Relativity Simply Explained
3.5/5
()
About this ebook
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.
Martin Gardner
Martin Gardner, born in 1914, has written several reviews for The New York Review of Books and was a Scientific American columnist for over twenty-five years. His books include Calculus Made Easy and When You Were a Tadpole and I Was a Fish. He lives in Hendersonville, North Carolina.
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Reviews for Relativity Simply Explained
31 ratings3 reviews
- Rating: 4 out of 5 stars4/5This was a college honors textbook. I am of a decidely non-scientific bent, and this is the only lucid explanation of relativity I received in school. Therefore I'm giving it 4 stars for illuminating an (to me) impenatrable idea and making it readable and (almost) enjoyable.
- Rating: 4 out of 5 stars4/5Good book. Writing a little bit non-exciting for the dramatic material this book actually is about.
- Rating: 5 out of 5 stars5/5Such a very understandable book that an average reader like me could understand the majority of its contents.
Book preview
Relativity Simply Explained - Martin Gardner
1
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.
, 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.
* We disregard in this book, as in most popular science writing, a technical distinction between speed and velocity. Speed is a scalar (a magnitude expressed by one variable), whereas velocity is a vector, calling for a specified direction as well as distance divided by time. If a car spirals around a hill on its way to the top, its speed at any moment is indicated by the speedometer. But its average velocity from the bottom to the top of the hill is much less than its average speed because it is obtained by dividing the distance along the vector line (a straight line from bottom to top) by the time.
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