The Dancing Wu Li Masters

by Gary Zukav

  When the experiment was performed, not the slightest difference in velocity could be detected between the two beams of light. The interferometer was turned 90 degrees so that the beam going against the ether wind now was directed across it, and the beam going across the ether wind now was sent directly into it. Again not the slightest difference in velocity between the two beams could be detected.

  In other words, the Michelson-Morley experiment had failed to prove the existence of the ether. Unless an explanation could be found, physicists would be faced with choosing between two unsettling alternatives: either (1) the earth is not moving (and Copernicus was wrong), or (2) the ether does not exist. Neither of these was very acceptable.

  Michelson and Morley thought that perhaps the earth carried a layer of ether with it as it moved through the ether set, just as it carries its atmosphere with it as it travels through space and, therefore, close to the surface of the earth, the ether breeze cannot be detected. No one had a better hypothesis until an Irishman named George Francis FitzGerald proposed (in 1892) an outrageous explanation.

  FitzGerald reasoned that perhaps the pressure of the ether wind compresses matter just as an elastic object moving through water becomes shortened in the direction that it is traveling. If this were true, then the arm of the interferometer pointing into the ether wind would be somewhat shorter than the arm that is not pointing into it. Therefore, a reduction in the velocity of the light traveling into the ether wind and back might not be detected because the distance that the light travels also is reduced. In fact, if the amount by which the interferometer arm pointing into the ether wind is shortened just corresponds to the amount by which the velocity of the light traveling up that arm and back is reduced, then both beams of light in the experiment will reach the measuring device at exactly the same time (the beam with the higher velocity traversing a greater distance in the same time that the beam with the slower velocity traverses a lesser distance).

  FitzGerald’s hypothesis had a major advantage over all the others. It was impossible to disprove. It said simply that there is a one-dimensional contraction (in the direction of motion) that increases as velocity increases. The catch is that everything contracts. If we want to measure the length of an object that is moving very fast compared to the speed of light, we have to catch up with it first, and when we do, according to the theory, the measuring stick that we are carrying with us also contracts. If the object measured seventeen inches at rest, it still would measure seventeen inches. Nor would anything look contracted because the lenses in our eyes also would contract, distorting them just enough to make everything look normal.

  One year later a Dutch physicist, Hendrik Antoon Lorentz, while working on another problem, independently arrived at FitzGerald’s hypothesis. Lorentz, however, expressed his discovery in rigorous mathematical terms. This, of course, upgraded FitzGerald’s hypothesis to a position of respectability and it began to gain a surprising degree of acceptance, considering its fantasy-like quality. Lorentz’s mathematical formulations of the FitzGerald-Lorentz contraction became known as the Lorentz transformations.

  The stage was now set. All of the scenery was in place. The failure to detect the ether. The Michelson-Morley experiment.* The constancy of the speed of light. The FitzGerald-Lorentz contractions. The Lorentz transformations. These are the facts that continued to confuse physicists at the beginning of the century. All of them but Albert Einstein. When he looked at these pieces of scenery, what his beginner’s mind saw was the special theory of relativity.

  1

  Special Nonsense

  Einstein’s first professional act, upon reviewing the facts, was the equivalent of saying, “But the Emperor’s not wearing any clothes!” except what he said was, “The ether does not exist.”1 The first message of the special theory of relativity is that since the ether is undetectable and, in effect, useless, there is no reason to continue to search for it. It is undetectable because every attempt to measure it or determine its quality, culminating with the Michelson-Morley experiment, failed utterly even to indicate its presence. It is useless because light propagation can be envisioned as the propagation of energy through empty space (in vacuo) according to Maxwell’s field equations as well as it can be envisioned as a disturbance of the ether medium. Einstein stated clearly what already was implicit in Maxwell’s equations. (Maxwell was the discoverer of the electromagnetic field.) “The electromagnetic fields,” he wrote, “are not states of a medium [the ether] and are not bound down to any bearer, but they are independent realities which are not reducible to anything else…”2 This assertion was supported by the inability of physicists to detect the ether.

  With this statement, Einstein brought to a close the illustrious history of mechanics, the idea that physical events are explicable in terms of things. Classical mechanics is the story of objects and forces between them. It was a remarkable break from a three-century-old tradition to assert blatantly, in the early 1900s, that electromagnetic fields involve no object whatever, that they are not states of the ether medium, but “ultimate, irreducible realities”3 in themselves. Henceforth, as in quantum mechanics, there would be no concrete imagery associated with physical theory.

  Both relativity and quantum theory heralded the unprecedented remoteness from experience which has characterized physical theory ever since. In fact, the trend is continuing. As though governed by an inexorable law, physics is becoming more and more abstract as it covers wider and wider tracts of experience. Only the future will tell if this trend is reversible.

  The second victim of Einstein’s inability to see clothes that weren’t there was absolute nonmotion. Why should we make one particular frame of reference “privileged”4 in respect to all others by saying that it alone absolutely is not moving? It may be desirable theoretically, but since such a frame of reference does not constitute a part of our experience, it should be disregarded. It is “intolerable”5 to place in a theoretical structure a characteristic which has no corresponding characteristic in our system of experience.

  In one stroke, Einstein eliminated the two major physical and philosophical blocks to a radically new way of perceiving reality. With no ether and no concept of absolute motion to confuse the situation, the situation became much simpler.

  Einstein’s next step was to confront the puzzle which had come to light (no pun) in the Michelson-Morley experiment, namely, the constancy of the speed of light. How could the speed of light always be 186,000 miles per second regardless of the state of motion of the observer?

  In an ingenious mental turnaround, Einstein turned this puzzle into a postulate! Instead of worrying, for the moment, about how it can happen, he simply accepted the experimentally irrefutable fact that it does happen. This evident (to us) recognition of the obvious was the first step in a logical process, which, once set in motion, was to explain not only the puzzle of the constant speed of light, but a great deal more.

  The puzzle of the constancy of the velocity of light became the principle of the constancy of the velocity of light. The principle of the constancy of the velocity of light is the first foundation stone of the special theory of relativity.

  The principle of the constancy of the velocity of light is that whenever we make a measurement of the velocity of light, regardless of whether we are in motion or at rest relative to the light source, we always get the same result. The speed of light is invariably 186,000 miles per second.* This is what Michelson and Morley discovered in their famous experiment.

  From the point of view of classical mechanics, the principle of the constancy of the velocity of light makes no sense at all. In fact, it conflicts violently with common sense. Before Einstein, the totalitarian grasp of “common sense” held the constancy of the speed of light to the status of a paradox. (Whenever we bump into the limits of our self-imposed cognitive reality, the result is always paradox.) It took a pure beginner’s mind, such as Albert Einstein’s, to accept that if what is, is (the constancy of the veloci
ty of light), then common sense must be wrong.

  The most important victim of Einstein’s beginner’s mind was the whole structure of classical (Galilean) transformations, that sweet but illusory fruit of a common sense anchored in macroscopic dimensions and velocities. To give up common sense is not an easy task. Einstein was the first person to do it in such a wholesale manner that his perception of the very nature of space and time changed radically. Moreover, when all was said and done, Einstein’s vision of space and time turned out to be more useful than that of common sense.

  The second foundation stone of the special theory of relativity is the principle of relativity. When Einstein dismissed the idea of absolute nonmotion, his theory became, ipso facto, a theory of relativity. Since there was no better principle of relativity to be had than Galileo’s, Einstein simply borrowed it, but first, of course, he brought it up to date.

  Galileo’s principle of relativity says that the laws of mechanics (such as the laws governing falling bodies) that are valid in one frame of reference are valid in all frames of reference that move uniformly (without jerkiness) in relation to it. Another way of saying the same thing is that it is impossible to determine, by doing experiments involving the laws of mechanics, whether or not our frame of reference is moving or at rest in relation to another frame of reference in which the laws of mechanics also are valid.

  Einstein expanded the Galilean relativity principle to include all the laws of physics, and not just the laws of classical mechanics. In particular he included the laws governing electromagnetic radiation, which were unknown in Galileo’s time.

  Einstein’s updated principle of relativity, then, is that all the laws of nature are exactly identical in all frames of references that move uniformly relative to each other and that, therefore, there is no way of distinguishing absolute uniform motion (or nonmotion).

  In short, the two foundation stones of the special theory of relativity are the principle of the constancy of the velocity of light (the Michelson-Morley experiment) and the principle of relativity (Galileo). Said more specifically, the special theory of relativity rests upon these two postulates:

  The velocity of light in a vacuum is the same in all frames of reference (for all observers) moving uniformly, relative to each other, and

  All laws of nature are the same in all frames of reference moving uniformly, relative to each other.

  Of these two postulates, the first one, the principle of the constancy of the velocity of light, is the troublemaker. There is no way that it and the classical transformation laws both can be true. According to the classical transformation laws (and common sense) the speed of light must be its velocity as it is emitted from a source plus or minus the velocity of the observer, if the observer is moving toward the source or away from the source. According to experiment, the speed of light remains constant regardless of the state of motion of the observer. Common sense and experimental findings are in violent disagreement.

  Einstein’s beginner’s mind told him that, since we cannot argue with what is (the experimental evidence), then our common sense must be wrong. With this decision to disregard common sense and to base his new theory on the only clothes he could see that the emperor was wearing (the constant speed of light and the principle of relativity) Einstein stepped boldly into the unknown, in fact, into the unimaginable. Already on new territory, he proceeded to explore where no person had gone before.

  How could it be that to every observer the speed of light is the same regardless of their state of motion? To measure speed, it is necessary to use a clock and ruler (a rigid rod). If the speed of light as measured by an observer at rest relative to a light source is the same as the speed of light as measured by an observer in motion relative to the source, then it must be that, somehow, the measuring instruments change from one frame of reference to the other in just such a way that the speed of light always appears to be the same.

  The speed of light appears constant because the rods and clocks used to measure it vary from one frame of reference to another depending upon their motion. In short, to an observer at rest, a moving rod changes its length and a moving clock changes its rhythm. At the same time, to an observer traveling along with a moving rod and clock, there is no apparent change at all in length or rhythm. Therefore, both observers measure the speed of light to be the same, and neither can detect anything unusual in the measurement or in the measuring apparatus.

  This is very similar to the case of the Michelson-Morley experiment. According to FitzGerald and Lorentz, the arm of the interferometer that faces into the ether wind (now dismissed from our theory) is shortened by the pressure of the ether wind. Therefore, the light that travels the interferometer arm facing into the “ether wind” has less distance to travel and more time to do it in than does the light traveling the other arm. As a result, the speed of light traveling both arms appears to be the same. This is what the Lorentz transformations describe. Come to think of it, the Lorentz transformations can be used to describe contractions due to motion as well as contractions due to a fictitious ether wind.

  FitzGerald and Lorentz imagined that rigid rods were compressed under the pressure of the ether wind, but according to Einstein, it is motion itself that causes contraction, and, in addition, time dilation.

  Here is another way of looking at it. A “constant velocity of light” is exactly what would result if moving measuring rods became shorter and moving clocks ran more slowly because a moving observer would measure the speed of light with a shorter measuring rod (less distance for the light to travel) and a slower clock (more time to do it in) than an observer at rest. Each observer, however, would consider his own rod and clock to be quite normal and unimpaired. Therefore, both observers would find the speed of light to be 186,000 miles per second and both of them would be puzzled by this fact if they were still bound by the classical transformation laws.

  These were the initial fruits of Einstein’s basic assumptions (the principle of the constancy of the velocity of light and the principle of relativity): First, a moving object appears to contract in its direction of motion and become shorter as its velocity increases until, at the speed of light, it disappears altogether. Second, a moving clock runs more slowly than a clock at rest and continues to slow its rhythm as its velocity increases until, at the speed of light, it stops running altogether.

  These effects only appear to a “stationary” observer; one who is at rest relative to the moving clock and rod. They do not appear to an observer who is traveling along with the clock and rod. To make this clear, Einstein introduced the labels “proper” and “relative.” What we see when we observe our stationary rod and our stationary clock, if we ourselves are stationary, is their proper length and proper time. (“Proper” means “one’s own.”) Proper lengths and proper times always appear normal. What we see if we are stationary and observe a rod and a clock traveling very fast relative to us is the relative length of the moving rod and the relative time of the moving clock. The relative length is always shorter than the proper length, and the relative time is always slower than the proper time.

  The time that you see on your own watch is your proper time, and the time that you see on the watch of the person moving past you is the relative time (which appears to you—not to the person moving past you—to run more slowly). The length of the measuring rod in your own hand is its proper length, and the length of the measuring rod in the hand of the person moving past you is its relative length (which appears to you—but not to the other person—to be shorter). From the point of view of the person moving past you, he is at rest, you are moving, and the situation is reversed.

  Suppose that we are aboard a spacecraft outward bound on an exploration. We have made arrangements to press a button every fifteen minutes to send a signal back to earth. As our speed steadily increases our earthbound colleagues notice that instead of every fifteen minutes, our signals begin to arrive seventeen minutes apart, and then twenty-five minutes apart. After se
veral days, our colleagues, to their distress, find that our signals arrive every two days. As our velocity continues to increase our signals become years apart. Eventually, generations of earthlings come and go between our signals.

  Meanwhile, on the spacecraft, we are entirely unaware of the predicament back on earth. As far as we are concerned, everything is proceeding according to plan, although we are becoming bored with the routine of pressing a button every fifteen minutes. When we return to earth, a few years older (our proper time) we may find that we have been gone, according to earth time, for centuries (their relative time). Exactly how long depends upon how fast we have been going.

  This scene is not science fiction. It is based upon a well-known (to physicists) phenomenon called the Twin Paradox of the special theory of relativity. Part of the paradox is that one twin remains on earth while the other goes on a space voyage and returns younger than his brother.

  There are many examples of proper time and relative time. Suppose that we are in a space station observing an astronaut who is traveling at a speed of 161,000 miles per second relative to us. As we watch him, we notice a certain sluggishness in his movements, as though he were moving in slow motion. We also notice that everything in his spaceship also seems to function in slow motion. His rolled cigarette, for example, lasts twice as long as one of ours.