Why Beauty is Truth Page 21

  Earlier, in his 1678 Treatise on Light, the Dutch physicist Christiaan Huygens had proposed a different theory: light is a wave. This theory neatly explains reflection, refraction, and diffraction—similar effects can be seen, for instance, in water waves. The aether was to light as water was to waves on the ocean—the thing that moved when the wave passed. But now Newton disagreed. The debate got very confused, because both scientists were making incorrect assumptions about the nature of the alleged waves.

  Everything changed when Maxwell got in on the act. And he stood on the shoulders of another giant.

  Electric heating, lighting, radio, television, food processors, microwave ovens, refrigerators, vacuum cleaners, and endless items of industrial machinery all derive from the insights of one man, Michael Faraday. Faraday was born in Newington Butts, London (now the Elephant and Castle), in 1791. He was a blacksmith’s son who rose to scientific eminence in the Victorian era. His father belonged to the Sandemanians, a minority Christian sect.

  Faraday became an apprentice bookbinder in 1805 and began performing scientific experiments, especially in chemistry. His interest in science grew significantly when, in 1810, he became a member of the City Philosophical Society, a group of young people who met to talk science. In 1812, he was given tickets to hear the final lectures of Sir Humphry Davy, Britain’s leading chemist, at the Royal Institution. Soon thereafter, he asked Davy for a job; he was given an interview, but no position was available. But after Davy’s chemical assistant was soon fired for starting a fight, Faraday got his job.

  From 1813 to 1815 Faraday toured Europe with Davy and his wife. Napoleon had given Davy a passport, which included a valet, so Faraday accepted that position. He was annoyed to find that Davy’s wife, Jane, took the title literally and expected him to act as her servant. In 1821, events took a more favorable turn: he was promoted, and he married Sarah Barnard, the daughter of a prominent Sandemanian. Better still, his research into electricity and magnetism was starting to take off. Following previous research of the Danish scientist Hans Ørsted, Faraday discovered that electricity flowing through a coil near a magnet produces a force. This is the basic principle underlying the electric motor.

  His research interests then became swamped under administrative and teaching duties, though these had a very favorable impact. In 1826, he started a series of evening discourses on science and also initiated the Christmas lectures for young people, both of which are still running. Today the Christmas lectures are broadcast on television, one of the gadgets that Faraday’s discoveries eventually made possible. In 1831, back at his experiments, he discovered electromagnetic induction. This was the discovery that changed the industrial face of the nineteenth century, because it led to electrical transformers and generators. The experiments convinced him that electricity must be some kind of force acting between material particles, and not a fluid as generally thought.

  Eminence in science typically leads to the honor of an administrative post, which promptly kills off the scientific activities that are being recognized. Faraday was made scientific adviser to Trinity House, whose mission is to keep the British seaways safe for shipping. He invented a new, more efficient kind of oil-burning lamp, which produced a brighter light. By 1840, he had become an elder of the Sandemanian sect, but his health was starting to worsen. In 1858 he was given free lodgings in a “grace and favor” house at Hampton Court, the former palace of King Henry VIII. He died in 1867 and was buried in Highgate Cemetery.

  Faraday’s inventions revolutionized the Victorian world, but (perhaps because of his early lack of education) he was weak on theory, and his explanations of how his inventions worked were based on curious mechanical analogies. In 1831, the year Faraday discovered how to turn magnetism into electricity, a Scottish lawyer was presented with a son—his only child, as it turned out. The lawyer was more interested in managing his land holdings, but he took considerable interest in the education of young “Jamesie,” more formally known as James Clerk Maxwell.

  Jamesie was bright and fascinated by machines. “How it doos?” was his standard question: How does it do that? Another was “What’s the go of that?” His father, who had similar fascinations, did his best to explain. And if the father failed to go far enough, Jamesie would ask a supplementary question: “What’s the particular go of that?”

  James’s mother died of cancer when the child was nine; the loss brought father and son closer together. The boy was sent to the Edinburgh Academy, which specialized in the classics and wanted its pupils to be neat and tidy, proficient in the standard subjects, and totally lacking in original thought because that got in the way of orderly teaching. Jamesie wasn’t quite what the schoolteachers wanted, and it did not help that his father, obsessed with cleanliness, had designed special clothes and shoes for the boy, including a frilly tunic bedecked with lace. The other kids nicknamed James “Dafty.” But James was stubborn and earned their respect, though he still baffled them.

  The school did one good thing for James: it gave him an interest in mathematics. A letter to his father talks of making “a tetra hedron, a dodeca hedron, and two more hedrons that I don’t know the wright names for.” (Presumably these were the octa and icosa.) By the age of 14 he had won a prize for independently inventing a class of mathematical curves known as Cartesian ovals, after its original inventor Descartes. His paper was read to the Royal Society of Edinburgh.

  James also wrote poetry, but his mathematical talents were greater. He started at the University of Edinburgh at 16 and later continued his studies at the University of Cambridge, Britain’s leading institution for mathematics. William Hopkins, who coached him for his exams, said that James was “the most extraordinary man I have ever met.”

  James earned his degree and remained at Cambridge as a postgraduate student, doing experiments on light. Then he read Faraday’s Experimental Researches and started studying electricity. To cut a long story very short, he took Faraday’s mechanical models of electromagnetic phenomena and by 1864 had distilled them into a system of four mathematical laws. (In the notation of the day there were more than four, but we now use vector notation to group them into four. Some formalisms reduce these down to one.) The laws describe electricity and magnetism in terms of two “fields,” one electric and one magnetic, which pervade the whole of space. These fields describe not just the strength of electricity or magnetism at each location but the direction as well.

  The four equations have simple physical meanings. Two tell us that electricity and magnetism can be neither created nor destroyed. The third describes how a time-varying magnetic field affects the surrounding electric field, and it embodies in mathematical form Faraday’s discovery of induction. The fourth describes how a time-varying electric field affects the surrounding magnetic field. Even in words, these equations are elegant.

  A simple mathematical manipulation of Maxwell’s four equations confirmed something that Maxwell had long suspected: light is an electromagnetic wave, a propagating disturbance in the electric and magnetic fields.

  The mathematical reason was that from Maxwell’s equations it is easy to derive something that all mathematicians could recognize: the “wave equation,” which as its name suggests describes how waves propagate. Maxwell’s equations also predict the speed of such waves: they must travel at the speed of light.

  Only one thing travels at the speed of light.

  In those days it was assumed that waves had to be waves in something. There had to be a medium to transmit them; waves were vibrations of that medium. The obvious medium for light waves was the aether. The mathematics said that light waves had to vibrate at right angles to the direction of travel. This explained why Newton and Huygens had been so confused: they thought the waves vibrated along the direction of travel.

  The theory made another prediction: that the “wavelength” of electromagnetic radiation, the distance from one wave to the next, could be anything. The wavelength of light is extremely short, but there ough
t to exist electromagnetic waves of much greater length. It was a good enough theory to inspire Heinrich Hertz to generate such waves, which we now call radio waves. Guglielmo Marconi quickly followed up with a practical transmitter and receiver, and suddenly we could talk to each other, almost instantly, across the entire planet. Now we send pictures the same way, monitor the skies with radar, and navigate with the Global Positioning System.

  Unfortunately, the concept of the aether was problematic. If the aether existed, then the Earth, which revolves round the Sun, must be moving with respect to the aether. It ought to be possible to detect that motion—or else the very concept of the aether would have to be abandoned as inconsistent with experiment.

  The answer to this conundrum would completely change the face of physics.

  In the summer of 1876, the firm of Israel and Levi, run by two Jewish merchants in the city of Ulm in the state of Württemberg, gained a new partner, Hermann Einstein. In his youth, Hermann had shown considerable ability in mathematics, but his parents could not afford to send him to university. Now he was becoming a partner in a firm that sold featherbeds.

  In August, Hermann married Pauline Koch in Cannstadt synagogue, and the couple eventually made a home in Bahnhofstrasse—Station Road. Less than eight months later, their first child was born. According to the birth certificate, “A child of the male sex, who has received the name Albert, was born in Ulm, in [Hermann’s] residence, to his wife Pauline Einstein, née Koch, of the Israelitic faith.” Five years later, Albert was presented with a sister, Maria, and the two became very close.

  Albert’s parents had a relaxed attitude to their religion and made efforts to integrate themselves into the regional culture. At that time, many German Jews were “assimilationist,” toning down their cultural traditions so that they would fit in better with fellow citizens of other faiths. The names that Hermann and Pauline chose for their children were not traditional Jewish names, although they maintained that Albert was named “after” his grandfather Abraham. Religion was not a frequent topic of discussion in Hermann’s house, and the Einsteins did not observe traditional Jewish rituals.

  Maria’s childhood recollections, published in 1924, are our main source of information about Albert’s early experiences and personality. Apparently, he frightened his mother at birth because the back of his head was strangely angular and unusually large. “Much too heavy! Much too heavy!” she cried, when she first saw her baby. Fears that the boy would turn out to be mentally handicapped grew when it took him a long time to start to speak. But Albert was merely waiting until he was confident that he knew what he was doing. He later said that he only began to talk when he could master complete sentences. He would try them out in his head, and then utter them once he was sure the words were correct.

  Albert’s mother was an accomplished piano player. Between the ages of six and thirteen, Albert was given violin lessons from a teacher named Schmied. In later life, he was devoted to his violin, but in childhood he found the lessons boring.

  The featherbed business having flopped, Hermann turned his hand to gas and water supplies, in collaboration with his brother Jakob. Jakob was an engineer and an entrepreneur, and the Einsteins invested heavily in the new venture. Then Jakob decided to diversify into electricity—not installing utilities but manufacturing equipment for power stations. The company officially came into being in 1885, and the two brothers moved into the same house in Munich, with financial help from Pauline’s father and other family members. At first, the business did well, and the Elektronische Fabrik J. Einstein und Co. sold power stations in the Munich area and as far afield as Italy.

  Einstein tells us that his interest in physics was triggered when his father showed him a compass. Then aged four or five, Albert was fascinated by its ability to point in the same direction no matter how it was turned, and he gained his first glimpse of the hidden wonders of the physical universe. He found the experience almost mystical.

  At school, Albert was competent but initially showed no special brilliance. He was slow and methodical, received good grades, but was a poor mixer. He much preferred to play on his own; he was particularly fond of building houses of cards. He disliked sports. When he moved to the gymnasium in 1888 he developed a talent for Latin, and until he left at fifteen he always was at the top of his class in Latin and mathematics. His mathematical abilities were stimulated by Uncle Jakob, who as an engineer would have studied quite a bit of higher mathematics. Jakob would set young Albert mathematical problems, and Albert was delighted when he solved them. A family friend, Max Talmud, also had a significant effect on Albert’s education. Talmud was a poverty-stricken medical student, and Hermann and Pauline had him over for dinner every Thursday evening. He gave Albert several books on popular science; then he initiated the young man into the philosophical writings of Immanuel Kant. The two would discuss philosophy and mathematics for hours. Talmud wrote that he never saw Einstein playing with other children, and that his reading material was always serious, nothing lightweight. His sole relaxation was to play music, including Beethoven and Mozart sonatas accompanied by Pauline.

  Albert’s enthusiasm for mathematics received a boost in 1891 when he acquired a copy of Euclid that he later called his “holy geometry book.” What impressed him most was the clarity of the logic, the way Euclid had organized the flow of ideas. For a time, Albert became very devout, thanks to compulsory school instruction (in Catholicism, as it happened—there was no choice) and home tuition in the Jewish faith. But all this was brushed aside when he found out about science. His studies of Hebrew and his progress towards his bar mitzvah ground abruptly to a halt; Albert had found a different calling.

  By the early 1890s, all was not well in the Elektronische Fabrik J. Einstein und Co. Sales were becoming more difficult in Germany, and the company’s Italian agent Lorenzo Garrone suggested that it should move to Italy. In June 1894, the German company was wound up, the family home went on the market, and the Einsteins moved to Milan—with the sole exception of Albert, who had his schooling to complete. While “Einstein and Garrone” set up shop in Pavia, where the family subsequently moved, Albert was left on his own in Munich.

  It was a depressing experience, and he hated it. Not only that: the prospect of military service was looming. Without telling his parents, he decided to join them in Italy. He persuaded the family doctor to provide a certificate stating that he suffered from nervous disorders, which may well have been true; permitted to leave school early, he turned up unannounced in Pavia in the spring of 1895. His parents were horrified, so he promised to continue his studies so that he could take the entrance examination to ETH (the Eidgenossische Technische Hochschule, then as now a leading Swiss institution of higher education) in Zurich.

  Albert blossomed in the Italian sunshine. In October he took the ETH entrance examination and failed. He passed easily in mathematics and science but fell down on the humanities. His essay writing was none too good either. But it turned out that there was another way into ETH, which was to start by gaining a high-school diploma, the Matura, which was an automatic entry route. He therefore went to a school in Aarau as a paying guest of the Winteler family. The Wintelers had seven children, and Albert enjoyed their company, developing a lasting affection for his substitute parents. He praised the school’s “liberal spirit” and excellent teachers—saying pointedly that the teachers did not bow to outside authority.

  For the first time in his life, he was happy at school. He grew in confidence and made his opinions known. One of his school essays, in French, laid out his plans for the future, which were to study mathematics and physics.

  In 1896 he entered ETH, renouncing his Württemberg citizenship and becoming stateless. He saved one-fifth of his monthly allowance to pay for his eventual Swiss naturalization. But now the electrical factory owned by his father and uncle Jakob went bankrupt, taking much of the family fortune with it. Jakob took a regular job with a big company, but Hermann was determined to start
yet another business. He ignored Albert’s advice to the contrary, started again in Milan, and lasted only two years before that enterprise, too, failed. Albert once more became depressed by his family’s misfortunes, until his father followed Jakob’s lead and took a job installing power stations.

  Albert spent much of his time at ETH in the physics laboratory, performing experiments. His professor, Heinrich Friedrich Weber, was unimpressed. “You are a smart boy, Einstein, a very smart boy,” he told the young man. “But you have one great fault: you do not let yourself be told anything.” He stopped Albert from carrying out an experiment to find out whether the Earth was moving relative to the aether—the hypothetical all-pervading fluid that was supposed to transmit electromagnetic waves.

  Nor was Einstein greatly impressed by Weber, whose courses he found old-fashioned. He was especially disappointed not to be told more about Maxwell’s theory of electromagnetism and taught it to himself, using a German text of 1894. He took lecture courses from two famous mathematicians, Hurwitz and Hermann Minkowski. Minkowski, a brilliantly original thinker, had introduced fundamental new methods into the theory of numbers, and was later to make important mathematical contributions to relativity. Albert also read some of Charles Darwin’s works on evolution.

  In order to proceed at ETH, he now needed to land an assistantship—what we would now call a teaching assistant position—so that he could finance his further studies while remaining at ETH. Weber hinted that he might offer Albert such a post, but failed to follow through, and Albert never entirely forgave him. He wrote a letter to Hurwitz inquiring whether such a post might be available, and apparently received a positive reply, but again nothing happened. By the end of 1900 he was unemployed. He did, however, publish his first research paper, on the forces acting between molecules. Soon thereafter, he attained Swiss citizenship, which he kept for the rest of his life, even after moving to the United States.