In phrases so simple as to be seductive, Einstein pointed out that time itself can be defined only by referring to simultaneous events, such as the small hand of a watch pointing to 7 as a train arrives. The obvious yet still astonishing conclusion: with no such thing as absolute simultaneity, there is no such thing as “real” or absolute time. As he later put it, “There is no audible tick-tock everywhere in the world that can be considered as time.”56
Moreover, this realization also meant overturning the other assumption that Newton made at the beginning of his Principia. Einstein showed that if time is relative, so too are space and distance: “If the man in the carriage covers the distance w in a unit of time—measured from the train—then this distance—as measured from the embankment—is not necessarily also equal to w.”57
Einstein explained this by asking us to picture a rod that has a certain length when it is measured while it is stationary relative to the observer. Now imagine that the rod is moving. How long is the rod?
One way to determine this is by moving alongside the rod, at the same speed, and superimposing a measuring stick on it. But how long would the rod be if measured by someone not in motion with it? In that case, a way to measure the moving rod would be to determine, based on synchronized stationary clocks, the precise location of each end of the rod at a specific moment, and then use a stationary ruler to measure the distance between these two points. Einstein shows that these methods will produce different results.
Why? Because the two stationary clocks have been synchronized by a stationary observer. But what happens if an observer who is moving as fast as the rod tries to synchronize those clocks? She would synchronize them differently, because she would have a different perception of simultaneity. As Einstein put it, “Observers moving with the moving rod would thus find that the two clocks were not synchronous, while observers in the stationary system would declare the clocks to be synchronous.”
Another consequence of special relativity is that a person standing on the platform will observe that time goes more slowly on a train speeding past. Imagine that on the train there is a “clock” made up of a mirror on the floor and one on the ceiling and a beam of light that bounces up and down between them. From the perspective of a woman on the train, the light goes straight up and then straight down. But from the perspective of a man standing on the platform, it appears that the light is starting at the bottom but moving on a diagonal to get to the ceiling mirror, which has zipped ahead a tiny bit, then bouncing down on a diagonal back to the mirror on the floor, which has in turn zipped ahead a tiny bit. For both observers, the speed of the light is the same (that is Einstein’s great given). The man on the track observes the distance the light has to travel as being longer than the woman on the train observes it to be. Thus, from the perspective of the man on the track, time is going by more slowly inside the speeding train.58
Another way to picture this is to use Galileo’s ship. Imagine a light beam being shot down from the top of the mast to the deck. To an observer on the ship, the light beam will travel the exact length of the mast. To an observer on land, however, the light beam will travel a diagonal formed by the length of the mast plus the distance (it’s a fast ship) that the ship has traveled forward during the time it took the light to get from the top to the bottom of the mast. To both observers, the speed of light is the same. To the observer on land, it traveled farther before it reached the deck. In other words, the exact same event (a light beam sent from the top of the mast hitting the deck) took longer when viewed by a person on land than by a person on the ship.59
This phenomenon, called time dilation, leads to what is known as the twin paradox. If a man stays on the platform while his twin sister takes off in a spaceship that travels long distances at nearly the speed of light, when she returns she would be younger than he is. But because motion is relative, this seems to present a paradox. The sister on the spaceship might think it’s her brother on earth who is doing the fast traveling, and when they are rejoined she would expect to observe that it was he who did not age much.
Could they each come back younger than the other one? Of course not. The phenomenon does not work in both directions. Because the spaceship does not travel at a constant velocity, but instead must turn around, it’s the twin on the spaceship, not the one on earth, who would age more slowly.
The phenomenon of time dilation has been experimentally confirmed, even by using test clocks on commercial planes. But in our normal life, it has no real impact, because our motion relative to any other observer is never anything near the speed of light. In fact, if you spent almost your entire life on an airplane, you would have aged merely 0.00005 seconds or so less than your twin on earth when you returned, an effect that would likely be counteracted by a lifetime spent eating airline food.60
Special relativity has many other curious manifestations. Think again about that light clock on the train. What happens as the train approaches the speed of light relative to an observer on the platform? It would take almost forever for a light beam in the train to bounce from the floor to the moving ceiling and back to the moving floor. Thus time on the train would almost stand still from the perspective of an observer on the platform.
As an object approaches the speed of light, its apparent mass also increases. Newton’s law that force equals mass times acceleration still holds, but as the apparent mass increases, more and more force will produce less and less acceleration. There is no way to apply enough force to push even a pebble faster than the speed of light. That’s the ultimate speed limit of the universe, and no particle or piece of information can go faster than that, according to Einstein’s theory.
With all this talk of distance and duration being relative depending on the observer’s motion, some may be tempted to ask: So which observer is “right”? Whose watch shows the “actual” time elapsed? Which length of the rod is “real”? Whose notion of simultaneity is “correct”?
According to the special theory of relativity, all inertial reference frames are equally valid. It is not a question of whether rods actually shrink or time really slows down; all we know is that observers in different states of motion will measure things differently. And now that we have dispensed with the ether as “superfluous,” there is no designated “rest” frame of reference that has preference over any other.
One of Einstein’s clearest explanations of what he had wrought was in a letter to his Olympia Academy colleague Solovine:
The theory of relativity can be outlined in a few words. In contrast to the fact, known since ancient times, that movement is perceivable only as relative movement, physics was based on the notion of absolute movement. The study of light waves had assumed that one state of movement, that of the light-carrying ether, is distinct from all others. All movements of bodies were supposed to be relative to the light-carrying ether, which was the incarnation of absolute rest. But after efforts to discover the privileged state of movement of this hypothetical ether through experiments had failed, it seemed that the problem should be restated. That is what the theory of relativity did. It assumed that there are no privileged physical states of movement and asked what consequences could be drawn from this.
Einstein’s insight, as he explained it to Solovine, was that we must discard concepts that “have no link with experience,” such as “absolute simultaneity” and “absolute speed.”61
It is very important to note, however, that the theory of relativity does not mean that “everything is relative.” It does not mean that everything is subjective.
Instead, it means that measurements of time, including duration and simultaneity, can be relative, depending on the motion of the observer. So can the measurements of space, such as distance and length. But there is a union of the two, which we call spacetime, and that remains invariant in all inertial frames. Likewise, there are things such as the speed of light that remain invariant.
In fact, Einstein briefly considered calling his creation Invarianc
e Theory, but the name never took hold. Max Planck used the term Relativtheorie in 1906, and by 1907 Einstein, in an exchange with his friend Paul Ehrenfest, was calling it Relativitätstheorie.
One way to understand that Einstein was talking about invariance, rather than declaring everything to be relative, is to think about how far a light beam would travel in a given period of time. That distance would be the speed of light multiplied by the amount of time it traveled. If we were on a platform observing this happening on a train speeding by, the elapsed time would appear shorter (time seems to move more slowly on the moving train), and the distance would appear shorter (rulers seem to be contracted on the moving train). But there is a relationship between the two quantities—a relationship between the measurements of space and of time—that remains invariant, whatever your frame of reference.62
A more complex way to understand this is the method used by Hermann Minkowski, Einstein’s former math teacher at the Zurich Polytechnic. Reflecting on Einstein’s work, Minkowski uttered the expression of amazement that every beleaguered student wants to elicit someday from condescending professors. “It came as a tremendous surprise, for in his student days Einstein had been a lazy dog,” Minkowski told physicist Max Born. “He never bothered about mathematics at all.”63
Minkowski decided to give a formal mathematical structure to the theory. His approach was the same one suggested by the time traveler on the first page of H. G. Wells’s great novel The Time Machine, published in 1895: “There are really four dimensions, three which we call the three planes of Space, and a fourth, Time.” Minkowski turned all events into mathematical coordinates in four dimensions, with time as the fourth dimension. This permitted transformations to occur, but the mathematical relationships between the events remained invariant.
Minkowski dramatically announced his new mathematical approach in a lecture in 1908. “The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength,” he said. “They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”64
Einstein, who was still not yet enamored of math, at one point described Minkowski’s work as “superfluous learnedness” and joked, “Since the mathematicians have grabbed hold of the theory of relativity, I myself no longer understand it.” But he in fact came to admire Minkowski’s handiwork and wrote a section about it in his popular 1916 book on relativity.
What a wonderful collaboration it could have been! But at the end of 1908, Minkowski was taken to the hospital, fatally stricken with peritonitis. Legend has it that he declared, “What a pity that I have to die in the age of relativity’s development.”65
Once again, it’s worth asking why Einstein discovered a new theory and his contemporaries did not. Both Lorentz and Poincaré had already come up with many of the components of Einstein’s theory. Poincaré even questioned the absolute nature of time.
But neither Lorentz nor Poincaré made the full leap: that there is no need to posit an ether, that there is no absolute rest, that time is relative based on an observer’s motion, and so is space. Both men, the physicist Kip Thorne says, “were groping toward the same revision of our notions of space and time as Einstein, but they were groping through a fog of misperceptions foisted on them by Newtonian physics.”
Einstein, by contrast, was able to cast off Newtonian misconceptions. “His conviction that the universe loves simplification and beauty, and his willingness to be guided by this conviction, even if it meant destroying the foundations of Newtonian physics, led him, with a clarity of thought that others could not match, to his new description of space and time.”66
Poincaré never made the connection between the relativity of simultaneity and the relativity of time, and he “drew back when on the brink” of understanding the full ramifications of his ideas about local time. Why did he hesitate? Despite his interesting insights, he was too much of a traditionalist in physics to display the rebellious streak in-grained in the unknown patent examiner.67 “When he came to the decisive step, his nerve failed him and he clung to old habits of thought and familiar ideas of space and time,” Banesh Hoffmann said of Poincaré. “If this seems surprising, it is because we underestimate the boldness of Einstein in stating the principle of relativity as an axiom and, by keeping faith with it, changing our notion of space and time.”68
A clear explanation of Poincaré’s limitations and Einstein’s boldness comes from one of Einstein’s successors as a theoretical physicist at the Institute for Advanced Studies in Princeton, Freeman Dyson:
The essential difference between Poincaré and Einstein was that Poincaré was by temperament conservative and Einstein was by temperament revolutionary. When Poincaré looked for a new theory of electromagnetism, he tried to preserve as much as he could of the old. He loved the ether and continued to believe in it, even when his own theory showed that it was unobservable. His version of relativity theory was a patchwork quilt. The new idea of local time, depending on the motion of the observer, was patched onto the old framework of absolute space and time defined by a rigid and immovable ether. Einstein, on the other hand, saw the old framework as cumbersome and unnecessary and was delighted to be rid of it. His version of the theory was simpler and more elegant. There was no absolute space and time and there was no ether. All the complicated explanations of electric and magnetic forces as elastic stresses in the ether could be swept into the dustbin of history, together with the famous old professors who still believed in them.69
As a result, Poincaré expressed a principle of relativity that contained certain similarities to Einstein’s, but it had a fundamental difference. Poincaré retained the existence of the ether, and the speed of light was, for him, constant only when measured by those at rest to this presumed ether’s frame of reference.70
Even more surprising, and revealing, is the fact that Lorentz and Poincaré never were able to make Einstein’s leap even after they read his paper. Lorentz still clung to the existence of the ether and its “at rest” frame of reference. In a lecture in 1913, which he reprinted in his 1920 book The Relativity Principle, Lorentz said, “According to Einstein, it is meaningless to speak of motion relative to the ether. He likewise denies the existence of absolute simultaneity. As far as this lecturer is concerned, he finds a certain satisfaction in the older interpretations, according to which the ether possesses at least some substantiality, space and time can be sharply separated, and simultaneity without further specification can be spoken of.”71
For his part, Poincaré seems never to have fully understood Einstein’s breakthrough. Even in 1909, he was still insisting that relativity theory required a third postulate, which was that “a body in motion suffers a deformation in the direction in which it was displaced.” In fact, the contraction of rods is not, as Einstein showed, some separate hypothesis involving a real deformation, but rather the consequence of accepting Einstein’s theory of relativity.
Until his death in 1912, Poincaré never fully gave up the concept of the ether or the notion of absolute rest. Instead, he spoke of the adoption of “the principle of relativity according to Lorentz.” He never fully understood or accepted the basis of Einstein’s theory. “Poincaré stood steadfast and held to his position that in the world of perceptions there was an absoluteness of simultaneity,” notes the science historian Arthur I. Miller.72
His Partner
“How happy and proud I will be when the two of us together will have brought our work on the relative motion to a conclusion!” Einstein had written his lover Mileva Mari back in 1901.73 Now it had been brought to that conclusion, and Einstein was so exhausted when he finished a draft in June that “his body buckled and he went to bed for two weeks,” while Mari “checked the article again and again.”74
Then they did something unusual: they celebrated together. As soon as he finished all fou
r of the papers that he had promised in his memorable letter to Conrad Habicht, he sent his old colleague from the Olympia Academy another missive, this one a postcard signed by his wife as well. It read in full: “Both of us, alas, dead drunk under the table.”75
All of which raises a question more subtle and contentious than that posed by the influences of Lorentz and Poincaré: What was Mileva Mari’s role?
That August, they took a vacation together in Serbia to see her friends and family. While there, Mari was proud and also willing to accept part of the credit. “Not long ago we finished a very significant work that will make my husband world famous,” she told her father, according to stories later recorded there. Their relationship seemed restored, for the time being, and Einstein happily praised his wife’s help. “I need my wife,” he told her friends in Serbia.“She solves all the mathematical problems for me.”76
Some have contended that Mari was a full-fledged collaborator, and there was even a report, later discredited,77 that an early draft version of his relativity paper had her name on it as well. At a 1990 conference in New Orleans, the American Association for the Advancement of Science held a panel on the issue at which Evan Walker, a physicist and cancer researcher from Maryland, debated John Stachel, the leader of the Einstein Papers Project. Walker presented the various letters referring to “our work,” and Stachel replied that such phrases were clearly romantic politeness and that there was “no evidence at all that she contributed any ideas of her own.”
The controversy, understandably, fascinated both scientists and the press. Columnist Ellen Goodman wrote a wry commentary in the Boston Globe, in which she judiciously laid out the evidence, and the Economist did a story headlined “The Relative Importance of Mrs. Einstein.” Another conference followed in 1994 at the University of Novi Sad, where organizer Professor Rastko Magli contended that it was time “to emphasize Mileva’s merit in order to ensure a deserved place in the history of science for her.” The public discussion culminated with a PBS documentary, Einstein’s Wife, in 2003, that was generally balanced, although it gave unwarranted credence to the report that her name had been on the original manuscript.78
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