Chapter II: Part 2

Now the sun being a big heavy body must extend its gravitational strain for a considerable distance around and a ray of light passing through this crumpled up space would not be able to pursue a straight course. And, according to the eclipse observations, it does not. Light like everything else follows “the easiest way” and this is not always the straight and narrow path. A river takes the easiest, not the shortest, way to the sea and this leads it through many meanderings. Most of us, I suppose, have a mental image of Newton’s gravitation as a sort of rope by which the sun pulls the earth into its orbit when it is disposed to fly off on a tangent. But from Einstein’s viewpoint we should rather think of the earth as picking its way as best it can through a space-and-time combination that has been strained and distorted by the power of the sun. I visualize Einstein’s solar system as a spider web with the sun in the middle like the spider and the planets like flies trying to get around through the tangled strands. But it is more complicated than that for each planet has its own lesser web of radiating influence to drag about with it wherever it goes.

Newton’s idea is simpler, but unfortunately light at least seems to follow Einstein’s law, not Newton’s. That is why Einstein is such a troublesome fellow. If he would confine himself to metaphysical speculation nobody need bother about these strange notions of his. But when he points how they can be proved and then British astronomers and American physicists find things according to his deductions he cannot be ignored. The man does not seem to have that decent respect for the opinions of mankind that leads most of us to limit our logic to the sphere of common sense. When he gets an idea in his head he follows it wherever it leads him even though he bumps up against Euclid and Newton and the rest of us. For instance, if you admit the second of his two fundamental postulates, that the speed of light is constant, regardless of the velocity of its source, you are irresistibly led--unless you let go of his hand somewhere on the way--to the conclusion that time is a local affair; that there is no way of telling by light signals whether two clocks at a distance are keeping the same time, or whether two events at different places occur simultaneously. You could not tell this even if you could shoot a watch from one place to the other with the speed of light, for no matter how many seconds--or years--the watch might be on its way it would register the same time. If instead of a watch a man could travel at that speed he would not grow old on the way. According to Einstein no man, watch or any other material thing can travel with the speed of light, for it would require an infinite force to give the smallest particle such a velocity. But let us suppose that a hollow projectile holding a man, such as Jules Verne and Wells used on their voyages to the moon, should be sent off into space with a velocity one twenty-thousandth less than light. If at the end of a year the projectile should be caught like a comet by the gravitation of some star and be swung around and sent back to the earth, the man on stepping out of his shell would be two years older but he would find the world two hundred years older. This would be, as Professor Langevin suggests in _Scientia_, 1911, an interesting way to study history, but it would be risky, not to say impossible. Still French scientists, like Napoleon, have no place in their dictionaries for so stupid a word as “impossible” and M. Esnault-Pelterie has figured out that a thousand pounds of radium would be sufficient to carry a man to Venus in 35 hours if a hollow projectile could be fitted up like a rocket with the radium in the rear sending out a rapid fire of electrons.

TURNING TIME BACKWARD

To loosen up our conventional ideas of the fixity of time and space we may accept the aid of the scientific romancers. Camille Flammarion, the famous French astronomer, wrote a fantastic little book called “Lumen” which tells of a man who died in 1864. His soul flew straight to its heaven which was one of the planets of Capella, the largest star in the constellation Auriga. Here he found the benevolent inhabitants of that sphere, who were endowed with superhuman powers of sight, watching with great distress the bloody scenes of the French revolution of 1793, and wondering how it would come out. To the visitor from the earth this was an old story, to the people of Alpha Aurigae it was a present spectacle, for the distance of the star was such that it took light 72 years to travel from the earth, so they were 72 years belated in their observation of current events on our planet.

The spirit of the defunct Parisian, having the power of flying through empty space at any speed he chose, found that he had thereby also acquired control of time and could hasten, retard, stop or reverse the course of events at will by simply varying his speed. If he remained stationary, scenes on the earth would unfold at their normal rate and in regular order. If he traveled away from the earth with the speed of light everything seemed to stand still. If he traveled faster than light he overtook the rays that had left the earth farther and farther back in the past so he saw through them events in the reverse order. For instance when he looked down on Waterloo he saw the battlefield strewn with corpses and Napoleon walking toward Waterloo backward pushing his horse by the bridle. This is how the battle looked to the interspatial observer:

When my sight was sufficiently habituated to the scene, I perceived some soldiers coming to life out of the eternal night, and by a single effort standing up. The dead horses revived like the dead cavaliers, and the latter remounted them. As soon as two or three thousand men had returned to life, I saw them form unconsciously in line of battle. The two armies took their places fronting one another, and began to fight desperately with a fury that one might have taken for despair. As the combat deepened on both sides, the soldiers came to life more rapidly....

At each gap made by the cannon in the serried ranks a group of resuscitated dead filled up the gaps immediately. When the belligerents had spent the whole day in tearing one another to pieces with grape-shot, with cannons and bullets, with bayonets, sabers and swords--when the great battle was over, there was not a single person killed, no one was even wounded; even uniforms that before it were torn and in disorder were in good condition, the men were safe and sound, and the ranks in correct form. The two armies slowly withdrew from one another, as if the heat of the battle and all its fury had no other object than the restoration to life, amid the smoke of the combat, of the two hundred thousand corpses which had lain on the field a few hours before. What an exemplary and desirable battle it was!

Another literary curiosity on the same theme is “Ignis” by Comte Didier de Chousy. This tells of certain engineers who attempted to utilize the internal heat of the earth by running the waters of a lake into a deep boring. The result was an explosion that blew off a piece of the planet. But the passengers on this artificial asteroid on looking down through their well at the earth they had left could see the lake and city undisturbed and watch themselves at work as they were before the place blew up. The explanation was that this fragment of the earth was projected into space more rapidly than the speed of light and so was catching up with the rays that had gone out before the explosion; these rays, of course, carried the picture of earlier scenes. But Einstein would say that this story--as we might ourselves have suspected--must be fiction for according to his theory the speed of light is the absolute limit of motion, the infinity of velocity, which no material body may excel or attain. He does not, however, say anything about the possible speed of a disembodied spirit such as Flammarion employed in his imaginary exploration of space.

THE METAPHYSICS OF THE MOVIES

But from such fantasies we can see that the order in which we view events depends upon how fast and in what direction we are moving and that past and future may be reversed to our vision. This is easily made apparent by means of motion pictures. If the film is reeled off in the wrong direction the action is reversed. So we see divers rising gracefully out of the water and landing on the spring board. Newly hatched chickens, dismayed at the sight of this unfriendly world, calmly tuck themselves back into their broken shells which close in upon them. When we have come to the close of a perfect Thanksgiving Day the obliging operator may give us an encore of the dinner reversed by running his machine backward. Then we see pieces of turkey politely picked out of the mouths of the diners with their forks and replaced upon the plates. When these are passed back to the carver he puts the slices neatly in their places and the fowl is then sent back to the oven to be unroasted. The cook then sticks on the feathers. The hired man carries the turkey out to the chopping block where with one swift stroke he restores the head and the fowl runs off backwards. This is just as correct as the ordinary order. The sequence of events is the same. Cause and effect are linked together as firmly as before, only they have exchanged places. A scientist knowing nothing of our world except from watching such reversed motion pictures might deduce from them the same consistent and logical system of natural laws that we now have although some of them, for instance, the second law of thermo-dynamics, would be reversed in form.

The motion-picture man has also the power to alter the speed of the passage of time as he will by turning the crank faster or slower. Sometimes he is quite too careless in the way he employs this prerogative. If he is behind time on his schedule he will rush through a lazy siesta scene in a Mexican plaza with all the fury of a Mack Sennett farce. But this telescoping of time can be used to advantage as when he shows us the growth of a plant, the unfolding of its flower and the ripening of its fruit, all in fifteen minutes. On the other hand motion may be slowed up by taking twice as many pictures a minute as usual and projecting them at the ordinary rate. For instance, if it is a dog jumping up to grab a piece of meat from his master’s hand, we see the dog rise slowly from the ground and, while poised in mid-air, eye the meat carefully to select the best point of attack, then deliberately take it between his jaws and gradually descend. Now notice that this is just as true a picture of the dog’s jump as any other. The movie man has simply expanded time measurements as he expands space measurements when he shows us a close-up. A close-up with a face covering a sixteen-foot screen is just as true as a smaller picture. It is what we should always see if the lens of our eyes were a bit more convex. We look through the small end of an opera-glass and objects seem magnified. We look through the large end and objects seem minified. This is not an illusion. The opera-glass _does_ actually enlarge or reduce _what we see_.

So, too, time intervals can be lengthened or shortened. Take a dose of hashish--no, don’t--I should say, if you did take a dose you would find that your perception of duration was prolonged. If while under the influence of the drug you drop a book it will seem an hour getting to the ground. De Quincey describes such experiences in his “Confessions of an Opium Eater.” But without entering into such abnormal states we all know by everyday experience how time flies or lags according to the number of our sensations. Bergson’s philosophy is built upon the distinction between the idea of duration as experienced by all of us and the idea of time as established by the physicists for comparative measurements.

We live in deeds not years; in thoughts not breaths;
In feelings not in figures on a dial.
--_Festus._

For all we know an ephemeral insect that dies in a day may live a longer life than a Galapagos turtle that exists for two centuries.

What Mark Twain said about classical music applies also to science; “It is not so bad as it sounds.” The thing that the chemist calls “sodium chloride” other folks call “salt”--and so does he when he is off duty. Don’t let the scientist bluff you by his polysyllabic propensity. Just try to see what he means by such language. Now what these new-fashioned non-Euclidean geometricians call “the four-dimensional space-time continuum” is essentially the same system of reference as you have used ever since you could toddle. Minkowski did not invent it. Everybody thinks that way unless he is an idiot. Each one of us has had to build up his own philosophy of the universe long before we went to school, mostly before we could talk. We had to study geometry while we were in our cradles--worse than that we had to work out a practical system of geometry for ourselves without the help of Euclid or anyone else. We had to excogitate a system of relationship between the sights and sounds and touches that came to us before we could get along in the world. Probably we all solve this riddle of the universe in about the same way although since there is no way of directly comparing notes we cannot be sure about that.

THE EGOCENTRIC THEORY OF THE UNIVERSE

But the framework that we construct to hold everything outside of ourselves is essentially of the following form:

You are the center of your universe. Everything and every event that you are considering is related to you here and now. Starting from this, your point of place and time, you imagine eight straight lines stretching out toward infinity in eight directions as divergent as possible. These lines--call them destinations or directions or dimensions or coördinates as you please--consist of four opposing pairs, right and left, up and down, forward and back, future and past. Somewhere along or between these four dimensional lines that cross in your brain you can find a place for anything that you need; your pencil, the discovery of America, the sun and next Friday. You can connect up all these things by lines which may represent changes, that is the tracks of movements in space and time. To connect the pencil in your hand with the discovery of America you would have to count back 428 years on the time line and measure off on the east-west and north-south lines whatever distance you may be from San Salvador--not to consider the motion of the earth.

Anything that exists, that is to say, persists, is moving along the time dimension at what appears to be a uniform rate. Of course you can, if you like, conceive of time itself as a stream flowing through things. Since all motion is relative, that way of looking at it is just as “true” as the other. But it is simpler and more sensible to think of things moving through a stationary time just as we think of them moving through a stationary space. A material point that is at rest, such as the dot of an _i_ on this page, (we continue to disregard the motion of the earth) is not moving about in space but is moving forward in time. Its track then is a straight line along the time dimension. That is, a material point is a line in the fourth dimension. If you move the page to the right the forward movement of the dot of the _i_ in the time dimension is combined with the sideways motion in a single slanting line. If you move the page simultaneously upward, rightward and backward the track of the point is a line combining the movement in all four dimensions. Such a track of a point moving through space and time is called its “world-line.” It is a continuity of one dimension. Any event is the point of intersection of one or more such world lines and we can never observe anything except such intersections. That is to say, everything happens somewhere and sometime.

A picture flashed on a cinema screen has three dimensions. It is, say, 10 feet long and 6 feet high and lasts ¹⁄₁₆ of a second, but it has no thickness. A man necessarily has four dimensions. He may measure from 24 to 72 inches in one dimension, from 8 to 18 inches in the second, from 4 to 9 inches in the third and 70 years in the fourth.

After all, the idea of the relativity of time ought to be easier to accept than that of space for it is in accord with experience instead of contrary to it. We drop off to sleep and wake the next instant if we credit our personal perceptions. Why should we believe the sun and the clock in preference to ourselves?

Bergson bases his whole philosophy upon the distinction between _duration_ as it is felt by the individual while he is living through it and _time_ as it is employed by the physicist in his calculations. The latter conception, physical time, is, as Bergson says, a mere invention of man and virtually a fourth dimension of space, so he concludes:

To sum up; every demand for explanation in regard to freedom comes back, without our suspecting it, to the following question: “Can time be adequately represented by space?” To which we answer: Yes, if you are dealing with time flown; No, if you speak of time flowing.[1]

Past and future are alike to the physicist, differing only in direction, like east and west. But to the living person they are altogether different things. For man rolls up his past, as a tourist his rug, and carries it with him wherever he goes. That is why Wells’s “Time Machine” and the reversed reels of the movies are so funny. There is nothing absurd about running a wheel backward but there is about running a man backward.[2] The physicist feels no reluctance about turning the stream of time backward for all physical phenomena are reversible under the proper conditions. If we interpret the universe as merely matter in motion and imagine at a certain instant that every individual particle reverses its motion and goes in just the opposite direction at the same speed, then the whole history of the world would be reënacted in the opposite order and the earth would return to its primeval nebulæ.

In Wells’s story, “The New Accelerator,” a professor invents an elixir that speeds up the rate of living a thousandfold. A person taking a dose of it sees people as wax figures apparently motionless in the midst of violent action. Falling objects seem to stand still in the air. The music of a band is reduced to “a low-pitched, wheezy rattle” or “the slow muffled ticking of some monstrous clock.” But in compensation for this the accelerated drug-fiend could watch at leisure the slow flapping of a bee’s wings.

But even Wells with his seven-league-boots imagination finds it difficult to keep ahead of the march of science. What he then saw only with his mind’s eye we can actually observe. By moving the accelerating lever on your phonograph toward the S end of the scale you can slow up the tune and lower its pitch until it becomes inaudible as music. The new Pathé ultra-rapid camera can take pictures at the rate of 160 to the second. When these are projected on the screen at the usual rate of 16 to the second all movement takes place ten times slower than in actual life. This gives opportunity for the study in detail of the action of a ballplayer pitching a curve or of the wing motion of a humming bird or of the splash of a marble falling into water or of the flight of a bullet. We can magnify motion or minify it as much as we will. The cinematograph owes its origin the desire of Senator Leland Stanford to study the movement of a horse’s legs so as to find out why one racer went faster than another.

Such playful flights of the scientific imagination as Wells and Flammarion indulge in and such freaks of projection as the camera man amuses us with are of use to those of us who find difficulty in translating a mathematical formula into terms of everyday life. There is no better place to study metaphysics than in the world of the flickering screen, for there man has complete control of time and space. He can enlarge and reduce any object. He can hasten, retard or reverse any action. He can throw upon the screen at the same time events happening months and miles apart. Therefore to those of us who have had the advantage of an education in the movies, Einstein’s ideas of the relativity of time and space do not seem startling or inconceivable.

Kant not only conceived the possibility of more than three dimensions but believed in the probability of it. His argument is based on greater insight into the intentions of the Almighty than we of this day would claim:

“If it is _possible_ that there be developments of other dimensions in space, it is also very _probable_ that God has somewhere produced them. For His works have all the grandeur and variety that can possibly be conceived.”

In this temporal, spatial and material world of ours reality requires that the four dimensions should hang together. But at an infinite distance from all matter this fourfold combination would be dissolved into a three-dimensional space and a one-dimensional time. In that extra-mundane realm time ceases to flow, gravitation no longer drags downward, matter is non-existent, light is immovable and change is impossible.[3] Thus the new mathematics leads to a state curiously like the conventional conception of heaven.

We talk as our forefathers did about “the ends of the earth” but we know that one might start from his home and walk forever in any direction without coming to an end of it. But though the earth’s surface is infinite in the sense of endless, yet one never can get more than 8,000 miles away from home where’er he may roam. If a man stood on the top of the highest mountain on earth and aimed a level gun in any direction, the bullet, if it could be given sufficient velocity to counteract the influence of gravity, would go around the world and hit him in the back of the head. Or if light were sufficiently deflected by gravitation to follow a level line around the earth--another absurd assumption--the man looking through a level telescope in any direction could see how his hair was combed in the back. Such happenings, though impossible, are not inconceivable but are logical consequences of our knowledge that the world is round and that what we call straight or level lines as measured on plain or sea are really great circles around a center four thousand miles below.

Now is it not also conceivable that the lines we call straight in astronomical space may also have an imperceptible curvature in some unknown fourth dimension? If this curve is closed like the circumferences of the earth a ray of light pursuing a straight course in a certain direction might eventually return upon its track, even though not refracted or reflected by the matter it passes through or by. A telescope of unlimited power pointed into space at a tangent might then show the observer his own back, if light were transmitted instantaneously, but, since it is not and since the curvature of space, if there be any, is exceedingly minute, what the observer would see, assuming that the earth had come back to its former position, might be the scenes of some geological age millions of years ago.

NON-EUCLIDEAN GEOMETRY

The idea that space itself may be curved and that the axioms and assumptions on which our geometry since the time of Euclid have been based, may not be absolutely and exactly and eternally and universally true has been diligently studied during the last fifty years. The Russian Lobatchewsky, the Hungarian Bolyai and the German Riemann have developed systems of geometry by starting from premises the opposite of those of Euclid and these systems are just as logical and consistent with themselves as the ordinary or Euclidean geometry. These non-Euclidean geometries were at first commonly regarded as mere freaks of the mathematical imagination, but they have already proved valuable in leading to a reconsideration of the fundamental principles of our thinking and, if Einstein is right, they may be necessary to explain physical phenomena. It is hard for the mathematician to discover anything useless. A distinguished American mathematician in announcing a new theorem exclaimed: “And thank Heaven, no possible use can ever be found for it.” But, whatever it was, he made a rash boast for nowadays the mechanic treads on the heels of the mathematician and uses imaginary quantities, actual only in the fourth dimension, like √-1, in figuring out the winding of his dynamo.

Readers whose mathematical faculty is weak or undeveloped and who like something concrete with “human interest” in it will find what they want in “Flatland by A Square,” a book published in Boston in 1891. The author, who turned out to be the Reverend Edwin Abbott, tells of a land in only two dimensions. The ruling class consisted of polygons, the bourgeoisie of squares and equilateral triangles, the lower class of isosceles triangles of narrow base, while the criminals had more irregular forms and the women were mere needles. Since all were confined to a surface, four lines set in a square made a tight prison. The inhabitants of Flatland, even the aristocratic and intellectual individuals who had so many sides as to be almost circular, could not conceive of a third dimension from which a person like ourselves could look down and see at a glance the insides of their houses, their safes and their bodies just as a being in the fourth dimension could see the insides of ours. The narrator, that is, A Square of Flatland, visits as a missionary the land of two dimensions where all the people lie in a line and refuse to believe in anything outside it and finally he encounters and endeavors to convert a solitary point of no dimensions but finds him, as we should expect, an incorrigible solipsist.

We should all of us have been familiar with the fourth dimension for years if Slade had not turned out a trickster. Slade was an American medium--the original of Browning’s “Mr. Sludge”--who fooled Professor Zöllner by giving him what purported to be experimental evidence of the fourth dimension. Zöllner was a distinguished German physicist, Professor of Astronomy in the University of Leipzig, old, near-sighted, pre-disposed to spiritualism, and unskilled in legerdemain. Any proofs that Zöllner asked for, Slade was usually able at the next séance to produce. All the things that one might do in four dimensions but could not do in three were forthcoming by the obliging spirits whom Slade had at call.

Zöllner tied the ends of a string together and sealed them on the table top, letting the loop hang down under the table out of sight. He then asked to have a single knot tied in the string and the spirits tied four. Zöllner also reports that the coins he put into a sealed box were taken out and writing produced inside sealed slates.

On the basis of these experiments Zöllner wrote a volume on “Transcendental Physics” to prove the existence of another world in the fourth dimension. But when Slade tried his tricks in London he was caught at them by Professor E. Ray Lankester. He was convicted of deception with intent to defraud in the Bow Street Police Court and sentenced to three months’ imprisonment with hard labor. Nowadays the apparatus for Slade’s famous slate-writing trick can be purchased at any conjurer’s shop.

It is vain to expect anything scientific to come out of the séance room where the alleged phenomena are not reproducible under specified conditions but appear only occasionally and under circumstances prescribed by the medium who always may be and often is proved to be a sleight-of-hand--or sleight-of-foot--performer. The fourth dimension which Einstein and other scientists are now considering is not conceived of as the abode of departed spirits, a spare room for ghostly visitants, but merely as a new factor in a mathematical formula. It offers us no hope of ever being able to take coin out of a closed safe or put coin into an unopened coconut but it does promise to explain certain optical phenomena which, though rare and minute, are yet open to the observation of anybody, be he skeptical or credulous.

SOME SIMPLE EXAMPLES

Lisbon lies nearly straight east of New York but when a ship captain wants to go to Lisbon he does not sail straight east but sets his course a little northward in the beginning and a little southward toward the end and so gets there quicker than if he had followed a line of latitude. Draw his course on a flat map and you would think he was taking a roundabout route, but trace it on a globe and you will see that he is following a great circle, the geodetic line, which is the shortest distance between any two points on the earth’s surface.

An airman looking down on a rocky, hilly, woody country sees it as a flat plain and if he watched a hunter returning home with his bag of game would wonder that he did not go straight instead of wandering around in such an irregular way. Yet the hunter, being tired, is taking what is for him the shortest way home as he dodges rocks and circumambulates the hills. The easiest way is the shortest way.

A river in its desire to reach the sea always takes the shortest possible way. Its meanderings are not meaningless but determined by a law as rigid as a law of geometry, that is, the law of gravitation which prevents the river from taking a short cut over the hill.

If you look at a landscape over a heated plain or bonfire or through uneven glass you will see that the image is distorted and confused because the rays of light are refracted and entangled as they pass through this unequal medium. Yet each ray is going just as straight as it can toward your eye.

Now to such familiar cases where a ray of light is bent out of its straight course by the uneven density of the air or glass through which it passes Einstein has added another and unsuspected effect, namely, that light is likewise deflected in passing through a strong gravitational field such as the vicinity of a large body like the sun.

It has long been known that the displacement of the earth in space and time (that is to say, its motion) causes an apparent displacement of the stars in space.

The astronomer does not point his telescope straight at a star. If he did, he would not see it, for, owing to the forward motion of the earth, the telescope moves out of range of the rays that otherwise would have reached it.

If you have ever tried to shoot a bird on the wing, or, better, a prairie-dog from a train you will get the idea. Or, if you have not had this experience, you have doubtless watched the raindrops running down a car window and have noticed that when the rain is falling straight down the drops strike the pane on a slant when the car is moving forward. The faster the car moves the greater the deviation from the perpendicular. If the train runs backward the rain-streaks slant in the opposite direction. If then you should be asked to point out the direction of the cloud from which the rain is coming you would--unless you knew and made allowance for the movement of the train--point in a line with the streaks on the pane, sometimes backward, sometimes forward, but not straight upward where the raincloud really is.

Now the astronomer is on a moving train, the earth, which is rushing around a ring about 186,000,000 miles across. Consequently every star appears to wabble around in a little ellipse and the astronomer has to aim his telescope, now on one side, then on the other, of the real position of the star in order to bring it on the cross-hairs of his object glass. This apparent displacement of the stars is known as “the aberration of light” was explained by Fresnel in 1818--to everybody’s satisfaction until recently--on the assumption that all space is filled with an immovable medium, the ether, which transmits the rays of light in straight lines in the form of wave motion, and that the earth moves through the ether without displacing it, somewhat as an airplane moves through still air. But the aviator knows how fast he is moving by the current of air streaming back in his face. Why then, since the ether is in perfect repose, could we not determine the absolute motion of the earth through space by measuring the drift of the ether as it streams through the pores of the earth? Light appears to afford us a means of measuring such a drift of the ether through matter, if there be such. Since light is conveyed by the ether we should naturally expect it to take less time to travel a certain distance if the receiving instrument is carried toward the source of the light by the earth motion than if it is being carried away from it. This question was put to the crucial test by two American physicists, Michelson and Morley, who devised an instrument so delicate that it could detect differences of one-25,000,000th of an inch in the path of a light ray. But although this delicacy was ten times greater than was necessary to detect the ether drift, if there were any, no evidence of such drift could be discovered.

THE ECLIPSE OBSERVATIONS

In the history of science the year 1919 is likely to be known, not as the year of the overthrow of the German Empire, but as the year of the overthrow of Newton’s law of gravitation. The British astronomers who went to Africa to observe the eclipse of the sun May 29, 1919, came back with the proof that a ray of light passing close by the sun is bent out of its straight course. The photographs taken during the six minutes when the sun was shadowed show the surrounding stars in different positions from where they are seen when the sun’s disk is not in their midst. This is the second time that Einstein has scored over Newton. The first was in regard to the orbit of Mercury. If the sun and Mercury were alone in the universe the planet, according to Newton’s law, would revolve forever around the sun in the same elliptical track. But the presence of the other planets makes Mercury deviate from this regular route so the ellipse it describes is never quite the same but slowly shifts around so that in the course of centuries its longer diameter would be pointing in a different direction. Calculating by Newton’s law, the influence exerted by the other planets astronomers found that it would shift the orbit of Mercury 532 seconds of arc in a century. But when they took observations on Mercury they found that its orbit was shifting at the rate of 574 seconds. The discrepancy between observation and theory, 42 seconds, is thirty times greater than could be accounted for by errors of instruments or observation. But according to Einstein’s theory, if the sun and Mercury were alone in space with no other planets interfering, the orbit of Mercury would not remain the same, but would advance at the rate of 43 seconds a century. This, as the reader will observe, is in substantial agreement with the discrepancy which has for two centuries puzzled astronomers, since it was inexplicable on the Newtonian theory.

The electro-magnetic theory of light, thought out by Clerk Maxwell forty-five years ago, has proved to be an excellent guide to research and led to many practical applications, such as wireless telegraphy. According to this theory the miles-long Marconi waves, the infinitesimal waves that we feel as heat or see as light and the still more minute waves of the X-rays are movements of the same sort, though differing in length, and all travel at the same speed in space of 186,000 miles a second. It was one of the implications of Maxwell’s theory, though it was not perceived until later, that light and all such waves must exercise a certain pressure upon a body against which they strike, just as a jet of water from a fireman’s hose pushes against the side of a house. The pressure of light is so exceedingly slight that it had never been noticed, but it has been actually detected and measured by Professors E. F. Nichols of Yale and G. F. Hull of Dartmouth. The sunshine falls upon the earth with a force of 160 tons. Both theory and experiment have shown that a beam of light has inertia or mass, that is to say, a beam of light pushes like a water jet, and it has now been proved, by the eclipse expedition, that the pull of gravity deflects a beam of light as it does a water jet. That is to say, a beam of light has weight, is attracted by gravity. This deflection of a beam of light by gravity is extremely small, but photographs taken during the recent total eclipse of the sun show that star beams that passed near the sun are bent out of a straight path.

A better illustration of the eclipse observation than I could word is given by Sir Oliver Lodge in his interesting article on “The New Theory of Gravitation” in The _Nineteenth Century_ of December, 1915, from which I therefore quote:

Take a fine silk thread of indefinite length, and stretch it straight over the surface of a smooth table or floor. Imagine a star at one end of the thread, and an eye at the other; and let the thread typify one of the rays of light emitted in all directions by the star, viz. the ray emitted in the direction of the observing eye.

Now take a halfpenny [or an American quarter,] place it on the table close to the thread, so that the eye end of the thread is ten feet away; and then push the halfpenny gently forward, till it has displaced the thread the barely perceptible amount of one thousandth of an inch. The eye looking along the thread will now see that the ray is no longer absolutely straight; in other words, the star whose apparent position is determined by that ray will appear slightly shifted. The scale is fixed by the size of the halfpenny, whose diameter, one inch, is used to represent the Sun’s diameter of 800,000 miles. The ten-foot distance between eye and Sun practically supposes that the eye is on the Earth, which would be a spot one hundredth of an inch in diameter, or about the size of this full stop.

As for the distance of the star, at the other far end of the thread, that does not matter in the least: but, on this scale, it may be interesting to note that one of the nearest stars, about eight light-years away, would require the thread to be a thousand miles long.

The ray is now bent or deflected as it passes the neighborhood of the Sun on its long journey, so that it is out of place one thousandth of an inch at a distance of ten feet; and the effect of this tilt of the ray, upon the observer, is to make him just able to see a star upon the Sun’s ‘limb’ when it is really behind it, or to make him see a star slightly further off the ‘limb’ or rim of the Sun than it really is. The shift of one thousandth of an inch at a distance of ten feet corresponds to an angle of one and three-quarter seconds of arc, which is just the optical shift that actually ought to occur, according to Einstein, when a ray from a star nearly grazes the Sun’s limb on its way to a telescope; and this is the optical shift which we now know does occur. That may be taken as the definite result of the recent eclipse observations. The effect, both in magnitude and direction, had been predicted four years before, on the strength of a mathematical investigation, by Professor Einstein.

The images of two stars, one on each side of the sun’s disk, will apparently be crowded a little apart when the sun comes between them. A star that would be just eclipsed by the edge of the sun’s disk if its rays came straight may still be visible since the rays are curved. In other words we can “see around a corner” as every good teacher is said to do. If the sun were encircled by a ring of stars, or a nebula, like a halo, the circle of light would be contracted as it passed the sun and would come to a focus at a place seventeen times the distance of Neptune, or 47,600,000,000 miles beyond the sun.

The observations made by the British expeditions during the eclipse of May 29, 1919, were not altogether satisfactory. At Principe, on account of a cloud that drifted by at an inopportune time, only a few photographs could be obtained. At Sobral one of the object glasses gave distorted plates, but the other gave a very good series of seven star images. These when measured at the Greenwich Observatory gave the following figures which are in accordance with those calculated by Einstein’s formula:

RADIAL DISPLACEMENT OF STARS IN SECONDS OF ANGLE

As observed by the British astronomers:
.20 .32 .56 .54 .84 .97 1.02

As predicted by Einstein:
.32 .33 .40 .53 .75 .85 .88

This is regarded by the astronomers of the British Eclipse Expedition as sufficiently close to confirm Einstein’s law but those who hesitate to accept so far-reaching and subversive a theory on the basis of these few minute measurements may hold their judgment in suspense until 1922 when the next solar eclipse, visible in Australia, takes place. Or possibly some means may be found to take star photographs close to the sun while shining. Our California mountain observatories may be of service in this since they are perched above much of the dust and mist and denser air that cause a strong light to irradiate and fog the photographic plate. Doubtless, too, the old photographs of earlier eclipses will now be got out to see if they contain any stars suitable for measuring.

Some of the opponents of Einstein suggest that the observed deflection of the starlight may be due to a solar atmosphere that refracts the rays like our earthly air. But it is hardly probable that an enveloping atmosphere sufficiently dense and so far-extending as to produce such an effect would have remained unobserved and it is highly improbable that the density of such an atmosphere should have just the density and decrease with the distance at just the rate to produce the deflection predicted by Einstein’s calculation.[4]

The discovery is rather disconcerting to astronomers, for all their calculations for the last three hundred years have been based upon the assumption that light travels in straight lines at even speed through empty space or, what is the same thing, through the ether. If now light is pulled aside by gravitation as it goes by a solid body the rays from a distant star having to pass through the tangled throng of the Milky Way might travel a very devious route and the star would appear to us to be located in a different place from where it really is. In fact it is possible that a star which we see double may actually be single but that rays starting out from it in different directions may be so deflected by passing near other stars that when they reach us they appear to come from different points of space and so appear to us as twin stars. There may, too, be dead or dark stars on the way whose existence we cannot discern and allow for.

Now those of us who are not astronomers are not much concerned over a discrepancy of a few hundredths of a second in the measurement of an angle by the telescope. We do not care much where Mercury will be five centuries hence, for we do not know quite where it is now. If astronomers made the laws of Nature instead of merely discovering them we might be afraid that at their next congress they might repeal Newton’s law of gravitation and send us all flying off into space. But fortunately they have no such power and even though they should all become adherents of Einstein’s most revolutionary theories, Newton’s laws of mechanics and Euclid’s laws of geometry would remain as true as they ever were, not perhaps absolutely and universally true, as we have assumed, but sufficiently accurate for all practical purposes. Deviations from them can only become detectable when we come to consider movements as swift as light waves or electrons.

How a heavy object can alter space relations may be seen from this simple illustration: Stretch a sheet of rubber over a hoop like a drumhead. It is now level and flat and if parallel lines are drawn across it in two directions so as to divide it up into squares like a checkerboard all these lines are straight and equidistant and all the squares are of equal size.

A row of worms, starting in an even rank and crawling along the parallel lines across the drumhead, would keep even all the way. Now lay a bullet on the center of the drumhead. The rubber sags down and stretches, most in the middle, least at the edges. The “parallel” lines are no longer equidistant. The squares are no longer equal. The lines are no longer of the same length. If now we repeat our worm race we shall find that those worms following lines close to the weight have to go down hill and up again and so travel a greater distance to traverse the same number of squares than those following lines nearer the edge which lie comparatively flat and are nearly as short as before. Consequently the worms will be slowed up in proportion to their nearness to the center and the row of their heads will be swung around at an angle to their former frontage.

We might “explain” this by assuming that the worms on seeing the bullet to one side were drawn by their curiosity a little toward it, those nearest of course being drawn the most. Or if we had got beyond this crude animistic method of explanation we might assume that the bullet was attached to the head of each worm by an invisible lariat which being pulled by the bullet drew the worms more or less to one side, the shorter the lariat the stronger the pull. Or if we had outgrown this crude mechanical method of explanation we might assume the existence of a “force” in the lead which in some mysterious manner attracts the heads of the worms inversely as the square of their distance. But instead of inventing a wormhead psychology or an invisible cord or an incomprehensible force is it not simpler to consider the space between and to suppose that the lines to be traversed are lengthened in the neighborhood of the weight?

Now these four successive methods of explanation have been used to account for gravitation. First it was assumed by the ancient Babylonians and Hebrews that the sun and stars were living beings, gods or angels, moving of their own volition around the earth, or at least that each was guided in its orbit by its particular god or angel. The later Greeks of Ptolemy’s time supposed the heavenly bodies to be set in concentric crystal spheres and so revolved; I presume by somebody turning a crank behind the scenes. Then came Newton and said: “Let’s discard the Ptolemaic spheres and all mechanical connection and assume a _force_ of gravitation attracting all bodies in proportion to their masses and inversely proportional to the squares of the distances separating them.” Now comes Einstein and says: “Let’s discard this hypothetical force and simply assume that the field of time and space traversed by a moving body is altered if there is another body in the vicinity.” In Einstein’s view gravitation is not a force; it is a distortion of space and time in the presence of matter. A comet sweeping past the sun cannot pursue a straight course, as it could in interstellar space, but follows a curved path about the sun which is for the comet the shortest way it can go under the circumstances.

So, too, a row of light waves coming from a distant star keeps an even front as they pass through empty space but as they come close to the sun they find their paths impeded, or, we may say, stretched. Those going nearest the sun are slowed up the most; those farthest off the least. Consequently the wavefront is slued around a bit and the direction of the ray is slightly altered.

If now light waves have difficulty getting past the sun we should expect that they would experience like difficulty getting away from the sun. They would be slowed up a bit by its gravitational pullback. The frequency would be reduced; the interval of time between wave-crests lengthened. This means, in the case of sound, lowering the pitch. Touch your finger to the turntable of your phonograph and you flat the tone. In the case of light, it means change of color toward the red. This effect, according to Einstein, should be, but has not been, observed.

“If Einstein’s third prediction is verified,” says Sir Oliver Lodge, “Einstein’s theory will dominate all higher physics and the next generation of mathematical physicists will have a terrible time of it. For university courses and for all practical purposes we shall have the Galilean and Newtonian dynamics but they will reign as a limited monarchy and sooner or later the Einstein physics cannot fail to influence every intelligent man. If these complications are to come into science we must leave them to the younger men. I hope that gravitation, now that it has begun to interact with light, will begin to give up its secrets, but in my time I must be content to get secrets out dynamically and leave transcendental methods to others.”

One English scientist, Thomas Case, writes to _The Times_ to protest that it would have been in much better taste for the Royal Society to have adjourned its discussion “before bringing into question the reputation of Newton, who was President of the Royal Society for the last twenty-five years of his life and raised the society to the acme of its fame.”

WHO IS EINSTEIN?