From NEWTON to EINSTEIN Changing Conceptions of THE UNIVERSE BY BENJAMIN HARROW
IV.
NEWTON
“Newton was the greatest genius that ever existed.”—Lagrange, one of the greatest of French mathematicians.
“The efforts of the great philosopher were always superhuman; the questions which he did not solve were incapable of solution in his time.”—Arago, famous French astronomer.
EINSTEIN
“This is the most important result obtained in connection with the theory of gravitation since Newton’s day. Einstein’s reasoning is the result of one of the highest achievements of human thought.”—Sir J. J. Thomson, president of the British Royal Society and professor of physics at the University of Cambridge.
“It surpasses in boldness everything previously suggested in speculative natural philosophy and even in the philosophical theories of knowledge. The revolution introduced into the physical conceptions of the world is only to be compared in extent and depth with that brought about by the introduction of the Copernican system of the universe.”—Prof. Max Planck, professor of physics at the University of Berlin and winner of the Nobel Prize.
I
NEWTON
II n speaking of Newton we are tempted to paraphrase a line from the Scriptures: Before Newton the Solar System was without form, and void; then Newton came and there was light. To have discovered a law not only applicable to matter on this earth, but to the planets and sun and stars beyond, is a triumph which places Newton among the super-men.
What Newton’s law of gravitation must have meant to the people of his day can be pictured only if we conceive what the effect upon us would be if someone—say Marconi—were actually to succeed in getting into touch with beings on another planet. Newton’s law increased confidence in the universality of earthly laws; and it strengthened belief in the cosmos as a law-abiding mechanism.
Newton’s Law. The attraction between any two bodies is proportional to their masses and inversely proportional to the square of the distance that separates them. This is the concentrated form of Newton’s law. If we apply this law to two such bodies as the sun and the earth, we can state that the sun attracts the earth, and the earth, the sun. Furthermore, this attractive power will depend upon the distance between these two bodies. Newton showed that if the distance between the sun and the earth were doubled the attractive power would be reduced not to one-half, but to one-fourth; if trebled, the attractive power would be reduced to one-ninth. If, on the other hand, the distance were halved, the attractive power would be not merely twice, but four times as great. And what is true of the sun and the earth is true of every body in the firmament, and, as Professor Rutherford has recently shown, even of the bodies which make up the solar system of the almost infinitesimal atom.
This mysterious attractive power that one body possesses for another is called “gravitation,” and the law which regulates the motion of bodies when under the spell of gravitation is the law of gravitation. This law we owe to Newton’s genius.
Newton’s Predecessors. We can best appreciate Newton’s momentous contribution to astronomy by casting a rapid glance over the state of the science prior to the seventeenth century—that is, prior to Newton’s day. Ptolemy’s conception of the earth as the center of the universe held undisputed sway throughout the middle ages. In those days Ptolemy was in astronomy what Aristotle was in all other knowledge: they were the gods who could not but be right. Did not Aristotle say that earth, air, fire and water constituted the four elements? Did not Ptolemy say that the earth was the center around which the sun revolved? Why, then, question further? Questioning was a sacrilege.
Copernicus (1473–1543), however, did question. He studied much and thought much. He devoted his whole life to the investigation of the movements of the heavenly bodies. And he came to the conclusion that Ptolemy and his followers in succeeding ages had expounded views which were diametrically opposed to the truth. The sun, said Copernicus, did not move at all, but the earth did; and far from the earth being the center of the universe, it was but one of several planets revolving around the sun.
The influence of the church, coupled with man’s inclination to exalt his own importance, strongly tended against the acceptance of such heterodox views. Among the many hostile critics of the Copernican system, Tycho Brahe (1546–1601) stands out pre-eminently. This conscientious observer bitterly assailed Copernicus for his suggestion that the earth moved, and developed a scheme of his own which postulated that the planets revolved around the sun, and planets and sun in turn revolved around the earth.
The majority applauded Tycho; a small, very small group of insurgents had faith in Copernicus. The illustrious Galileo (1564–1642) belonged to the minority. The telescope of his invention unfolded a view of the universe which belied the assertions of the many, and strengthened his belief in the Copernican theory. “It (the Copernican theory) explains to me the cause of many phenomena which under the generally accepted theory are quite unintelligible. I have collected arguments for refuting the latter, but I do not venture to bring them to publication.” So wrote Galileo to his friend, Kepler. “I do not venture to bring them to publication.” How significant of the times—of any time, one ventures to add.
Galileo did overcome his hesitancy and published his views. They aroused a storm. “Look through my telescope,” he pleaded. But the professors would not; neither would the body of Inquisitors. The Inquisition condemned him: “The proposition that the sun is in the center of the earth and immovable from its place is absurd, philosophically false and formally heretical; because it is expressly contrary to the Holy Scriptures.” And poor Galileo was made to utter words which were as far removed from his thoughts as his oppressors’ ideas were from the truth: “I abjure, curse and detest the said errors and heresies.”
The truth will out. Others arose who defied the majority and the powerful Inquisition. Most prominent of all of these was Galileo’s friend, Kepler. Though a student of Tycho, Kepler did not hesitate to espouse the Copernican system; but his adoption of it did not mean unqualified approval. Kepler’s criticism was particularly directed against the Copernican theory that the planets revolve in circles. This was boldness in the extreme. Ever since Aristotle’s discourse on the circle as a perfect figure, it was taken for granted that motion in space was circular. Nature is perfect; the circle is perfect; hence, if the sun revolves, it revolves in circles. So strongly were men imbued with this “perfection,” that Copernicus himself fell victim. The sun no longer moved, but the earth and the planets did, and they moved in a circle. Radical as Copernicus was, a few atoms of conservatism remained with him still.
Not so Kepler. Tycho had taught him the importance of careful observation,—to such good effect, that Kepler came to the conclusion that the revolution of the earth around the sun takes the form of an ellipse rather than a circle, the sun being stationed at one of the foci of the ellipse.
To picture this ellipse, we shall ask the reader to stick two pins a short distance apart into a piece of cardboard, and to place over the pins a loop of string. With the point of a pencil draw the loop taut. As the pencil moves around the two pins the curve so produced will be an ellipse. The positions of the two pins represent the two foci.
Kepler’s observation of the elliptical rotation of the planets was the first of three laws, quantitatively expressed, which paved the way for Newton’s law. Why did the planets move in just this way? Kepler tried to answer this also, but failed. It remained for Newton to supply the answer to this question.
Newton’s Law of Gravitation. The Great Plague of 1666 drove Newton from Cambridge to his home in Lincolnshire. There, according to the celebrated legend, the philosopher sitting in his little garden one fine afternoon, fell into a deep reverie. This was interrupted by the fall of an apple, and the thinker turned his attention to the apple and its fall.
It must not be supposed that Newton “discovered” gravity. Apples had been seen to fall before Newton’s time, and the reason for their return to earth was correctly attributed to this mysterious force of attraction possessed by the earth, to which the name “gravity” had been given. Newton’s great triumph consisted in showing that this “gravity,” which was supposed to be a peculiar property residing in the earth, was a universal property of matter; that it applied to the moon and the sun as well as to the earth; that, in fact, the motions of the moon and the planets could be explained on the basis of gravitation. But his supreme triumph was to give, in one sublime generalization, quantitative expression to the motion regulating heavenly bodies.
Let us follow Newton in his train of thought. An apple falls from a tree 50 yards high. It would fall from a tree 500 yards high. It would fall from the highest mountain top several miles above sea level. It would probably fall from a height much above the mountain top. Why not? Probably the further up you go the less does the earth attract the apple, but at what distance does this attraction stop entirely?
The nearest body in space to the earth is the moon, some 240,000 miles away. Would an apple reach the earth if thrown from the moon? But perhaps the moon itself has attractive power? If so, since the apple would be much nearer the moon than the earth, the probabilities are that the apple would never reach the earth.
But hold! The apple is not the only object that falls to the ground. What is true of the apple is true of all other bodies—of all matter, large and small. Now there is the moon itself, a very large body. Does the earth exert any gravitational pull on the moon? To be sure, the moon is many thousands of miles away, but the moon is a very large body, and perhaps this size is in some way related to the power of attraction?
But then if the earth attracts the moon, why does not the moon fall to the earth?
A glance at the accompanying figure will help to answer this question. We must remember that the moon is not stationary, but travelling at tremendous speed—so much so, that it circles the entire earth every month. Now if the earth were absent the path of the moon would be a straight line, say MB. If, however, the earth exerts attraction, the moon would be pulled inward. Instead of following the line MB it would follow the curved path MB′. And again, the moon having arrived at B′, is prevented from following the line B′C, but rather B′C′. So that the path instead of being a straight line tends to become curved. From Kepler’s researches the probabilities were that this curve would assume the shape of an ellipse rather than a circle.
The only reason, then, why the moon does not fall to the earth is on account of its motion. Were it to stop moving even for the fraction of a second it would come straight down to us, and probably few would live to tell the tale.
Newton reasoned that what keeps the moon revolving around the earth is the gravitational pull of the latter. The next important step was to discover the law regulating this motion. Here Kepler’s observations of the movements of the planets around the sun was of inestimable value; for from these Newton deduced the hypothesis that attraction varies inversely as the square of the distance. Making use of this hypothesis, Newton calculated what the attractive power possessed by the earth must be in order that the moon may continue in its path. He next compared this force with the force exerted by the earth in pulling the apple to the ground, and found the forces to be identical! “I compared,” he writes, “the force necessary to keep the moon in her orb with the force of gravity at the surface of the earth, and found them answer pretty nearly.” One and the same force pulls the moon and pulls the apple—the force of gravity. Further, the hypothesis that the force of gravity varies inversely as the square of the distance had now received experimental confirmation.
The next step was perfectly clear. If the moon’s motion is controlled by the earth’s gravitational pull, why is it not possible that the earth’s [11]motion, in turn, is controlled by the sun’s gravitational pull? that, in fact, not only the earth’s motion, but the motion of all the planets is regulated by the same means?
Here again Kepler’s pioneer work was a foundation comparable to reinforced concrete. Kepler, as we have seen, had shown that the earth revolves around the sun in the form of an ellipse, one of the foci of this ellipse being occupied by the sun. Newton now proved that such an elliptic path was possible only if the intensity of the attractive force between sun and planet varied inversely as the square of the distance—the very same relationship that had been applied with such success in explaining the motion of the moon around the earth!
Newton showed that the moon, the sun, the planets—every body in space conformed to this law. The earth attracts the moon; but so does the moon the earth. If the moon revolves around the earth rather than the earth around the moon, it is because the earth is a much larger body, and hence its gravitational pull is stronger. The same is true of the relationship existing between the earth and the sun.
Further Developments of Newton’s Law of Gravitation. When we speak of the earth attracting the moon, and the moon the earth, what we really mean is that every one of the myriad particles composing the earth attracts every one of the myriad particles composing the moon, and vice versa. If in dealing with the attractive forces existing between a planet and its satellite, or a planet and the sun, the power exerted by every one of these myriad particles would have to be considered separately, then the mathematical task of computing such forces might well appear hopeless. Newton was able to present the problem in a very simple form by pointing out that in a sphere such as the earth or the moon, the entire mass might be considered as residing in the center of the sphere. For purposes of computation, the earth can be considered a particle, with its entire mass concentrated at the center of the particle. This viewpoint enabled Newton to extend his law of inverse squares to the remotest bodies in the universe.
If this great law of Newton’s found such general application beyond our planet, it served an equally useful purpose in explaining a number of puzzling features on this planet. The ebb and flow of the tides was one of these puzzles. Even in ancient times it had been noticed that a full moon and a high tide went hand in hand, and [13]various mysterious powers, were attributed to the satellite and the ocean. Newton pointed out that the height of the water was a direct consequence of the attractive power of the moon, and, to a lesser extent, because further away, of the sun.
One of his first explanations, however, dealt with certain irregularities in the moon’s motion around the earth. If the solar system would consist of the earth and moon alone, then the path of the moon would be that of an ellipse, with one of the foci of this ellipse occupied by the earth. Unfortunately for the simplicity of the problem, there are other bodies relatively near in space, particularly that huge body, the sun. The sun not only exerts its pull on the earth but also on the moon. However, as the sun is much further away from the moon than is the earth, the earth’s attraction for its satellite is much greater, despite the fact that the sun is much huger and weighs far more than the earth. The greater pull of the earth in one direction, and a lesser pull of the sun in another, places the poor moon between the devil and the deep sea. The situation gives rise to a complexity of forces, the net result of which is that the moon’s orbit is not quite that of an ellipse. Newton was able to account for all the forces that come into play, and he proved that the actual path of the moon was a direct consequence of the law of inverse squares in actual operation.
The “Principia.” The law of gravitation, embodying also laws of motion, which we shall discuss presently, was first published in Newton’s immortal “Principia” (1686). A selection from the preface will disclose the contents of the book, and, incidentally, the style of the author: “… We offer this work as mathematical principles of philosophy; for all the difficulty in philosophy seems to consist in this—from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena; and to this end the general propositions in the first and second book are directed. In the third book we give an example of this in the explication of the system of the world; for by the propositions mathematically demonstrated in the first book, we there derive from the celestial phenomena the forces of gravity with which bodies tend to the sun and the several planets. Then, from these forces, by other propositions which are also mathematical, we deduce the motions of the planets, the comets, the moon and the sea. I wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other.…”
At this point we may state that neither Newton, nor any of Newton’s successors including Einstein, have been able to advance even a plausible theory as to the nature of this gravitational force. We know that this force pulls a stone to the ground; we know, thanks to Newton, the laws regulating the motions due to gravity; but what this force we call gravity really is we do not know. The mystery is as deep as the mystery of the origin of life.
“Prof. Einstein,” writes Prof. Eddington, “has sought, and has not reached, any ultimate explanation of its [that is, gravitation] cause. A certain connection between the gravitational field and the measurement of space has been postulated, but this throws light rather on the nature of our measurements than on gravitation itself. The relativity theory is indifferent to hypotheses as to the nature of gravitation, just as it is indifferent to hypotheses as to the nature of light.”
Newton’s Laws of Motion. In his Principia Newton begins with a series of simple definitions dealing with matter and force, and these are followed by his three famous laws of motion. The nature and amount of the effort required to start a body moving, and the conditions required to keep a body in motion, are included in these laws. The Fundamentals, mass, time and space, are exhibited in their various relationships. Of importance to us particularly is that in these laws, time and space are considered as definite entities, and as two distinct and widely separated manifestations. We shall see that in Einstein’s hands a very close relationship between these two is brought about.
Both Newton and Einstein were led to their theory of gravitation by profound studies of the mathematics of motion, but as Newton’s conception of motion differed from Einstein’s, and as, moreover, important discoveries into the nature of matter and the relationship of motion to matter were made subsequent to Newton’s time, we need not wonder that the two theories show divergence; that, as we shall see, Newton’s is probably but an approximation of the truth. If we confine our attention to our own solar system, the deviation from Newton’s law is, as a rule, so small as to be negligible.
Newton’s laws of motion are really axioms, like the axioms of Euclid: they do not admit of direct proof; but there is this difference, that the axioms of Euclid seem more obviously true. For example, when Euclid informs us that “things which are equal to the same thing are equal to one another,” we have no hesitation in accepting this statement, for it seems so self-evident. When, however, we are told by Newton that “the alteration of motion is ever proportional to the motive force impressed,” we are at first somewhat bewildered with the phraseology, and then, even when that has been mastered, the readiness with which we respond will probably depend upon the amount of scientific training we have received.
“Every body continues in its state of rest or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed thereon.” So runs Newton’s first law of motion. A body does not move unless something causes it to move; to make the body move you must overcome the inertia of the body. On the other hand, if a body is moving, it tends to continue moving, as witness our forward movement when the train is brought to a standstill. It may be asked, why does not a bullet continue moving indefinitely once it has left the barrel of the gun? Because of the resistance of the air which it has to overcome; and the path of the bullet is not straight because gravity acts on it and tends to pull it downwards.
We have no definite means of proving that a body once set in motion would continue moving, for an indefinite time, and along a straight line. What Newton meant was that a body would continue moving provided no external force acted on it; but in actual practise such a condition is unknown.
Newton’s first law defines force as that action necessary to change a state of rest or of uniform motion, and tells us that force alone changes the motion of a body. His second law deals with the relation of the force applied and the resulting change of motion of the body; that is, it shows us how force may be measured. “The alteration of motion is ever proportional to the motive force impressed, and is made in the direction of the right line in which that force is impressed.”
Newton’s third law runs—“To every action there is always opposed an equal reaction.” The very fact that you have to use force means that you have to overcome something of an opposite nature. The forward pull of a horse towing a boat equals the backward pull of the tow-rope connecting boat and horse. “Many people,” says Prof. Watson, “find a difficulty in accepting this statement … since they think that if the force exerted by the horse on the rope were not a little greater than the backward force exerted by the rope on the horse, the boat would not progress. In this case we must, however, remember that, as far as their relative positions are concerned, the horse and the boat are at rest, and form a single body, and the action and reaction between them, due to the tension on the rope, must be equal and opposite, for otherwise there would be relative motion, one with respect to the other.”
It may well be asked, what bearing have these laws of Newton on the question of time and space? Simply this, that to measure force the factors necessary are the masses of the bodies concerned, the time involved and the space covered; and Newton’s equations for measuring forces assume time and space to be quite independent of one another. As we shall see, this is in striking contrast to Einstein’s view.
Newton’s Researches on Light. In 1665, when but 23 years old, Newton invented the binomial theorem and the infinitesimal calculus, two phases of pure mathematics which have been the cause of many a sleepless night to college freshmen. Had Newton done nothing else his fame would have been secure. But we have already glanced at his law of inverse squares and the law of gravitation. We now have to turn to some of Newton’s contributions to optics, because here more than elsewhere we shall find the starting point to a series of researches which have culminated so brilliantly in the work of Einstein.
Newton turned his attention to optics in 1666 when he proved that the light from the sun, which appears white to us, is in reality a mixture of all the colors of the rainbow. This he showed by placing a prism between the ray of light and a screen. A spectrum showing all the colors from red to violet appeared on the screen.
Another notable achievement of his was the design of a telescope which brought objects to a sharp focus and prevented the blurring effects which had occasioned so much annoyance to Newton and his predecessors in all their astronomical observations.
These and other discoveries of very great interest were brought together in a volume on optics which Newton published in 1704. Our particular concern here is to examine the views advanced by him as to the nature of light.
That the nature of light should have been a subject for speculation even to the ancients need not surprise us. If other senses, as touch, for example, convey impressions of objects, it is true to say that the sense of sight conveys the most complete impression. Our conception of the external world is largely based upon the sense of sight; particularly so when we deal with objects beyond our reach. In astronomy, therefore, a study of the properties of light is indispensable.1
But what is this light? We open our eyes and we see; we close our eyes and we fail to see. At night in a dark room we may have our eyes open and yet we do not see; light, then, must be absent. Evidently, light does not wholly depend upon whether our eyes are open or closed. This much is certain: the eye functions and something else functions. What is this “something else”?
Strangely enough, Plato and Aristotle regarded light as a property of the eye and the eye alone. Out of the eye tentacles were shot which intercepted the object and so illuminated it. From what has already been said, such a view seems highly unlikely. Far more consistent with their philosophy in other directions would have been the theory that light has its source in the object and not in the eye, and travels from object to eye rather than the reverse. How little substance the Aristotelian contribution possesses is immediately seen when we refer to the art of photography. Here light rays produce effects which are independent of any property of the eye. The blind man may click the camera and produce the impression on the plate.
Newton, of course, could have fallen into no such error as did Plato and Aristotle. The source of light to him was the luminous body. Such a body had the power of emitting minute particles at great speed, and these when coming in contact with the retina produce the sensation of sight.
This emission or corpuscular theory of Newton’s was combated very strongly by his illustrious Dutch contemporary, Huyghens, who maintained that light was a wave phenomenon, the disturbance starting at the luminous body and [23]spreading out in all directions. The wave motions of the sea offer a certain analogy.
Newton’s strongest objection to Huyghens’ wave theory was that it seemed to offer no satisfactory explanation as to why light travelled in straight lines. He says: “To me the fundamental supposition itself seems impossible, namely that the waves or vibrations of any fluid can, like the rays of light, be propagated in straight lines, without a continual and very extravagant bending and spreading every way into the quiescent medium, where they are terminated by it. I mistake if there be not both experiment and demonstration to the contrary.”
In the corpuscular theory the particles emitted by the luminous body were supposed to travel in straight lines. In empty space the particles travelled in straight lines and spread in all directions. To explain how light could traverse some types of matter—liquids, for example—Newton supposed that these light particles travelled in the spaces between the molecules of the liquid.
Newton’s objection to the wave theory was not answered very convincingly by Huyghens. Today we know that light waves of high frequency tend to travel in straight lines, but may be prevented from doing so by gravitational forces of bodies near its path. But this is Einstein’s discovery.
A very famous experiment by Foucault in 1853 proved beyond the shadow of a doubt that Newton’s corpuscular theory was untenable. According to Newton’s theory, the velocity of light must be greater in a denser medium (such as water) than in a lighter one (such as air). According to the wave theory the reverse is true. Foucault showed that light does travel more slowly in water than in air. The facts were against Newton and in favor of Huyghens; and where facts and theory clash there is but one thing to do: discard the theory.
Some Facts about Newton. Newton was a Cambridge man, and Newton made Cambridge famous as a mathematical center. Since Newton’s day Cambridge has boasted of a Clerk Maxwell and a Rayleigh, and her Larmor, her J. J. Thomson and her Rutherford are still with us. Newton entered Trinity College when he was 18 and soon threw himself into higher mathematics. In 1669, when but 27 years old, he became professor of mathematics at Cambridge, and later represented that seat of learning in Parliament. When his friend Montague became Chancellor of the Exchequer, Newton was offered, and accepted, the lucrative position of Master of the Mint. As president of the Royal Society Newton was occasionally brought in contact with Queen Anne. She held Newton in high esteem, and in 1705 she conferred the honor of knighthood on him. He died in 1727.
“I do not know,” wrote Newton, “what I may appear to the world, but, to myself, I seem to have been only like a boy playing on the seashore, and directing myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”
Such was the modesty of one whom many regard as the greatest intellect of all ages.
II
THE ETHER AND ITS CONSEQUENCES
Huyghens’ wave theory of light, now so generally accepted, loses its entire significance if a medium for the propagation of these waves is left out of consideration. This medium we call the ether.1
Huyghens’ reasoning may be illustrated in some such way as this: If a body moves a force pushes or pulls it. That force itself is exemplified in some kind of matter—say a horse. The horse in pulling a cart is attached to the cart. The horse in pulling a boat may not be attached to the boat directly but to a rope, which in turn is attached to the boat. In common cases where one piece of matter affects another, there is some direct contact, some go-between.
But cases are known where matter affects matter without affording us any evidence of contact. Take the case of a magnet’s attraction for a piece of iron. Where is the rope that pulls the iron towards the magnet? Perhaps you think the attraction due to the air in between the magnet and iron? But removing the air does not stop the attraction. Yet how can we conceive of the iron being drawn to the magnet unless there is some go-between? some medium not readily perceptible to the senses perhaps, and therefore not strictly a form of matter?
If we can but picture some such medium we can imagine our magnet giving rise to vibrations in this medium which are carried to the iron. The magnet may give rise to a disturbance in that portion of the medium nearest to it; then this portion hands over the disturbance to its neighbor, the next portion of the medium; and so on, until the disturbance reaches the iron. You see, we are satisfying our sense-perception by arguing in favor of action by actual contact rather than some vague action at a distance; the go-between instead of being a rope is the medium called the ether.
Foucault’s experiment completely shattered the corpuscular theory of light, and for want of any other more plausible alternative, we are thrown back on Huyghens’ wave theory. It will presently appear that this wave theory has elements in it which make it an excellent alternative. In the meantime, if light is to be considered as a wave motion, then the query immediately arises, what is the medium through which these waves are propagated? If water is the medium for the waves of the sea, what is the medium for the waves of light? Again we answer, the medium is the ether.
What Is This “Ether”? Balloonists find conditions more and more uncomfortable the higher they ascend, for the density of the air (and therefore the amount of oxygen in a given volume of air) becomes less and less. Meteorologists have calculated that traces of the air we breathe may reach a height of some 200 miles. But what is beyond? Nothing but the ether, it is claimed. Light from the sun and stars reaches us via the ether.
But what is this ether? We cannot handle it. We cannot see it. It fails to fall within the scope of any of our senses, for every attempt to show its presence has failed. It is spirit-like in the popular sense. It is Lodge’s medium for the souls of the departed.
Helmholtz and Kelvin tried to arrive at some properties of this hypothetical substance from a careful study of the manner in which waves were propagated through this ether. If, as the wave theory teaches us, the ether can be set in motion, then according to laws of mechanics, the ether has mass. If so it is smaller in amount than anything which can be detected with our most accurate balance. Further—and this is a difficulty not easily explained—if this ether has any mass, why does it offer no detectable resistance to the velocity of the planets in it? Why is not the velocity of the planets reduced in time, just as the velocity of a rifle bullet decreases owing to the resistance of the air?
Lodge, in arguing in favor of an ether, holds that its presence cannot be detected because it pervades all space and all matter. His favorite analogy is to point out the extreme unlikelihood of a deep-sea fish discovering the presence of the water with which it is surrounded on all sides;—all of which tells us nothing about the ether, but does try to tell us why we cannot detect it.
In short, answering the query at the head of this paragraph, we may say that we do not know.
Waves Set up in This Ether. The waves are not all of the same length. Those that produce the sensation of sight are not the smallest waves known, yet their length is so small that it would take anywhere from one to two million of them to cover a yard. Curiously enough, our eye is not sensitive to wave lengths beyond either side of these limits; yet much smaller, and much larger waves are known. The smallest are the famous X-rays, which are scarcely one ten-thousandth the size of light waves. Waves which have a powerful chemical action—those which act on a photographic plate, for example—are longer than X-rays, yet smaller than light waves. Waves larger than light waves are those which produce the sensation of heat, and those used in wireless telegraphy. The latter may reach the enormous length of 5,000 yards. X-ray, actinic, or chemically active ray, light ray, heat ray, wireless ray—they differ in size, yet they all have this in common: they travel with the same speed (186,000 miles per second).
The Electromagnetic Theory of Light. Powerful support to the conception that space is pervaded by ether was given when Maxwell discovered light to be an electromagnetic phenomenon. From purely theoretical considerations this gifted English physicist was led to the view that waves could be set up as a result of electrical disturbances. He proved that such waves would travel with the same velocity as light waves. As air is not needed to transmit electrical phenomena—for you can pump all air out of a system and produce a vacuum, and electrical phenomena will continue—Maxwell was forced to the conclusion that the waves set up by electrical disturbances and transmitted with the same velocity as light, were enabled to do so with the help of the same medium as light, namely, the ether.
It was now but a step for Maxwell to formulate the theory that light itself is nothing but an electrical phenomenon, the sensation of light being due to the passage of electric waves through the ether. This theory met with considerable opposition at first. Physicists had been brought up in a school which had taught that light and electricity were two entirely unrelated phenomena, and it was difficult for them to loosen the shackles that bound them to the older school. But two startling discoveries helped to fasten attention upon Maxwell’s theory. One was an experimental confirmation of Maxwell’s theoretical deduction. Hertz, a pupil of Helmholtz, showed how the discharge from a Leyden jar set up oscillations, which in turn gave rise to waves in the ether, comparable, in so far as velocity is concerned, to light waves, but differing from the latter in wave length, the Hertzian waves being much longer. At a later date these waves were further investigated by Marconi, with the result that wireless messages soon began to be flashed from one place to another.
Just as there is a close connection between light and electricity, so there is between light and magnetism. The first to point out such a relationship was the illustrious Michael Faraday, but we owe to Zeeman the most extensive investigations in this field.
If we throw some common salt into a flame, and, with the help of a spectroscope, examine the spectrum produced, we are struck by two bright lines which stand out very prominently. These lines, yellow in color, are known as the D-lines and serve to identify even minute traces of sodium. What is true of sodium is true of other elements: they all produce very characteristic spectra. Now Zeeman found that if the flame is placed between a powerful magnet, and then some common salt thrown into the flame, the two yellow lines give place to ten yellow lines. Such is one of the results of the effect of a magnetic field on light.
The Electron. The “Zeeman effect” led to several theories regarding its nature. The most successful of these was one proposed by Larmor and more fully treated by Lorentz. It has already been pointed out that the only difference between wireless and light waves is that the former are much “longer,” and, we may now add, their vibrations are much slower. Light and wireless waves bear a relationship to one another comparable to the relationship born by high and low-pitched sounds. To produce wireless waves we allow a charge of electricity to oscillate to and fro. These oscillations, or oscillating charges, are the cause of such waves. What charges give rise to light waves? Lorentz, from a study of the Zeeman effect, ascribed them to minute particles of matter, smaller than the chemical atom, to which the name “electron” was given.
The unit of electricity is the electron. Electrons in motion give rise to electricity, and electrons in vibration, to light. The Zeeman effect gave Lorentz enough data to calculate the mass of such electrons. He then showed that these electrons in a magnetic field would be disturbed by precisely the amount to which Zeeman’s observations pointed. In other words, the assumption of the electron fitted in most admirably with Zeeman’s experiments on magnetism and light.
In the meantime, a study of the discharge of electricity through gases, and, later, the discovery of radium, led, among other things, to a study of beta or cathode rays—negatively charged particles of electricity. Through a series of strikingly original experiments J. J. Thomson ascertained the mass of such particles or corpuscles, and then the very striking fact was brought out that Thomson’s corpuscle weighed the same as Lorentz’s electron. The electron was not merely the unit of electricity but the smallest particle of matter.
The Nature of Matter. All matter is made up of some eighty-odd elements. Oxygen, copper, lead are examples of such elements. Each element in turn consists of an innumerable number of atoms, of a size so small, that 300 million of them could be placed alongside of one another without their total length exceeding one inch.
John Dalton more than a hundred years ago postulated a theory, now known as the atomic theory, to explain one of the fundamental laws in chemistry. This theory started out with an old Greek assumption that matter cannot be divided indefinitely, but that, by continued subdivision, a point would be reached beyond which no further breaking up would be possible. The particles at this stage Dalton called atoms.
Dalton’s atomic hypothesis became one of the pillars upon which the whole superstructure of chemistry rested, and this because it explained a number of perplexing difficulties so much more satisfactorily than any other hypothesis.[36]
For nearly a century Dalton stood as firm as a rock. But early in the nineties some epoch-making experiments on the discharge of electricity through gases were begun by a group of physicists, particularly Crookes, Rutherford, Lenard, Roentgen, Becquerel, and, above all, J. J. Thomson, which pointed very clearly to the fact that the atoms are not the smallest particles of matter at all; that, in fact, they could be broken up into electrons, of a diameter one one-hundred-thousandth that of an atom.
It remained for the illustrious Madame Curie to confirm this beyond all doubt by her isolation of radium. Here, as Madame Curie showed, was an element whose atoms were actually breaking up under one’s very eyes, so to speak.
So far have we advanced since Dalton’s day, that Dalton’s unit, the atom, is now pictured as a complex particle patterned after our solar system, with a nucleus of positive electricity in the center, and particles of negative electricity, or electrons, surrounding the nucleus.
All this leads to one inevitable conclusion: matter is electrical in nature. But now if matter and light have the same origin, and matter is subject to gravitation, why not light also? So reasoned Einstein.
Summary. Newton’s studies of matter in motion led to his theory of gravitation, and, incidentally, to his conception of time and space as definite entities. As we shall see, Einstein in his theory of gravitation based it upon discoveries belonging to the post-Newtonian period. One of these is Minkowski’s theory of time and space as one and inseparable. This theory we shall discuss at some length in the next chapter.
Other important discoveries which led up to Einstein’s work are the researches which culminated in the electron theory of matter. The origin of this theory may be traced to studies dealing with the nature of light.
Here again Newton appears as a pioneer. Newton’s corpuscular theory, however, proved wholly untenable when Foucault showed that the velocity of light in water is less than in air, which is the very reverse of what the corpuscular theory demands, but which does agree with Huyghens’ wave theory.
But Huyghens’ wave theory postulated some medium in which the waves can act. To this medium the name “ether” was given. However, all attempts to show the presence of such an ether failed. Naturally enough, some began to doubt the existence of an ether altogether.
Huyghens’ wave theory received a new lease of life with Maxwell’s discovery that light is an electromagnetic phenomenon; that the waves set up by a source of light were comparable to waves set up by an electrical disturbance.
Zeeman next showed that magnetism was also, closely related to light.
A study of Zeeman’s experiments led Lorentz to the conclusion that electrical phenomena are due to the motion of charged particles called “electrons,” and that the vibrations of these electrons give rise to light.
The conception of the electron as the very fundamental of matter was arrived at in an entirely different way: from studies dealing with the discharge of electricity through gases and the breaking up of the atoms of radium.
If matter and light have the same origin, and if matter is subject to gravitation, why not light also?
ALBERT EINSTEIN
C. Wide World
III
EINSTEIN
“This is the most important result obtained in connection with the theory of gravitation since Newton’s day. Einstein’s reasoning is the result of one of the highest achievements of human thought.”
These words were uttered by Sir J. J. Thomson, the president of the Royal Society, at a meeting of that body held on November 6, 1919, to discuss the results of the Eclipse Expedition.
Einstein another Newton—and this from the lips of J. J. Thomson, England’s most illustrious physicist! If ever man weighed words carefully it is this Cambridge professor, whose own researches have assured him immortality for all time.
What has this Albert Einstein done to merit such extraordinary praise? With the world in turmoil, with classes and races in a death struggle, with millions suffering and starving, why do we find time to turn our attention to this Jew? His ideas have no bearing on Europe’s calamity. They will not add one bushel of wheat to starving populations.
The answer is not hard to find. Men come and men go, but the mystery of the universe remains. It is Einstein’s glory to have given us a deeper insight into the universe. Our scientists are Huxley’s agnostics: they do not deny activities beyond our planet; they merely center their attention on the knowable on this earth. Our philosophers, on the other hand, go far afield. Some of them soar so high that, like one poet’s opinion of Shelley, the bubble bursts. Einstein, using the tools of the scientist—the experimentalist—builded a skyscraper which ultimately reached the philosophical school. His rôle is the rôle of alcohol in causing water and ether (the anæsthetic) to mix. Ether and water will mix no better than oil and water, without the presence of alcohol; in its presence a uniform mixture is obtained.
The Object of the Eclipse Expedition. Einstein prophesied that a ray of light passing near the sun would be pulled out of its course, due to the action of gravity. He went even further. He predicted how much out of its course the ray would be deflected. This prediction was based on a theory of gravitation which Einstein had developed in great mathematical detail. The object of the British Eclipse Expedition was either to prove or disprove Einstein’s assumption.
The Result of the Expedition. Einstein’s prophecy was fulfilled almost to the letter.
The Significance of the Result. Since Einstein’s theory of gravitation is intimately associated with certain revolutionary ideas concerning time and space, and, therefore, with Fundamentals of the Universe, the net result of the expedition was to strengthen our belief in the validity of his new view of the universe.
It is our intention in the following pages to discuss the expedition and the larger aspects of Einstein’s theory that follow from it. But before we do so we must have a clear idea of our solar system.
Our Solar System. In the center of our system is the sun, a flaming mass of fire, much bigger than our own earth, and very, very far away. The sun has its family of eight planets—of which the earth is one—which travel around the sun; and around some of the planets there travel satellites, or moons. The earth has such a satellite, the moon.
Now we have good reasons for believing that every star which twinkles in the sky is a sun comparable to our own, having also its own planets and its own moons. These stars, or suns, are so much further away from us than our own sun, that but a speck of their light reaches us, and then only at night, when, as the poets would say, our sun has gone to its resting place.
The distances between bodies in the solar system is so immense that, like the number of dollars spent in the Great War, the number of miles conveys little, or no impression. But picture yourself in an express train going at the average rate of 30 miles an hour. If you start from New York and travel continuously you would reach San Francisco in 4 days. If you could continue your journey around the earth at the same rate you would complete it in 35 days. If now you could travel into space and to the moon, still with the same velocity, you would reach it in 350 days. Having reached the moon, you could circumscribe it with the same express train in 8 days, as compared to the 35 days it would take you to circumscribe the earth. If instead of travelling to the moon you would book your passage for the sun you, or rather your descendants, would get there in 350 years, and it would then take them 10 additional years to travel around the sun.
Immense as these distances are, they are small as compared to the distances that separate us from the stars. It takes light which, instead of travelling 30 miles an hour, travels 186,000 miles a second, about 8 minutes to get to us from the sun, and a little over 4 years to reach us from the nearest star. The light from some of the other stars do not reach us for several hundred years.
The Eclipse of the Sun. Now to return to an infinitesimal part of the universe—our solar system. We have seen that the earth travels around the sun, and the moon around the earth. At some time in the course of these revolutions the moon must come directly between the earth and the sun. Then we get the eclipse of the sun. As the moon is smaller than the earth, only a portion of the earth’s surface will be cut off from the sun’s rays. That portion which is so cut off suffers a total eclipse. This explains why the eclipse of May, 1919, which was a total one for Brazil, was but a partial one for us.
Einstein’s Assertion Re-stated. Einstein claimed that a ray of light from one of the stars, if passing near enough to the surface of the sun, would be appreciably deflected from its course; and he calculated the exact amount of this deflection. To begin with, why should Einstein suppose that [46]the path of a ray of light would be affected by the son?
Newton’s law of gravitation made it clear that bodies which have mass attract one another. If light has mass—and very recent work tends to show that it has—there is no reason why light should not be attracted by the sun, or any other planetary body. The question that agitated scientists was not so much whether a ray of light would be deviated from its path, but to what extent this deviation would take place. Would Einstein’s figures be confirmed?
Of the bodies within our solar system the sun is by far the largest, and therefore it would exert a far greater pull than any of the planets on light rays coming from the stars. Under ordinary conditions, however, the sun itself shines with such brilliancy, that objects around it, including rays of light passing near its surface, are wholly dimmed. Hence the necessity of putting our theory to the test only when the moon covers up the sun—when there is a total eclipse of the sun.
A Graphical Representation. Imagine a star A, so selected that as its light comes to us the ray just grazes the sun. If the path of the ray is straight—if the sun has no influence on it—then the path can be represented by the line AB. If, however, the sun does exert a gravitational pull, then its real path will be AB′, and to an observer on the earth the star will have appeared to shift from A to A′.
What the Eclipse Expedition Set Out to Do. Photographs of stars around the sun were to be taken during the eclipse, and these photographs compared with others of the same region taken at night, with the sun absent. Any apparent shifting of the stars could be determined by measuring the distances between the stars as shown on the photographic plates.
Three Possibilities Anticipated. According to Newton’s assumption, light consists of corpuscles, or minute particles, emitted from the source of light. If this be true these particles, having mass, should be affected by the gravitational pull of the sun. If we apply Newton’s theory of gravitation and make use of his formula, it can be shown that such a gravitational pull would displace the ray of light by an average amount equal to 0.75 (seconds of angular distance.)1 On the other hand, where light is regarded as waves set in motion in the “ether” of space (the wave theory of light), and where weight is denied light altogether, no deviation need be expected. Finally there is a third alternative: Einstein’s. Light, says Einstein, has mass, and therefore probably weight. Mass is the matter light contains; weight represents pull by gravity. Light rays will be attracted by the sun, but according to Einstein’s theory of gravitation the sun’s gravitational pull will displace the rays by an average amount equal to 1.75 (seconds of angular distance).
The Expeditions. That science is highly international, despite many recent examples to the contrary, is evidenced by this British Eclipse Expedition. Here was a theory propounded by one who had accepted a chair of physics in the university of Berlin, and across the English Channel were Germany’s mortal enemies making elaborate preparations to test the validity of the Berlin professor’s theory.
The British Astronomical Society began to plan the eclipse expedition even before the outbreak of the Great War. During the years that followed, despite the destinies of nations which hung on threads from day to day, despite the darkest hours in the history of the British people, our English astronomers continued to give attention to the details of the proposed expedition. When the day of the eclipse came all was in readiness.
One expedition under Dr. Crommelin was sent to Sobral, Brazil; another, under Prof. Eddington, to Principe, an island off the west coast of Africa. In both these places a total eclipse was anticipated.
The eclipse occurred on May 29, 1919. It lasted for six to eight minutes. Some 15 photographs, with an average exposure of five to six seconds, were taken. Two months later another series of photographs of the same region were taken, but this time the sun was no longer in the midst of these stars.
The photographs were brought to the famous Greenwich Observatory, near London, and the astronomers and mathematicians began their laborious measurements and calculations.
On November 6, at the meeting of the Royal Society, the result was announced. The Sobral expedition reported 1.98; the Principe expedition 1.62. The average was 1.8. Einstein had predicted 1.75, Newton might have predicted 0.75, and the orthodox scientists would have predicted 0. There could now no longer be any question as to which of the three theories rested on a sure foundation. To quote Sir Frank Dyson, the Astronomer Royal: “After a careful study of the plates I am prepared to say that there can be no doubt that they confirm Einstein’s prediction. A very definite result has been obtained that light is deflected in accordance with Einstein’s law of gravitation.”2
Where Did Einstein Get His Idea of Gravitation? In 1905 Einstein published the first of a series of papers supporting and extending a theory of time and space to which the name “the theory of relativity” had been given. These views as expounded by Einstein came into direct conflict with Newton’s ideas of time and space, and also with Newton’s law of gravitation. Since Einstein had more faith in his theory of relativity than in Newton’s theory of gravitation, Einstein so changed the latter as to make it harmonize with the former. More will be said on this subject.
Let not the reader misunderstand. Newton was not wholly in the wrong; he was only approximately right. With the knowledge existing in Newton’s day Newton could have done no more than he did; no mortal could have done more. But since Newton’s day physics—and science in general—has advanced in great strides, and Einstein can interpret present-day knowledge in the same masterful fashion that Newton could in his day. With more facts to build upon, Einstein’s law of gravitation is more universal than Newton’s; it really includes Newton’s.
But now we must turn our attention very briefly to the theory of relativity—the theory that led up to Einstein’s law of gravitation.
The Theory of Relativity. The story goes that Einstein was led to his ideas by watching a man fall from a roof. This story bears a striking similarity to Newton and the apple. Perhaps one is as true as the other.
However that may be, the principle of relativity is as old as philosophical thought, for it denies the possibility of measuring absolute time, or absolute space. All things are relative. We say that it takes a “long time” to get from New York to Albany; long as compared to what? long, perhaps, as compared to the time it takes to go from New York City to Brooklyn. We say the White House is “large”; large when compared to a room in an apartment. But we can just as well reverse our ideas of time and distance. The time it takes to go from New York to Albany is “short” when compared to the time it takes to go from New York to San Francisco. The size of the White House is “small” when compared to the size of the city of Washington.
Let us take another illustration. Every time the earth turns on its axis we mark down as a day. With this as a basis, we say that it takes a little over 365 days for the earth to complete its revolution around the sun, and our 365 days we call a year. But now consider some of our other planets. With our time as a basis, it takes Jupiter or Saturn 10 hours to turn on its axis, as compared to the 24 hours it takes the earth to turn. Saturn’s day is less than one-half our day, and our day is more than twice Saturn’s—that is, according to the calculations of the inhabitants of the earth. Mercury completes her circuit around the sun in 88 days; Neptune, in 164 years. Mercury’s year is but one-fourth ours, Neptune’s, 164 times ours. And observers at Mercury and Neptune would regard us from their standard of time, which differs from our standard.
You may say, why not take our standard of time as the standard, and measure everything by it? But why should you? Such a selection would be quite arbitrary. It would not be based on anything absolute, but would merely depend on our velocity around the sun.
These ideas are old enough in metaphysics. Einstein’s improvement of them consists not merely in speculating about them, but in giving them mathematical form.
The Origin of the Theory of Relativity. A train moves with reference to the earth. The earth moves with reference to the sun. We say the sun is stationary and the earth moves around the sun. But how do we know that the sun itself does not move with reference to some other body? How do we know that our planetary system, and the stars, and the cosmos as a whole is not in motion?
There is no way of answering such a question unless we could get a point of reference which is fixed—fixed absolutely in space.
We have already alluded to our view of the nature of light, known as the wave theory of light. This theory postulates the existence of an all-pervading “ether” in space. Light sets up wave disturbances in this ether, and is thus propagated. If the ocean were the ether, the waves of the ocean would compare with the waves set up by the ether.
But what is this ether? It cannot be seen. It defies weight. It permeates all space. It permeates all matter. So say the exponents of this ether. To the layman this sounds very much like another name for the Deity. To Sir Oliver Lodge it represents the spirits of the departed.
To us, of importance is the conception that this ether is absolutely stationary. Such a conception is logical if the various developments in optics and electricity are considered. But if absolutely stationary, then the ether is the long-sought-for point of reference, the guide to determine the motion of all bodies in the universe.
The Famous Experiment Performed by Prof. Michelson. If there is an ether, and a stationary ether, and if the earth moves with reference to this ether, the earth, in moving, must set up ether “currents”—just as when a train moves it sets up air currents. So reasoned Michelson, a young Annapolis graduate at the time. And forthwith he devised a crucial experiment the explanation of which we can simplify by the following analogy:
Which is the quicker, to swim up stream a certain length, say a hundred yards, and back again, or across stream the same length and back again? The swimmer will answer that the up-and-down journey is longer.4
Our river is the ether. The earth, if moving in this ether, will set up an ether stream, the up stream being parallel to the earth’s motion. Now suppose we send a beam of light a certain distance up this ether stream and back, and note the time; and then turn the beam of light at right angles and send it an equal distance across the stream and back, and note the time. How will the time taken for light to travel in these two directions compare? Reasoning by analogy, the up-and-down stream should take longer.
Michelson’s results did not accord with analogy. No difference in time could be detected between the beam of light travelling up-and-down, and across-and-back.
But this was contrary to all reason if the postulate of an ether was sound. Must we then revise our ideas of an ether? Perhaps after all there is no ether.
But if no ether, how are we to explain the propagation of light in space, and various electrical phenomena connected with it, such as the Hertzian, or wireless waves?
There was another alternative, one suggested by Larmor in England and Lorentz in Holland,—that matter is contracted in the direction of its motion through the ether current. To say that bodies are actually shortened in the direction of their motion—by an amount which increases as the velocity of these bodies approaches that of light—is so revolutionary an idea that Larmor and Lorentz would hardly have adopted such a viewpoint but for the fact that recent investigations into the nature of matter gave basis for such belief.
Matter, it has been shown, is electrical in nature. The forces which hold the particles together are electrical. Lorentz showed that mathematical formulas for electrical forces could be developed which would inevitably lead to the view that material bodies contract in the direction of their motion.5
“But this is ridiculous,” you say; “if I am shorter in one direction than in another I would notice it.” You would if some things were shortened and others were not. But if all things pointing in a certain direction are shortened to an equal extent, how are you going to notice it? Will you apply the yard stick? That has been shortened. Will you pass judgment with the help of your eyes? But your retina has also contracted. In brief, if all things contract to the same amount it is as if there were no contraction at all.
Lorentz’s Plausible Explanation Really Deepens the Mystery. The startling ideas just outlined have opened up several new vistas, but they have left unanswered the two problems we set out to solve: whether there is an ether, and if so, what is the velocity of the earth in reference to this ether? Lorentz maintains that there is an ether, but the velocities of bodies relative to it must forever remain a mystery. As you change your position your distances change; you change; everything about you changes accordingly; and all basis for comparison is lost. Nature has entered into a conspiracy to keep you ignorant.
Einstein Comes upon the Scene. Einstein starts with the assumption that there is no possible way of identifying this ether. Suppose we ignore the ether altogether, what then?6
If we do ignore the ether we no longer have any absolute point of reference; for if the ether is considered stationary the velocity of all bodies within the ether may be referred to it; any point in space may be considered a fixed point. If, however, there is no ether, or if we are to ignore it, how are we to get the velocity of bodies in space?
The Principle of Relativity. If we are to believe in the “causal relationship between only such things as lie within the realm of observation,” then observation teaches us that bodies move only relative to one another, and that the idea of absolute motion of a body in space is meaningless. Einstein, therefore, postulates that there is no such thing as absolute motion, and that all we can discuss is the relative motion of one body with respect to another. This is just as logical a deduction from Michelson’s experiment as the attempt to explain Michelson’s anomalous results in the light of an all-pervading ether.
Consider for a moment Newton’s scheme. This great pioneer pictured an absolute standard of position in space relative to which all velocities are measured. Velocities were measured by noting the distance covered and dividing the result by the time taken to cover the distance. Space was a definite entity; and so was time. “Time,” said Newton, “flows evenly on,” independent of aught else. To Newton time and space were entirely different, in no way to be confounded.
Just as Newton conceived of absolute space, so he conceived of absolute time. From the latter standard of reference the idea of a “simultaneity of events” at different places arose. But now if there is no standard of reference, if the ether does not exist or does not function, if two points A and B cannot be referred to a third, and fixed point C, how can we talk of “simultaneity of events” at A and B?7
In fact, Einstein shows that if all you can speak about is relative motion, then one event which takes say one minute on one planet would not take one minute on another. For consider two bodies in space, say the planets Venus and the earth, with an observer B on Venus and another A on the earth. B notes the time taken for a ray of light to travel from B to the distance M. A on the earth has means of observing the same event. B records one minute. A is puzzled, for his watch records a little more than one minute. What is the explanation? Granting that the two clocks register the same time to start with, and assuming further Einstein’s hypothesis that the velocity of light is independent of its source, the difference in time is due to the fact that the planet Venus moves with reference to the observer on the earth; so that A in reality does not measure the path BM and MB, but BM′ and M′B′, where BB′ represents the distance Venus itself has moved in the interval. And if you put yourself in B’s position on Venus the situation is exactly reversed. All of which is simply another way of saying that what is a certain time on one body in space is another time on another body in space. There is nothing definite in time.
Prof. Cohen’s Illustration. Further bewildering possibilities are clearly outlined in this apt illustration: “If when you are going away on a long and continuous journey you write home at regular intervals, you should not be surprised that with the best possible mail service your letters will reach home at progressively longer intervals, since each letter will have a greater distance to travel than its predecessor. If you were armed with instruments to hear the home clock ticking, you would find that as your distance from home keeps on increasing, the intervals between the successive ticks (that is, its seconds) grow longer, so that if you travelled with the velocity of sound the home clock would seem to slow down to a standstill—you would never hear the next tick.
“Precisely the same is true if you substitute light rays for sound waves. If with the naked eye or with a telescope you watch a clock moving away from you, you will find that its minute hand takes a longer time to cover its five-minute intervals than does the chronometer in your hand, and if the clock travelled with the velocity of light you would forever see the minute hand at precisely the same point. That which is true of the clock is, of course, also true of all time intervals which it measures, so that if you moved away from the earth with the velocity of light everything on it would appear as still as on a painted canvas.”
Your time has apparently come to a standstill in one position and is moving in another! All this seems absurd enough, but it does show that time alone has little meaning.
Minkowski’s Conclusion. The relativity theory requires that we thoroughly reorganise our method of measuring time. But this is intimately associated with our method of measuring space, the distance between two points. As we proceed we find that space without time has little meaning, and vice versa. This leads Minkowski to the conclusion that “time by itself and space by itself are mere shadows; they are only two aspects of a single and indivisible manner of coordinating the facts of the physical world.” Einstein incorporated this time-space idea in his theory of relativity.
How We Measure a Point in Space. Suppose I say to you that the chemical laboratory of Columbia University faces Broadway; would that locate the laboratory? Hardly, for any building along Broadway would face Broadway. But suppose I add that it is situated at Broadway and 117th Street, south-east? there could be little doubt then. But if, further, this laboratory would occupy but part of the building, say the third floor; then the situation would be specified by naming Broadway, 117th Street S. E., third floor. If Broadway represents length, 117th Street width, and third floor height, we can see what is meant when we say that three dimensions are required to locate a position in space.
The Fourth Dimension. A point on a line may be located by one dimension; a point on a wall requires two dimensions; a point in the room, like the chemical laboratory above ground, needs three. The layman cannot grasp the meaning of a fourth dimension; yet the mathematician does imagine it, and plays with it in mathematical terms. Minkowski and Einstein picture time as the fourth dimension. To them time occupies no more important position than length, breadth, or thickness, and is as intimately related to these three as the three are to one another. H. G. Wells, the novelist, has beautifully caught this spirit when in his novel, “The Time Machine,” he makes his hero travel backwards and forwards along time just as a man might go north or south. When the man with his time machine goes forward he is in the future; when he goes backwards he is in the past.
In reality, if we stop to think a minute, there is no valid reason for the non-existence of a fourth dimension. If one, two and three dimensions, why not four—and five and six, for that matter? Theoretically at least there is no reason why the limit should be set at three. However, our minds become sluggish when we attempt to picture dimensions beyond three; just as an extraordinary effort on our part is needed to follow Einstein when he “juggles” with space and time.
Our difficulty in imagining four dimensions may be likened to the difficulty two-dimensioned beings would experience in imagining us, beings of the conventional three dimensions. Suppose these two-dimensional beings were living on the surface of the earth; what could they see? They could see nothing below and nothing above the surface. They would see shifting surfaces as we walked about, but being sensitive to length and breadth only, and not to height, they could gain no notion whatsoever of what we really look like. It is thus with us when we attempt to picture four-dimensional space.
Perhaps the analogy of the motion picture may help us somewhat. As everybody knows, these motion pictures consist of a series of photographs which are shown in rapid succession on the screen. Each photograph by itself conveys a sensation of space, that is, of three dimensions; but one photograph rapidly following another conveys the sensation of space and time—four dimensions. Space and time are interlinked.
The Time-space Idea Further Developed. We have already alluded to the fact that objects in space moving with different velocities build up different time intervals. Thus the velocity of the star Arcturus, if compared with reference to the earth, moves at the rate of 200 miles a second. Its motion through space is different from ours. Objects which, according to Lorentz, contract in the direction of their motion to an extent proportional to their velocity, will contract differently on the surface of Arcturus than on the earth. Our space is not Arcturus’ space; neither is Arcturus’ time our time. And what is true of the discrepancies existing between the space and time conceptions of the earth and Arcturus is true of any other two bodies in space moving at different velocities.
But is there no relationship existing between the space and time of one body in the universe as compared to the space and time of another? Can we not find something which holds good for all bodies in the universe? We can. We can express it mathematically. It is the concept of time and space interlinked; of time as the fourth dimension, length, breadth and thickness being the other three; of time as one of four co-ordinates and at right angles to the other three (a situation which requires a terrific stretch of the imagination to visualize). The four dimensions are sufficient to co-ordinate the time-space relationships of all bodies in the cosmos, and hence have a universality which is totally lacking when time and space are used independently of one another. The four components of our time-space are up-and-down, right-and-left, backwards-and-forwards, and sooner-and-later.
“Strain” and “Distortion” in Space. The four-dimensional unit has been given the name “world-line,” for the “world-line” of any particle in space is in reality a complete history of that particle as it moves about in space. Particles, we know, attract one another. If each particle is represented by a world-line these world-lines will be deflected from their course owing to such attraction.
Imagine a bladder representing the universe, with lines on it representing world-lines. Now squeeze the bladder. The world-lines are bent in various directions; they are “distorted.” This illustrates the influence of gravity on these world-lines; it is the “strain” brought about due to the force of attraction. The distorted bladder illustrates even more, for it is a true representation of the real world.
How Einstein’s Conception of Time and Space Led to a New View of Gravitation. In our conventional language we speak of the sun as exerting a “force” on the earth. We have seen, however, that this force brings about a “distortion” or “strain” in world-lines; or, what amounts to the same thing, a “distortion” or “strain” of time and space. The sun’s “force,” the “force” of any body in space, is the “force” due to gravity; and these “forces” may now be treated in terms of the laws of time and space. “The earth,” Prof. Eddington tells us, “moves in a curved orbit, not because the sun exerts any direct pull, but because the earth is trying to find the shortest way through a space and time which have been tangled up by an influence radiating from the sun.”8
At this point Newton’s conceptions fail, for his views and his laws do not include “strains” in space. Newton’s law of gravitation must be supplanted by one which does include such distortions. It is Einstein’s great glory to have supplied us with this new law.
Einstein’s Law of Gravitation. This appears to be the only law which meets all requirements. It includes Newton’s law, and cannot be distinguished from it if our experiments are confined to the earth and deal with relatively small velocities. But when we betake ourselves to some orbits in space, with a gravitational pull much greater than the earth’s, and when we deal with velocities comparable to that of light, the differences become marked.
Einstein’s Theory Scores Its First Great Victory. In the beginning of this chapter we referred to the elaborate eclipse expedition sent by the British to test the validity of Einstein’s new theory of gravitation. The British scientists would hardly have expended so much time and energy on this theory of Einstein’s but for the fact that Einstein had already scored one great victory. What was it?
Imagine but a single planet revolving about the sun. According to Newton’s law of gravitation, the planet’s path would be that of an ellipse—that is, oval—and the planet would travel indefinitely along this path. According to Einstein the path would also be elliptical, but before a revolution would be quite completed, the planet would start along a slightly advanced line, forming a new ellipse slightly in advance of the first. The elliptic orbit slowly turns in the direction in which the planet is moving. After many years—centuries—the orbit will be in a different direction.
The rapidity of the orbit’s change of direction depends on the velocity of the planet. Mercury moving at the rate of 30 miles a second is the fastest among the planets. It has the further advantage over Venus or the earth in that its orbit, as we have said, is an ellipse, whereas the orbits of Venus and the earth are nearly circular; and how are you going to tell in which direction a circle is pointing?
Observation tells us that the orbit of Mercury is advancing at the rate of 574 seconds (of arc) per century. We can calculate how much of this is due to the gravitational influence of other planets. It amounts to 532 seconds per century. What of the remaining 42 seconds?
You might be inclined to attribute this shortcoming to experimental error. But when all such possibilities are allowed for our mathematicians assure us that the discrepancy is 30 times greater than any possible experimental error.
This discrepancy between theory and observation remained one of the great puzzles in astronomy until Einstein cleared up the mystery. According to Einstein’s theory the mathematics of the situation is simply this: in one revolution of the planet the orbit will advance by a fraction of a revolution equal to three times the square of the ratio of the velocity of the planet to the velocity of light. When we allow mathematicians to work this out we get the figure 43, which is certainly close enough to 42 to be called identical with it.
Still Another Victory? Einstein’s third prediction—the shifting of spectral lines toward the red end of the spectrum in the case of light coming to us from the stars of appreciable mass—seems to have been confirmed recently (March, 1920). “The young physicists in Bonn,” writes Prof. Einstein to a friend, “have now as good as certainty (so gut wie sicher) proved the red displacement of the spectral lines and have cleared up the grounds of a previous disappointment.”
Summary. Velocity, or movement in space, is at the basis of Einstein’s work, as it was at the basis of Newton’s. But time and space no longer have the distinct meanings that they had when examined with the help of Newton’s equations. Time and space are not independent but interdependent. They are meaningless when treated as separate entities, giving results which may hold for one body in the universe but do not hold for any other body. To get general laws which are applicable to the cosmos as a whole the Fundamentals of Mechanics must be united.
Einstein’s great achievement consists in applying this revised conception of space and time to elucidate cosmical problems. “World-lines,” representing the progress of particles in space, consisting of space-time combinations (the four dimensions), are “strained” or “distorted” in space due to the attraction that bodies exhibit for one another (the force of gravitation). On the other hand, gravitation itself—more universal than anything else in the universe—may be interpreted in terms of strains on world-lines, or, what amounts to the same thing, strains of space-time combinations. This brings gravitation within the field of Einstein’s conception of time and space.
That Einstein’s conception of the universe is an improvement upon that of Newton’s is evidenced by the fact that Einstein’s law explains all that Newton’s law does, and also other facts which Newton’s law is incapable of explaining. Among these may be mentioned the distortion of the oval orbits of planets round the sun (confirmed in the case of the planet Mercury), and the deviation of light rays in a gravitational field (confirmed by the English Solar Eclipse Expedition).
Einstein’s Theories and the Inferences to be Drawn from Them. Einstein’s theories, supported as they are by very convincing experiments, will probably profoundly influence philosophic and perhaps religious thought, but they can hardly be said to be of immediate consequence to the man in the street. As I have said elsewhere, Einstein’s theories are not going to add one bushel of wheat to war-torn and devastated Europe, but in their conception of a cosmos decidedly at variance with anything yet conceived by any school of philosophy, they will attract the universal attention of thinking men in all countries. The scientist is immediately struck by the way Einstein has utilized the various achievements in physics and mathematics to build up a co-ordinated system showing connecting links where heretofore none were perceived. The philosopher is equally fascinated with a theory, which, in detail extremely complex, shows a singular beauty of unity in design when viewed as a whole. The revolutionary ideas propounded regarding time and space, the brilliant way in which the most universal property of matter, gravitation, is for the first time linked up with other properties of matter, and, above all, the experimental confirmation of several of his more startling predictions—always the finest test of scientific merit—stamps Einstein as one of those super-men who from time to time are sent to us to give us a peep into the beyond.
Some Facts about Einstein Himself. Albert Einstein was born in Germany some 45 years ago. At first he was engaged at the Patent Bureau in Berne, and later became professor at the Zürich Polytechnic. After a short stay at Prague University he accepted one of those tempting “Akademiker” professorships at the university of Berlin—professorships which insure a comfortable income to the recipient of one of them, little university work beyond, perhaps, one lecture a week, and splendid facilities for research. A similar inducement enticed the chemical philosopher, Van ’t Hoff, to leave his Amsterdam, and the Swedes came perilously near losing their most illustrious scientist, Arrhenius.
Einstein published his first paper on relativity in 1905, when not more than 30 years old. Of this paper Planck, the Nobel Laureate in physics this year, has offered this opinion: “It surpasses in boldness everything previously suggested in speculative natural philosophy and even in the philosophical theories of knowledge. The revolution introduced into the physical conceptions of the world is only to be compared in extent and depth with that brought about by the introduction of the Copernican system of the universe.”
Einstein published a full exposition of the relativity theory in 1916.
