“dogmatic faith” in mechanics alone as the basis of the physical world, and now, in May 1905, this was the argument that led Einstein to wonder whether mechanics and electromagnetism together could accommodate a principle of relativity—whether a synthesis of those two systems might in fact be historically next.
He tried it. First Einstein proposed that just as Newton’s mechanics don’t allow observers either on a dock or on a ship to consider themselves to be the ones absolutely at rest, neither should electrodynamics and optics. “We shall raise this conjecture (whose content will hereafter be called ‘the principle of relativity’) to the status of a postulate,” he wrote in the second paragraph of his paper. Then he accepted the constancy of the speed of light in empty space as another given—a second postulate: that the speed of light in a vacuum is always the same “independent of the state of motion of the emitting body.”
And that was all. It worked. Einstein now had two mutually reinforcing postulates, “only apparently irreconcilable”: a principle of relativity, allowing us to conduct experiments involving light either on the ship or on the dock with equal validity; and a principle of constancy, allowing the ship (or the dock, for that matter) to approach the speed of light without any light onboard (or on the dock)—including electromagnetic waves bringing images from objects to our eyes—slowing to a stop and thereby revealing whether the ship (or dock) is the one “really” in motion. In which case, as Einstein promised his readers in that same second paragraph, the “introduction of a ‘light ether’ will prove to be superfluous, inasmuch as the view to be developed here will not require a ‘space at absolute rest’ endowed with special properties.”
The rest was math—high-school-level algebra, at that. Suppose that you’re standing on a dock watching our old Galilean ship, still anchored 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,
