4 1 ADVENTURES OF THE MIND 27.

Einstein's Great Idea By JAMES R. NEWMAN

To the eyes of the man of imagination, nature is imagination itself. must tramp one's own road. Nevertheless, relativity is in some -WILLIAM BLAKE. respects simpler than the theory it supplanted. It makes the 4 instein died less than four years ago. Fifty years ear- model of the physical world more susceptible to proof by lier, when he was twenty-six, he put forward an experiment; it replaces a grandiose scheme of space and time F idea which changed the world. His idea revolution- with a more practical scheme. Newton's majestic system was ized our conception of the physical universe; its consequences worthy of the gods; Einstein's system is better suited to crea- have shaken human society. Since the rise of science in the tures like ourselves, with limited intelligence and weak eyes. seventeenth century, only two other men, Newton and Dar- But relativity is radically new. It forces us to change deeply win, have produced a comparable upheaval in thought. rooted habits of thought. It requires that we free ourselves Einstein, as everyone knows, did something remarkable, from a provincial perspective. It demands that we relinquish but what exactly did he do? Even among educated men and convictions so long held that they are synonymous with com- women, few can answer. We are resigned to the importance of mon sense, that we abandon a picture of the world which his theory, but we do not comprehend it. It is this circum- seems as natural and as obvious as that the stars are overhead. stance which is largely responsible for the isolation of modern It may be that in time Einstein's ideas will seem easy; but our science. This is bad for us and bad for science; therefore more generation has the severe task of being the first to lay the old than curiosity is at stake in the desire to understand Einstein. aside and try the new. Anyone who seeks to understand the Relativity is a hard concept, prickly with mathematics. world of the twentieth century must make this effort. There are many popular accounts of it, a small number of In 1905 while working as an examiner in the Swiss Patent which are good, but it is a mistake to expect they will carry the Office, Einstein published in the Annalen der Physik, a thirty- reader along—like a prince stretched on his palanquin. One page paper with the CONTINUED ON PAGE 102

James R. Newman has achieved equal distinction as the Imagination (written with Edward Kasner), The a lawyer and a writer on mathematics. In the former Control of Atomic Energy (with Byron Milner), and capacity he taught at Yale Law School, served as recently the monumental four-volume World of About the Author adviser to the White House on scientific legislation, Mathematics, published by Simon & Schuster. He is and as counsel to the Senate Special Committee on currently at work on a biography of Michael Faraday. Atomic Energy. His books include Mathematics and Photograph by Philippe Halsman 1 02 THE SATURDAY EVENING POST

He seated them at a table near the what you and Della are going to eat-1 "Hold the drinks," Mason said, "until dance floor, summoned a waiter and di- have a hunch we may have to bolt this he gets back from the phone, but you rected him to take good care of Mason meal, even if we're going to get it at can bring the menus." Bridge Clubs and his party. all." Mason smiled across at Della Street. "You wish drinks before seeing the Mason's eyes narrowed thoughtfully "Paul can't believe he's really going to menu?" the waiter asked. as he thought about what Drake had said. relax and have some good food. Usually Mason glanced at Della Street, nodded, "Hold everything for a minute, waiter... . he's chained down to that office of his." LOVE said, "Bring a manhattan for the lady.... Call your office, Paul. Let them know The waiter brought menus. Mason What do you want, Paul?" where we are and see if there's a report studied his menu carefully. Della Street "A double manhattan, sweet," Drake on anything urgent." glanced at it, made up her mind, put the them Can't keep said. "You wait right there," Drake said to menu aside, looked up toward the phone the dishes filled! Nobody "I'll take a rum cocktail," Mason said, the waiter. "I'll be back and confirm that booth and said, "Oh-oh." "and then you can bring the menu." order." "What's the matter?" Mason asked. can resist the melt-on-the- "Now wait a minute," Drake said. "I Drake started for the phone booth, "Paul," Della Street said. "Look at tongue goodness of have a horrible hunch about this thing. and the waiter said to Mason and Della him." pure creamery butter, I would prefer to give my order right Street, "I'll bring the menus. Shall I Drake was hurrying toward their table. fresh-mint flavor, and now. I don't need any menu, and I know bring the drinks now?" TO BE CONTINUED other prized ingredients.

Einstein's Great Idea (Continued from Page 41)

title On the Electrodynamics of Moving The wave theory of light appeared to This reasoning was the basis of the Bodies. The paper embodied a vision. answer this question. A wave is a pro- Michelson-Morley experiment. They car- Poets and prophets are not alone in their gressive motion in some kind of medium; ried out a number of trials in which they visions; a young scientist—it happens a sound wave, for example, is a move- compared the velocity of a beam of light mostly to the young—may in a flash ment of air particles. Light waves, it was moving through the ether in the direction glimpse a distant peak which no one else supposed, move in an all-pervasive me- of the earth's motion, and another beam has seen. He may never see it again, but dium called the ether. The ether was as- traveling at right angles to this motion. the landscape is forever changed. The sin- sumed to be a subtle jelly with marvelous There was every reason to believi that gle flash suffices; he will spend his life de- properties. It was colorless, odorless, these velocities would be different. Yet no scribing what he saw, interpreting and without detectable features of any kind. difference was observed. The light beam elaborating his vision, giving new direc- It could penetrate all matter. It quivered seemed to move at the same velocity in tions to other explorers. in transmitting light. Also, the body of either direction. The possibility that the At the heart of the theory of relativity the ether as a whole was held to be sta- earth dragged the ether with it having are questions connected with the velocity tionary. To the physicist this was its most been ruled out, the inquiry had come to a of light. The young Einstein began to important property, for being absolutely dead end. Perhaps there was no differ- brood about these while still a high- at rest the ether offered a unique frame of ence; perhaps there was no ether. The school student. Suppose, he asked him- reference for determining the velocity of Michelson-Morley findings were a major self, a person could run as fast as a beam light. Thus while it was hopeless to at- paradox. of light, how would things look to him? tempt to determine the absolute motion Various ideas were advanced to resolve Imagine that he could ride astride the of a physical body because one could it. The most imaginative of these, and beam, holding a mirror just in front of find no absolutely stationary frame of also the most fantastic, was put forward him. Then, like a fictional vampire, he by the Irish physicist, G. F. Fitzgerald.

would cause no image; for since the light • • • • • • • • • • • • • • • • • • • • • He suggested that since matter is elec- and the mirror are traveling in the same trical in essence and held together by direction at the same velocity, and the electrical forces, it may contract in the mirror is a little ahead, the light can never Lament for direction of its motion as it moves catch up to the mirror and there can be a Shining Past through the ether. The contraction would no reflection. be very small; nevertheless in the direc- But this applies only to his mirror. tion of motion the unit of length would Imagine a stationary observer, also Oh, for those carefree days be shorter. This hypothesis would ex- equipped with a mirror, who watches the when I plain the Michelson-Morley result. The rider flashing by. Obviously the observ- Was youthful, dashing, arms of their interferometer might con- er's mirror will catch the rider's image. In lusty ! tract as the earth rotated; this would shorten the unit of length and cancel out other words, the optical phenomena sur- I'm not the blade I used to rounding this event are purely relative. the added velocity imparted to the light They exist for the observer; they do not be; by the rotation of the earth. The veloc- exist for the rider. This was a trouble- I've gotten pretty rusty. ities of the two beams—in the direction some paradox, which flatly contradicted Richard Wheeler of the earth's motion and at right angles the accepted views of optical phenomena. to it—would appear equal. Fitzgerald's We shall have to see why. idea was elaborated by the famous Dutch • • • • • • • • • • • • • • • • • • • • • The speed of light had long engaged physicist, H. A. Lorentz. He put it in the attention of physicists and astron- mathematical form and connected the omers. In the seventeenth century the reference against which to measure it, the contraction caused by motion with the Danish astronomer Romer discovered attempt was not hopeless for light; the velocity of light. According to his arith- that light needed time for its propagation. ether, it was thought, met the need. metic, the contraction was just enough to Thereafter, increasingly accurate meas- The ether, however, did not meet the account for the negative results of the urements of its velocity were made and need. Its marvelous properties made it a Michelson-Morley experiment. There the by the end of the nineteenth century the terror for experimentalists. How could subject rested until Einstein took it up established opinion was that light always motion be measured against an ecto- anew. travels in space at a certain constant rate, plasm, a substance with no more sub- He knew of the Michelson-Morley about 186,000 miles a second. stantiality than an idea? Finally, in 1887, findings. He knew also of other incon- But now a new problem arose. In the two American physicists, A. A. Michel- sistencies in the contemporary model of mechanics of Galileo and Newton, rest son and E. W. Morley, rigged up a beau- the physical world. One was the slight but and uniform motion (i.e., constant ve- tifully precise instrument, called an inter- persistent misbehavior (by classical stand- locity) are regarded as indistinguishable. ferometer, with which they hoped to dis- ards) of the planet Mercury as it moved in its orbit; it was losing time (at a trifling within easy reach at Of two bodies, A and B, it can only be cover some evidence of the relationship said that one is in motion relative to the between light and the hypothetical ether. rate, to be sure—forty-three seconds of your nearby supermarket other. The train glides by the platform; If the earth moves through the ether, a arc per century), but Newton's theory of or the platform glides by the train. The beam of light traveling in the direction of its motion was exact and there was no earth approaches the fixed stars; or they the earth's motion should move faster way of accounting for the discrepancy. approach it. There is no way of deciding through the ether than a beam traveling Another was the bizarre antics of elec- VerneIN which of these alternatives is true. And in the opposite direction. Moreover, just trons, which, as W. Kaufmann and J. J. in the science of mechanics it makes no as one can swim across a river and back Thomson discovered, increased in mass *MUTTER MINTS difference. more quickly than one can swim the same as they went faster. The question was, VANILLA or CHOCOLATE One of the questions, therefore, was distance up and down stream, it might could these inconsistencies be overcome whether, in respect to motion, light itself be expected that a beam of light taking by patching and mending classical the- Vemell-Thompson Candy Co., Seattle was like a physical body; that is, whether analogous paths through the ether would ories? Or had the time come for a Coper- its motion was relativistic in the New- complete the to-and-fro leg of the journey nican renovation? tonian sense, or absolute. more quickly than the up-and-down leg. (Continued on Page 104) 104 THE SATURDAY EVENING POST

(Continued from Page 102) Making his integrate: neither space nor time is what of nature, unaffected by the motion of the own way, Einstein turned to another as- it seems. observer or of the source of the light. pect of the velocity problem. Velocity The clarification of the concept of si- The hypothesis of the ether thus be- measurements involve time measure- multaneity thrust upon Einstein the task came unnecessary. One did not have to ments, and time measurements, as he of challenging two assumptions, assump- try to measure the velocity of light perceived, involve the concept of simul- tions hedged with the divinity of Isaac against an imaginary frame of reference, taneity. Is this concept simple and intui- Newton. "Absolute, true, and mathe- for the plain reason that whenever light tively clear? No one doubted that it was; matical time, of itself and from its own is measured against any frame of refer- but Einstein demanded proof. nature, flows equably without relation to ence its velocity is the same. Why then I enter my study in the morning as the anything external. . . ." This was New- conjure up ethereal jellies? The ether clock on the wall begins to strike. Ob- ton's sonorous definition in his great simply lost its reason for being. viously these events are simultaneous. book, Principia Mathematica. To this TR1-EX REFINED Assume, however, that on entering the definition he added the equally majestic, A second postulate was needed. New- study I hear the first stroke of the town- "Absolute space, in its own nature, with- tonian relativity applied to the motion of hall clock, half a mile away. It took time out relation to anything external, remains material bodies; but light waves, as I for the sound to reach me; therefore always similar and immovable." These mentioned earlier, were thought not to while the sound wave fell on my ears at assumptions, as Einstein saw, were mag- be governed by this principle. Einstein the moment I entered the study, the event nificent but untenable. They were at the pierced the dilemma in a stroke. He that produced the wave was not simul- bottom of the paradoxes of contemporary simply extended Newtonian relativity to taneous with my entry. physics. They had to be discarded. Ab- include optical phenomena. The second Consider another kind of signal. I see solute time and absolute space were con- postulate says: In any experiment involv- the light from a distant star. An astron- cepts which belonged to an outworn met- ing mechanical or optical phenomena it omer tells me that the image I see is not aphysic. They went beyond observation makes no difference whether the laboratory Wolf's Head Oil of the star as it is today, but of the star as and experiment; indeed, they were re- where the experiment is being performed is it was the year Brutus killed Caesar. futed by the nasty facts. Physicists had to at rest or in uniform motion; the results of What does simultaneity mean in this live with these facts. the experiments will be the same. More case? Is my here-now simultaneous with To live with them meant nothing less generally, one cannot by any method dis- there-then? provides the star's Can I speak mean- than to accept the Michelson-Morley tinguish between rest and uniform mo- WOLF'S HEAD ingfully of the star as it was the day Joan - the kind of difference paradox, to incorporate it into physics tion, except in relation to each other. that really counts. of Arc was burned, even though ten gen- rather than try to explain it away. From Is that all there is to the special theory With WOLF'S HEAD, you erations will have to pass before the light the point of view of common sense the of relativity? The postulates are decep- get smoother engine emitted by the star on that day reaches results were extraordinary, yet they had tively simple. Moreover, to the sharp- operation . . . fewer repair bills . . . add the earth? How can 1 be sure it will ever been verified. It was not the first time that eyed reader they may appear to contra- less oil between drains. That's because get here? In short, is the concept of si- science had had to overrule common dict each other. The contradictions, how- WOLF'S HEAD is 100% Pure Pennsylvania multaneity for different places exactly sense. The evidence showed that the ever, are illusory, and the consequences . . . Tri-Ex refined three important extra equivalent to the concept for one and the speed of light measured by any observer, are revolutionary. steps . . . and scientifically fortified for same place? whether at rest or in motion relative to Consider the first point. From the superior premium quality. WOLF'S HEAD is Einstein soon convinced himself that the light source, is the same. Einstein em- postulates one may infer that on the one tough . . . long-lasting . . . gives you more the answer is no. Simultaneity, as he re- bodied this fact in a principle from which hand light has the velocity c, and, on the miles of complete protection per quart. Prove the difference yourself—try WOLF'S alized, depends on signals; the speed of a satisfactory theory of the interaction be- other hand, even when according to our HEAD, today. light (or other signal) must therefore enter tween the motion of bodies and the traditional way of calculating it should into the meaning of the concept. Not propagation of light could be derived. have the velocity c q (where q is the only does the separation of events in This principle, or first postulate, of his velocity of the source), its velocity is still WOLF'S HEAD OIL space becloud the issue of simultaneity in Special Theory of Relativity states that c. Concretely, light from a source in mo- REFINING CO., INC. OIL CITY, PA. time, but relative motion may do so. A the velocity of light in space is a constant tion with (Continued on Page 106) pair of events which one observer pro- nounces simultaneous may appear to an- other observer, in motion with respect to the first, to have happened at different times. In his own popular account of rel- ativity (see box on Page 108), Einstein CorNo Other Method gave a convincing and easy example, Pain stops last 1. Acts Like which showed that any measurement of 2. Corns quickly time is a measurement with respect to a removed Dr. Scholl's given observer. A measurement valid for Corns, sore toes 3. one observer may not be valid for an- prevented other. Indeed, the measurement is certain 4. New or tight not to be valid if one attempts to extend shoes eased it from the system where the measure- ment was made to a system in motion No waiting for the kind of relief you want relative to the first. when you avail yourself of the multiple Einstein was now aware of these facts. action of Dr. Scholl's Zino-pads. Relief Measuring the speed of light requires a starts in seconds . . . corns are removed in time measurement. This involves a judg- a jiffy ... new or tight shoes are eased. Get ment of simultaneity. Simultaneity is not this fast relief today. Sold everywhere. an absolute fact, the same for all observ- ers. The individual observer's judgment depends on relative motion. You be the Judge 519* AO! SchollS Zino-pads But the sequence does not end here. A By FLORENCE K. PALMER Calk those cracks further inference suggests itself, namely, that simultaneity may also be involved in To salvage what he could when he lost his small apartment house with measuring distances. A passenger on a moving train who wants to measure the through foreclosure, Boswell removed the electric ranges. The length of his car has no difficulty. With a mortgage holder sued to halt him. LCALKING COMPOUND yardstick he can do the job as easily as if "Whatever is attached to a building is part of the real estate," L. Use handy Speed Loads for he were measuring his room at home. Not the mortgagor contended. "The vents above these stoves, and the ! fastest, easiest way to seal so for a stationary observer watching the fact that the stoves rested flush with the sink drainboards, go to cracks around windows train go by. The car is moving and he show that they were permanent fixtures." and doors. Stays put. Will cannot measure it simply by laying a L not dry out, run or crack! yardstick end on end. He must use light "Not so," Boswell replied. "They belong to me personally, as (Also in Squeeze Tubes) they were connected to the kitchen wall only by an ordinary elec- At Hardware & Lumber Dealers signals, which will tell him when the ends of the car coincide with certain arbitrary tric plug like those of floor lamps and radios." MACKLANBURG-DUNCAN CO. points. Therefore, problems of time arise. If you were the judge, would you let Boswell get away with OKLAHOMA CITY 1, OKLA. Suppose the thing to be measured is an the stoves? electron, which is in continual motion at • • • • • • • • • • • • • • • • • • • • • high speed. Light signals will enter the DOGS — CATS — BIRDS experiment, judgments of simultaneity Boswell kept the stoves. The court property. It added, "An ordinary STOP Misery! Itch, Eczema, Dry coat will have to be made, and once again it is ruled that if an object can be moved plug cannot change personal prop- dLe to lack SKIN VITAMIN—Linoleic oil obvious that observers of the electron without material damage to itself or erty into realty." (5VZ- in Rex). Add to food. Give Beauty, who are in motion relative to each other the building, it remains personal Based upon a 1956 Oregon decision. Brilliant Sheen to Coat or Feathers. will get different results. The whole com- Write for free folder. REX, Monticello, Illinois. fortable picture of reality begins to dis- o6 THE SATURDAY EVENING POST

(Continued from Page 104) respect to a time characteristics of a physical event given frame of reference has the same ve- which, though perceived by him, are in- Won't you make this simple experiment ? locity as light from a source at rest with dependent of the observer and might respect to the same frame. (As one physi- therefore be expected to appear the same cist suggested, this is as if we were to say to all observers. The constancy principle that a man walking up a moving stairway of the velocity of light provided Einstein does not get to the top any sooner than with the invariant he needed. It could be a man standing still on the moving stair- maintained, however, only at the expense way.) This seems absurd. But the reason it of the traditional notion of time. And seems absurd is that we take it for granted even this offering was not enough. Space that the velocity of the moving source and time are intertwined. They are part must be added to the normal velocity of of the same reality. Tinkering with the light to give the correct velocity of the measure of time unavoidably affects the beam emitted by the source. Suppose we measure of space. abandon this assumption. We have al- Einstein, you will notice, arrived at the ready seen, after all, that motion has a same conclusion as Fitzgerald and Lo- queer effect on space and time measure- rentz without adopting their electrical ments. It follows that the established hypotheses. It was a consequence of his notions of velocity must be reconsidered. postulates that clocks and yardsticks The postulates were not inherently con- yield different measurements in relative tradictory; the trouble lay with the clas- motion than at rest. Is this due to an sical laws of physics. They had to be actual physical change in the instru- changed. Einstein did not hesitate. To ments? The question may be regarded as preserve his postulates he consigned the irrelevant. The physicist is concerned only old system to the flames. In them were with the difference in measurements. If consumed the most cherished notions of clock springs and yardsticks contract, space, time and matter. why is it not possible to detect the change? One of the cliches about Einstein's Because any scales used to measure it theory is that it shows that everything is would suffer the same contraction. What relative. The statement that everything is is at issue is nothing less than the relative is as meaningful as the statement foundations of rational belief. that everything is bigger. As Bertrand Earlier I mentioned Kaufmann's and Russell pointed out, if everything were Thomson's discovery that a moving elec- relative there would be nothing for it to tron increases in mass as it goes faster. be relative to. The name relativity is Relativity explains this astonishing fact. misleading. Einstein was in fact concerned The first postulate sets an upper limit to with finding something that is not relative, the velocity of light, and permits of the something that mathematicians call an deduction that no material body can ex- invariant. With this as a fixed point, it ceed this speed limit. In Newton's system might be possible to formulate physical there were no such limits; moreover, the laws which would incorporate the "ob- mass of a body—which he defined as its jective residue" of an observer's experi- "quantity of matter"—was held to be the ence; that is, that part of the space and same whether the body was at rest or in

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EASIEST TO PLAY OP ALL MUSICAL INSTRUMENTS! THE SATURDAY EVENING POST Its patented and exclusive features make the difference "Yes, dear . . . right, dear . . . will do, dear . . ." May 16, 1959 107 motion. But just as his laws of motion servations made within a system, it seems fact that the forces arise from the inertia the deflection one could compute the have been shown not to be universally quite possible, under the same circum- of a mass, i.e., its resistance to changes in acceleration. true, his concept of the constancy of stances, to determine changes in velocity its state. It would seem then that any one When Einstein turned these points over mass turns out to be flawed. According to or direction, i.e., acceleration. In a train of several simple experiments should in his mind, he perceived a loose end in Einstein's Special Theory, the resistance moving smoothly in a straight line, at furnish evidence of such acceleration, the reasoning, which others had not of a body to changes in velocity increases constant velocity, one feels no motion. and distinguish it from uniform motion or noticed. How is it possible in either a with velocity. Thus, for example, more But if the train speeds up, slows down or rest. Moreover, it should even be possible mechanical or an optical experiment to force is required to increase a body's takes a curve, the change is felt immedi- to determine the effect of acceleration on distinguish between the effects of gravity, velocity from 50,000 to 50,001 miles per ately. One has to make an effort to keep a beam of light. For example, if a beam and of acceleration produced by inertial hour than from 100 to 101 miles per hour. from falling, to prevent the soup from were set parallel to the floor of a labora- forces? Take the light-beam experiment. The scientific name for this resistance is sloshing out of the plate, and so on. tory at rest or in uniform motion, and the At one point the beam is parallel to the inertia, and the measure of inertia is These effects are ascribed to what are laboratory were accelerated upward or floor of the laboratory; then suddenly it mass. (This jibes with the intuitive notion called inertial forces, producing accelera- downward, the light would no longer be is deflected. The observer ascribes the de- that the amount of force needed to tion—the name is intended to convey the parallel to the floor, and by measuring flection to acceleration caused by inertial accelerate a body depends on its "quan- tity of matter.") The ideas fall neatly into place: with increased speed, inertia in- creases; increased inertia evinces itself as increased mass. The increase in mass is, to be sure, very small at ordinary speeds, and therefore undetectable, which ex- plains why Newton and his successors, though a brilliant company, did not dis- cover it. This circumstance also explains why Newton's laws are perfectly valid for all ordinary instances of matter in mo- tion: even a rocket moving at 10,000 miles an hour is a tortoise compared to a beam of light at 186,000 miles a second. But the increase in mass becomes a major factor where high-speed nuclear particles are concerned; for example, the electrons in a hospital X-ray tube are speeded up to a point where their normal mass is doubled, and in an ordinary TV-picture tube the electrons have 5 per cent extra mass due to their energy of motion. And at the speed of light the push of even an unlimited accelerating force against a body is completely frustrated, because the mass of the body, in effect, becomes infinite. It is only a step now to Einstein's fate- ful mass-energy equation. The quantity of additional mass, mul- tiplied by an enormous number—namely, the square of the speed of light—is equiv- alent to the energy which was turned into mass. But is this equivalence of mass and energy a special circumstance attendant upon motion? What about a body at rest? Does its mass also represent energy? Ein- stein boldly concluded that it does. "The mass of a body is a measure of its energy content," he wrote in 1905, and gave his now-famous formula, E = mc2, where E is energy content, m is mass (which varies according to speed) and c is the velocity of light. "It is not impossible," Einstein said in this same paper, "that with bodies whose energy content is variable to a high Bouquet from Mr. Big degree (e.g., with radium salts) the theory may be successfully put to the test." In "Our Treasurer does a fine job of keeping close tabs on our expenses. Recently Other postage meter advantages the 1930's many physicists were making this test, measuring atomic masses and he stopped by to compliment me on asking for the little postage meter. 'Saves time • Meters seal as well as stamp your the energy of products of many nuclear and postage,' he says, 'first real postage accounting we ever had.' Saves me from envelopes; most models do both simultaneously. Some also sign checks. reactions. All the results verified his idea. being stuck, too, with slow, sloppy lick-and-stick mailing. Good deal all around!" A distinguished physicist, Dr. E. U. • Postage in the meter eliminates the Condon, tells a charming story of Ein- A postage meter prints postage as you need it for any kind or class of mail need for inventories of adhesive stein's reaction to this triumph: "One of —directly on the envelope or on special gummed tape for parcel post. Prints stamps of different denominations. my most vivid memories is of a seminar at • your own small ad, if you want one, at the same time. No minimum mail volume Princeton (1934) when a graduate student is required. And anyone can was reporting on researches of this kind easily use a postage meter. and Einstein was in the audience. Einstein The meter is set by the postoffice for as much postage as you want to buy. had been so preoccupied with other Your postage is protected from loss, damage, misuse, and automatically FREE: Handy desk or wall chart studies that he had not realized that such accounted for. Metered mail needs less handling time in the postoffice, can of new postal rates with parcel post confirmation of his early theories had often catch earlier trains and planes. map and zone,finder. become an everyday affair in the physical laboratory. He grinned like a small boy One out of 3 users of the low-cost, desk model (the DM) averages less than Larger electric and kept saying over and over, '1st das models stamp wirk/ich so?' Is it really true?—as more $1 a day for postage. Call the nearest Pitney-Bowes office for a demonstration. and seal up to 175 letters a minute. and more specific evidence of his E = mc2 Or send coupon for free illustrated booklet. relation was being presented." For ten years after he formulated the Special Theory, Einstein grappled with PITNEY-BOWES PITNEY-BOWES, INC. M.Ibrat the task of generalizing relativity to in- PB 2872 Pacific St., clude accelerated motion. 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o8 THE SATURDAY EVENING POST forces, but how can he be sure? He ally fall into one of the hollows. Now must make his determination entirely on think of space-time as corresponding to the basis of what he sees within the labora- the sheet of rubber, and large gravita- tory, and he is therefore unable to tell V V tional masses to the lead weights; think whether inertial forces are at work—as in M' also of any "event"—a moving particle, the moving train—or whether the ob- EINSTEIN'S OWN Train a beam of light, a planet—as the counter- served effects are produced by a large part of the marble rolling on the mem- (though unseen) gravitating mass. EXAMPLE OF brane. Where there are no masses, space- Here then, Einstein realized, was the time is "flat" and paths of motion are clue to the problem of generalizing rela- THE RELATIVITY Embankment straight lines. But in the neighborhood of tivity. As rest and uniform motion are in- large masses space-time is distorted into OF TIME distinguishable, so are acceleration and M "slopes" and "hollows," which affect the the effects of gravitation. Neither mechan- A B path of any object entering upon them. ical nor optical experiments conducted This is what used to be called the within a laboratory can decide whether attraction of gravitation. But gravitation the system is accelerated or in uniform The diagram shows a long railroad the embankment. But MI is not station- in Einstein's theory is merely an aspect of motion and subjected to a gravitational train traveling along the rails with veloc- ary; it is moving toward the right with space-time. The starlight bent toward field. (The poor wretch in tomorrow's ity V, in the direction toward the right of the velocity V of the train. Therefore the sun "dips" into the "slope" around it, space ship, suddenly thrown to the floor, the page. The bottom line denotes the (considered with reference to the em- but has enough energy not to be trapped will be unable to tell whether his vehicle embankment running parallel to the rails. bankment) the passenger is moving to- in the "hollow"; the earth circling the sun is starting its rocket motor for the home The letters A and B mark two places on ward the beam of light coming from B, is riding on the "rim" of its "hollow" like journey or falling into the gravitational the rails, and the letter M marks a point and away from the beam coming from A. a cyclist racing round a velodrome; a clutches of Arcturus.) Einstein formu- on the embankment directly midway be- It seems clear then that he will see the planet which gets too deep into the lated his conclusion in 1911 in his "prin- tween A and B. At M stands an observer beam emitted by the flash at B sooner "hollow" may fall to the bottom. (This is ciple of equivalence of gravitational forces equipped with a pair of mirrors which are than the beam emitted by the flash at one of the hypotheses astronomers make and inertial forces." joined in a V and inclined at 90°. By A. Accordingly he will pronounce the about collisions which may have formed His ideas invariably had startling con- means of this device he can observe both flash at B as earlier in time than the flash new planets in our universe.) There are sequences. From the principle of equiv- places, A and B, at the same time. We at A. slopes and hollows wherever there is alence he deduced, among others, that imagine two events at A and B, say two Which of the two pronouncements is matter; and since astronomical evidence gravity must affect the path of a ray of flashes of lightning, which the observer correct, the observer's or the passenger's? seems to favor the hypothesis that mat- light. This follows from the fact that ac- perceives in his mirror device at the same The answer is that each is right in its own ter is on average uniformly distributed celeration would affect the ray, and grav- time. These he pronounces to be simul- system. The observer is right with respect throughout the universe, and finite— ity is indistinguishable from acceleration. taneous, by which he means that the rays to the embankment, the passenger with though not necessarily constant—Ein- Einstein predicted that this gravity effect of light emitted at A and B by the light- respect to the train. The observer may stein suggested the possibility that the would be noticeable in the deflection of ning bolts meet at the midpoint M of the say that he alone is right because he is at whole of space-time is gently curved, the light from the fixed stars whose rays length A B along the embankment. rest while the passenger is moving and his finite, but unbounded. It is not incon- pass close to the huge mass of the sun. Now consider the moving train, and impressions are therefore distorted. To sistent with this hypothesis that the uni- He realized, of course, that it would not imagine a passenger seated in it. As the this the passenger can reply that motion verse is expanding, in which case the be easy to observe the bending because train proceeds along the rails, the passen- does not distort the signals, and that, in density of matter would decrease. A under ordinary conditions the sun's bril- ger will arrive at a point MI, which is any case, there is no more reason to be- finite but unbounded universe is roughly liant light washes out the light of the directly opposite M, and therefore ex- lieve that he was moving and the observer analogous—though it is of higher dimen- stars. But during a total eclipse the stars actly midway between the length A —›- B at rest than that the passenger was at rest sion—to the two-dimensional curved sur- near the sun would be visible, and circum- along the rails. Assume further that the and the observer moving. face of the earth. The area is finite with- stances would be favorable to checking passenger arrives at MI just when the There is nothing to choose between out boundaries, and if one travels in a his prediction. "It would be extremely de- flashes of lightning occur. We have seen these views, and they can be logically "straight line" in a given direction one sirable," Einstein wrote in his paper that the observer at M correctly pro- reconciled only by accepting the principle must, after a time, return to the original enunciating the equivalence principle, "if nounces the lightning bolts as simultane- that simultaneity of events is meaningful point of departure. astronomers would look into the problem ous; the question is, Will the train passen- only with respect to a particular reference Einstein's achievement is one of the presented here, even though the consid- ger at MI make the same pronouncement? system; moreover, that every such system glories of man. Two points about his eration developed above may appear in- It is easily shown that he will not. Obvi- has its own particular time, and unless, work are worth making. The first is that sufficiently founded or even bizarre." ously if the point MI were stationary as Einstein says, we are told the reference his model of the world was not a machine Eight years later, in 1919, a British eclipse with respect to M, the passenger would system to which the statement of time with man outside it as observer and inter- expedition headed by the famous astron- have the same impression of simultaneity refers, a bare statement of the time of an preter. The observer is part of the reality omer Arthur Eddington, confirmed Ein- of the lightning flashes as the observer on event is meaningless. he observes; therefore by observation he stein's astounding prediction. shapes it. In 1916 Einstein announced his Gen- The second point is that his theory did eral Theory of Relativity, a higher syn- much more than answer questions. As a thesis incorporating both the Special living theory it forced new questions upon Theory and the principle of equivalence. must also be discarded. In the new world be curved? Once again we must think not us. Einstein challenged unchallengeable Two profound ideas are developed in the of Minkowski and Einstein, there is in terms of metaphysical abstractions, but writs; he would have been the last to General Theory: the union of time and neither absolute past nor absolute future; of testable concepts. claim that his own writs were beyond space into a four-dimensional continuum nor is there an absolute present dividing Light rays in empty space move in challenge. He broadened the human mind. (a consequence of the Special Theory), past from future and "stretching every- straight lines. Yet in some circumstances and the curvature of space. where at the same moment through (e.g., where the ray is close to the sun) For readers who may wish to pursue It was to one of his former professors space." The motion of an object is repre- the path of motion is seen to be curved. this subject further, the following books at Zurich, the Russian-born mathema- sented by a line in space-time, called a A choice of explanations offers itself. We are recommended: tician, Hermann Minkowski, that Ein- "world-line." The event makes its own may, for example, say that a gravitational stein owed the idea of the union of space history. The signals it emits take time to mass in the neighborhood of the ray has Newman, James R. (editor) and time. "From henceforth," Minkow- reach the observer; since he can record bent it; or we may say that this gravita- WHAT IS SCIENCE? ski had said in 1908, "space in itself and only what he sees, an event present for tional mass has curved the space through Simon & Schuster time in itself sink to mere shadows, and one observer may be past for another, which the ray is traveling. There is no $4.95 only a kind of union of the two preserves future for a third. In Eddington's words, logical reason to prefer one explanation (See chapter What is Physics? an independent existence." To the three the absolute "here-now" of former be- to the other. Gravitational fields are no by E. U. Condon.) familiar dimensions of space, a fourth, of liefs has become a merely relative "seen- less an imaginary concept than space- time, had to be added, and thus a single now." time. The only concrete evidence comes Whitehead, Alfred North new medium, space-time, replaced the But this must not be taken to mean that from measuring the path of the light it- SCIENCE AND THE MODERN WORLD orthodox frame of absolute space and every observer can portray only his own self—not the field or space-time. It turns New American Library absolute time. An event within this me- world, and that in place of Newtonian out to be more fruitful to explain the $.50 dium—one may, for example, think of a order we have Einsteinian anarchy. Just curved path of the light ray as an effect of moving object as an "event"—is identi- as it was possible in the older sense to fix curved space-time, rather than as an ef- Frank, Philipp fied not only by three spatial co-ordinates precisely the distance between two points fect of the direct action of gravity on light. EINSTEIN: HIS LIFE AND TIMES denoting where it is, but by a time co- in three-dimensional space, so it is pos- Let me suggest an analogy. A thin sheet Knopf ordinate denoting when the event is there. sible in the four-dimensional continuum of rubber is stretched over a large drum- $5.00 Where and when are, as we have seen, of space-time to define and measure dis- kettle. I take a very light marble and per- judgments made by an observer, depend- tance between events. This distance is mit it to roll over the sheet. I observe that Eddington, Sir Arthur ing on certain interchanges of light sig- called an "interval" and has a "true, ab- the path of its motion is a straight line. I THE NATURE OF THE PHYSICAL WORLD nals. It is for this reason that the time co- solute value," the same for all who meas- now take several lead weights and place Cambridge University Press ordinate includes as one of its elements ure it. Thus, after all, "we have found them at different points on the rubber $4.25 the number for the velocity of light. something firm in a shifting world." sheet. Their weight dimples it, forming With absolute space and time dis- How is the concept of curved space re- small slopes and hollows. Suppose I re- Dampier, Sir William carded, the old picture of the universe lated to this picture? The concept itself lease the marble on this surface. The path A HISTORY OF SCIENCE proceeding moment by moment from the sticks in the craw. A vase, a pretzel, a line of motion will no longer be straight, but Cambridge University Press past through the present into the future can be curved. But how can empty space will curve toward the slopes and eventu- $4.95