EINSTEIN AND THE UNIVERSE
EINSTEIN AND THE UNIVERSE
CHAPTER ITHE METAMORPHOSES OFSPACE AND TIME
THE METAMORPHOSES OFSPACE AND TIME
Removing the mathematical difficulties—The pillars of knowledge—Absolute time and space, from Aristotle to Newton—Relative time and space, from Epicurus to Poincaré and Einstein—Classical Relativity—Antinomy of stellar aberration and the Michelson experiment.
“Have you read Baruch?” La Fontaine used to cry, enthusiastically. To-day he would have troubled his friends with the question “Have you read Einstein?”
But, whereas one needs only a little Latin to gain access to Spinoza, frightful monsters keep guard before Einstein, and their horrible grimaces seem to forbid us to approach him. They stand behind strange moving bars, sometimes rectangular and sometimes curvilinear, which are known as “co-ordinates.” They bear names as frightful as themselves—“contravariant and covariant vectors, tensors, scalars, determinants, orthogonal vectors, generalised symbols of three signs,” and so on.
These strange beings, brought from the wildest depths of the mathematical jungle, join together or part from each other with a remarkable promiscuity, by means of some astonishing surgery which is calledintegrationanddifferentiation.
In a word, Einstein may be a treasure, but there is a fearsome troop of mathematical reptiles keeping inquisitive folk away from it; though there can be no doubt that they have, like our Gothic gargoyles, a hidden beauty of their own. Let us, however, drive them off with the whip of simple terminology, and approach the splendour of Einstein’s theory.
Who is this physicist Einstein? That is a question of no importance here. It is enough to know that he refused to sign the infamous manifesto of the professors, and thus brought upon himself persecution from the Pan-Germanists.[1]Mathematical truths and scientific discoveries have an intrinsic value, and this must be judged and appreciated impartially, whoever their author may chance to be. Had Pythagoras been the lowest of criminals, the fact would not in the least detract from the validity of the square of the hypotenuse. A theory is either true or false, whether the nose of its author has the aquiline contour of the nose of the children of Sem, or the flattened shape of that of the children of Cham, or the straightness of that of the children of Japhet. Do we feel that humanity is perfect when we hear it said occasionally: “Tell me what church you frequent, and I will tell you if your geometry is sound.” Truth has no need of a civil status. Let us get on.
All our ideas, all science, and even the whole of our practical life,are based upon the way in which we picture to ourselves the successive aspects of things. Our mind, with the aid of our senses, chiefly ranges these under the headings of time and space, which thus become the two frames in which we dispose all that is apparent to us of the material world. When we write a letter, we put at the head of it the name of the place and the date. When we open a newspaper, we find the same indications at the beginning of each piece of telegraphic news. It is the same in everything and for everything. Time and space, the situation and the period of things, are thus seen to be the twin pillars of all knowledge, the two columns which sustain the edifice of men’s understanding.
So felt Leconte de Lisle when, addressing himself to “divine death,” he wrote, in his profound, philosophic way:
Free us from time, number, and space:Grant us the rest that life hath spoiled.
Free us from time, number, and space:Grant us the rest that life hath spoiled.
Free us from time, number, and space:Grant us the rest that life hath spoiled.
Free us from time, number, and space:
Grant us the rest that life hath spoiled.
He inserts the word “number” only in order to define time and space quantitatively. What he has finely expressed in these famous and superb lines is the fact that all that there is for us in this vast universe, all that we know and see, all the ineffable and agitated flow of phenomena, presents to us no definite aspect, no precise form, until it has passed through those two filters which are interposed by the mind, time and space.
The work of Einstein derives its importance from the fact that he has shown, as we shall see, that we have entirely to revise our ideas of time and space. If that is so, the whole of science, including psychology, will have to be reconstructed. That is the first part of Einstein’s work, but it goes further. If that were the whole of his work it would be merely negative.
Once he had removed from the structure of human knowledge what had been regarded as an indispensable wall of it, though it was really only a frail scaffolding that hid the harmony of its proportions, he began to reconstruct. He made in the structure large windows which allow us now to see the treasures it contains. In a word, Einstein showed, on the one hand, with astonishing acuteness and depth, that the foundation of our knowledge seems to be different from what we had thought, and that it needs repairing with a new kind of cement. On the other hand, he has reconstructed the edifice on this new basis, and he has given it a bold and remarkably beautiful and harmonious form.
I have now to show in detail, concretely, and as accurately as possible, the meaning of these generalities. But I must first insist on a point which is of considerable importance: if Einstein had confined himself to the first part of his work, as I have described it, the part which shatters the classical ideas of time and space, he would never have attained the fame which now makes his name great in the world of thought.
The point is important because most of those—apart from experts—who have written on Einstein have chiefly, often exclusively, emphasised this more or less “destructive” side of his work. But, as we shall see, from this point of view Einstein was not the first, and he is not alone. All that he has done is to sharpen, and press a little deeper between the badly joined stones of classical science, a chisel which others, especially the great Henri Poincaré, had used long before him. My next point is to explain, if I can, the real, the immortal, title ofEinstein to the gratitude of men: to show how he has by his own powers rebuilt the structure in a new and magnificent form after his critical work. In this he shares his glory with none.
The whole of science, from the days of Aristotle until our own, has been based upon the hypothesis—properly speaking, the hypotheses—that there is an absolute time and an absolute space. In other words, our ideas rested upon the supposition that an interval of time and an interval of space between two given phenomena are always the same, for every observer whatsoever, and whatever the conditions of observation may be. For instance, it would never have occurred to anybody as long as classical science was predominant, that the interval of time, the number of seconds, which lies between two successive eclipses of the sun, may not be the fixed and identically same number of seconds for an observer on the earth as for an observer in Sirius (assuming that the second is defined for both by the same chronometer). Similarly, no one would have imagined that the distance in metres between two objects, for instance the distance of the earth from the sun at a given moment, measured by trigonometry, may not be the same for an observer on the earth as for an observer in Sirius (the metre being defined for both by the same rule).
“There is,” says Aristotle, “one single and invariable time, which flows in two movements in an identical and simultaneous manner; and if these two sorts of time were not simultaneous, they would nevertheless be of the same nature.... Thus, in regard to movements which take place simultaneously, there is one and the same time, whether or no the movements are equal in rapidity; and this is true even if one of them isa local movement and the other an alteration.... It follows that even if the movements differ from each other, and arise independently, the time is absolutely the same for both.”[2]This Aristotelic definition of physical time is more than two thousand years old, yet it clearly represents the idea of time which has been used in classic science, especially in the mechanics of Galileo and Newton, until quite recent years.
It seems, however, that in spite of Aristotle, Epicurus outlined the position which Einstein would later adopt in antagonism to Newton. To translate liberally the words in which Lucretius expounds the teaching of Epicurus:
“Time has no existence of itself, but only in material objects, from which we get the idea of past, present, and future. It is impossible to conceive time in itself independently of the movement or rest of things.”[3]
Both space and time have been regarded by science ever since Aristotle as invariable, fixed, rigid, absolute data. Newton thought that he was saying something obvious, a platitude, when he wrote in his celebrated Scholion: “Absolute, true, and mathematical time, taken in itself and without relation to any material object, flows uniformly of its own nature.... Absolute space, on the other hand, independent by its own nature of any relation to external objects, remains always unchangeable and immovable.”
The whole of science, the whole of physics and mechanics, as they are still taught in our colleges and in most of our universities, are based entirely upon these propositions, these ideas of an absolute time andspace, taken by themselves and without any reference to an external object, independent by their very nature.
In a word—if I may venture to use this figure—time in classical science was like a river bearing phenomena as a stream bears boats, flowing on just the same whether there were phenomena or not. Space, similarly, was rather like the bank of the river, indifferent to the ships that passed.
From the time of Newton, however, if not from the time of Aristotle, any thoughtful metaphysician might have noticed that there was something wrong in these definitions. Absolute time and absolute space are “things in themselves,” and these the human mind has always regarded as not directly accessible to it. The specifications of space and time, those numbered labels which we attach to objects of the material world, as we put labels on parcels at the station so that they may not be lost (a precaution that does not always suffice), are given us by our senses, whether aided by instruments or not, only when we receive concrete impressions. Should we have any idea of them if there were no bodies attached to them, or rather to which we attach the labels? To answer this in the affirmative, as Aristotle, Newton, and classical science do, is to make a very bold assumption, and one that is not obviously justified.
The only time of which we have any idea apart from all objects is the psychological time so luminously studied by M. Bergson: a time which has nothing except the name in common with the time of physicists, of science.
It is really to Henri Poincaré, the great Frenchman whose death has left a void that will never be filled, that we must accord the merit ofhaving first proved, with the greatest lucidity and the most prudent audacity, that time and space, as we know them, can only be relative. A few quotations from his works will not be out of place. They will show that the credit for most of the things which are currently attributed to Einstein is, in reality, due to Poincaré. To prove this is not in any way to detract from the merit of Einstein, for that is, as we shall see, in other fields.
This is how Poincaré, whose ideas still dominate the minds of thoughtful men, though his mortal frame perished years ago, expressed himself, the triumphant sweep of his wings reaching further every day:
“One cannot form any idea of empty space.... From that follows the undeniable relativity of space. Any man who talks of absolute space uses words which have no meaning. I am at a particular spot in Paris—the Place du Panthéon, let us suppose—and I say: ‘I will come backhereto-morrow.’ If anyone asks me whether I mean that I will return to the same point in space, I am tempted to reply, ‘Yes.’ I should, however, be wrong, because between this and to-morrow the earth will have travelled, taking the Place du Panthéon with it, so that to-morrow the square will be more than 2,000,000 kilometres away from where it is now. And it would be no use my attempting to use precise language, because these 2,000,000 kilometres are part of our earth’s journey round the sun, but the sun itself has moved in relation to the Milky Way, and the Milky Way in turn is doubtless moving at a speed which we cannot learn. Thus we are entirely ignorant, and always will be ignorant, how far the Place du Panthéon shifts its position in space in a single day. What I really meant to say was: ‘To-morrow I shallagain see the dome and façade of the Panthéon.’ If there were no Panthéon, there would be no meaning in my words, and space would disappear.”
Poincaré works out his idea in this way:
“Suppose all the dimensions of the universe were increased a thousandfold in a night. The world would remain the same, giving the word ‘same’ the meaning it has in the third book of geometry. Nevertheless, an object that had measured a metre in length will henceforward be a kilometre in length; a thing that had measured a millimetre will now measure a metre. The bed on which I lie and the body which lies on it will increase in size to exactly the same extent. What sort of feelings will I have when I awake in the morning, in face of such an amazing transformation? Well, I shall know nothing about it. The most precise measurements would tell me nothing about the revolution, because the tape I use for measuring will have changed to the same extent as the objects I wish to measure. As a matter of fact, there would be no revolution except in the mind of those who reason as if space were absolute. If I have argued for a moment as they do, it was only in order to show more clearly that their position is contradictory.”
It would be easy to develop Poincaré’s argument. If all the objects in the universe were to become, for instance, a thousand times taller, a thousand times broader, we should be quite unable to detect it, because we ourselves—our retina and our measuring rod—would be transformed to the same extent at the same time. Indeed, if all the things in the universe were to experience an absolutely irregular spatial deformation—if some invisible and all-powerful spirit were to distortthe universe in any fashion, drawing it out as if it were rubber—we should have no means of knowing the fact. There could be no better proof that space is relative, and that we cannot conceive space apart from the things which we use to measure it. When there is no measuring rod, there is no space.
Poincaré pushed his reasoning on this subject so far that he came to say that even the revolution of the earth round the sun is merely a more convenient hypothesis than the contrary supposition, but not a truer hypothesis, unless we imply the existence of absolute space.
It may be remembered that certain unwary controversialists have tried to infer from Poincaré’s argument that the condemnation of Galileo was justified. Nothing could be more amusing than the way in which the distinguished mathematician-philosopher defended himself against this interpretation, though one must admit that his defence was not wholly convincing. He did not take sufficiently into account the agnostic element.
Poincaré, in any case, is the leader of those who regard space as a mere property which we ascribe to objects. In this view our idea of it is only, so to say, the hereditary outcome of those efforts of our senses by means of which we strive to embrace the material world at a given moment.
It is the same with time. Here again the objections of philosophic Relativists were raised long ago, but it was Poincaré who gave them their definitive shape. His luminous demonstrations are, however, well known, and we need not reproduce them here. It is enough to observe that, in regard to time as well as space, it is possible to imagine either a contraction or an enlargement of the scale which would becompletely imperceptible to us; and this seems to show that man cannot conceive an absolute time. If some malicious spirit were to amuse itself some night by making all the phenomena of the universe a thousand times slower, we should not, when we awake, have any means of detecting the change. The world would seem to us unchanged. Yet every hour recorded by our watches would be a thousand times longer than hours had previously been. Men would live a thousand times as long, yet they would be unaware of the fact, as their sensations would be slower in the same proportion.
When Lamartine appealed to time to “suspend its flight,” he said a very charming, but perhaps meaningless, thing. If time had obeyed his passionate appeal, neither Lamartine nor Elvire would have known and rejoiced over the fact. The boatman who conducted the lovers on the Lac du Bourget would not have asked payment for a single additional hour; yet he would have dipped his oars into the pleasant waters for a far longer time.
I venture to sum up all this in a sentence which will at first sight seem a paradox: in the opinion of the Relativists it is the measuring rods which create space, the clocks which create time. All this was maintained by Poincaré and others long before the time of Einstein, and one does injustice to truth in ascribing the discovery to him. I am quite aware that one lends only to the rich, but one does an injustice to the wealthy themselves in attributing to them what does not belong to them, and what they need not in order to be rich.
There is, moreover, one point at which Galileo and Newton, for all their belief in the existence of absolute space and time, admitted a certain relativity. They recognised that it is impossible todistinguish between uniform movements of translation. They thus admitted the equivalence of all such movements, and therefore the impossibility of proving an absolute movement of translation.
That is what is called the Principle of Classic Relativity.
An unexpected fact served to bring these questions upon a new plane, and led Einstein to give a remarkable extension to the Principle of Relativity of classic mechanics. This was the issue of a famous experiment by Michelson, of which we must give a brief description.
It is well known that rays of light travel across empty space from star to star, otherwise we should be unable to see the stars. From this physicists long ago concluded that the rays travelled in a medium that is devoid of mass and inertia, is infinitely elastic, and offers no resistance to the movement of material bodies, into which it penetrates. This medium has been named ether. Light travels through it as waves spread over the surface of water at a speed of something like 186,000 miles a second: a velocity which we will express by the letterV.
The earth revolves round the sun in a veritable ocean of ether, at a speed of about 18 miles a second. In this respect the rotation of the earth on its axis need not be noticed, as it pushes the surface of the globe through the ether at a speed of less than two miles a second. Now the question had often been asked: Does the earth, in its orbital movement round the sun, take with it the ether which is in contact with it, as a sponge thrown out of a window takes with it the water which it has absorbed? Experiment—or rather, experiments, for many have beentried with the same result—has shown that the question must be answered in the negative.
This was first established by astronomical observation. There is in astronomy a well-known phenomenon discovered by Bradley which is called aberration. It consists in this: when we observe a star with a telescope, the image of the star is not precisely in the direct line of vision. The reason is that, while the luminous rays of the star which have entered the telescope are passing down the length of the tube, the instrument has been slightly displaced, as it shares the movement of the earth. On the other hand, the luminous ray in the tube does not share the earth’s motion, and this gives rise to the very slight deviation which we call aberration. This proves that the medium in which light travels, the ether which fills the instrument and surrounds the earth, does not share the earth’s motion.
Many other experiments have settled beyond question that the ether, which is the vehicle of the waves of light, is not borne along by the earth as it travels. Now, since the earth moves through the ether as a ship moves over a stationary lake (not like one floating on a moving stream), it ought to be possible to detect some evidence of this speed of the earth in relation to the ether.
One of the devices that may be imagined for the purpose is the following. We know that the earth turns on itself from west to east, and travels round the sun in the same way. It follows that in the middle of the night the revolution of the earth round the sun means that Paris will be displaced, in the direction from Auteuil toward Charenton, at a speed of about thirty kilometres a second. During the day, of course, it is precisely the opposite. Paris changes its placeround the sun in the direction from Charenton toward Auteuil. Well, let us suppose that at midnight a physicist at Auteuil sends a luminous signal. A physicist receiving this ray of light at Charenton, and measuring its velocity, ought to find that the latter isV+ 30 kilometres. We know that, as a result of the earth’s motion, Charenton recedes before the ray of light. Consequently, since light travels in a medium, the ether, which does not share the earth’s motion, the observer at Charenton ought to find that the ray reaches him at a less speed than it would if the earth were stationary. It is much the same as if an observer were travelling on a bicycle in front of an express train. If the express travels at thirty metres a second and the cyclist at three metres a second, the speed of the train in relation to the cyclist will be 30-3 = 27 metres a second. It would benilif the train and the cyclist were travelling at the same rate.
On the other hand, if the cyclist were going toward the train, the speed of the train in relation to him would be 30 + 3 = 33 metres a second. Similarly, when the physicist at Charenton sends out a luminous message at midnight, and the physicist of Auteuil receives it, the latter ought to find that the ray of light has a velocity ofV+ 30 kilometres.
All this may be put in a different way. Suppose the distance between the observer at Auteuil and the man at Charenton were exactly twelve kilometres. While the ray of light emitted at Auteuil speeds toward Charenton, that town is receding before it to a small extent. It follows that the ray will have to travel a little more than twelve kilometres before it reaches the man of science at Charenton. It will travel a little less than that distance if we imagine it proceeding in the opposite direction.
Now the American physicist Michelson, borrowing an ingenious idea from the French physicist Fizeau, succeeded, with a high degree of accuracy, in measuring distances by means of the interference-bands of light. Every variation in the distance measured betrays itself by the displacement of a certain number of these bands, and this may easily be detected by a microscope.
Let us next suppose that our two physicists work in a laboratory instead of between Charenton and Auteuil. Let us suppose that they are, by means of the interference-bands, measuring the space traversed by a ray of light produced in the laboratory, according as it travels in the same direction as the earth or in the opposite direction. That is Michelson’s famous experiment, reduced to its essential elements and simplified for the purpose of this essay. In those circumstances Michelson’s delicate apparatus ought to reveal a distinctly measurable difference according as the light travels with the earth or in the opposite direction.
But no such difference was found. Contrary to all expectation, and to the profound astonishment of physicists, it was found that light travels at precisely the same speed whether the man who receives it is receding before it with the velocity of the earth or is approaching it at the same velocity. It is an undeniable consequence of this thatthe ether shares the motion of the earth. We have, however, seen that other experiments, not less precise, had settled thatthe ether does not share the motion of the earth.
Out of this contradiction, this conflict of two irreconcilable yet indubitable facts, Einstein’s splendid synthesis, like a spark of light issuing from the clash of flint and steel, came into being.