Einstein on the Run Read online

  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.

  In a related vein, Jürgen Renn and Robert Schulmann, two historians of science, identified Einstein’s unwillingness to adopt received ideas simply on the authority of a scientist’s reputation – even if the scientist was Newton or Maxwell. For example, Einstein examined the highly influential works of Ernst Mach, a leading physicist of his formative years. Mach did not accept the concept of either the ether or the atom, neither of which had been experimentally observed in the late nineteenth century. Though Einstein did not share Mach’s positivist philosophy, he liked Mach’s scepticism. ‘[Einstein] would carefully study Mach’s arguments against burdening physics with unnecessary concepts,’ noted Renn and Schulmann, ‘and eventually discard the ether concept, while accepting Mach’s criticism of atomism as a challenge and trying to provide evidence for the existence of atoms.’ This Einstein effectively achieved in his 1905 paper on atomic theory. It explained the puzzling phenomenon of ‘Brownian movement’ – the erratic fluctuations of microscopic particles suspended in a fluid, such as fine pollen in water, observed by a British botanist, Robert Brown, in 1827 – in terms of the kinetic motion of atoms and molecules. According to this kinetic theory, the invisible fluctuations of atoms/molecules produce visible fluctuations of particles via collisions between atoms/molecules and particles.

  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 reme
mbered 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 perso
n 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.