Part 7

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: