Einstein in time and spa.., p.7
Einstein in Time and Space, page 7
Using some of the statistics he had developed for his dissertation, Albert was able to calculate that, through all of its zigging and zagging, a standard particle suspended in water would be displaced by 0.006 millimeter in one minute. His prediction, he pointed out, could be tested. A lot hung on whether or not an experiment verified his result.
At the time, atoms and molecules were far from being regarded as real. Many physicists and chemists believed in them and they had proved to have a theoretical use. But it was still wondered whether they actually existed, or whether they were much like what Planck thought of his quanta—a convenient fiction. Einstein’s predicted value for displacement was very specific, and his method of obtaining it had direct links to the science of atoms. If Einstein’s result was proved right, atoms and molecules existed; if it was wrong, they didn’t.
There was no shortage of responses to this paper—it garnered attention and correspondence from theorists and experimentalists alike. An attempt to verify Einstein’s prediction was undertaken within months, and it was confirmed four years later, with extreme precision, by the French physicist Jean Perrin. The atomic skeptics ceded their position. Atoms were now, to all intents and purposes, conclusively real. Perrin was later awarded the Nobel Prize for his work confirming Einstein’s theory.
At the end of this initial outpouring of work, Einstein took a moment to write to his friend Conrad Habicht, who had moved from Bern to Schaffhausen toward the end of 1903. They hadn’t written to each other in a little while, and Einstein joked that he was almost committing sacrilege by breaking their solemn silence with the “inconsequential babble” of his letter.
“So, what are you up to, you frozen whale, you smoked, dried, canned piece of soul, or whatever else I would like to hurl at your head?” he wrote. “Why have you still not sent me your dissertation? Don’t you know that I am one of the 1 ½ fellows who would read it with interest and pleasure, you wretched man? I promise you four papers in return.” The first, he said, “deals with radiation and the energy properties of light and is very revolutionary, as you will see if you send me your work first.” The second paper, he explained, was “a determination of the true sizes of atoms,” and the third accounted for the random movements of molecules in liquid.
The last paper wasn’t finished, but he was sure it would be of particular interest. “The fourth paper is only a rough draft at this point, and is an electrodynamics of moving bodies which employs a modification of the theory of space and time.”
Habicht could not know it, but his friend was about to tear down another veil and force the world to be seen anew.
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Imagine that you have shut yourself belowdecks on a ship. The main cabin is in a curious state: the air is thick with butterflies; on a table there stands a large bowl of water containing some fish; a bottle suspended from the ceiling is emptying drop by drop into a vessel beneath it. The ship is still in harbor, at rest, and so you see the fish swimming this way and that, the butterflies floating with equal speed in any direction, the drops from the bottle splashing into the vessel. Now imagine that the ship has set sail, traveling at a constant velocity on remarkably calm seas. You wouldn’t be able to tell the difference. Nothing would change.
This thought experiment was described by Galileo in 1632. He used it to defend the Copernican view of the solar system from its detractors, who argued that if Earth were spinning around the sun, people would surely feel it. Galileo’s ship exemplifies what is known as the “special case” of relativity. The general principle of relativity states that the laws of physics remain the same no matter what your motion, which is simple to understand, though difficult to accept. Special relativity, on the other hand, only relates to reference frames at a constant velocity, which is to say that it only relates to things either at rest or moving with a uniform speed and direction. Acceleration is not taken into account in special relativity.
Although the “special case” sounds contrived due to its strict limitations, it is much easier to grasp as a concept because we experience the effects of it in everyday life. On the Shinkansen bullet train, for example, commuters are not flung about the carriage at two hundred miles per hour, careering down the aisle, but stay comfortably in their seats. They could hold an archery tournament, bake a Breton cake, or broadcast radio waves, and the laws of physics would operate just as if they were standing on the ground.
Intrinsic to relativity is the idea that one reference frame is not privileged over another. If someone stood at a station and saw the train speed past them, then logically enough it would look to them as if the train and all its passengers were moving in a certain direction. However, to someone on the train, it would look as if the station were speeding past them in the opposite direction. Both of these interpretations are in fact valid. There is no way to discern which is “correct.” As the laws of physics operate in exactly the same way for both the person on the train and the person at the station, no experiment can determine which of them is truly at rest or in motion. It all depends on your reference frame.
By 1905, the principle of relativity was a long-accepted part of physics. Einstein did not invent the idea. What separated his theory of special relativity from Galileo’s ship was his consideration of light.
Sound waves wouldn’t exist without something to oscillate through, such as the air or a piece of wood. Water waves wouldn’t exist without water. For physicists of the early twentieth century, a wave was, by definition, a disturbance propagating through some medium. While Newton had envisioned light to be composed of particles, by the late nineteenth century it was considered instead to be a wave. James Clerk Maxwell had brilliantly shown that light was part of a whole spectrum of electromagnetic waves, the combination of electric and magnetic fields. Moreover, light consistently acted like a wave in experiments—it diffracted and reflected, and it had a measurable frequency. It was therefore assumed that light must be propagating through some medium, like all other waves. This unknown substance was named the “ether.”
For the ether to accord with observable reality, it needed to be somewhat strange. For one thing, it had to pervade the entire universe, otherwise starlight wouldn’t be able to reach Earth. It also had to be so thin and spectral that it had no effect on anything within it, and yet so rigid that it allowed light to travel through it at immense speed. Much of late nineteenth-century physics was concerned with searching for this ether. It proved most elusive.
One way in which it was thought possible to discover the ether was to detect variations in the speed of light. It was assumed that Earth, moving through the ether, would create an “ether wind” that would blow in the direction opposite to Earth’s motion, just as would happen if the planet were moving through air or water. Light, it was reasoned, would have a harder time traveling against the ether wind than if it were traveling with it. In 1887, the American physicists Albert Michelson and Edward Morley conducted what became a famous experiment based on this idea, splitting a light beam in two so that one half traveled with the movement of Earth and the other half traveled transverse to it. Try as they might, they could not detect the slightest difference between the speeds of the two light beams.
Of all the many experiments conducted to find evidence of the ether, none succeeded. Something was obviously wrong. However, to scientists of the late nineteenth and early twentieth centuries, the ether remained real—as real as air. The thought that light could propagate without a medium, through nothing, was preposterous.
By 1905, Einstein had grown skeptical of the ether’s existence. In his June paper, “On the Electrodynamics of Moving Bodies,” he discarded it with hardly a backward glance. “The introduction of a ‘light ether’ will prove to be superfluous,” he wrote, doing away with two hundred years’ worth of received scientific wisdom as if it were an old coat.
Einstein’s paper was based on two principles only. Everything else in the theory developed directly from these immutable truths. The first was the “principle of relativity”: that the laws of physics are the same in all non-accelerating reference frames. The second principle was that the speed of light traveling in empty space is constant. Light travels at 299,792,458 meters per second, or 670,616,629 miles per hour; or, if you prefer, one light-year per year. A pretty close approximation of this speed was known by the late 1800s. Einstein dared to propose that this speed remained the same no matter what the motion of a light source. In other words, the speed of light was constant in all reference frames.
If, back on our train moving with a constant velocity, you threw a ball down your passenger car, in the direction the train was moving, you would see the ball traveling with whatever speed you had thrown it at. However, someone standing at the train station, looking in through the windows at your reckless behavior as the train passed them, would see something different. They would see the ball traveling at the speed of the train plus your throwing speed. The same would be true if you threw a piece of the Great Sphinx, or indeed if you talked—the sound waves produced would seem to the person on the station platform to travel at the speed of the train plus the speed of sound.
Before Einstein, it was assumed that light would behave just like everything else. If you fired a laser down the train or held up a lantern, it was believed that, in your reference frame, the emitted light would travel at the speed of light, but for the person at the station, the light would travel at the speed of the train plus the speed of light.
Einstein took it to be a law of nature that light—unlike everything else—traveled at the same velocity for both the person on the train and the person at the station. He was sure this was correct. He was equally sure that the principle of relativity was correct, and that to develop his theory, it needed to be built up from these two postulates.
He had reached this conclusion sometime before 1905. Unfortunately for him, however, as he admitted in his June paper, these two principles were “seemingly incompatible,” and as a result he had spent “almost a year fruitlessly thinking about it.” Then, one beautiful day in Bern, he went to visit his good friend Michele Besso and told him about his problem. “I’m going to give it up,” he said. But the friends discussed it, and all at once the ivy was pulled from the edifice and Einstein understood. The very next day Albert visited Besso again and, without any greeting, said, “Thank you. I’ve completely solved my problem.”
And so he had. Five weeks later, at the end of June, Einstein submitted his paper. What he’d grasped in his talk with Michele was that what was a simultaneous event in one reference frame needn’t be a simultaneous event in another. If a person sees two lightning strikes happening simultaneously, what that effectively means is that they are standing at a midpoint between the strikes and the light from each reaches them at the same time. But if that person were standing in the same position on a train moving toward one of the strikes, then the light from that strike would reach them before the other. One strike would happen first. Under the principle of relativity both of these views are as valid as each other. True simultaneity does not exist. One might say that simultaneity is a relative concept.
And what this means, as Einstein saw, is that there is no absolute time. As he put it later, “There is no audible tick-tock everywhere in the world.” Every reference frame has its own time. It was this new concept of time that allowed Einstein to reconcile his two principles, and it had some strange consequences.
Einstein pointed out that if time is relative, then so is space. Imagine two people, each with their own set of synchronized clocks—one in a train, one at the station. Imagine that the train passenger has a shiny golden rod with them. To measure the length of this fantastic rod, the passenger would simply use a measuring stick. To the person at rest, however, the rod is moving. For them to be able to measure its length, a more convoluted process is required. First they need to determine where the two ends of the rod are at a particular instant in time. Once they know the position of the front and back of the rod, they can mark those points with flags and measure the distance between them. Common sense tells us that the two lengths would be the same. They’re not. The golden rod appears shorter for the person at rest than for the person moving with it. The reason for this is that the person at the station has a different notion of simultaneity than the train passenger. The passenger would argue that the person at rest located the two ends of the rod at different times, not in the same instant. This phenomenon is known as “length contraction.”
The other counterintuitive outcome of special relativity is called “time dilation.” Imagine now that the person on the train has got rid of their rod and has upgraded it for two mirrors. One mirror is attached to the floor, the other to the ceiling. A light beam is bouncing between the two. To the train passenger, the light bounces in a straight line, up and down. But to the person at the station the light travels in a zigzag. It looks to them as if the light has to travel diagonally upward from the floor to reach the ceiling mirror, which has moved ahead a little with the train, and it travels diagonally downward to reach the floor mirror, which has moved ahead in turn. For the person at the station, then, the light seems to have traveled a greater distance than for the person on the train. But the speed of light—as is very much a given in Einstein’s relativity—travels at the same speed for both observers. It can only be concluded that for the person at rest more time has elapsed than for the person on the train.
The faster the train goes, the farther the light beam has to travel from ceiling to floor. Which is another way of saying that the faster the train goes, the slower time passes. The passengers age less, plants take longer to germinate and grow, atoms decay at a slower rate. On Earth, all these effects are barely perceptible—indeed, the effects of relativity only really become interesting at very high speeds.
Einstein’s June paper was unusual not only for its new and profound oddities, but also for the more mundane fact that it contained not one citation. Many of the paper’s ideas were already in the scientific air of the time. George F. FitzGerald and Hendrik Lorentz, for example, both independently developed the concept of length contraction, while Henri Poincaré had questioned the concept of absolute time. But all had done so as a patch for the problems of the ether. Einstein had come to this startling vision of the world alone—or very nearly alone. “In conclusion,” he wrote, “let me note that my friend and colleague M. Besso steadfastly stood by me in my work on the problem here discussed, and that I am indebted to him for many an invaluable suggestion.”
After finishing his paper, Einstein took to his bed for a fortnight, while Marić checked and rechecked his work.
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As part of his application for Swiss citizenship, Einstein officially declared himself a teetotaler. As a rule, he didn’t drink alcohol. He didn’t like it. Once, when offered a glass of champagne, he chose to sniff the golden, bubbling liquid and leave it at that. “I do not need wine,” he said, “because my brain is acquainted with intellectual drunkenness.”
After Albert completed his paper on special relativity, however, he and Mileva celebrated. During their festivities they sent a postcard to their friend Conrad Habicht, which read in its entirety:
Both of us, alas, dead drunk under the table. Your poor
Backside and wife
A few months later, he sent Habicht another letter. An extraordinary upshot of his theory had crossed his mind, he wrote, one that was most unexpected. It seemed that mass and energy were in some way connected. “The consideration is amusing and seductive,” he wrote, “but for all I know, God Almighty might be laughing at the whole matter and might have been leading me around by the nose.”
In September, Albert scribbled down a follow-up to his June paper, just three pages long. By considering a body emitting radiation first from a reference frame at rest and then from one in uniform motion, he was able to develop equations relating speed and mass, and he quickly arrived at this theorem: “If a body releases the energy L in the form of radiation, its mass decreases by L/V2.” Which is to say that “the mass of a body is a measure of its energy content.” Energy and mass are in fact the same thing, in different masks.
Updating Einstein’s symbols, and keeping things in their simplest form, what the special theory of relativity therefore implied was the equation E = mc2. The most famous equation in all of science simply fell out of Einstein’s work, an afterthought to his already miraculous year.
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Mileva Marić, Hans Albert Einstein, and Albert Einstein, ca.1904–5.
In April 1906, Einstein was promoted to Technical Expert II Class and his salary raised to 4,500 francs. He had more than proved himself as an adept bureaucrat and talented patent examiner. What’s more, as his boss pointed out when he recommended the promotion, Einstein was now Herr Doktor.
The family moved again, renting the top floor of a house on the tree-lined Aegertenstrasse, where they had their own furniture and views of the Bernese Oberland mountains. Einstein was twenty-seven, professional, proper. Because of their move, he and Besso no longer walked home together. Habicht and Solovine had long moved away. Those dancing days were gone, and he missed them. He and Marić only socialized on Sundays.
“I am doing fine,” he wrote to a friend. “I am a respectable Federal ink pisser with a decent salary.”
He had time enough for fiddling on his violin and indulging in a little physics, although both activities were performed within the narrow constraints set by his two-year-old. Not that Einstein minded the tyranny of his son that much. Hans Albert had grown into “quite an imposing, impertinent fellow” and Mileva and Albert often had to check themselves from laughing at his clowning around. They were so taken with him that at home they would communicate with him only in imitation of his baby talk, and it was not until the age of five that Hans Albert learned to speak proper German.
