Einstein’s use of an aesthetic criterion—symmetry—is quite important. The chain of reasoning that would eventually lead him to relativity did not begin with a specific experiment or a mathematical calculation. It began with a sense of the way the universe should be, of what a scientific explanation should look like. It did not seem right that there was this split between what could be seen and the concepts used as explanations. These objections did not spring spontaneously into Einstein’s mind. Rather, they were the result of several years of intense thought and consideration. We do know, though, what triggered the avalanche. It was a pair of philosophers.
Einstein loved to read and debate philosophy with his friends. Even though their focus was science, they came from a generation where intellectual training was still broad and technical expertise was expected to be grounded in the liberal arts. Epistemology—the study of how we gain knowledge—seemed to them a basic part of physics. They read Kant along with their Newton. One of the books they read was a classic by David Hume, the eighteenth-century Scottish iconoclast known for his aggressive approach to questioning everything from miracles to causality. Hume located all our ideas in sense impressions and demanded close scrutiny of any entities beyond what could be directly experienced.
Along with the influence of Hume, Einstein had been interested in the work of Ernst Mach for some time. Mach, an impressively bearded Austrian physicist and philosopher, put forward an approach often called positivism. Mach argued that scientific concepts needed to be grounded not only in direct experience but specifically in measurement. One should not talk about “force,” for instance, but instead specifically about how one measured force (springs, scales, and so on). He warned that scientists often held on to ideas not for good reasons but simply out of tradition and habit. Einstein took away the lesson that it was necessary to critically examine the roots of all of our basic concepts. Once we forget the origin of our ideas, we might try to base our progress on dangerously unstable foundations. Between Mach and Hume, Einstein was primed, as he said to Besso, to “stamp out vermin” hiding within physics.
So Einstein’s objection about asymmetry came from this Machian question: how do we measure these electromagnetic phenomena? Or as Hume would demand: what is our actual experience of induction? Einstein, the son of a dynamo maker, answered: measuring an electrical current. We do not see a magnetic field. We do not see an electrical field. We do not see the ether. We see a magnet and coil get closer together, and then a needle shift on a device that measures current or a lightbulb start to glow. We can’t even really know which of the magnet or the coil is “really” moving—Galileo’s principle of relativity demanded that either one could be seen as moving, just like the observers on the train and on the station platform. And if we look only at what can be measured with our electrical equipment, that is true. Either way, we see the same current. Our conclusions about whether the magnet or the coil was moving could not be separated from a careful analysis of the way we measured that movement. Einstein realized he needed a new way of thinking that could make sense of these ambiguities and keep physics close to that which could be directly observed.
This sparked several weeks of what he called his “struggle.” The crucial moment came one evening in the middle of May 1905. After a frantic conversation with Besso about these problems, Einstein wandered off in a haze of thought. The next day when he saw Besso he simply said, “Thank you. I’ve completely solved the problem.” He declared that an analysis of time was the key. The historian Peter Galison has richly demonstrated that this moment was not a fluke. To live in Switzerland in 1905 was to be steeped in the technologies of time. Clocks were mounted everywhere on public buildings. Trains were coordinated by electrical time signals. Every day, Einstein passed underneath the most famous clock in Bern as he walked from his apartment to the patent office. At his desk, he examined a steady stream of devices for measuring, marking, and synchronizing time.
So when Einstein decided that time was the key, he meant something very specific. Sitting at the intersection of Hume, Mach, and the patent office, he meant one thing by “time”: clocks. Time as an abstract or metaphysical concept was unacceptable. A scientific, positivist notion of time needed to be built on how one measured time, and nothing more.
The heart of Einstein’s theory of relativity was one of these clocks, albeit a strange one. You can make a clock out of any kind of repetitive physical process—the motion of the sun, the swinging of a pendulum, or the pulsing of the quartz crystal in a digital watch. We can understand the theory of relativity by thinking about a light clock, where the repetitive process is a pulse of light bouncing back and forth between two mirrors. Every time the pulse finishes one cycle, the clocks tick; one second has passed. It is important to note that this is not a real clock (it would be far larger than the Earth). Einstein was proposing a “thought experiment.” Thought in that it takes place entirely in your head. Experiment in the sense that you don’t know what the outcome will be before you start. It is a rigorous and careful thinking through of the consequences of some initial idea or postulate, in much the same style as Albert’s sacred geometry book. You need no laboratory or equipment, only imagination and mental discipline.
Einstein’s scientific paper “On the Electrodynamics of Moving Bodies” dates from June 1905. This was the first appearance of what we now call the theory of special relativity. If Einstein’s goal with this paper was to irritate other physicists, he was well on his way. It had no footnotes, no references to other papers, and only a brief note thanking his friend Besso for helpful conversations. Instead of building on an experiment or an existing theory, the paper simply began with his objection to the asymmetry of the magnet-wire situation. He then proposed two postulates that would govern his thought experiments. First, that the laws of nature should be the same for observers in any inertial frame of reference (“inertial frame of reference” is just a technical way of saying sitting still or coasting at a steady velocity). Einstein thought of this as a simple extension of Galileo’s principle of relativity—if the observers on the train and on the platform are truly equivalent, this has to be true. Indeed, few scientists of 1905 would have objected to it. It was simply saying that no one person had access to the “correct” laws of physics. The physics jargon is to say that there are no “privileged reference frames.” More simply it states that everyone should agree on the basic operations of nature.
The second postulate stated that the speed of light should be the same for all observers in inertial reference frames. This seems in flat contradiction to our ordinary experience—if I throw a ball from a moving train, the speed of the train and my throw are added together, and the ball is going faster than if I threw it from the platform. Similarly, if I turn on a flashlight on the train, surely the speed of the train should be added to the speed of the light beam? This harkens back to Einstein’s youthful imagining of running alongside an electromagnetic wave and seeing it frozen in place. If the second postulate is true, the wave would always seem to be moving at 186,292 miles per second regardless of how he was running. Despite this strangeness, Einstein asked for the reader to be patient and follow his reasoning.
Now, armed with our two postulates, we revisit the light clock. We give two of our friends, Alice and Bob, their own light clocks. Being good Swiss citizens, they synchronize their clocks—that is, their clocks always tick at exactly the same moment. They watch the light pulses for a little while to confirm that they are, in fact, synchronized. However, strange things begin to happen if we set Alice on a train moving quickly (the train is coasting, so she is still in an inertial reference frame). As the train passes the platform where Bob is standing, they compare the ticking of their clocks. Bob sees his light pulse tick up and down (the clock on the top). But as he watches Alice’s mirror carried along by the train he sees the light pulse move at an angle (the clock on the bottom).
This means that the overall distance tha
t Bob sees Alice’s light pulse travel is longer than the distance he sees his own light pulse travel. The natural solution to this is for him simply to say that the movement of the train is changing the speed the light is traveling at, just as with the thrown ball. That fixes the extra distance, and the clocks still tick at the same time. But suddenly Einstein’s second postulate lunges in and reminds Bob that the speed of light can’t change, even with the motion of the train. Instead, Alice’s light pulse has farther to go at the same speed, and Bob’s light pulse finishes its cycle first. Bob’s clock ticks before Alice’s. Bob is startled to realize that Alice’s clock—formerly synchronized with his—is now running slow.
Einstein’s hypothetical light clock
ORIGINAL ILLUSTRATION BY JACOB FORD
Bob’s reflex will be to claim that his clock is right, and Alice’s is wrong. He thinks her clock is not running correctly because of her motion. Now Einstein’s first postulate enters the picture, which warns that neither Bob nor Alice is allowed to say they are the one that is “really moving.” According to Galileo, Alice is perfectly entitled to say that her train is standing still and it is the platform that is moving. So now Alice follows exactly the same chain of reasoning that Bob just did, and arrives at the conclusion that Bob’s clock is running slow. Now, here is the perverse core of relativity: they are both right. There is no one correct position from which to watch clocks. Any observer will see a moving clock running slow compared to their own. And since time is nothing more than the ticking of a clock, time itself changes with motion.
If time truly changes, then we are in a strange place. People can disagree about whether two events are simultaneous. Identical twins can find themselves to be different ages. Our most basic experience of the world around us—the passage of time—is suddenly relative.
Einstein then performs exactly the same kind of positivist analysis with space instead of time. How does one measure space? With measuring rods—rulers, meter sticks, and so on. Running through the process of measuring length with a rod, just as we did with time and the light clock, results in the conclusion that the rods shrink as they go faster and faster. So as time seems to slow down, length seems to be compressed. The former phenomenon is called time dilation, the latter length contraction. One further Machian inquiry, this time about mass, concluded that mass, too, changed with the speed of the observer (an interesting result of this calculation was the simple formula m = L/c2, more often written today as E = mc2).
Einstein’s postulates are, on the surface, basic statements of the universality of science. They are guarantees that any scientist, no matter their point of view, will be able to discover Maxwell’s equations or Newton’s law of gravity. But Einstein’s thought experiment with the light clocks shows that there is a cost to this universality. The cost is that, while the laws remain the same, the measurements we make—of time, space, and mass—are all malleable. Motion changes them all. And since motion is relative—thanks, Galileo—time, space, and mass are themselves all relative. These categories, assumed since Newton (and demonstrated by Kant) to be immutable and absolute, were no longer so.
A completely reasonable objection to Einstein’s outrageous claims is that you never see any of these things happen. Train stations do not seem to shrink as my subway car passes through them. I will not be able to persuade my boss that time dilation means I should get to go home early. A quick glance at the formulas, though, shows why this is (see page 34). These effects can only be seen when moving very, very close to the speed of light—you need to go about 90 percent the speed of light to see a clock running at half speed. For comparison, the fastest any human being has ever traveled relative to the Earth is about 0.0004 percent of the speed of light (the Apollo 10 lunar module, if you are wondering). Even today, time dilation can be demonstrated only with hyper-precise atomic clocks. Relativity was not amenable to being tested in 1905.
Time dilation and length contraction. Note that the effects only become significant close to the speed of light.
ORIGINAL ILLUSTRATION BY JACOB FORD
It is important to realize that these are all the results of thought experiments, not anything done in the physical world. Einstein had no tests he could perform, no predictions that could be reliably checked. The best he could do was to say that his theory was compatible with the unusual results of certain experiments. These were the ether-drift experiments intended to measure the movement of the Earth through the electromagnetic ether, the most famous of which today is the Michelson–Morley interferometer. These experiments always returned what is called a “null result”—no apparent motion through the ether. This never made any sense. The Earth’s direction of movement through the ether should be constantly shifting as it moved around the sun every year.
The null results were a genuine puzzle. Einstein’s new theory had an explanation, though. The ether-drift experiments assumed that the ether was an absolute reference frame against which all motion could be measured, a place truly at rest in the universe. Einstein argued that this was impossible—if we wanted the laws of physics to be truly universal, there could be no such place. Special relativity dictated that any attempt to measure absolute rest would fail. The very concept of the ether was, in the positivist sense, unscientific because it could not be measured. Thus the twenty-six-year-old patent clerk in Bern, Switzerland, never having held an academic position, dismissed the fundamental hypothesis of nineteenth-century physics as “superfluous.” Not wrong, not disproven. Superfluous. No longer needed, thanks to Einstein’s insistence on the symmetry of the universe.
It is extraordinary that Einstein was able to arrive at these results on his own, and, some say, suspicious. Surely Michele Besso could not have been his only collaborator? What of Mileva, herself a physicist? She must have been a part of the genesis of relativity. Perhaps, even, Albert stole the theory from her and passed it off as his own? The evidence for this claim essentially comes down to a single word in Einstein’s letters: “our.” On one occasion he wrote to Mileva referring to “our work on relative motion.” On others he mentioned “our theory of molecular forces.” But there is no evidence beyond this. It seems clear that “our” was used here in the sense of “the theory we were discussing.” Mileva never claimed responsibility for any of Albert’s work. She was certainly a sounding board for his ideas in the same way that Besso and Grossmann were, and special relativity would no doubt have been different if any of them had not been present—Einstein needed his friends, as we will see over and over again. It would be strange, though, to say that special relativity was created by Besso, even though he was essential to its creation. Similarly with Mileva. There is really no reason to credit her with any of Einstein’s work (he had productive decades of work without her, so he was hardly a fraud). There is no question that as a woman in physics circa 1900, Mileva had a nearly impossible road to success. Her social context essentially did not allow her to excel, regardless of her ability. But that does not mean her work was stolen; it simply means that she was one of vast numbers of women denied opportunities by an intensely patriarchal society.
The molecular theory Einstein referred to above is an important reminder that relativity was only one facet of his work at this time. 1905 is sometimes referred to as his “miracle year,” an astoundingly productive time for the young man. He published six papers in the prestigious Annalen der Physik, all of which changed the world. In March, a paper on the photoelectric effect, which he described to his friends as “very revolutionary,” proposed the notion that light can be treated as a particle, a small packet of energy called a quantum. This essentially jump-started the new field of quantum physics. In April, his doctoral thesis provided a new way to estimate the sizes and motions of molecules. Less than two weeks later, and then more completely in December, he put those estimates to work in an analysis of Brownian motion (the observed zigzag motion of tiny particles suspended in liquid). Einstein was
able to explain these motions as collisions with molecules, and predict their behavior startlingly well—this was essentially the final nail in the coffin for skeptics of the reality of molecules. In June, his first paper on relativity appeared. September saw his second paper on relativity presenting E = mc2.
As is often the case, the process of publication created the illusion of a sudden wave of discovery, when in fact each of these papers was the culmination of years of hard work. Nonetheless, their appearance en masse attracted serious attention, particularly from the editor responsible for their approval in the Annalen: Max Planck. By 1905 Planck was already the most important person in German physics. The wild, unkempt hair of his youth had long since given way to extensive balding, but his thoughtful, hooded gaze remained. His theoretical skill was unquestioned, especially having cracked the fundamental problem of so-called black-body radiation (how hot objects give off light). This theory was the groundwork on which Einstein built his own quantum calculations. It was the beginning of what we now call modern physics.
Planck was the very model of the German professor: morally upstanding, bureaucratically skilled, politically conservative. Colleagues remembered him for his “sense of duty and deliberateness of action.” He was a mentor to countless young scientists, and as a three-time president of the Physical Society, essentially ran the field of physics in Germany. The publication of Einstein’s papers was, for the most part, Planck’s own decision—this was in the days before peer review. Despite their unconventional style, he saw something important in them and called the attention of physicists to this obscure patent clerk. It is sometimes said that Einstein was Planck’s second great discovery.
Einstein's War Page 4