Einstein and the universe: A popular exposition of the famous theory — Context and Discussion

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 to distinguish 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 letter =V=.

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 been tried 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 place round 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 is =V= + 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 be _nil_ if 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 of =V= + 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 that _the ether shares the motion of the earth_. We have, however, seen that other experiments, not less precise, had settled that _the 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.

SCIENCE IN A NO-THOROUGHFARE

_Scientific truth and mathematics—The precise function of Einstein—Michelson’s experiment, the Gordian knot of science—The hesitations of Poincaré—The strange, but necessary, Fitzgerald-Lorentz hypothesis—The contraction of moving bodies—Philosophical and physical difficulties._

It would be foolish to pretend that we can penetrate the most obscure corners of Einstein’s theories without the aid of mathematics. I believe, however, that we can give in ordinary language—that is to say, by means of illustrations and analogies—a fairly satisfactory idea of these things, the intricacy of which is usually due to the infinitely subtle and supple play of mathematical formulæ and equations.

After all, mathematics is not, never was, and never will be, anything more than a particular kind of language, a sort of shorthand of thought and reasoning. The purpose of it is to cut across the complicated meanderings of long trains of reasoning with a bold rapidity that is unknown to the mediæval slowness of the syllogisms expressed in our words.

However paradoxical this may seem to people who regard mathematics as _of itself_ a means of discovery, the truth is that we can never get from it anything that was not implicitly inherent in the data which were thrust between the jaws of its equations. If I may use a somewhat trivial illustration, mathematical reasoning is very like certain machines which are seen in Chicago—so bold explorers in the United States tell us—into which one puts living animals that emerge at the other end in the shape of appetising prepared meats. No spectator could have, or would wish to have, eaten the animal alive, but in the form in which it issues from the machine it can at once be digested and assimilated. Yet the meat is merely the animal conveniently prepared. That is what mathematics does. By means of a marvellous machinery the mathematician extracts the valuable marrow from the _given facts_. It is a machinery that is particularly useful in cases where the wheels of verbal argument, the chain of syllogisms, would soon be brought to a halt.

Does it follow that, properly speaking, mathematics is not a science? Does it follow at least that it is only a science in so far as it is based upon reality, and fed with experimental data, since “experience is the sole source of truth.” I refrain from answering the question, as I am one of those who believe that everything is material for science. Still, it was worth while to raise the question because many are too much disposed to regard a purely mathematical education as a scientific education. Nothing could be further from the truth. Pure mathematics is, in itself, merely an abbreviated form of language and of logical thought. It cannot, of its own nature, teach us anything about the external world; it can do so only in proportion as it enters into contact with the world. It is of mathematics in particular that we may say: _Naturæ non imperatur nisi parendo._

Are not Einstein’s theories, as some imperfectly informed writers have suggested, only a play of mathematical formulæ (taking the word in the meaning given to it by both mathematicians and philosophers)? If they were only a towering mathematical structure in which the _x_’s shoot out their volutes in bewildering arabesques, with swan-neck integrals describing Louis XV patterns, they would have no interest whatever for the physicist, for the man who has to examine the nature of things before he talks about it. They would, like all coherent schemes of metaphysics, be merely a more or less agreeable system of thought, the truth or falseness of which could never be demonstrated.

Einstein’s theory is very different from that, and very much more than that. It is based upon facts. It also leads to facts—new facts. No philosophical doctrine or purely formal mathematical construction ever enabled us to discover new phenomena. It is precisely because it has led to such discovery that Einstein’s theory is neither the one nor the other. That is the difference between a scientific theory and a pure speculation, and it is that which, I venture to say, makes the former so superior.

Like some suspension bridge boldly thrown across an abyss, Einstein’s theory rests, on the one side, on experimental phenomena, and it leads, at the other side, to other, and hitherto unsuspected, phenomena, which it has enabled us to discover. Between these two solid experimental columns the mathematical reasoning is like the marvellous network of thousands of steel bars which represent the elegant and translucent structure of the bridge. It is that, and nothing but that. But the arrangement of the beams and bars might have been different, and the bridge—though less light and graceful, perhaps—still have been able to join together the two sets of facts on which it rests.

In a word, mathematical reasoning is only a kind of reasoning in a special language, from experimental premises to conclusions which are verifiable by experience. Now there is no language which cannot in some degree be translated into another language. Even the hieroglyphics of Egypt had to give way before Champollion. I am therefore convinced that the mathematical difficulties of Einstein’s theories will some day be replaced by simpler and more accessible formulæ. I believe, indeed, that it is even now possible to give by means of ordinary speech an idea, rather superficial perhaps, but accurate and substantially complete, of this wonderful Einsteinian structure which ranges all the conquests of science, as in some well-ordered museum, in a new and superb unity. Let us try.

We may resume in the few following words the story of the origin, the starting-point, of Einstein’s system.

1. Observation of the stars proves that interplanetary space is not empty, but is filled with a special medium, ether, in which the waves of light travel.

2. The fact of aberration and other phenomena seems to prove that the ether is not displaced by the earth during its course round the sun.

3. Michelson’s experiment seems to prove, on the contrary, that the earth bears the ether with it in its movement.

This contradiction between facts of equal authority was for years the despair and the wonder of physicists. It was the Gordian knot of science. Long and fruitless efforts were made to untie it until at last Einstein cut it with a single blow of his remarkably acute intelligence.

In order to understand how that was done—which is the vital point of the whole system—we must retrace our steps a little and examine the precise conditions of Michelson’s famous experiment.

I pointed out in the preceding chapter that Michelson proposed to study the speed of a ray of light produced in the laboratory and directed either from east to west or west to east: that is to say, in the direction in which the earth itself moves, at a speed of about eighteen miles a second, as it travels round the sun, or in the opposite direction. As a matter of fact, Michelson’s experiment was rather more complicated than that, and we must return to it.

Four mirrors are placed at an equal distance from each other in the laboratory, in pairs which face each other. Two of the opposing mirrors are arranged in the direction east-west, the direction in which the earth moves in consequence of its revolution round the sun. The other two are arranged in a plane perpendicular to the preceding, the direction north-south. Two rays of light are then started in the respective directions of the two pairs of mirrors. The ray coming from the mirror to the east goes to the mirror in the west, is reflected therefrom, and returns to the first mirror. This ray is so arranged that it crosses the path of the light which goes from north to south and back. It interferes with the latter light, causing “fringes of interference” which, as I said, enable us to learn the exact distance traversed by the rays of light reflected between the pairs of mirrors. If anything brought about a difference between the length of the two distances, we should at once see the displacement of a certain number of interference-fringes, and this would give us the magnitude of the difference.

An analogy will help us to understand the matter. Suppose a violent steady east wind blew across London, and an aviator proposed to cross the city about twelve miles from extreme west to east and back: that is to say, going with the wind on his outward journey and against it on the return journey. Suppose another aviator, of equal speed, proposed at the same time to fly from the same starting-point to a point twelve miles to the north and back, the second aviator will fly both ways at right angles to the direction of the wind. If the two start at the same time, and are imagined as turning round instantaneously, will they both reach the starting-point together? And, if not, which of them will have completed his double journey first?

It is clear that if there were no wind, they would get back together, as we suppose that they both do twenty-four miles at the same speed, which we may roughly state to be 200 yards a second.

But it will be different if, as I postulated, there is a wind blowing from east to west. It is easy to see that in such circumstances the man who flies east to west will take longer to complete the journey. In order to get it quite clearly, let us suppose that the wind is travelling at the same speed as the aviator (200 yards a second). The man who flies at right angles to the wind will be blown twelve miles to the west while he is doing his twelve miles from south to north. He will therefore have traversed _in the wind_ a real distance equal to the diagonal of a square measuring twelve miles on each side. Instead of flying twenty-four miles, he will really have flown thirty-four in the wind, the medium in relation to which he has any velocity.

On the other hand, the aviator who flies eastward will never reach his destination, because in each second of time he is driven westward to precisely the same extent as he is travelling eastward. He will remain stationary. To accomplish his journey he would need to cover _in the wind_ an infinite distance.

If, instead of imagining a wind equal in velocity to the aviator (an extreme supposition in order to make the demonstration clearer), I had thought of it as less rapid, we should again find, by a very simple calculation, that the man who flies north and south has less distance to cover in the wind than the man who flies east and west.

Now take rays of light instead of aviators, the ether instead of the wind, and we have very nearly the conditions of the Michelson experiment. A current or wind of ether—since the ether has been already shown to be stationary in relation to the earth’s movement—proceeds from one to the other of our east-west mirrors. Therefore the ray of light which travels between these two mirrors, forth and back, must cover a longer distance in ether than the ray which goes from the south mirror to the north and back. But how are we to detect this difference? It is certainly very minute, because the speed of the earth is ten thousand times less than the velocity of light.