The Invisible Century: Einstein, Freud and the Search for Hidden Universes. Richard Panek
just offshore after all these centuries. And suppose that the ship is absolutely motionless in the water. And suppose that instead of dropping a stone, someone on board is dropping a light signal—sending a beam of light from the top of the mast to the deck. If you time this simple event and get an answer of, say, one second, then you know that the distance between the top of the mast and the deck must be the distance that light travels in one second, or 186,282 miles. (It’s a big ship.)
The complications begin, just as they did in Galileo’s day, once that ship lifts anchor and sets sail. Suppose that it’s moving at a constant speed across your line of sight. If the person at the top of the mast sends a second light signal in the same manner as the first, what will you see from your vantage on the dock? The Aristotelian answer: a streak of light heading straight for the center of the Earth and therefore landing some distance behind the base of the mast—a distance corresponding to how far the ship has traveled along the water during the signal’s journey. The Galilean answer: a streak of light heading straight for the base of the mast—which is the Einsteinian answer as well. From your point of view, the base of the mast will have moved out from under the top of the mast during the descent of the beam of light, just as it did during the descent of a stone. Which means the distance the light has traveled, from your point of view, has lengthened. It’s not 186,282 miles. It’s more.
How much more you can easily find out by measuring the time of its journey—and that’s where the Einsteinian interpretation begins to depart from the Galilean. What is velocity? Nothing but distance divided by time, whether inches divided by—or, in the vernacular, per—day or kilometers per hour or miles per second. But if we accept Einstein’s second postulate, then the velocity in question isn’t just 186,282 miles per second. It’s always 186,282 miles per second. It’s constant—indeed, a constant. In the equation “velocity equals distance divided by time,” this constant is over on one side of the equals sign, off by itself, humming along at its own imperturbable rate. On the opposite side of the equals sign are the parts of the equation that can vary, that are indeed the variables—distance and time, also known as miles and seconds. They can undergo as many permutations as you can imagine, as long as they continue to divide in such a way that the result is 186,282 miles per second, or the equivalent—372,564 miles per two seconds, or 558,846 miles per three seconds, or 1,862,820 per ten seconds, and so on. Change the distance, and you have to change the time.
You have to change the time.
For more than two centuries, though, you didn’t. Now, on an evening in May 1905, you suddenly did, because on that evening Einstein, having talked the problem through with his friend Besso, realized that he needed to take into account something he’d never before adequately considered: the “inseparable connection between time and the signal velocity.” Time was a variable, a measurement that passed at different rates according to where you were. To an observer on the dock, the second light signal would had to have lasted longer than one second. To an observer on the ship, however, the second light signal would have appeared to do what the first one had done, back when the ship was anchored in the water: travel straight down to the base of the mast, 186,282 miles away. For this observer, the distance wouldn’t have differed from one signal to the next, so the time wouldn’t have, either. The shipboard observer would be measuring one second while you on the dock would have been counting two seconds or three seconds or more, depending on the speed of the ship along the water. For this reason, you would have every right to say that clocks on board the ship were moving slowly. And there it is: a new principle of relativity.
Of course, such an effect wouldn’t become noticeable unless the ship were moving at a significant fraction of the speed of light. At more modest speeds, the Galilean interpretation holds to a high degree of accuracy; as Einstein later wrote, “it supplies us with the actual motion of the heavenly bodies with a delicacy of detail little short of wonderful.” Still, according to Einstein’s math, as long as a ship is in motion at all, the distance the light travels on its angular path would have to be greater than the simple perpendicular drop you would see when the ship is at rest relative to you, and therefore the time to cover that distance would have to be greater, too. Through similar reasoning, Einstein also established that for an observer in a relative state of rest, back on the dock, the measurement of the length of a rod aboard a moving ship would have to shorten in the direction of motion, and to grow shorter the faster the ship is moving relative to the dock. And vice versa: Someone on the supposedly moving ship would have every right to consider that system to be the one at rest, and you and your so-called resting system to be the one whose dimensions would also appear to have shortened, and whose time would also appear to have slowed.
So which observer would be “right”? The observer on the ship, or you on the dock? The answer: Both—or, maybe more accurately, either, depending on who’s doing the measuring. But how much time passed really? How long is the rod really? The answer: There is no “really”—no absolute space, no ether, against which to measure the motions of all matter in the universe. There is only the relative motions of the two systems.
“For the rest of my life I want to reflect on what light is,” Einstein once said. If Einstein were correct, the universe wasn’t quite a clockwork mechanism; it didn’t function only according to the visible motions of matter. Instead it was electromagnetic, operating according to heretofore hidden principles. On a fundamental level, it was less a pocket watch than a compass.
Not that this new understanding of the universe was complete. Einstein knew that all he’d done was take into account the measurements of objects moving at uniform, or nonvarying, velocities relative to one another—a highly specialized situation. He hadn’t yet taken into account the measurements of objects moving at nonuniform, or varying, velocities relative to one another—a far more representative sampling of the universe as we know it.
Still, it was a start. In a way, Einstein’s light-centered universe was as physically distinct from the Galilean one he’d inherited as Galileo’s sun-centered universe was from the Aristotelian one he’d inherited. But like Galileo, Einstein knew his had to be true—or truer than the one it was replacing, anyway—because he had seen the evidence for himself, if only in his mind’s eye.
Listen.
And so the boy listened. His father had something to tell him. Hand in hand, they were going for a walk during which, in the manner they’d recently adopted, the father would attempt to impart to his son some lesson about life. On this occasion, the story concerned an incident that had happened to the father years earlier, on the streets of the city of Freiberg, the boy’s birthplace. The father, then a young man, had been walking along minding his own business when a stranger came up to him and in one swift motion knocked his new fur hat off his head, called him a Jew, and told him to get off the pavement. The boy dutifully listened to his father describe this scene, and he had to wonder: So what did you do? His father answered quietly that he had simply stepped into the roadway and picked up his cap. The boy and his father then walked along in silence. The boy was considering this answer. He knew his father was trying to tell him something about how times had changed and how the treatment of Jews was better today. But that’s not what the boy was thinking. Some three decades later, when Sigmund Freud recalled this scene, he couldn’t remember whether he had been ten or twelve at the time, but the impression he’d taken away from that encounter he could still summon and summarize drily: “This struck me as unheroic conduct on the part of the big, strong man who was holding the little boy by the hand.”
An impression, anyway. By the time Freud was committing this memory to paper, he was beginning to understand that any interpretation of the encounter on that long-ago day depended as much on what the boy had wanted to hear as on what the man had been trying to say, or even on what he, by now a father several times over, wished to believe about his father or himself, or about fathers and sons—depended, that is, on the vagaries of the human thought process. Not necessarily because of that conversation with his father