It is remarkable how willing Michelson was to throw out centuries of accepted wisdom on the basis of a single experiment, but while he was supremely confident in his results, the rest of the world was not. The eminent Dutch physicist Hendrik Lorentz, who was one of the few who seemed to even consider Michelson’s data seriously, uncovered an error in Maxwell’s theoretical analysis and thus distrusted the rest of the work. Both he and the eminent British physicist Lord Rayleigh urged Michelson to repeat the experiment with higher accuracy.
Thus it was that in 1887 Michelson, who had moved to Case School of Applied Science in Cleveland, teamed with chemist Edward Morley, from nearby Western Reserve University—a collaboration that presaged the merger eighty years later of Case and Western Reserve into my home institution, Case Western Reserve University—to perform one of the most celebrated experiments in modern physics.
The Michelson-Morley experiment definitively established that the velocity of light as measured on Earth was independent of a light ray’s direction relative to the earth’s motion around the sun. While Michelson jumped to the conclusion that this implied the ether did not exist (ultimately the correct conclusion), it is, in fact, not the only logical possibility. Rather, the results could have implied that for some reason the ether may have affected the measurement of light’s velocity in ways that no one had yet understood. Indeed, Lorentz’s first question following the experiment, in a letter to Rayleigh, was whether there could be some error in the dynamic theory of electromagnetism that might explain the Michelson-Morley data. Lorentz continued to think deeply about this paradox, and in 1892 he argued that there was only one way he had come up with to reconcile their findings with commonsense notions about what should happen for observers moving with respect to each other. They would measure precisely the same round-trip travel time for light rays going in different directions with respect to the earth’s motion through a stationary ether if, somehow, lengths along the direction of motion with respect to the ether were foreshortened.
What Lorentz was in effect arguing was that the only way light rays would be measured to take the same time for round-trip travels independent of whether or not they were fighting an ether headwind would be if somehow lengths were also shortened along the direction of motion as the earth moved against any such headwinds. Since the distance the light ray traveled is calculated by its velocity multiplied by the time it travels, shortening the distance would cancel what would otherwise have been an extra travel time due to the slowing of light in these directions. It was not so radical an idea to imagine that dynamic electromagnetic effects could cause lengths to so change. After all, if light is an electromagnetic phenomenon, and electric and magnetic forces are conveyed via the medium of the ether, then perhaps the electrically charged particles that make up the constituents of all atoms could be affected by their interactions with the ether as they pushed through it in a way that would move the atoms closer together. (In fact, the Irish physicist George Fitzgerald made precisely this argument in 1889, to derive precisely the same result, although it was unknown to Lorentz in 1892.)
Over the next twelve years Lorentz continued to think about the nature of electromagnetism in this context, and also about the mathematical properties of the theory that might determine what different observers moving with respect to each other would measure. In the process he made an observation that is implicit in Maxwell’s equations but that had never been explicitly described. In 1895 he demonstrated that a moving charged particle would experience a force in a background magnetic field, because moving charges produce magnetic fields, and are therefore magnets and so must also experience forces due to other magnets.
I have always felt that it is precisely this revelation that carries the key to understanding why it was electromagnetism, and not some other force, that led Einstein to cause us to rethink our ideas of space, time, and motion. Ultimately, what the “Lorentz force,” as it has become known, tells us is that what one observer measures as uniquely an electric force, another observer can measure as a magnetic force.
Think about it this way. If you are at rest with respect to some charged particle, and you observe it to move, you know it must have experienced a force, because things do not suddenly start moving without a force having acted on them. But the only force that a charged particle at rest can respond to is an electric force. Now, instead, imagine that you are moving at a constant velocity away from the charged particle. Relative to you the particle is moving backward, away from you. The laws of electromagnetism say that in your reference frame this moving charge must produce a magnetic field. If such a particle is then suddenly deflected in its path, you can measure this deflection and infer that the cause of this deflection was due to an external magnetic field acting on this current.
Thus, one person’s electricity can be another person’s magnetism. That is really the beauty of Maxwell’s theory of electromagnetism. It demonstrated that electricity and magnetism are not only related, they are identical—merely different sides of the same coin. Different observers would measure the same phenomena, and ascribe them to either magnetic or electric effects, depending upon their state of motion. Since it is motion that relates electric and magnetic fields, it is perhaps not so surprising that light, an electromagnetic phenomenon, would cause us to rethink the nature of motion itself. Albert Einstein was only five years old when the Michelson-Morley experiment was performed, but over the next eighteen years, while Lorentz, Fitzgerald, Rayleigh, and other well-known physicists were puzzling over the null results of Michelson and Morley, Einstein came to realize that the real problem was not reconciling Maxwell’s theory with the MichelsonMorley finding (which he would later often claim not even to have known about at the time), but rather reconciling Maxwell’s theory with the understanding of space and time that had prevailed in physics since the days of Galileo.
Again, with hindsight, the problem can be simply stated. One of Maxwell’s greatest discoveries was that if light was an electromagnetic wave, one could calculate its speed from first principles, using solely quantities that could be measured in any laboratory associated with the strength of electric and magnetic forces.
But there is a fundamental, hidden problem with this result. It had long been recognized—indeed, since the time of Galileo and later Newton—that the laws of motion as measured by an observer moving at a constant velocity (say, a person on a train or plane) are the same as for an observer standing still. Think about throwing a ball in the air or playing catch. If you are on a plane or train that is moving in a straight line, and you throw a ball up in the air, you will see exactly the same thing that you would see if you threw the ball while standing still. This is to say, you won’t feel as if you are moving. If the windows are covered, and there are no bumps, and the engines are not making any noise, there is, in fact, really no way to know if you are moving or standing still.
Galileo first recognized this fact about motion and codified it, stating that there is no way to distinguish between observers at rest and observers in constant motion. That principle is literally the foundation on which all of our understanding of modern physics was based. We now call this “Galilean relativity.”
However, as Einstein realized from his teenage years onward, there is a problem reconciling Galilean relativity with Maxwell’s discovery about light. For, if the speed of light can be calculated from fundamental constants that can be measured in a laboratory, and if observers in laboratories moving at a constant velocity with respect to each other should observe the same results as observers in laboratories at rest, then this would imply something remarkable. Since all such observers should measure the same fundamental constants of nature, in terms of which they could each calculate the speed of light rays that they would measure in their laboratories, then all observers, regardless of their state of motion with respect to an ether background, should measure the same speed of light. This result is, of course, precisely what the Michelson-Morley experiment seemed to demo
nstrate, but it also leads to a paradox if light is a wave in an ether. It is like saying that, if you are driving a car along a river, the waves moving in the water would appear to move along relative to you at the same speed that they would be measured to move relative to someone sitting on the shore. That is silly, because if your car is moving along at the same speed as the waves, they will be stationary with respect to you, but not to an observer on the shore.
This is so counterintuitive that it perhaps explains why the best physics minds in the world spent much of the two decades after the Michelson-Morley experiment trying to find a way to dynamically change the predictions of Maxwell’s theory in different ways to accommodate it, rather than accepting that the theory in fact required this result. Einstein, on the other hand, accepted this implication of Maxwell’s theory at face value, because the theory perfectly described all other measured aspects of electromagnetism. Instead, he recognized that to accommodate it one would have to revise other aspects of our understanding of the world.
The first person to suggest that one must begin to think along these lines was not Albert Einstein, but the famous French mathematical physicist, Jules Henri Poincaré. A leading scientific intellect who had a philosophical bent as well, Poincaré realized as early as 1898 that we might have to alter basic notions regarding the objective meaning of various concepts of space and time to account for the fact that the occurrence of events at distant points could only be relayed to us after a finite time. It was in this context that he uttered the words quoted at the beginning of this chapter.
Poincaré even discovered in 1905, the same year that Einstein published his first paper on special relativity, that the equations of electromagnetism remained unchanged if measurements of space and time change for different observers in relative motion in precisely such a way as to reproduce the “Lorentz contraction”—as he then referred to it—which Lorentz had earlier proposed to reconcile the negative result of the MichelsonMorley experiment. Poincaré even demonstrated that the different observers who synchronize their clocks by light signals may have different notions of simultaneity.
It is remarkable that in spite of discovering all of these pieces, Poincaré never fully put the puzzle together. He remained committed both to the ether and to a dynamic origin for the contraction of bodies along their direction of motion relative to the ether. It remained for Einstein to demonstrate that Maxwell’s equations, when combined with the ideas of Galilean relativity, provided all that was necessary to resolve the paradoxes of electrodynamics without additional dynamic hypotheses. All that one had to do was dispense with the absolute
C H A P T E R 4
THE FOURTH DIMENSION
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.
—Hermann Minkowski
Physicists at the turn of the twentieth century were understandably reluctant to abandon the security of a sensible worldview that up to that point had appeared to successfully describe the universe. But ultimately, once the hidden connections that underlie electromagnetism came into clear focus, there was no turning back, and the road that began at “Let there be light” led straight into a fourth dimension. First, the sensible worldview: If I am running away from you, and someone behind you throws a ball at you, I would expect that the ball would appear to be traveling faster relative to you than it would to me. Common sense similarly suggests that two different observers in relative motion will measure the same light ray to travel at different speeds relative to each of them in, say, one second.
Now the problem: Electromagnetism only makes sense, in a world where all laboratories measure the same strength of magnetism and electricity, if the light ray mentioned above approaches each observer by the same distance in the same time, even if the observers are moving apart. Now for Einstein’s solution: If the light ray is to be so measured, then each observer must use different measures of distance or time. Upon careful analysis Einstein determined that both measurements must differ. Specifically, Einstein demonstrated the following implications of the strange behavior of light, in what we now call Einstein’s special theory of relativity:
(i) Remote events that are simultaneous to one observer will not be simultaneous to another observer moving with respect to the first. (ii) Clocks carried by an observer moving with respect to another observer will be measured by the latter to be running slowly.
(iii) Objects carried by an observer moving with respect to another observer will be measured by the latter to be foreshortened along the direction of their motion.
Einstein arrived at each of these bizarre conclusions by doing what he called gedanken, or “thought experiments,” that get around the fact that on human scales our perceptions of space and time are vastly different from what they would be if we could travel at near light-speed. In this, he followed the spirit of Poincaré’s thinking. As Poincaré first pointed out, our knowledge of remote events is always indirect, because remote events are, after all, remote. We may feel like something we see happening across the room is happening at the same moment as we see it, so that we are a “part” of the event, but that is merely an illusion brought about by the incredibly fast speed of light.
Consider a class photograph. We are accustomed to thinking that it reflects a single frozen instant in time, when all of the bright young faces are captured as an enduring memory. But, strictly speaking, this is not accurate. Just as the different rows of students are spread out in space, the photograph reflects an image that is also spread out in time. The light reflected from the faces of the children in the back row arrives at the camera lens at the same instant as the light from the faces of the children in the front row only if the light from the back row began its voyage slightly earlier. The time difference is imperceptible, perhaps a billionth of a second or so, but it isn’t zero. If each row were separated from the row in front by, say, a hundred million miles, instead of a few feet, then the students in the back row could easily have left their seats by the time the students in the front row had begun to pose for one and the same photograph. This is because the light from the back row would take about ten minutes to reach the front row, and would thus reach the camera at the same time as light emitted from the front row ten minutes later. In an astronomical context, this is always true. When we look up at the sky at night, the images of the individual stars reflect moments spread out by hundreds if not thousands of years.
We are accustomed to this phenomenon in a reverse context because of the fact that sound travels much more slowly than light. When we see lightning strike in the distance, and we hear the thunder clap many seconds later, we know that they relate to one and the same event, even though we experience its different aspects at different times. It is equally true however, that things we experience in a single instant can reflect not one event, but many separate ones.
Einstein imagined a scenario where this would be explicit. Picture, for example, a train so long that light from one end of it would take several seconds to reach the other. Now picture that you are in the middle of the train. Now picture, finally, another implausible series of events: Lightning strikes both ends of the train at exactly the same instant. How do you know that the two lightning bolts hit either end of the train at the same time? Simple: You see the two flashes in your car at the same instant. Since you are in the middle of the train, you know that, even accounting for the fact that it has taken some time for the images to reach you, since the time for both images to reach you is the same, the flashes must have been simultaneous.
Now, what about someone on the ground whom you see directly opposite you at exactly the instant when the lightning bolts struck the ends of the train (not later, when you actually see the flashes!)? What would she see (assuming the flashes were bright enough for her to see them as well)?
Well, since you are moving with respect to her, by the time you see the flashes she must now be closer
to one end of the train than the other.
Thus, the light from one of the flashes must have passed her location before it made its way to you. Hence, she will see one of the flashes before the other. But since she was opposite you when the lightning hit either end of the train, and was thus also midway between the flashes, and since she sees one before the other, she must infer that one of the flashes hit before the other.
What is wrong with this picture? Well, in a sensible universe the person on the ground would indeed see one flash before the other, and the person on the train would see both flashes at the same time. But the person on the train, whom the person on the ground would see moving toward one flash and away from the other, would also be able to (if she had the proper apparatus) measure that the light ray from the side of the train that she was moving toward would be traveling relative to her faster than the other light ray, which she would be moving away from. Thus, although she saw both flashes at the same time, she would indeed be able to infer from her measurements that one event had to have occurred before the other in order for her to experience them simultaneously, in agreement with the assessment of the person on the ground.
Hiding in the Mirror: The Quest for Alternate Realities, From Plato to String Theory (By Way of Alicein Wonderland, Einstein, and the Twilight Zone) Page 4
