Like Poincaré, Einstein decided that the only way out is by “convention.”28 Einstein argued that the equality of the speeds of light in opposite directions is “a stipulation which I can make of my own free will in order to arrive at a definition of simultaneity.”29 He also decided that the speed of light is the same in opposite directions essentially as a matter of “definition.”30
In March 1905 Einstein had been reading the Treatise on Human Nature (1739–1740) by the Scottish philosopher David Hume.31 Hume argued that even basic physical notions, like the notion of cause and effect, involve certain assumptions.32 In no case do we really know whether one thing is the cause of something else, we only know that the two occur in a regular sequence. That is, when we believe that x is the cause of y, it is mainly a matter of habit. While studying these ideas, Einstein concluded: “All concepts, even those which are closest to experience, are from the point of view of logic freely chosen conventions.”33
Thus Einstein posited that the speed of all light rays is equal and constant—that the time it takes light to travel from A to B is the same as it takes to travel from B to A—as a fundamental assumption. By contrast, some books simply claim that the constancy of the speed of light is “an experimental fact.”34 But they give no evidence about how the speed of light rays traveling in opposite directions can be measured and compared. Contrary to the myth that the postulates of special relativity are experimental facts, a very few good books do note the essential difference between the velocity of a light ray and the average round-trip speed of light.35
Einstein also considered the question of simultaneity. To understand the synchrony of clocks, we need to have some way to verify whether any two events happen at once. The morning after his conversation with Besso, it occurred to Einstein, just as he was getting out of bed, that events that are simultaneous to one observer might not be simultaneous to another moving relative to the first.36 To explain this notion, Einstein envisioned an imaginary experiment with a train.37 Suppose that lightning strikes at two distant places on a railroad track. How can we decide whether these two events are simultaneous? Einstein argued that you should stand at the midpoint between the two events, holding an angled mirror to reflect light to you from both directions. So, suppose you see both light flashes at the same time. Then you say: the two lightning bolts were simultaneous events.
But consider now a train that, in the meantime, travels along the railroad tracks. Now, when lightning strikes, it burns marks on the train. So there can be no doubt regarding where on the train the lightning struck. And there are people sitting inside all the train cars, so we seek and find the one passenger who happened to be sitting exactly midway between the two burnt marks, and we ask: Did you see the lightning strokes?
“Yes.”
“Did they happen at the same time?”
And the passenger replies: “No, the lightning on the front struck first, clearly.”
We might argue: “The lightning strokes happened at the same time; the reason why you on the train saw one of them first is just because you were moving forward along its direction.”
But then the passenger objects: “I wasn't moving at all, I was just sitting here.”
We reply: No, you were moving, the entire train was moving.
The passenger might insist: “No it wasn't, I didn't feel it to be moving at all. I had a cup of hot coffee in my hand. And actually, what I saw was that all the trees and the guy outside were moving.”
Maybe we smile and reply that that was just an illusion, really, that the trees weren't moving at all.
But then the passenger might continue: “How do you know? I say they were moving because the entire planet is moving, just like you say I was moving because of the train.”
For Einstein, it didn't matter at all that the train is smaller than Earth. Both observers applied the same method to determine simultaneity. Yet they obtained different results. Einstein says both are right. Simultaneity is relative.
Einstein argued that the usual notion of simultaneity is a prejudice. We usually think that if events are simultaneous, then they are simultaneous for everyone. Einstein reasoned that that is just an assumption, that there is no evidence for it. For one observer, A happens before B; for another observer, A happens after B; and for another, they happen at the same time. Einstein said that they're all right, so long as they each applied the same procedure to determine simultaneity.
This relativity business is not entirely arbitrary; there should be actual visual evidence to correspond with it. Suppose that each door on either end of a train car is rigged to open automatically at the very instant when light hits it, and that the car is moving quickly when a lightbulb inside, at its center, gets turned on. We're outside, and suppose we see that the rear door opens first. We reason that the rear door opened first because it raced to meet the light, while the front door moved away. An important point is that this would be empirical data: we saw the rear door open first; it's not an opinion.
But what about someone inside the train car? According to the assumption that the speed of light is equal in opposite directions, a passenger expects that light should reach both doors at the same time, making the respective mechanisms open each door. We expect that a person standing in the car, midway between the two doors, should actually see both doors open at once.
But how can that happen, since we, standing outside, actually saw that the rear door opened first? Well, suppose that the train car is moving to the right, so that light takes less time to reach one door than the other, as it seems to us, standing outside. We say that the rear door opened first. But for the passenger inside the car, the only way to know whether a door opens is by seeing it. Light needs to travel from the door to the passenger. So, if the rear door opened first, light has to travel back to the observer at the center. But the observer is moving with the car. Both light rays will return to the middle observer at the same time. It doesn't matter whether one door opened first; he will literally see that both doors opened simultaneously. He will judge that the outside observers, us, see that the rear door opens first only because we are moving to the rear.38
So who's right, the person inside or outside? Both, says Einstein. That's the relativity of simultaneity. Events that are simultaneous for one observer are not necessarily simultaneous for another moving relative to the first.
The relativity of simultaneity has some bizarre consequences. Consider one example. We see that a ruler is twelve inches long. But what's the length of that ruler when it's moving? We might say that its length is the same. But unless we establish and carry out some procedure for actually measuring its length, the claim that it is still twelve inches long is just an assumption. So how do we measure a moving body? One way is to project a flash of light to cast its shadow on photographic film. Another way is to shoot a series of inkjets toward the ruler, such that they outline its shape on a backboard.
The result of this process, we expect, would be that the outline or shadow has the same length as the ruler. We then measure the length of that shadow and call it “the length of the ruler.”
But suppose the ink jets to the right were shot first, and the rest in a sequence. Then the resulting shadow will be shorter.
Thus, the length of the shadow depends on whether all the ink jets are fired simultaneously. But how can we fire them simultaneously? If one procedure satisfies us, then that procedure might not satisfy an observer moving relative to us. Since we disagreed about the simultaneity of distant events, the moving observer would say that the inkjets were not emitted simultaneously, and will conclude that our measurement is wrong.
Lengths depend on simultaneity; if we disagree about simultaneity, we'll disagree about the lengths of moving objects. Furthermore, if we disagree about lengths, we'll disagree about volumes. If we disagree about volumes, we'll disagree about density. Plus, if we disagree about simultaneity, we'll disagree about time intervals. When we disagree about time intervals, we'll disagree about a
ccelerations. Moving observers disagree about forces, energy, mass, and so on. That's why Einstein formulated a so-called theory of relativity, to interrelate systematically how various physical quantities compare and vary among reference systems.
Einstein established that measurements should depend on the postulates of relativity and the constancy of the speed of light. To derive the equations of his theory, the so-called Pythagorean theorem is useful. Consider just one example, the relativity of durations, or time intervals. Suppose that a light ray is emitted from the ceiling of a train car straight to the floor, and let us call its vertical speed c' (we call it “c prime” because we have not yet assumed that it is equal to the speed of light outside the train). If t' is the time interval it takes to go from the ceiling to the floor as determined by clocks inside the train car, then it covers a vertical distance c't'. But meanwhile, from the embankment outside, the train is seen to move forward at a speed v, measured by clocks on the ground, and from the instant when the light ray is emitted downward, the train covers a distance vt, as measured by those clocks on the ground. Then, to observers standing on the embankment, the ray did not just travel downward, it traveled diagonally forward and down, covering a distance ct, where c is the speed of light as measured by clocks on the ground. By relating these displacements into the so-called Pythagorean theorem, we have:
which can be rewritten as:
If we now assume, with Einstein, that the speed of light is the same on both the train and the embankment, c' = c, we have:
This equation states that the time interval marked by clocks inside the train differs from the time interval marked by clocks on the embankment.
Einstein's equations hardly implied any measurable anomalies in the behavior of bodies moving in everyday circumstances, such as trains and clocks, because most things move at speeds far slower than light. But the equations applied aptly to describe the motions of electrons. Their implications seemed most fascinating when applied to larger objects.
Returning to the start, relative to a spaceship traveling at an immensely high speed, planet Earth is contracted by a certain amount. Is that wrong? Not according to Einstein's theory, and neither does Earth seem to be contracted. Instead, Earth does not have a single length of diameter, nothing does. Objects all have various lengths in relation to various systems of reference. If we like the idea that the real length is the length relative to an observer at rest, then Einstein would disagree; we have a preference for a relative speed of zero, but that's just one speed, one perspective. It's just like the relativity of motion. What's the speed of the floor? Zero miles per hour, but only relative to you on your chair—relative to the moon, the floor beneath your feet moves very fast, and relative to the sun it moves at another speed, and relative to another star at yet another. Just as speed is relative, Einstein argued, the simultaneity of distant events is also relative, and lengths too, and so on.
And what about the guy in the spaceship? He turns on his flashlight which sends a beam of light forward. He moves relative to Earth at 160,000 miles per second. And the light moves relative to him at 186,282 mps. One might expect that the light ray moves relative to Earth at a speed of 346,282 mps. But Einstein would say that we're just assuming that velocities combine according to the simple addition rule:
He argued that this is just an assumption, that there is no evidence that this rule is exactly right. Instead, he managed to show that given the relativity of simultaneity, we can derive a different rule for the composition of velocities, namely:
If the speed of the spaceship is v, and the speed to be added is c, then the speed of the light ray relative to Earth is:
And this becomes:
So the speed of the light ray relative to Earth is the same as relative to the spaceship, 186,282 miles per second. It looks like magic, but it isn't. We can grasp this seemingly impossible result once we remember that speed, simply put, is just distance divided by time; and since the people on Earth and the guy on the spaceship disagree about times and distances, they can therefore agree about the speed of light.
The point is that throughout time, scientists have had to distinguish between the properties that belong to objects and the properties that exist only as relations among objects. People used to think (and many still do) that objects have certain colors, intrinsically, say, that a given apple is really red. But it turns out, as we know thanks to Newton, that colors are not in objects, they're in the light. If we turn off the lamp, an apple ceases to be red. Colors also vary depending on the speed with which we move relative to each object. Similarly, we used to think that weight is something that is an intrinsic attribute of a body. But again, thanks to Newton, we know that weight is a relational property. Your favorite book would weigh much more if it were sitting on the surface of Jupiter. And its weight there is no less real than its weight here. Einstein argued that notions such as length and time are also relational properties. If we're going to state the length of a body, then we'd better specify the reference frame. And events that are simultaneous relative to you, strictly speaking, need not be simultaneous relative to other observers.
Einstein showed that despite such disagreements, one could still formulate a physics in which certain relations hold generally. The net result was that physics as a whole became reformulated and statements that we used to know as laws became just approximations, while new statements came to replace them. Space and time, which for ages had been imagined as absolute, like mythical gods indifferent and unaffected by human affairs, came to be construed instead as variable relative concepts. Although Einstein based his theory on convenient assumptions, the old habit of viewing physics as based on universal facts continued. To this day, many scientists tend to construe, in particular, the constancy of the speed of light as a brute experimental fact. While Einstein construed his special theory of relativity as a makeshift and preliminary construct, many of his followers did not. Einstein became religiously devoted to the spirit of scientific inquiry, but many scientists remained devoted to scientific doctrine, even if it changed.
11
The Cult of the Quiet Wife
HERE'S an intriguing tale: having enjoyed decades of extraordinary fame, Albert Einstein never admitted that his acclaimed theory of relativity owed partly to the secret contributions of his modest wife. Not only had they lived together during his most creative year, they had studied physics together and when he won the Nobel Prize he gave the money to her. Was she his secret collaborator? It's a good story, but is it true?
Proponents of Einstein's wife have been arguing about this for years. It would be awful to discover that historians and physicists have systematically lied, based on some sexist bias, to deny credit where it is long overdue. If you trust authoritative historians you might simply disbelieve the story, dismiss it as a modern myth. Personally, I'd be glad to learn that Mileva Marić was Einstein's secret collaborator. I want her to be the secret coauthor. But we should set aside our speculative preferences and instead look at the evidence.
Better yet, we can trace how stories evolve. People sell reams of print by taking historical tidbits and stretching and sculpting them into provocative shapes. In 2003, television stations in the United States and other countries began to broadcast a documentary called Einstein's Wife.1 It dramatized the life of Mileva Marić, highlighting the idea that she contributed to Einstein's scientific works. It was accompanied by a PBS website (since updated in response to concerns about historical accuracy) that featured an online poll that asked: “Was it really possible for Albert alone to produce all the phenomenal physics generated during 1905?” It continued: “Did Mileva Marić collaborate with Einstein? You Decide! Take our online poll.” Thus viewers were invited to decide the past by voting. In a couple of years, more than 75 percent of the people polled had replied that Marić did collaborate with Einstein.2 How did so many people come to believe that?
The fuss began in 1987, when historians, led by John Stachel, began publishing comprehe
nsive compilations of Einstein's works, manuscripts, and correspondence. Among the documents, they published old letters between Einstein and Marić. In a few of those letters, written around 1900, Einstein briefly used expressions such as “our research,” “our paper,” and once, “our work on the relative motion.”3 Historians of physics were fascinated as they analyzed such letters, but concluded that they are just too vague and insufficient to establish whether Marić contributed to Einstein's publications.
Still, plenty of non-specialists also pondered roles that Marić could have played. The lure to speculate was understandable. For example, Einstein's most intriguing comment, translated, reads: “How happy and proud will I be, when we both together have brought our work on the relative motion victoriously to its end!”4 Non-specialists quickly concluded that this letter refers to the theory of relativity. Written by Einstein's own hand, could it be any clearer?
But wait. The letter was written in 1901, and Einstein had no concept of the theory that he later formulated which became known as relativity. At that time he still believed in the invisible ether and sought ways to detect its relative motion experimentally. This problem of “the relative motion” was a widespread concern; many physicists aimed to solve it. As a college student in 1899, Einstein began trying to design experiments to exhibit the relative motion of the ether. As he mentioned to Marić: “I also wrote to Professor Wien in Aachen about my paper on the relative motion of the luminiferous ether against ponderable matter.”5 Then in 1901, Einstein shared his speculations or aspirations with Marić. But by 1902, he had abandoned the idea of detecting the ether motion. He abandoned the concept of the ether and hypothesized instead that light behaves like bullets—its speed is affected by the speed of its source.6 Later, in 1904, he discarded those conjectures too and hypothesized instead that the speed of light is independent of its source.7 He struggled to modify the leading theory, that of Hendrik Lorentz, to improve it.8 But he failed again, and only in spring 1905 did he abruptly formulate a radically new theory that became known as special relativity, after ten years of reflection, including more than seven years of intensive struggles.9 On the basis of abundant documentary evidence, we know that Einstein obsessively worked on physics before 1905 and for decades afterward. What about Marić?
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