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Since the publication of Einstein's Special Theory of Relativity in 1905, the discovery of such astronomical phenomena as quasars, pulsars, and black holes — all intimately connected to relativity — has provoked a tremendous upsurge of interest in the subject.
This volume, a revised version of Martin Gardner's earlier Relativity for the Million, brings this fascinating topic up to date. Witty, perceptive, and easily accessible to the general reader, it is one of the clearest and most entertaining introductions to relativity ever written.
Mr. Gardner offers lucid explanations of not only the special and general theories of relativity, but of the Michelson-Morley experiment, gravity and spacetime, Mach's principle, the twin paradox, models of the universe, and other topics. A new Postscript, examining the latest developments in the field, and specially written for this edition, is also included.
The clarity of the text is especially enhanced by the brilliant graphics of Anthony Ravielli, making this "by far the best layman's account of this difficult subject." — Christian Science Monitor.
Absolute or Relative?
Two sailors, Joe and Moe, were cast away on a deserted island. Several years went by. One day Joe found a bottle that had washed ashore. It was one of those new king-size bottles of Coca-Cola. Joe turned pale.
"Hey, Moe!" he shouted. "We've shrunk!"
There is a serious lesson to be learned from this joke. The lesson is: There is no way of judging the size of an object except by comparing it with the size of something else. The Lilliputians thought Gulliver a giant. The Brobdingnagians thought Gulliver tiny. Is a billiard ball large or small? Well, it is extremely large relative to an atom, but extremely small relative to the earth.
Jules Henri Poincaré, a famous nineteenth-century French mathematician who anticipated many aspects of relativity theory, once put it in this way (scientists call his way of putting it a "thought experiment": an experiment that can be imagined but not actually performed). Suppose, he said, that during the night, while you were sound asleep, everything in the universe became a thousand times larger than before. By everything, Poincaré meant everything: electrons, atoms, wavelengths of light, you yourself, your bed, your house, the earth, the sun, the stars. When you awoke, would you be able to tell that anything had changed? Is there any experiment you could perform that would prove you had altered in size?
No, said Poincaré, there is no such experiment. In fact, the universe really would be the same as before. It would be meaningless even to say it had grown larger. "Larger" means larger in relation to something else. In this case there is no "something else." It would be just as meaningless, of course, to say that the entire universe had shrunk in size.
Size, then, is relative. There is no absolute way to measure an object and say that it is absolutely such-and-such a size. It can be measured only by applying other sizes, such as the length of a yardstick or meter rod. But how long is a meter rod? Originally it was defined as one ten-millionth of the distance from the earth's equator to one of its poles. This soon gave way to the length of a platinum bar kept in a cellar near Paris. Today it is defined as the distance light travels through a vacuum in one 299,792,458th of a second. How is a second defined? It is 9,192,631,770 vibrations of a cessium atom excited by microwaves. Of course, if everything in the universe were to grow larger or smaller in the same proportion, including the distance light travels in a second, there would still be no experimental way to detect the change.
The same is true of periods of time. Does it take a "long" or "short" time for the earth to make one trip around the sun? To a small child, the time from one Christmas to the next seems like an eternity. To a geologist, accustomed to thinking in terms of millions of years, one year is but a fleeting instant. A period of time, like distance in space, is impossible to measure without comparing it to some other period of time. A year is measured by the earth's period of revolution around the sun; a day by the time it takes the earth to rotate once on its axis; an hour by the time it takes the long hand of a clock to make one revolution. Always one period of time is measured by comparing it with another.
There is a famous science-fiction story by H. G. Wells called "The New Accelerator." It teaches the same lesson as the joke about the two sailors, only the lesson is about time instead of space. A scientist discovers a way to speed up all the processes of his body. His heart beats more rapidly, his brain operates faster, and so on. You can guess what happens. The world seems to slow down to a standstill. The scientist walks outside, moving slowly so the friction of the air will not set fire to his pants. The street is filled with human statues. A man is frozen in the act of winking at two passing girls. In the park, a band plays with a low-pitched, wheezy rattle. A bee buzzes through the air with the pace of a snail.
Let us try another thought experiment. Suppose that at a certain instant everything in the cosmos begins to move at a slower speed, or a faster speed,* or perhaps stops entirely for a few million years, then starts up again. Would the change be perceivable? No, there is no experiment by which it could be detected. In fact, to say that such a change had occurred would be meaningless. Time, like distance in space, is relative.
Many other concepts familiar in everyday life are relative. Consider "up" and "down." In past ages it was hard for people to understand why a man on the opposite side of the earth was not hanging upside down, with all the blood rushing to his head. Children today have the same difficulty when they first learn that the earth is round. If the earth were made of transparent glass and you could look straight through it with a telescope, you would in fact see people standing upside down, their feet sticking to the glass. That is, they would appear upside down relative to you. Of course, you would appear upside down relative to them. On the earth, "up" is the direction that is away from the center of the earth. "Down" is toward the center of the earth. In interstellar space there is no absolute up or down, because there is no planet available to serve as a "frame of reference."
Imagine a spaceship on its way through the solar system. It is shaped like a giant doughnut and is rotating so that centrifugal force creates an artificial gravity field. Inside the ship, spacemen can walk about the outer rim of the doughnut as if it were a floor. "Down" is now away from the center of the ship, "up" is toward the center: just the opposite of how it is on a rotating planet.
So you see, there are no absolute "ups" and "downs" in the universe. Up and down are directions relative to the direction in which a gravitational field is acting. It would be meaningless to say that while you were asleep the entire cosmos turned upside down, because there is nothing to serve as a frame of reference for deciding which position the cosmos has taken.
Another type of change that is relative is the change of an object to its mirror image. If a capital R is printed in reverse form like this, , you recognize it immediately as the mirror image of an R. But if the entire universe (including you) suddenly became its mirror image, there would be no way that you could detect such a change. Of course, if only one person became his mirror image (H. G. Wells wrote a story about this also, "The Plattner Story") while the cosmos remained the same, then it would seem to him as if the cosmos had reversed. He would have to hold a book up to a mirror to read it, the way Alice behind the looking-glass managed to read the reversed printing of "Jabberwocky" by holding the poem up to a mirror. But if everything reversed, there would be no experiment that could detect the change. It would be just as meaningless to say that such a reversal had occurred as it would be to say that the universe had turned upside down or doubled in size.
Is motion absolute? Is there any type of experiment that will show positively whether an object is moving or standing still? Is motion another relative concept that can be measured only by comparing one object with another? Or is there something peculiar about motion, something that makes it different from the relative concepts just considered?
Stop and think carefully about this for a while before you go on to the next chapter. It was in answer to just such questions that Einstein developed his famous theory of relativity. This theory is so revolutionary, so contrary to common sense that even today there are thousands of scientists (including physicists) who have as much difficulty understanding its basic concepts as a child has in understanding why the people of China do not fall off the earth.
If you are young, you have a great advantage over these scientists. Your mind has not yet developed those deep furrows along which thoughts so often are forced to travel. But whatever your age, if you are willing to flex your mental muscles, there is no reason why you cannot learn to feel at home in the strange new world of relativity.CHAPTER 2
The Michelson-Morley Experiment
Is motion relative? After some first thoughts you may be inclined to answer, "Of course it is!" Imagine a train moving north at 100 kilometers per hour. On the train a man walks south at 4 kilometers per hour. In what direction is he moving and at what speed? It is immediately obvious that this question cannot be answered without choosing a frame of reference. Relative to the train, the man moves south at 4 kilometers per hour. Relative to the ground, he moves north at 100 - 4 = 96 kilometers per hour.
Can we say that the man's "ground speed" (96 kilometers per hour) is his true, absolute speed? No, because there are other, larger frames of reference. The earth itself is moving. It both rotates and swings around the sun. The sun, with all its planets, speeds through the galaxy. The galaxy rotates and moves relative to other galaxies. The galaxies in turn form galactic clusters that move relative to each other. No one really knows how far this chain of motions can be carried. There is no apparent way to chart the absolute motion of anything; that is to say, there is no fixed, final frame of reference by which all motions can be measured.* Motion and rest, like large and small, slow and fast, up and down, left and right, seem to be completely relative. There is no way to measure the motion of one object except by comparing it with the motion of some other object.
Alas, it is not so simple! If this were all there is to say about the relativity of motion, there would have been no need for Einstein to develop his theory of relativity. Physicists would have had the theory all along!
The reason it is not simple is this: there appear to be two very easy ways to detect absolute motion. One method makes use of the speed of light; the other makes use of various inertial effects that occur when a moving object alters its path or velocity. Einstein's special theory of relativity deals with the first, his general theory of relativity with the second. In this and the next two chapters the first method that might serve as a clue to absolute motion, the method that makes use of the speed of light, will be considered.
In the nineteenth century, before the time of Einstein, physicists thought of space as containing a kind of fixed, invisible substance called the ether. Often it was called the "luminiferous ether," meaning that it was the bearer of light waves. It filled the entire universe. It penetrated all material substances. If all the air were pumped out of a glass bell jar, the jar would still be filled—filled with ether. Otherwise, how could light travel through the vacuum? Light is a wave motion; there had to be something there to transmit the waving. The ether itself, although it must vibrate, seldom (if ever) would move with respect to material objects; rather, all objects would move through it, like the movement of a sieve through water. The absolute motion of a star, planet, or any object whatever was (so these early physicists were convinced) simply its motion with respect to this motionless, invisible, etherial sea.
But, you may ask, if the ether is an invisible, nonmaterial substance—a substance that cannot be seen, heard, felt, smelled or tasted—how can the movement of, say, the earth ever be measured with respect to it? The answer is simple. The measurement can be made by comparing the earth's motion with the motion of a beam of light.
To understand this, consider for a moment the nature of light. Actually, light is only the small visible portion of a spectrum of electromagnetic radiation which includes radio waves, radar waves, infrared light, ultraviolet light, and gamma rays. Everything said about light in this book applies equally to any type of electromagnetic wave, but "light" is a shorter term than "electromagnetic wave," so this term will be used throughout. Light is a wave motion. To think of such a motion without thinking also of a material ether seemed to the early physicists as preposterous as thinking about water waves without thinking of water.
If a bullet is fired straight ahead from the front of a moving jet plane, the ground speed of the bullet is faster than if it were fired from a gun held by someone on the ground. The ground speed of the bullet fired from the plane is obtained by adding the speed of the plane to the speed of the bullet. In the case of light, however, the velocity of a beam is not affected by the speed of the object that sends out the beam. This was strongly indicated by experiments in the late nineteenth and early twentieth centuries, and has since been amply confirmed, especially by recent tests on the decay of neutral pi mesons. One famous test was made by Russian astronomers in 1955, using light from opposite sides of the rotating sun. One edge of our sun is always moving toward us, the other edge always moving away. It was found that light from both edges travels to the earth with the same velocity. Similar tests had been made decades earlier with light from revolving double stars. Regardless of the motion of its source, the speed of light through empty space is always the same: about 299,800 kilometers (186,300 miles) per second.
Do you see how this fact provides a means by which a scientist (we will call him the observer) could calculate his own absolute motion? If light travels through a fixed, stationary ether with a certain speed, c, and if this velocity is independent of the velocity of its source, then the speed of light can be used as a kind of yardstick for measuring the observer's absolute motion. An observer moving in the same direction as a beam of light should find the beam passing him with a speed less than c; an observer moving toward a beam of light should find the beam approaching him with a velocity greater than c. In other words, measurements of the velocity of a beam of light should vary, depending on the observer's motion relative to the beam. These variations would indicate his true, absolute motion through the ether.
Physicists often describe this situation in terms of what they call an "ether wind." To understand just what they mean by this, consider again that moving train. We have seen how the speed of a man walking through the train at 4 kilometers per hour is always the same relative to the train, regardless of whether he walks toward the engine or toward the rear of the train. The same is true of the speed of sound waves inside a closed car. Sound is a wave motion transmitted by molecules of air. Because the air is carried along by the car, sound will travel north in the car with the same velocity (relative to the car) with which it travels south.
The situation alters if we move from the closed passenger car to an open flatcar. The air is no longer trapped inside the car. If the train moves at 100 kilometers per hour, there will be a wind of 100 kilometers per hour blowing back across the flatcar. Because of this wind, the speed of sound moving from the back to the front of the car will be less than normal. The speed of sound from front to back will be greater than normal.
Physicists of the nineteenth century believed that the ether surely must behave like the air that rushes over a moving flatcar. How could it be otherwise? If the ether is motionless, any object moving through it would have to encounter an "ether wind" blowing in the opposite direction. Light is a wave motion in this fixed ether. The velocity of light, measured on a moving object, would of course be influenced by such an ether wind.
The earth is hurtling through space, on its trip around the sun, at a speed of about 30 kilometers per second. This motion, the physicists reasoned, should create an ether wind of 30 kilometers per second, blowing past the earth and through the spaces between its atoms. To measure the absolute motion of the earth—its motion with respect to the fixed ether—all that would be necessary would be to measure the speed of light as it travels back and forth in different directions on the earth's surface. Because of the ether wind, light would surely move faster in one direction than another. By comparing the various speeds of light as it is sent in different directions, it should then be possible to calculate the absolute direction and velocity of the earth's motion at any given instant. Such an experiment was first proposed in 1875, four years before Einstein was born, by the great Scottish physicist James Clerk Maxwell.
Excerpted from Relativity Simply Explained by Martin Gardner, Anthony Ravielli. Copyright © 1997 Martin Gardner. Excerpted by permission of Dover Publications, Inc..
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