Bohr and Einstein were already deep in conversation when they boarded one of Copenhagen’s trams. Although Bohr enjoyed a good quarrel, Einstein preferred to pass by fools in silence and rarely rebutted even published opinions. “I do not have to read the thing,” Einstein once said of a book that denigrated his role in creating relativity theory. “If he manages to convince others, that is their own affair.” So it was a mark of great admiration that Einstein was willing to talk endlessly with a man he disagreed with so deeply. Bohr was always looking for converts; Einstein was not.

What Einstein wanted was encouragement and new ways of thinking. “My friend and colleague M. Besso,” Einstein had written at the end of his first relativity paper, “steadfastly stood by me in my work on the problem discussed here, and I am indebted to him for several valuable suggestions.” Steadfastly stood by … that was the kind of thing Einstein appreciated, and when you look at the major people in Einstein’s life—Ehrenfest, von Laue, Lorentz, Planck, and Elsa, too—the quality they all shared was a steadfast support for Herr Professor Einstein.

Bohr was not that way, but Einstein appreciated the vigorous workout given his ideas whenever the two men talked. We naturally focus on imagination’s grand moments, the steps and insights that cre-

ate new things, but the long talking and wrestling was critical. Einstein told a friend it would be wrong to consider his great step in relativity “as a birthday, because earlier the arguments and building blocks were being prepared over a period of years, although without bringing about the fundamental decision.” For Einstein, the long tram talk with Bohr was not idle. He was always preparing his garden, always looking for the insight that would make sense of two contradictory ideas.

Bohr, too, disliked contradictions, although he was closer in spirit to Ernst Mach’s worries than to Einstein’s. Mach used to complain about the contradictions between the ways people talked about physics and about themselves. Bohr, too, wanted a unified way of talking about things, which is not quite the same as saying the things themselves are unified.

The contradiction that Einstein had once faced when he worked on relativity was as baffling as those that later plagued the quantum. The laws of motion were well established, but they contradicted demonstrated facts of electromagnetism. He had titled his relativity paper, “On the Electrodynamics of Moving Bodies,” indicating that it would be about the way electrical bodies moved. In 1905, when Einstein published that paper, the electron’s discovery was less than 10 years old, and questions about its movement were in the avant-garde of theoretical physics. The leading thinker on the subject in those days was Hendrik Lorentz, a Dutchman already past 50 and yet still the trail scout who found the clearest routes through the wilderness. In old age, Einstein often said relativity would have been impossible for him without Lorentz. Indeed, into the 1920s many physicists still referred to relativity as “Lorentz-Einstein theory.”

Bohr’s work also focused on how the electron moved. Bohr’s approach, however, saw quantum jumps as intrinsic to the story while relativity rejected the possibility of discontinuous changes that Bohr demanded. Even so, many physicists hoped to see the theories united. In 1916, Arnold Sommerfeld had shown that by including relativistic mathematics in Bohr’s theory he could solve certain puzzles that Bohr’s equation alone could not calculate.

Einstein never seemed much interested in Bohr’s side of electron movement. Although Einstein’s explanations could be very abstract,

the phenomena he started with tended to be remarkably straightforward. Bohr’s work assumed a particular kind of atomic structure and a particular explanation for the source of atomic spectra. Einstein preferred the kind of phenomena that a garage mechanic might notice. For instance, Einstein began his relativity paper with two objects, a magnet and an electrical conductor. They could be found in any commercial garage of that day or this and yet, when used together, they produce contradictory results. When motion produces an effect, physicists do not care what moves and what stays still. If you strike a match against a matchbox, you get a flame. Also, if you hold the match steady and rub the box against it, you still get a flame. If wind moves through a wind chime, you get a sound. Likewise, sound comes if the air is still and the wind chime sails through it. We would be startled if wind caused the chime to sound, but moving the chime caused it to glow. Yet conductors and magnets produce exactly this kind of surprise. If a magnet moves past a resting conductor, you get one effect. You get a different effect if the conductor moves and the magnet lies still.

The first effect is an electric field measured as energy. This energy field appears around a magnet if you move the magnet near a resting conductor.

The second effect, known as electromagnetic induction, produces an electromotive force, measured in volts. When a conductor moves past a resting magnet, this electromotive force (voltage) appears in the conductor and begins “pushing” electrons.

Both of these effects were well known before Einstein’s day. They were discovered and defined by two heroes of nineteenth century British physics, Michael Faraday and James Clerk Maxwell. Einstein’s father had been in the electrical equipment business, producing dynamos and other machines, so this matter of electrical fields and forces was old news in the Einstein home. But Einstein, unlike the majority of physicists, worried about this “asymmetry” in which one motion produced one effect while an equal and opposite motion produced a second effect. Turn-of-the-century physics could not account for such a contradiction.

Several times before in the history of science the theory of motion had needed enlarging. The ancient Greeks produced a notorious

error remembered as Zeno’s paradox that purported to show motion was impossible. To get from my bed to the doorway, the argument went, I first have to cover half the distance between the two points. Then half the distance again. Then half again … and so on forever. A person can never reach the goal because there is always another half distance to cross. It requires a certain temperamental attachment to reasoning before you can take this argument seriously, and most people probably dismiss it out of hand. Clearly, we do not really move in that half-again style. But the challenge is in coming up with some better account of motion. Where had Zeno gone wrong?

Zeno was philosophically attracted to the idea that the world is stable and all change is illusion. He used his paradox to “prove” that although the world seemed full of change and motion, it really stayed the same, and he felt content to keep the argument as it stood. It was a profoundly unscientific argument because it sought to deny the facts of experience. It did not look for a deeper truth that explained the facts, but instead required a faith in logic so strong that a person would accept it instead of everyday experience. A physicist like Einstein would never be content to simply defy the facts, but as a believer in logic, Einstein also would have refused to brush Zeno’s reasoning aside.

To overcome Zeno you will get nowhere by looking for a flaw in the logic he used. In these days of moving film we know full well that motion can be broken down into an infinite number of steps. There is no theoretical limit to the number of movie frames we could use in capturing the motion from bed to doorway. Instead of looking for a logical error, the solution was to find a deeper idea that Zeno had left out. At first glance, movement may seem to be merely a change in position. A second look, however, shows that Zeno overlooks part of the story. Motion involves both a change in position and a change in time. Zeno’s argument, Einstein would have said, was not illogical, it was incomplete.

True, I could go halfway between bed and doorway and stop so that no further change in location occurred, but I cannot stop time’s winged chariot. Take another look at that movie reel. Each frame shows a snippet of motion through space, but any two frames show a span of time. Zeno might have cried, wait, time is an illusion too. Before

you can have a second, you need half a second and then before you can have the last half second you need a quarter second … and so boringly on. But now we have caught Zeno in his error. He insists on separation instead of unity, on arguing only about space or only about time when we know that motion concerns both space and time changing together. No matter how short a space we consider, there is always a speck of time changing as well, so that even if we are down to tracing a millionth of an inch, we still have the change in a millionth of a second (or whatever) giving us a rate of change. If the rate is kept up, the traveler will arrive at its destination. Zeno might have overlooked the point, but Archimedes knew it well enough. Movement is measured by distance and time. The phrase “60 miles per hour” brings space and time into a single concept. The point had been settled before the Christian era began.

The Copernican theory of a moving earth forced some still-deeper thinking about movement. If the earth is really spinning at a speed measured at the equator of about 1,000 miles per hour, my ability to drop a ball on my foot becomes a puzzle. Let’s say I hold a ball about 5 feet above my toe and drop it. It takes perhaps a quarter of a second for it to land. During that time the earth rotates about 367 feet, yet the ball still hits my toe. Why doesn’t it miss? Many people today secretly wonder about this sort of thing. When I ride in an airplane going hundreds of miles per hour, why doesn’t the back of the plane swat anything thrown in the air?

Galileo solved this one by adding what we can call relative systems to our idea of motion. Einstein called them coordinate systems and many physicists call them inertial systems. The name does not matter so much, but the point is crucial. Motion can appear differently to different observers, depending on whether they share the same relative system. Galileo showed what he meant by using a ship as an example; we can do the same, modernizing the armada.

Suppose some sailors play baseball on the deck of an aircraft carrier. The pitcher throws the ball. Behind the catcher is a baseball scout with a radar gun that measures the ball’s speed at 80 miles per hour. It happens, however, that the carrier is passing a lighthouse where another fellow with a radar gun measures the same pitch and gets 100

miles per hour. The extra 20 miles per hour was added by the carrier, which is cruising at that speed.

The players and scout aboard the carrier are together in the same relative system. They are all at rest relative to one another. For them, things move as though the ship really were at rest. The same principle applies to a rotating earth and flying airplanes. I don’t miss my toe because both my hand and foot share the same relative system. I don’t have to take my foot’s motion into account when I drop the ball because, as far as I am concerned, my foot is not moving. Likewise, the back of the plane and my seat share a relative system. If I toss a magazine to a person across the aisle, I need not worry about the way the back of the plane is moving because, from my perspective, it is not moving.

Getting back to shipboard baseball: the fellow in the lighthouse does not share a relative system with the aircraft carrier, so he measures the effect of the ship’s motion on the ball. Likewise, an observer in a spacecraft watching me drop a ball onto my toe would see the ball arc 5 feet to the ground while flying more than 100 yards eastward along with the spinning earth.

Linking time to motion has an intuitive feel to it, making Zeno seem a little silly for having forgotten it, but Galileo’s relative motion does not harmonize so readily with our psychology. We don’t see ourselves as perpetually at rest. Even Einstein and Bohr, talking eagerly, paying no attention to the city outside the window, perceived (if only they had looked) the tram as moving through Copenhagen and not vice-versa. Nevertheless, physics in Galileo’s day divorced psychology and made it an established principle that uniform motion is always relative. Something is moving, but whether it is one thing or the other is just an arbitrary choice. But Einstein had noticed a simple motion involving magnets and conductors that seemed absolute. You get different accounts of what happens depending on what you view as being at rest.

Einstein’s instinct was to deny that this contradiction could be correct. He needed a rule that overcame electromagnetic logic, so he asserted what he ever after referred to as the “relativity principle.” According to this notion, “the same laws of electrodynamics and op-

tics will be valid” in all relative systems where Newton’s laws of motion are valid. The principle was not a theory or hypothesis so much as it was a prayer. If science was to work, its laws have to be the same in every relative system. Otherwise behavior will appear random. Suppose, for example, a scientist conducts an experiment in a relative system where a conductor seems to move past a magnet, but “really” the magnet is moving past the conductor. This scientist will see that when the conductor moves, an electric field appears around the magnet, and the scientist will develop electromagnetic laws that are exactly the opposite from those found by earthling scientists.

On his walks through Bern and evenings chatting with Besso, Einstein worried for years about such differences and the problem of making Newton’s mechanical rules fit together with the laws of electromagnetism. The persistence of his wonder suggests that either he was a young man of astonishing faith in nature’s lawfulness, or he was a crazy man unable to stop charging windmills of his own invention. Possibly right from the beginning, Einstein had guessed the solution—electromotive forces are really just electromagnetic fields with a 0 energy measure—but like Detective Columbo, who always guessed the culprit at the beginning of his investigation, he still had to prove it.

In Copenhagen, crossing the tracks, Bohr and Einstein waited for a return ride. Fifty years earlier it would have seemed impossible that the world’s leading physicists would still be disputing the nature of light. The matter had appeared settled in 1873 when Maxwell joined electricity, magnetism, and light into one unified phenomenon—as decisive an achievement as uniting distance and time. It had seemed then that centuries of dispute about light had been resolved.

Galileo had raised the question of whether the arrival of a flash of light is “instantaneous or whether, although extremely rapid, it still occupies time.” He even proposed experiments to measure the speed of light. Not until the nineteenth century, however, could machines be made precise enough to allow the experiments. The research had es-

tablished that light travel does take time, but the same work led to some other questions. In particular physicists wondered why light’s relative speed was not as easy to detect as relative motions on a ship deck. A Frenchman named Armand Fizeau measured the speed of light in water and found that the expected equations for relative speed were not as straightforward as those for a ball thrown on a ship’s deck. Two Americans, Albert Michelson and Edward Morley, conducted very precise measurements that showed no change in speed relative to the ether that carried the light wave. Experiments like these were complex and subject to interpretation, but the results were plainly not the simple ones expected.

Einstein, when he was 16, had also recognized something odd. He had imagined what it would be like to travel at the speed of light while chasing after a light beam. When two streetcars travel side by side at the same speed, they become part of the same relative system and don’t appear to move at all. The passengers in separate cars can talk with each other or even play catch if they have a mind to, exactly as though the trams were resting side by side in a railway yard. In his mind’s eye, Einstein saw what a motionless beam of light would look like when viewed that way, but he realized that no such thing as standing light ever turns up in nature. There were no experiments where light could be brought to a standstill. Furthermore, Maxwell’s equations would not work if the speed of light were equal to zero.

That imaginary ride appears to have been the first time Einstein began chasing after a serious split between logic and nature’s laws. It marked the birth of his lifelong technique; find the point where two sets of ideas rub against one another and then discover what the existing theory leaves out. When Einstein and Besso talked together, Einstein was looking for a way to unite electromagnetic and mechanical motion, just as, 20 years later, riding back and forth through Copenhagen with Niels Bohr, he was looking for a way to unite waves and particles, or gravity and electromagnetism.

Bohr, for his part, was still resisting the photon, despite the Compton effect, because it was going to force disunity on physics. Light would not be one thing or its opposite; it would become one thing and its opposite. Mach had worried that people talked one way

when they discussed physics and another when talking about anything else. Now Bohr feared people would be forced to talk about physics one way, and then, without even changing the subject, talk in another way. The solution, Einstein felt, was to find out what light really is. Bohr thought the solution was to find a coherent way of talking about light.

Most other physicists were not so single-minded about how an explanation should work. Their approach was professional, grabbing what worked and letting the philosophical side of the question look after itself. The generation of physicists before Einstein did well with that professional approach. They had to resolve the mystery of the electromagnetic fields that are inherent in Maxwell’s equations. Most physicists had a hard time grasping the idea of a physical field, a region of empty space that somehow produces effects. It was Lorentz who clarified the concept by stressing two realities—electrons and the ether. Electrons were theoretical atoms of electricity that carried an electric charge. They existed in Lorentz’s theory years before the English physicist, J.J. Thomson showed them to be fact. Equally important to Lorentz was the ether that supported light. The ether had no normal physical properties and was difficult to detect, but it permeated everything. “Empty space” really did not exist. Every point contained the ether. Furthermore, the ether provided a way to see beyond relative motions to absolute movement. Ships move one way, planets go another, but the ether is not moving anywhere. Motion relative to the ether is true motion because it is relative to the whole universe.

For Lorentz, therefore, the Michelson and Morley experiments that failed to find an ether were a serious problem. He saved his theory by proposing that movements against the ether force objects to contract. The molecules literally press together. Normally these contractions would go unobserved because everything, including measuring sticks, contract at the same rate. They became apparent only when measuring the speed of light because the contractions eliminated the relativistic velocities of light, creating the illusion that light moves at the same speed regardless of relative systems. Lorentz also produced a set of equations that compared the sizes of normal and contracted objects, publishing them in final form in 1904.

This work by Lorentz led some to deny that Einstein discovered

relativity. Iconoclasts, anti-Semites, and congenital contrarians are always “discovering” Lorentz’s theory. Many years later, Serbian nationalists would even argue that Einstein’s first wife was the real genius behind relativity and that Einstein had simply appropriated her labor. Contemporary historians and biographers know they can get into trouble by dismissing charges against their main figures. The scholars who devoted their careers to studying Thomas Jefferson look foolish for having rejected out of hand the claims that their man used one or more of his slaves sexually. An example like that can frighten other writers into hesitant “balance,” making wishy-washy stands: Well, of course there is no clear proof in Mileva’s favor, but neither is there a smoking gun against her. You cannot go wrong that way. Except there is a smoking gun. It is the style of Einstein’s thought.

Einstein was, his whole life through, obsessed with ironing the logical contradictions out of physics, especially the contradictions related to electromagnetics and particle mechanics. Mileva had no such obsession. The issues Einstein tackled in 1905 recurred in 1907 and in 1909 and in 1915, 1916, 1923, and on and on. They were part of his fabric. By contrast, if Einstein had, in 1904, somehow produced the Lorentz paper, we would know something was wrong. Even though Lorentz’s math is very similar to Einstein’s work in 1905, its reasoning was most unEinsteinian. Yes, the Lorentz theory was visualizable and Einstein liked visualizability. Lorentz’s ether forced molecules closer just the way a hand squeezes together the holes in a sponge. The contractions were fully predictable in a mathematically precise way. They were also absolute. Lorentz’s equations predicted contractions along all three dimensions as they would appear from the ether’s objective viewpoint. One thing, however, became unknowable, unvisualizable. That was the ether itself. Its effects were clear, its importance undeniable, but movement through the ether became in principle beyond all measuring. Movement relative to the ether forced a contraction in the very devices needed to discover these movements. The ether became like one of God’s angels, acting everywhere while discoverable nowhere. Einstein never liked angels, and if they had ever turned up in one of his theories, we would wonder whose influence we were seeing.

Lorentz’s work was typical of a professional scientist. He had a

theory. Experiments raised difficulties with a critical part of the theory. He revised his idea to resolve the problem and save the theory, but Lorentz had paid no attention to the issues that haunted Einstein. Lorentz’s new equations did not address the contradictions between electromagnetism and ordinary motion, and there was still the business of Einstein’s personal vision of the impossible light-beam-at-rest.

Einstein, in thinking endlessly about these puzzles came to a guiding assumption, one that he set right up there with his relativity principle: “light always propagates in empty space with a distinct velocity that is independent of the state of the motion of the emitting body.” It is amusing to remember how many street philosophers say that Einstein proved everything is relative when his guiding axioms assert absolutes. The relativity principles asserts that the laws of physics are absolute and do not change as one travels from one relative system to another. The second axiom holds that the speed of light is unchanging whether the light is coming from a speeding ship or a standing lighthouse.

It was a bold idea, but not entirely new. In 1904, Henri Poincaré told an audience in St. Louis that physics needed “an entirely new kind of dynamics which will be characterized above all by the rule that no velocity can exceed the velocity of light.”

Although in the spring of 1905, as Einstein chattered with Besso, Lorentz’s rules and Poincaré’s speed limit had already appeared, Einstein, stuck in Bern, Switzerland, with no decent physics library on hand, knew nothing of those things. Even if he had known he would not have been satisfied. It is not enough to assert that the speed of light is a fixed limit on how fast anything can move; you have to explain how such a rule can make sense. Absolute speed leads to mathematical contradictions. There are good reasons for finding different speeds in different relative systems. If you measure the distance from pitcher to home plate in our aircraft-carrier ballgame, you find 60 feet 6 inches. The speed of the ball equals the distance traveled to reach home plate divided by the 0.52 seconds required for the ball to arrive at home

plate. Viewed from a lighthouse, however, the ball travels 75.6 feet—the 60.5 feet to the home plate plus the 15.1 feet that the ship covers while the ball is in flight. It doesn’t take too many math skills to see that 60.5 feet divided by 0.52 seconds gives us a different number from 75.6 feet divided by 0.52 seconds. So how can any speed, even a very high one, ever be absolute? Problems like this made Einstein suspect the absolute speed of light was untenable and that he would have to drop it.

Lorentz, of course, had seen the problem and had found a solution, or at least he had found what today’s computer programmers call a “workaround.” Along with the three equations that showed how objects seemed to change size, Lorentz had a fourth that showed how time seemed to change too. He called these distortions local time to distinguish them from true time, but Einstein was never interested in workarounds because they obscure the real meaning of things. Historians who like to play what if games can entertain themselves by asking what would have happened if Einstein had been buried in an avalanche during one of his schoolday jaunts up into the Alps. Lorentz had developed a coherent mathematics that produced correct answers for movements involving the speed of light. How long would it have been before somebody bothered to rethink the matter? Would Lorentz’s ether have become as embedded into twentieth-century physics as the crystalline spheres had been in medieval astronomy?

As it was, Einstein was still very much alive, still wracking his brains, and still ignorant of Lorentz’s 1904 publication. One afternoon he poured out the whole of his troubles to Besso. They went over the paradoxes and contradictions between effects and principles. With it all stretched out before him Einstein at last took his great step. Snap, the relativity principle will hold if time tick-tocks differently for different observers. Snap, the speed of light can be the same in all equations if the pace of time varies between relative systems. Einstein’s step was the realization that the pace of time is as relative as distance. If one observer sees light travel 10,000 feet and another sees it travel 12,500 feet, the only way 10,000 feet per unit of time and 12,500 feet per unit of time can equal the same rate is if the times are different for the two observers. Mathematically it may seem obvious that the time part

of the fraction must change if you need to calculate the same speed for changing distances, but physically the step took enormous imagination because we have always believed that time is absolute. Just as shipboard and lighthouse surveyors will measure different distances for the same flying ball, so too, timekeepers in different relative systems will measure different times. The distance between events depends on relative systems. The time between events also depends on relative systems.

With the realization that time is as relative as distance, Einstein stepped beyond Lorentz. Lorentz understood what had happened to him and admitted that the source of his “failure” to discover relativity, despite the years of work, had been his “clinging to the idea” of a true time and his thinking that local time was not real. Poincaré had missed it for the same reason, thinking there was one true time throughout the universe. Now Einstein’s step was really carrying him toward the invisible face that hid behind the moving compass.

Still in Copenhagen, Bohr and Einstein again made their way across the tracks and again began to wait for another tram. The fact that they were having trouble reaching their destination was no mark against their achievements. From the beginning, a few physicists had recognized in Einstein’s relativity paper the work of a new Copernicus. The original Copernicus, too, had defied one of the most universal experiences. The sun can be seen rising and setting every day. Even very bright, very imaginative people responded to Copernicus by demanding to know just how it could be that the sun really stands still and that its motion is a relativistic illusion. Our experience of time is similar. Time flies but keeps to a faithful schedule. It was and is hard to grasp how that steadiness could be just another relativistic illusion. Very few people can abandon their belief in true time. The fact that the watch on my arm runs slow does not persuade me that my time is just as good as anybody else’s.

Newton would have said that God knows which time is true.

No, Einstein would have replied, God knows which equations are true. The measurements are transitory and local; the relationships enduring and universal.

So I was right about change being illusory after all, Zeno might have chimed in, allowing Newton and Einstein to join forces and hurl sticks at the ancient Greek.

Einstein was thrilled with his step and the next day said to Besso, “Thank you, I’ve completely solved the problem.” The two concepts—laws of electrodynamics hold true in all relative systems, and the speed of light is absolute—now formed an arch strong enough to support a multitude of shifting facts. Einstein spent the next five weeks in a frenzy of labor, putting the whole theory down on paper. When he was done, he collapsed. He spent the next two weeks in bed while Mileva checked his article closely before telling him, “It’s a very beautiful piece of work.”

Much of his effort during those five intense weeks had been mathematical, deriving equations that expressed time’s relativity. He produced the same four equations that Lorentz had published the year before, but in Einstein’s paper their meaning was quite different. Lorentz’s equations predicted how objects would contract along their direction of motion; Einstein’s told how anything measurable in one relative system would appear to another relative system. Mechanical contraction played no role in Einstein’s theory.

Lorentz’s theory was dynamic, using the ether to squeeze molecules. Einstein’s theory was mathematical, describing what happens but including no angels to make it happen. Lorentz’s theory made the universe more complicated; Einstein’s made it simpler.

Einstein’s simplicity clarified what he meant by reality. Ultimately, the face of truth was natural law, the description of nature’s givens and how their relationships make the world appear to its observers. The appearances themselves—say, the speed of a baseball—might vary, depending on local circumstances, but the phenomenon is real. After all, the distance between the baseball and the pitcher does change and no observer will deny that fact, but the appearance’s measurable details are relative.

The purely qualitative part of the phenomenon remains a given. If

the batter gets a hit, it remains true for all observers. We can imagine a broadcaster moving relative to a pitch in such a way that the ball appears to have been traveling at 125 miles per hour. “Wow!” shrieks the announcer, “How can a batter be so quick?” Meanwhile, another broadcaster in a different observation perch might say, “Well, of course, he hit that ball. The radar gun shows it was only going 35 miles an hour.” The measurable parts of the event are relative, facts that change with circumstances, but the collision of bat and ball is one of the givens of existence.

Relative natures are not trivial. If a baseball passes my head at 125 m.p.h., it will sound and look different from one going 35 m.p.h., yet these differences depend entirely on local circumstances. Many things that people have taken to be absolutely real turn out to be such dependent phenomena. The wind we feel when we poke our hand out a moving car’s window is another example of a dependent phenomenon. It is so real that even dogs love putting their heads out of car windows to feel the wind bat their faces, but this sensuous wind is obviously created by the moving car. Its properties come from circumstances, not from nature itself. The earth is turning even more rapidly, yet because the atmosphere turns with the earth we do not feel that breeze. The highway’s air, however, does not move with the car and seems to fly past us. If the air were moving along with the car, the wind would fade, even disappear.

A car passing a pedestrian at 60 m.p.h. has a special sound, a kind of quick rising thud that fades just as quickly, and there is a brief wind blast as well. When that same car passes another automobile, one doing 55 m.p.h., the sound is different and the wind is different. None of these sounds or winds is an illusion, but we make a serious error about the physics of the case if we treat such dependent phenomena as the independent givens of reality.

The fact that striking effects can depend entirely on their relative systems finally explained Einstein’s paradox of magnets and conductors. As he had guessed, the electromotive force that appears when a conductor moves through a magnetic field is a secondary phenomenon. When you solve the electromagnetic equations for different relative systems, you discover that an electromagnetic field around the

magnet has no strength when a magnet appears at rest and the conductor appears to move past it. That is not to say voltage is not real. It is as real as the wind your dog loves to enjoy, but it depends on appearances. Every scientist in any lab in the universe will find the same law at work. If a magnet appears to move, the magnetic field appears as well.

“What kept you,” Margrethe Bohr might have asked when the two geniuses finally arrived at the Bohr home. Possibly they explained their delay, or possibly they just laughed, their approaches to explanation being so contradictory.