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  Throughout 1901, Albert kept trying to obtain a university position, writing letters, sending out copies of his paper, applying for any position that was open. No luck. In desperation he took a job as a temporary high-school teacher. To his surprise, he discovered that he enjoyed teaching; in addition, it left him ample spare time to continue his research into physics. He told his friend Marcel Grossmann that he was working on the theory of gases, and—once again—the motion of matter through the aether. He moved to another temporary teaching post in another school.

  Now Grossmann came to Albert’s rescue: Marcel’s father was persuaded to recommend Albert to the director of the Federal Patent Office in Bern. When the job was officially advertised, Einstein applied. He resigned from school teaching and moved to Bern early in 1902, although he had not yet been told officially that he had secured the post. Perhaps he had been assured of this informally, or perhaps he was just very confident. The appointment was made official in June 1902. It was not the academic position that he coveted, but it earned enough money—3500 Swiss francs a year—to provide food, clothes, and lodging. And it left enough time for physics.

  At ETH he had encountered a young student named Mileva Maric, who had a strong interest in science—and in Albert. They fell in love. Unfortunately, Pauline Einstein disliked her prospective daughter-in-law, and this caused ill feeling. Then Hermann developed terminal heart disease. On his deathbed the father finally agreed to allow Albert and Mileva to marry, but then he asked everyone in the family to leave him, so that he could die alone. Albert felt guilty for the rest of his life. He and Mileva were married in January 1903; their only son, Hans Albert, was born in May 1904.

  The patent office job suited Einstein, and he carried out his duties so effectively that toward the end of 1904 his job was made permanent—but his boss warned that further promotion would depend on Einstein coming to grips with machine technology. His physics advanced too, with work on statistical mechanics.

  All of which led up to the “golden year” of 1905, when the patent office clerk wrote a paper that eventually earned him the Nobel Prize. In the same year he obtained his PhD from the University of Zurich. He was also promoted to technical expert second class, with a raise of 1000 Swiss francs per year—it seems he had managed to master machine technology.

  Even after he became famous, Albert always gave credit to Grossmann for paving the way to the job at the patent office. It was this, more than anything else, said Einstein, that had made his work in physics possible. It had been a stroke of genius, the perfect job, and he never forgot that.

  In that most remarkable year in the history of physics, Einstein published three major research papers.

  One was on Brownian motion, the random movements of very tiny particles suspended in a fluid. This phenomenon is named after its discoverer, the botanist Robert Brown. In 1827, he was looking through his microscope at grains of pollen floating in water. Inside holes in the pollen he noticed even tinier particles jiggling about at random. The mathematics of this kind of motion was worked out by Thorvald Thiele in 1880, and independently by Louis Bachelier in 1900. Bachelier’s inspiration was not Brownian motion as such, but the equally random fluctuations of the stock market—the mathematics proved identical.

  The physical explanation was still up for grabs. Einstein, and independently the Polish scientist Marian Smoluchowski, realized that Brownian motion might be evidence for the then-unproved theory that matter was made of atoms, which combined to form molecules. According to the so-called “kinetic theory,” molecules in gases and liquids are constantly bouncing off each other, effectively moving at random. Einstein worked out enough of the mathematics of such a process to show that it matched the experimental observations of Brownian motion.

  The second paper was on the photoelectric effect. Alexandre Becquerel, Willoughby Smith, Heinrich Hertz, and several others had observed that certain types of metal produce an electric current when exposed to light. Einstein started from the quantum-mechanical proposal that light is composed of tiny particles. His calculations showed that this assumption gives a very good fit to the experimental data. It was one of the first strong pieces of evidence in favor of quantum theory.

  Either of these articles would have been a major breakthrough. But the third outclassed them all. It was on special relativity, the theory that went beyond Newton to revolutionize our views of space, time, and matter.

  Our everyday view of space is the same as Euclid’s and Newton’s. Space has three dimensions, three independent directions at right angles to each other like the corner of a building—north, east, and up. The structure of space is the same at all points, though the matter that occupies space may vary. Objects in space can be moved in different ways: they can be rotated, reflected as if in a mirror, or “translated”—slid sideways without rotating. More abstractly, we can think of these transformations being applied to space itself (a change of the “frame of reference”). The structure of space, and the physical laws that express that structure and operate within it, are symmetric under these transformations. That is, the laws of physics are the same in all locations and at all times.

  In a Newtonian view of physics, time forms another “dimension” that is independent of those of space. Time has a single dimension, and its symmetry transformations are simpler. It can be translated (add a fixed period of time to every observation) or reflected (run time in reverse—as a thought-experiment only). The physical laws do not depend on the starting date for your measurements, so they should be symmetric under translations of time. Most fundamental physical laws are also symmetric under time reversal, though not all, a fact that is rather mysterious.

  But when mathematicians and physicists started to think about the newly discovered laws of electricity and magnetism, the Newtonian view seemed not to fit. The transformations of space and time that left the laws unchanged were not the simple “motions” of translation, rotation, and reflection; moreover, those transformations could not be applied to space or time independently. If you made a change in space alone, the equations got messed up. You had to change time in a compensating way.

  To some extent this problem could be ignored, as long as the system under study was not moving. But the problem came to a head with the mathematics of a moving electric particle such as an electron—and this problem was central to the physics of the late nineteenth century. The associated worries about symmetry could no longer be ignored.

  In the years leading up to 1905, a number of physicists and mathematicians had been puzzling about this strange feature of Maxwell’s equations. If you performed an experiment involving electricity and magnetism in a laboratory or on a moving train, how should the results compare?

  Of course, few experimentalists work on moving trains, but they all work on a moving Earth. For many purposes, though, the Earth can be considered to be at rest, because the experimental apparatus moves along with it, so the motion makes no real difference. Newton’s laws of motion, for example, remain exactly the same in any “inertial” frame of reference, one that is moving with constant speed in a straight line. The Earth’s speed is fairly constant, but it spins on its axis and revolves around the Sun, so the motion relative to the Sun is not straight. Still, the path the apparatus follows is almost straight; whether the curvature matters depends on the experiment, and often it does not matter at all.

  No one would have been worried if Maxwell’s equations had to take a different form in a rotating frame. What they discovered was more disturbing: Maxwell’s equations took a different form in an inertial frame. Electromagnetism on a moving train is different from electromagnetism in a fixed laboratory, even when the train is traveling in a straight line at constant speed.

  There was a further complication: it is all very well to say that a train, or the Earth, is moving, but the concept of motion is relative. Mostly we don’t notice the movement of the Earth, for example. The Sun’s rising in the morning and setting in the evening is explaine
d by the Earth’s rotation. But we don’t feel the rotation, we deduce it.

  If you sit in a train and look out of the window, you may get the impression that you are fixed and the countryside is rushing past you. Someone standing in a field watching you go past observes the opposite: she is stationary and the train is moving. When we say that the Earth goes around the Sun rather than the Sun going around the Earth, we are making a subtle distinction, because either description is valid, depending on which frame of reference you choose. If the frame is carried along with the Sun, then the Earth moves relative to that frame and the Sun does not. But if the frame is carried along with the Earth, as the planet’s inhabitants are, then the Sun is the object that moves.

  So what was all the fuss about the heliocentric theory, which holds that the Earth orbits the Sun, not the other way around? Poor Giordano Bruno was burnt to death because he said that one description was correct while the Church preferred the other one. Did he die because of a misunderstanding?

  Not exactly. Bruno made a number of claims that the Church viewed as heresies—small matters like the nonexistence of God. His fate would have been much the same if he had never mentioned the heliocentric theory. But there is an important sense in which “the Earth goes around the Sun” is superior to “the Sun goes around the Earth.” The important difference is that the mathematical description of the planets’ movements relative to the Sun is much simpler than that of their movements relative to the Earth. An Earth-centered theory is possible but very complicated. Beauty is more significant than mere truth. Many points of view yield true descriptions of nature, but some provide more insight than others.

  Now, if all motion is relative, then nothing can be absolutely “at rest.” Newtonian mechanics is consistent with the next-simplest proposal: that all inertial frames are on the same footing. But that is not true of Maxwell’s equations.

  As the nineteenth century drew to a close, one further intriguing possibility also had to be considered. Since light was believed to be a wave traveling through the aether, then perhaps the aether was at rest. Instead of all motions being relative, some motions—those relative to the aether—might be absolute. But that still did not explain why Maxwell’s equations are not the same in all inertial frames.

  The common theme here is symmetry. Changing from one frame of reference to another is a symmetry operation on space-time. Inertial frames are about translational symmetries; rotating frames are about rotational symmetries. Saying that Newton’s laws are the same in any inertial frame is to say that those laws are symmetric under translations at uniform speed. For some reason, Maxwell’s equations do not have this property. That seems to suggest that some inertial frames are more inertial than others. And if any inertial frames are special, surely it should be those that are stationary relative to the aether.

  The upshot of these problems, then, was two questions, one physical, one mathematical. The physical one was, can motion relative to the aether be detected in experiments? The mathematical one was, what are the symmetries of Maxwell’s equations?

  The answer to the first was found by Albert Michelson, a US Navy officer who was taking leave to study physics under Helmholtz, and the chemist Edward Morley. They built a sensitive device to measure tiny discrepancies in the speed of light moving in different directions, and concluded that there were no discrepancies. Either the Earth was at rest relative to the aether—which made little sense given that it was circling the Sun—or there was no aether, and light did not obey the usual rules for relative motion.

  Einstein attacked the problem from the mathematical direction. He didn’t mention the Michelson–Morley experiment in his papers, though he later said he was aware of it and that it had influenced his thinking. Instead of appealing to experiments, he worked out some of the symmetries of Maxwell’s equations, which have a novel feature: they mix up space and time. (Einstein did not make the role of symmetry explicit, but it is not far below the surface.) One implication of these weird symmetries is that uniform motion relative to the aether—assuming that such a medium exists—cannot be observed.

  Einstein’s theory acquired the name “relativity,” because it made unexpected predictions about relative motion and electromagnetism.

  “Relativity” is a very bad name. It’s misleading because the most significant feature of Einstein’s theory is that some things are not relative. Specifically, the speed of light is absolute. If you shine a beam of light past an observer standing in a field, and another one standing in a moving train, both will measure the same speed.

  This is distinctly counterintuitive, and at first sight it seems absurd. The speed of light is roughly 186,000 miles per second. Clearly this is what the observer in the field should measure. What about the person on the train?

  Suppose the train is traveling at 50 mph. First, imagine that there is a second train on a parallel line, also traveling at 50 mph. You look out of the window and watch it go past. How fast does it seem to you to be moving?

  If it is traveling in the same direction that you are, then the answer is 0 mph. The second train will keep pace with yours, it will stay alongside it, and seem not to be moving relative to your train. If it is traveling the opposite way, then it will appear to flash past at 100 mph, because your train’s 50 mph is in effect added to the speed of the oncoming train.

  If you do the measurements with trains, that is what you find.

  Now replace the second train by a beam of light. The speed of light, converted to the appropriate units, is 670,616,629 miles per hour. If your train were moving away from the source of the light, you would expect to observe a speed of 670,616,629 - 50 = 670,616,579 mph, because the light would have to “catch up” with the train. On the other hand, if your train were moving toward the source of the light, then you would expect the speed of light relative to the train to be 670,616,629 + 50 = 670,616,679 mph, because the movement of the train would add to the apparent speed.

  According to Einstein, both of those numbers are wrong. What you will observe, in either case, is light traveling at 670,616,629 mph—exactly the same speed that the woman in the field observes.

  This sounds mad. If the Newtonian rules for relative motion work for another train, why don’t they work for light? Einstein’s answer is that laws of physics are different from Newton’s for objects that move very fast.

  More precisely, the laws of physics are different from Newton’s, period. But the difference only becomes apparent when objects are moving at speeds very close to the speed of light. At low speeds like 50 mph, Newton’s laws are such a good approximation to Einstein’s proposed replacements that you cannot notice any difference. But as speeds increase, discrepancies become large enough to be observed.

  The basic physical point is that the symmetries of the Maxwell equations not only preserve the equations; they preserve the speed of light. Indeed, the speed of light is built into the equations. So the speed of light must be absolute.

  It is ironic that this proposal should be called “relativity.” Einstein actually wanted to name it “Invariantentheorie”: invariant theory. But the name “relativity” stuck, and in any case there already existed an area of mathematics called invariant theory, so Einstein’s preferred name might have been confusing. Though not half as confusing as using “relativity” to describe the invariance of the speed of light in all inertial frames.

  The consequences of “relativity” are bizarre. The speed of light is a limiting speed. You can’t travel faster than light, and you can’t send messages faster than light. No Star Wars hyperdrives. Near the speed of light, lengths shrink, time slows to a crawl, and mass increases without limit. But—and here’s the wonderful thing—you don’t notice, because your measuring instruments also shrink, slow down (in the sense that time passes more slowly), or get heavier. This is why the observer in the field and the one on the train measure your light at the same speed despite their relative motion: the changes in length and time compensate exactly for t
he expected effects of the relative movement. This is why Michelson and Morley could not detect the Earth’s motion relative to the aether.

  When you are moving, everything looks the same to you as it did when you weren’t moving. The laws of physics cannot tell you whether you are moving or stationary. They can tell you whether you are accelerating, but not how fast you are going if your speed is constant.

  It may still seem weird, but experiments confirm the theory in exquisite detail. Another consequence is Einstein’s famous formula E = mc2, linking mass to energy, which indirectly led to the atomic bomb, though its role there is often exaggerated.

  Light is so familiar to us that we seldom think about how weird it is. It seems to weigh nothing, it penetrates everywhere, and its enables us to see. What is light? Electromagnetic waves. Waves in what? The space-time continuum, which is a fancy way of saying, “we don’t know.” Early in the twentieth century, the medium for the waves was thought to be the luminiferous aether. After Einstein, we understood one thing about that aether: it doesn’t exist. The waves are not in anything.

  Quantum mechanics, as we will see, went further. Not only are light waves not in anything: all things are waves. In place of a medium to support the waves—a fabric of space-time that ripples as the waves pass—the fabric itself is made of waves.

  Einstein was not the only person to notice that the symmetries of space-time, as revealed in Maxwell’s equations, are not the obvious Newtonian symmetries. In a Newtonian view, space and time are separate and different. Symmetries of the laws of physics are combinations of rigid motions of space and an independent shift in time. But as I mentioned, these transformations do not leave Maxwell’s equations invariant.