it with its true significance. Planck considered the energy of heat that had been measured emerging from a glowing cavity, termed a ‘black body’ because the hole leading to the cavity behaves almost as a perfect absorber and emitter of energy with no reflecting power (like a black surface). Planck tried to devise a theory to explain how the heat energy of a black body varied over different wavelengths and at different temperatures of the cavity. But he found that if he treated the heat as a continuous wave, this wave model did not agree with experiment. Only when he assumed that the energies of the ‘resonators’ (atoms) in the walls of the cavity that were absorbing and emitting heat were not continuous but could take only discrete values, did theory match experiment. Instead of continuous absorption and emission of energy, energy was exchanged between heat and atoms in packets or quanta. Moreover, the size of a quantum was proportional to the frequency of the resonator, which meant that high-frequency quanta carried more energy than low-frequency quanta. As a believer in nature as a continuum, and as an innately conservative man, Planck did not feel at all comfortable with what his calculation had told him, but in 1900 he reluctantly published his theoretical explanation of black-body radiation.

Einstein was bolder than Planck. He was twenty years younger and had less stake than Planck in classical nineteenth-century physics. Probably encouraged by his disbelief in the ether, Einstein decided that it was not just the exchange of energy between heat/light and matter (i.e. absorption and emission) that was quantised – light itself was quantised. In his introduction to his April 1905 paper he radically stated: ‘According to the assumption to be contemplated here, when a light ray is spreading from a point, the energy is not distributed continuously over ever-increasing spaces, but consists of a finite number of energy quanta that are localised in points in space, move without dividing, and can be absorbed or generated as a whole.’ Instead of moving particles, Einstein visualised a light beam as moving packets of energy. When this avant-garde concept was finally accepted by reluctant physicists in the 1920s, the packets were termed ‘photons’.

Had there been no experimental support for Einstein’s assumption of quantised light, it would have met with an even more sceptical reaction than it in fact did. But fortunately there was at least some significant laboratory evidence. Though it was not detailed, Einstein audaciously interpreted the evidence with the quantum theory he had elaborated in the first part of his paper. The success of his theoretical explanation of the ‘photoelectric effect’ in his 1905 paper (which won him the Nobel prize) meant that light quanta could not be totally ignored, even if they were gravely distrusted.

The photoelectric effect had been discovered by Hertz around 1888 while investigating electromagnetic waves. Hertz noticed that in a spark gap the spark gained in brightness when illuminated by ultraviolet (high-frequency) light. With the discovery of X-rays in 1895, and of the electron in 1897, followed by the experiments of Philipp Lenard (a former assistant to Hertz), it was soon accepted that high-frequency light could knock electrons out of the surface of a metal producing photoelectrons, so-called cathode rays. ‘I just read a wonderful paper by Lenard on the generation of cathode rays by ultraviolet light. Under the influence of this beautiful paper I am filled with such happiness and joy that I absolutely must share some of it with you,’ Einstein wrote to his fiancée Mileva in 1901. It may have been this paper by Lenard that started Einstein speculating on the quantised nature of light. For Lenard’s published data were in major contradiction with those expected from classical physics.

With the wave theory of light, the more intense the light, the more energy it must have and the greater the number of electrons that should be ejected from the metal. This was observed by Lenard – yet only above a certain frequency of light. Below this frequency threshold, no matter how intense the light, it knocked out no electrons. Moreover, above the threshold, electron emission was observed even when the light was exceedingly weak. With the quantum theory, however, Einstein realised such behaviour was to be expected. One quantum of light (later called a photon) would knock out one electron, but only if the quantum carried enough energy to extract it from the surface of the metal. Since, as Planck had shown, the size of a quantum depended on its frequency, only quanta of a sufficiently high frequency or higher would knock out electrons – hence the existence of the threshold frequency. Moreover, even a very few quanta (a very weak intensity of light) would still eject a few electrons, provided that the quanta were above the threshold in frequency.

So truly revolutionary was this discontinuous view of nature, which owed almost nothing to earlier physics, that light quanta took much more experimentation and a lot of fresh thinking to be accepted by other physicists. This happened only in the late 1920s. So we shall leave the quantum theory for now, and return to it much later, after following the next phase in Einstein’s struggle with relativity.

GENERAL RELATIVITY

In 1908, Einstein’s former mathematics professor at Zurich, Minkowski, reformulated relativity mathematically and introduced the new concept of ‘space-time’. He enthusiastically announced:

The views of space and time which I wish to lay before you have sprung from the soil of experimental physics and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

More prosaically, events in four-dimensional space-time are analogous to points in three-dimensional space. There is an analogy, too, between the interval separating events in space-time and the straight-line distance between points on a flat sheet of paper. The space-time interval is absolute, in other words its value does not change with the reference frame used to compute it. In conventional space and time the stone falling from a uniformly moving train has two trajectories – straight down and parabolic – depending on whether it is observed from the train or from the embankment. But in the geometry of space-time it has only one trajectory, which Minkowski dubbed its ‘world line’.

‘Since the mathematicians pounced on the relativity theory I no longer understand it myself,’ Einstein apparently sighed on studying Minkowski’s treatment. As a physicist he was at this time somewhat ambivalent about pure mathematics. Even in his introduction to relativity for the general reader, he felt obliged to warn that mathematical talk of a ‘four-dimensional space-time continuum’ had nothing at all to do with the occult or with inducing ‘mysterious shuddering’. Yet, Einstein did admit that without Minkowski’s mathematics, the general theory of relativity might never have grown out of its infant state. ‘“Analytic” or “algebraically expressed” geometry is fundamental to modern theoretical physics, because of its ability to take the imagination way beyond everyday physical constraints,’ according to mathematician Robyn Arianrhod in Einstein’s Heroes: Imagining the World through the Language of Mathematics. ‘Newton used an early form of it (in his calculus) to visualise aspects of the mechanism that keeps “the stars in their courses”; Maxwell used it to imagine Faraday’s invisible fields; and Einstein used it to imagine the whole cosmos.’

The following year, 1909, with the growing fame of relativity, Einstein’s academic career took off. After seven years he left the Patent Office in Bern to become a (non-tenured) professor of theoretical physics at the University of Zurich; was the guest of honour at the next annual meeting of German scientists in Salzburg; and received his first honorary degree in Geneva at the age of just thirty. In early 1911, he moved to Prague as a full professor, but stayed only sixteen months before moving back to Zurich in 1912, now as full professor of theoretical physics. While based in Prague, in late 1911 he attended the first Solvay Congress in Brussels and lectured about his quantum theory on terms of equality with the world’s greatest scientists: Lorentz, Planck and Poincaré – already known to him – as well as Marie Curie, Ernest Rutherford, Walther Nernst and others. Nernst’s student, Frederick Lindemann, secretary of the Congress – who as a future professor of physics at the University of Oxford would host Einstein in England – meeting him for the first time, recalled Einstein as ‘singularly simple, friendly and unpretentious. He was invariably ready to discuss physical questions, even with a mere post-graduate student, as I then was. . . . But his pre-eminence among the eighteen greatest theoretical physicists of the day, who were there assembled, was clear to any unprejudiced observer.’ Finally, in the spring of 1914, Einstein left Switzerland – while remaining a Swiss citizen – and arrived in Berlin where he was elected a member of the Prussian Academy – thereby reacquiring, in effect, German citizenship – on the understanding that he could devote his entire time to research.

Solvay Congress in Brussels, Belgium, 1911: a gathering of the greatest scientists in the world at this time. Einstein, then only thirty-two years old, who gave the concluding address on his revolutionary quantum theory, stands second from right. Among the seated scientists are Walther Nernst (far left), Hendrik Lorentz (fourth from left), Marie Curie (second from right) and Henri Poincaré (far right). Those standing include Max Planck (second from left), Arnold Sommerfeld (fourth from left), Frederick Lindemann (fifth from left), James Jeans (fifth from right) and Ernest Rutherford (fourth from right).

At this point, the relativity theory of 1905 began to be known as ‘special’ relativity, to distinguish it from the later, more general theory, following Einstein’s own terminology introduced in 1915. Of course the ‘general’ theory subsumes the ‘special’ theory, indeed it reduces to the special theory under conditions of uniform motion with constant velocity (as with the example of the train and the falling stone). In such an idealised universe, without gravity, special relativity alone is sufficient. But in the real physical universe, which is pervaded by gravity and accelerations due to gravity as well as various other kinds of forces, there is no such thing as absolutely uniform motion, only approximations to it, so we need the more general theory.

Einstein’s aim was to make his 1905 relativity theory valid for all moving coordinate systems. Then, as he noted ironically, there would be an end to the violent disputes that had racked human thought since Copernicus, because ‘The two sentences, “the Sun is at rest and the Earth moves,” or “the Sun moves and the Earth is at rest,” would simply mean two different conventions concerning two different coordinate systems.’ In 1905, he had done away with Newton’s concepts of absolute space and absolute time. Now, using the concept of space-time introduced by Minkowski and radically developed by Einstein with the help of his mathematician friend Grossmann, Einstein would devise a more sophisticated theory which would also do away with gra-vity’s inexplicable instantaneous action at a distance, while at the same time retaining Newton’s laws of motion and his inverse-square law of gravitational attraction as a first approximation to physical reality.

The initial inkling of how to generalise relativity struck Einstein in 1907, and it is a moment reminiscent of Newton’s contemplation of the falling apple, though trickier to comprehend. ‘I was sitting on a chair in my Patent Office in Bern. Suddenly a thought struck me: if a man falls freely, he would not feel his weight,’ Einstein later recalled. In other words, if you were to jump off a rooftop or better still a high cliff, you would not feel gravity. ‘I was taken aback. The simple thought experiment made a deep impression on me. It was what led me to the theory of gravity.’ He called this ‘the happiest thought of my life’.

To drive home the point, he imagined that as you fall, you let go of some rocks from your hand. What happens to them? They fall at the same rate as you, side by side. If you were to concentrate only on the rocks (admittedly difficult!), you would not be able to tell if they were falling to the ground. An observer on the ground would see you and the rocks accelerating together for a smash, but to you the rocks, relative to your reference frame, would appear to be ‘at rest’.

Or imagine being inside a moving lift while standing on a weight scale. As the lift descends, the faster it accelerates, the less you will feel your weight and the lighter will be the weight reading on the scale. If the lift cable were to snap and the lift to go into free fall, your weight according to the scales would be zero. Then gravity would not exist for you in your immediate vicinity. In other words, the existence of gravity is relative to acceleration.

From such thinking, which became intensive only after he moved to Prague in 1911, Einstein restated a venerable idea that has become known as his ‘equivalence principle’ – the idea that gravity and acceleration are, in a certain sense, equivalent. It encompasses the fact, first observed by Galileo Galilei, that gravity accelerates all bodies equally. In more scientific language, inertial mass (as defined by Newton’s second law of motion) equals gravitational mass (as defined by gravity). Newton had simply assumed this equivalence as self-evident in formulating his gravitational equation, but Einstein felt that by understanding the physical reason for the equivalence he could gain insight into how to include gravity in relativity theory. Modern physicists have different ways to state the equivalence principle. For example, it is ‘the idea that the physics in an accelerated laboratory is equivalent to that in a uniform gravitational field’, according to Tony Hey and Patrick Walters.

For the next few years Einstein became obsessed with thoughts of accelerating closed boxes. On a Swiss Alpine hike with Marie Curie, her two daughters and their governess in the summer of 1913, Einstein toiled along crevasses and up steep rocks without seeing either, stopping periodically to discuss science. Once, Eve Curie remembered with amusement, Einstein seized her mother’s arm and burst out: ‘You understand, what I need to know is exactly what happens in a lift when it falls into emptiness.’ At a packed lecture in Vienna the following month, he entertained an audience of scientists by asking them to imagine two physicists awakening from a drugged sleep to find themselves standing in a closed box with opaque walls but with all their instruments. They would be unable to discover, he said, whether their box was at rest in the Earth’s gravity or was being uniformly accelerated upwards through empty space (in which gravity is taken to be negligible) by some mysterious external force.

The deflection of light by Earth’s gravity would be far too small to measure, Einstein realised. But deflection might be measurable, he reasoned, when light from distant stars passed close to a massive body like the Sun. Furthermore, the equivalence principle dictated that the light emitted from the Sun should feel the drag of solar gravity too. Its energy must therefore fall slightly, which meant that its frequency must fall and therefore its wavelength must get longer (since light’s velocity must remain constant, and the velocity of a wave equals its frequency multiplied by its wavelength). So light from atoms in the surface of the Sun, as compared with light emitted by the same atoms in interstellar space, should be shifted towards the red – longer wavelength – end of the visible spectrum when observed on Earth. The deflection of starlight by the Sun and the red shift of solar radiation were therefore possible tests of relativity.

But in order to introduce gravity into relativity, a major problem confronted Einstein in trying to apply the equivalence principle to the flat space-time visualised by Minkowski. The problem can be perceived, at least dimly, from a paradox about a simple merry-go-round that bothered Einstein. When a merry-go-round is at rest, its circumference is equal to π times its diameter. But when it spins, its circumference travels faster than its interior. According to relativity, the circumference should therefore shrink more than the interior (since space contraction increases with velocity), which must distort the shape of the merry-go-round and make the circumference less than π times the diameter. The result is that the surface is no longer flat; space is curved. Euclid’s geometry, based on flat surfaces and straight light rays, no longer applies. Einstein is said to have had a nice analogy for this curvature, which he gave to his young son, when the boy asked his father why he was so famous: ‘When a blind beetle crawls over the surface of a curved branch, it doesn’t notice that the track it has covered is indeed curved. I was lucky enough to notice what the beetle didn’t notice.’

In the mid-nineteenth century, the mathematician Bernhard Riemann had invented a geometry of curved space in which, said Einstein, ‘space was deprived of its rigidity, and the possibility of its partaking in physical events was recognised’. Now Einstein – initially with the help of his mathematician friend Grossmann but after he moved to Berlin in 1914 almost entirely alone – used Riemann’s geometry to create a new geometry of curved space-time. ‘His idea was that mass and energy would warp space-time in some manner yet to be determined,’ explained Hawking. Gravity would no longer be an interaction of bodies through a law of forces; it would be a field effect that emerged from the way in which mass curved space. When a marble is propelled across a flat, smooth trampoline on which sits a large and heavy ball, the marble follows a curved path around the depression caused by the ball. In the Newtonian view, a gravitational force emanates from the ball and somehow compels the marble to move in a curve. But according to general relativity it is the curvature of space – or rather space-time – that is responsible; there is no mysterious force. ‘Matter tells space-time how to curve, and curved space tells matter how to move’ – to quote a well-known summary of Einstein’s general theory of relativity by the physicist John Archibald Wheeler.

The light ‘corpuscles’ in a light ray from a distant star grazing the Sun on its way to our eyes could be interpreted like marbles moving past a ball. In 1911, before he had mastered curved space-time, Einstein had calculated the expected deflection of starlight on the basis of Newton’s law of gravitation. In 1915, however, having completed general relativity, he recalculated the deflection as twice the size of his 1911 calculation based on Newton. If the magnitude of the actual deflection were to be measured by astronomers, it would test which gravitational theory was correct: Newton’s or Einstein’s. ‘The examination of the correctness or otherwise of this deduction is a problem of the greatest importance, the early solution of which is to be expected of astronomers,’ wrote Einstein in his introduction to relativity in 1916. It was to be British astronomers who would answer his challenge, in 1919, and launch Einstein as a new star visible across planet Earth.