CHAPTER VGENERALISED RELATIVITY
GENERALISED RELATIVITY
Weight and inertia—Ambiguity of the Newtonian law—Equivalence of gravitation and accelerated movement—Jules Verne’s projectile and the principle of inertia—Why rays of light are subject to gravitation—How light from the stars is weighed—An eclipse as a source of light.
We are now on the threshold of the great mystery of gravitation.
In thepreceding chapterwe saw how Einstein brought under one magnificent law both the slow movements of massive objects and the far more rapid movements of light. They had hitherto been separate and anarchic provinces of the universe. We now know that the same laws govern mechanics and optics. If for a time it appeared otherwise, it was because at velocities which approach that of light the lengths and masses of objects experience in the eyes of the observer an alteration which is imperceptible at familiar speeds. It is in its power of synthesis that Einstein’s mechanics is so splendid. Thanks to it, we perceive more unity, more harmony, more beauty, than formerly in this astounding universe, in which our thoughts and our anxieties are so ephemeral.
The theory of Relativity, however, has up to the present not touched a phenomenon that is fundamental, essential, ubiquitous in our cosmos. Imean gravitation, the mysterious property of bodies which rules the tiny atom no less than the most gigantic star, and directs their paths in majestic curves.
The universal attraction which, as far as earth is concerned, we call weight was a kind of steep-cliffed island in the sea of phenomena, something unrelated to the rest of natural philosophy.
The Einsteinian mechanism, as we have described it up to now, passed by this island, taking no notice of it. For that reason it was, in this form, known as “the theory of Special Relativity.” In order to convert it into a perfect instrument of synthesis, the phenomenon of gravitation had to be introduced. It is thus that Einstein crowned his work, and his system assumed the form which is well called “the theory of General Relativity.”
Einstein has drawn gravitation from its “splendid isolation,” and has annexed it, docile and vanquished, to the triumphal chariot of his mechanics. He has, moreover, given Newton’s famous law a more correct form, and experiment, the supreme judge, has declared this the only just form.
How he did this, by what subtle and powerful chain of reasoning, by what calculations based upon facts, I will now endeavour to tell; and I will again do my best to avoid the network of barbed wire of mathematical terminology.
Why did Newton, followed by the whole of classical science, believe that gravitation, the fall of bodies, did not belong to the mechanics of which he formulated the laws? Why, in a word, did he regard gravitation as a force or—to use a vaguer but more general term—an action which prevents heavy bodies from changing their positionsfreelyin space?
Because of the principle of inertia.This principle, the foundation of the whole Newtonian mechanics, may be expressed thus: a body which is not acted upon by any force maintains its velocity and direction unchanged.
Why do we equip steam-engines with the heavy wheels which we call “fly-wheels,” which work nothing? Because the principle of inertia is certainly nearly true. When the engine experiences a sudden and sharp check, or an acceleration, the fly-wheel serves to keep it steady. Driven by the speed it has acquired, and driving the engine in its turn, it tends to preserve its velocity, and it prevents or modifies accidental checks or accelerations. The principle is therefore based upon experience, especially on the experiments of Galileo, who verified it by rolling balls down planes inclined at different angles.
For instance, we find that a ball set in motion on a highly polished horizontal plane keeps its direction, and would preserve its velocity if the resistance of the atmosphere and the friction of the plane did not gradually reduce it to zero. We find that, in proportion as we reduce the friction, the ball tends to maintain its speed so much the longer.
Newton’s principle of inertia is based upon a number of these experiments. It is by no means in the nature of a self-evident mathematical truth. This is so true that ancient thinkers believed, contrary to classical mechanics, that the movement ceases as soon as the cause of it is removed. Certain of the Greek philosophers even thought that all bodies travel in a circle, if nothing interferes with them, because the circular is the noblest of all movements.
We shall see later how the principle of inertia of Einstein’sgeneralised mechanics has a strange affinity to this idea, and at the same time to the curious declination, theclinamen, which the great and profound Lucretius attributed to the free path of the atoms. But we must not anticipate.
This belief, that an object left freely to itself and not acted upon by any force preserves its velocity and direction, cannot pretend to be more than an experimental truth. But the observations on which it is based, especially those of Galileo, but any that may be imagined by physicists, could not possibly be conclusive, because in practice it is impossible to protect a moving body from every external force, such as atmospheric resistance, friction, or other.
I am aware that Newton grounded his principle on astronomical as well as terrestrial observations. He noticed that,apart from any attraction by other celestial bodies, and as far as we can see, the planets seem to maintain their direction and velocity relatively to the vault of heaven. But Relativists think that the words I have italicised in the preceding sentence, which reflect Newton’s idea, really beg the question. His argument assumes that the planets do not circulatefreely; that they are governed in their motions by a force which he called universal attraction.
We shall see how Einstein came to think that this is not a force, and in that case the issue of the argument is very different. However that may be, the classical principle of inertia is a truth based upon (imperfect) experience, and it is therefore subject to the constant control of facts. All that we can say about it is that practically—that is to say, approximately—it harmonises with what we find.
Newton did not regard it as such, not as a more or less precise approximation, but as a strict truth. That is why, when he saw that the planets do not travel in straight lines but in curved orbits, he concluded—which is apetitio principii—that they were subject to a central force, gravitation. That is why heavy bodies did not seem to him amenable to the mechanical laws which he had formulated for bodies left freely to themselves. That is why, in a word, Newton’s law of gravitation and his laws of dynamics are two distinct and separate things.
The great genius, the mind which had no equal, was nevertheless human. The immortal Descartes put forward strange statements and very occult hypotheses (about the pineal gland and animal spirits), after he had expressly resolved to affirm nothing that he did not perceive clearly and distinctly. In the same way Newton, after laying down as his principleHypotheses non fingo, put the hypotheses of absolute time and space at the very basis of his mechanics. At the basis of his masterly theory of gravitation he put the hypothesis—which isa priorieasier to admit—that there is a special force of gravitation.
These are weaknesses which the greatest of men do not escape. They ought to make us admire all the more the finer aspects of their work. So deep is the furrow ploughed by these great students of the unknown that, even when it is not straight, it takes two centuries and a half before men dream of inquiring afresh whether Newton’s distinction between purely mechanical and gravitational phenomena was just.
It is the signal distinction of Einstein that he successfully accomplished this: that, after erasing many things which were supposed to be finally settled, he blended mechanics and gravitation in a superbsynthesis, and enabled us to see more clearly the sublime unity of the world.
To tell the truth—let us premise this before we go further into the profound and marvellous truths of General Relativity—it isa priorievident that Newton’s law of universal attraction can no longer be considered satisfactory.
It says:Bodies attract each other in direct proportion to their masses and in inverse proportion to the square of their distances.What does that mean? We saw that the mass of a body varies with its velocity. When, for instance, we introduce the mass of our planet into calculations which involve Newton’s law, what precisely do we mean? Do we mean the mass which the earth would have if it did not revolve round the sun? Or do we mean the larger mass which it has in virtue of its motion? This motion, however, is not always of the same speed, because the earth travels in an ellipse, not a circle. What value shall we give to this variable mass in the calculation? That which corresponds to perihelion or aphelion, the period when the earth travels most rapidly or most slowly? Moreover, ought we not also to take into account the velocity of translation of the solar system, which in turn increases or diminishes according to the season?
Again, under Newton’s law what shall we make the distance from the earth to the sun? Is it to be the distance relatively to an observer on the earth or on the sun, or to a stationary observer in the middle of the Milky Way who does not share the motion of our system across it? Here again we shall have different values in each case, because spatialdistances vary, as we saw with Einstein, according to the relative velocity of the observer.
Hence Newton’s law is, in spite of its simple and artistic form, ambiguous and far from clear. I am aware that the differences I have just noted are not very important, but our calculations show that they are by no means negligible. Einsteinians therefore regard it as indisputable, apart from the considerations which we shall see presently, that Newton’s law, in its classical form, is obscure, and must be modified and completed.
These preliminary remarks will serve to at least put us in the frame of mind that is required of iconoclasts; and in science the iconoclasts are often the makers of progress. The particular idols at which we are preparing to deal a few audacious blows are the conception of the Newtonian law and gravitation.
Laplace wrote, in hisExposition du Système du Monde: “It is impossible to deny that nothing is more fully proved in natural philosophy than the principle of universal gravitation in virtue of mass and in inverse proportion to the square of the distance.” Nothing can better show us than this sentence of the great mathematician the importance of the step taken by Einstein when he, as we shall see, improved what had been regarded as the very type, the most perfect example, of scientific truth: the famous Newtonian law.
Gravitation, or weight, has this in common with inertia, that it is a quite general phenomenon. All material objects, whatever may be their physical and chemical condition, are both inert (that is to say, according to their mass they resist forces which tend to displace them)and heavy (they fall when they are left to themselves). But it is a strange thing, noted by Newton, though he did not realise the significance of it—he regarded it merely as an extraordinary coincidence—that the same figure which defines the inertia of a body also defines its weight. This figure is the mass of the body.
Let us return to the illustration which I used in aprevious chapterin dealing with Einstein’s mechanics. If two trains drawn by two similar locomotives start in the same conditions, and if the velocity communicated to the first train at the end of a second is double that communicated to the second, we conclude that the inertia, the inert mass, of the second train (leaving out of account the friction with the rails) is twice as great as that of the first. If we afterwards weigh our two trains, we find that the weight of the second is similarly twice as great as that of the first.
This experiment, though crude enough in our illustration, has been made with great precision by physicists, who used delicate methods which we need not describe here. The result was the same. The inert mass and the weight of bodies are exactly expressed by the same figures. Newton saw in this a mere coincidence. Einstein found in it the key to the hermetically sealed and inviolate dungeon in which gravitation was isolated from the rest of nature. Let us see how.
There is one remarkable feature of weight or gravitation: whatever be the nature of the objects, they always fall at the same speed (apart from atmospheric resistance). This is easily proved by causing a number of different objects to fall, in the same period of time, down a long tube in which a vacuum has been created. They all reach the bottom of the tube at the same time. A ton of lead and a sheet of paper will, ifthey are launched into the void simultaneously from the summit of a tower, reach the ground simultaneously, with a velocity the acceleration of which is, near the ground, 981 centimetres a second. This fact was known to Lucretius. Two thousand years ago that profound and immortal poet wrote:
Nulli, de nulla parte, neque ulloTempore, inane potest vacuum subsistere rei,Quin sua quod natura petit concedere pergat.Omnia quapropter debent per inane quietumÆque ponderibus non æquis concita ferri.[8]
Nulli, de nulla parte, neque ulloTempore, inane potest vacuum subsistere rei,Quin sua quod natura petit concedere pergat.Omnia quapropter debent per inane quietumÆque ponderibus non æquis concita ferri.[8]
Nulli, de nulla parte, neque ulloTempore, inane potest vacuum subsistere rei,Quin sua quod natura petit concedere pergat.Omnia quapropter debent per inane quietumÆque ponderibus non æquis concita ferri.[8]
Nulli, de nulla parte, neque ullo
Tempore, inane potest vacuum subsistere rei,
Quin sua quod natura petit concedere pergat.
Omnia quapropter debent per inane quietum
Æque ponderibus non æquis concita ferri.[8]
Now if weight were aforceanalogous to electrical attraction, to the propulsion of a locomotive, or even to the propulsive action of a charge of powder, this ought not to be the case. The velocities which it communicates to different masses ought to be different from each other. The two trains of unequal mass in our illustration receive unequal accelerations from the same locomotive. Nevertheless, if a great trench suddenly opened before them, they would fall into it with the same velocity.
From this it is only one step to conclude that gravitation is not a force, as Newton thought, but simply a property of space in which bodies move freely. Einstein took this step without hesitation.
Imagine the cable of the lift in some colossal skyscraper suddenly breaking. The lift will fall with an accelerated movement, though less rapidly than it would in a vacuum, on account of the atmospheric resistance and the friction of the cage of the apparatus. But let us suppose, further, that the electrical engine which works the lift hasits commutator reversed at the same time, and this accelerates the fall to such an extent that the velocity of the descent increases 981 centimetres in every second. It would be quite easy for our engineers to carry out this experiment, though the interest of it has not up to the present seemed great enough to justify it. But we have the right, when it is necessary to make a subject clear, to say with the poet:
An thou wilt, let us dream a dream.
An thou wilt, let us dream a dream.
An thou wilt, let us dream a dream.
An thou wilt, let us dream a dream.
Let us suppose our dream fulfilled. The lift falls from above with precisely the accelerated velocity of an object falling in a vacuum.
If the passengers have kept cool enough in their giddy rush downward to observe what happens, they will notice that their feet cease to press against the floor of the lift. They can imagine themselves like La Fontaine’s charming and poetic princess:
No blade of grass had feltThe light traces of her steps.
No blade of grass had feltThe light traces of her steps.
No blade of grass had feltThe light traces of her steps.
No blade of grass had felt
The light traces of her steps.
Our passengers’ purses will, even if they are full of gold, no longer be heavy in their pockets—which may give them a momentary anxiety. If their hats are released from their hands, they will remain suspended in the air beside them. If they happen to have scales with them, they will notice that the pans remain poised at equal height, even if various weights are put in one pan. All this is because the objects, as a natural effect of their weight, fall toward the ground with the same velocity as the lift itself. Their weight has disappeared.
Jules Verne described this state of things in the projectile which he imagined taking his heroes from the earth to the moon, at the moment when the romantic projectile reaches the “neutral point”: that is to say, the point where it leaves the earth’s sphere of gravitation, but has not yet entered that of the moon. We might add that Jules Verne perpetrated a few little scientific heresies in connection with his projectile. In particular, he forgot that, in compliance with what is most conspicuously evident in the principle of inertia, the unfortunate passengers ought to have been flattened like pancakes against the bottom of the projectile when the charge was fired. He also wrongly supposed that objects ceased to have weight in the projectile only at the point where it was exactly between the two spheres of attraction, that of the earth and that of the moon.
But let us overlook these trifles and return to the admirable illustration he has prophetically provided for our convenience in explaining Einstein’s system.
Let us take the projectile when it begins to fall freely toward the moon.[9]It is evident that from this point onward, until it lands on the moon, it will behave exactly like the lift which we have described.
During this fall upon the moon the passengers, if they have miraculously escaped being flattened at the start, will see the various objects about them suddenly deprived of their weight, floating in the air, and, at the slightest shake, adhering to the walls or the vaulted roof of the projectile. They will feel themselves extraordinarilylight, and they will be able to make prodigious leaps without any effort. This is because they and all the objects about them fall toward the moon with the same velocity as the projectile. Hence the disappearance of weight or gravitation, which vanish as if spirited away by some magician. The magician is the properly accelerated movement, the unimpeded fall of the observers.
In a word, to get rid of the apparent effects of gravitation in any place whatever it is enough for the observer to acquire a properly accelerated velocity. That is what Einstein calls the “principle of equivalence”: equivalence of the effects of weight and of an accelerated movement. The one cannot be distinguished from the other.
Let us imagine Jules Verne’s projectile and its unfortunate passengers transported a long distance from the moon, the earth, and the sun, to some deserted and glacial region of the Milky Way where there is no matter, and so remote from the stars that there is no longer any weight or attraction. Let us suppose that our projectile is abandoned there, and motionless. It is clear that in these circumstances there will be no such thing as high or low—no such thing as weight—for the passengers. They will find themselves relieved of every inconvenience of weight. They may, if they choose, stand on the inner wall of the upper part of the projectile or on the floor, as it was when they were falling upon the moon.
Now let us suppose that the wizard Merlin quietly approaches and, fastening a cord to the ring on the top of the projectile, begins to drag it with a uniformly accelerated movement. What will happen to the passengers? They will notice that they have suddenly recovered theirweight, and that they are riveted to the floor of the projectile, much as they were drawn to the surface of our planet before they left it. Indeed, if the motion of Merlin is accelerated 981 centimetres a second, they will have exactly the same sensations of weight as they had on the earth.
They will notice that if they throw a plate into the air at a given moment, it will fall upon the floor and be broken. “This is,” they will think, “because we are again subject to weight. The plate falls in virtue of its weight, its inert mass.” But Merlin will say: “The plate falls because, on account of its inertia, it has retained the increasing velocity which it had at the moment when it was thrown. Immediately afterwards, as I drew the projectile with an accelerated movement, the ascending velocity of the projectile was greater than that of the plate. That is why the bottom of the projectile, in its accelerated ascending course, knocked against the plate and broke it.”
This proves that the weight or gravitation of a body is indistinguishable from its inertia. Inert mass and heavy mass are not, as Newton supposed, two things which happen by some extraordinary coincidence to be equal; they are identical and inseparable. The two things are really one.
And we are thus led to believe that the laws of weight and the laws of inertia, the laws of gravitation and those of mechanics, must be identical, or must at least be two modalities of one and the same thing: much as the full face and the profile of the same man are the same face seen under two different angles.
Even if the travellers in the projectile—who look rather like guinea-pigs—peep out of the window and see the cord that is drawing them, it will not alter their illusion. They will believe that they areat rest and floating at a point of space where weight has been restored: that is to say, in the language of the experts, at a point of space where there is a “gravitational field.” This phrase is analogous to the familiar “magnetic field,” which refers to a part of space in which there is magnetic action, a part in which the needle of the compass has a definite direction imposed upon it.
In sum, we can at any point replace a gravitational field, or the effects of weight, by a properly accelerated movement of the observer, and vice versa. There is a complete equivalence between the effects of weight and those of an appropriate movement.
This now enables us to establish very simply the following fundamental fact, unknown only a few years ago, but now brilliantly proved by experiment:Light does not travel in a straight line in those parts of the universe where there is gravitation, but its path is curved like that of heavy objects.
We showed in one of thepreceding chaptersthat in the four-dimensional continuum in which we live, which we might call “space-time” but which we more simply call the universe, there is something that remains constant, identical for observers who move at given and different velocities. It is the “Interval” of events.
It is natural to suppose that this “Interval” will remain identical even if the velocity of the observers changes—even if it is accelerated like the velocity of the lift in our illustration, or of Jules Verne’s projectile, during their fall.
In point of fact, if something in the universe is aninvariant, as physicists say, or invariable, for the observers who move atdifferent speeds, this something mustnaturallyremain the same for a third observer whose velocity changes gradually from that of the first to that of the second observer, and who is therefore in a state of uniformly accelerated movement. From this we deduce certain consequences of a fundamental character.
In the first place, one thing is evident, and is unanimously admitted by physicists: in a vacuum, and in a region of space where there is no force acting and no such thing as weight, light travels in a straight line. That is certain for many reasons—in the first place, on the mere ground of symmetry, because in a region of isotropic vacuum a ray which is uninfluenced will not depart from its rectilinear path in any direction whatever. That is evident, whatever hypothesis we adopt as to the nature of light, and even if, like Newton, we suppose that it consists of ponderable particles.
Admitting that, let us now suppose that at some point in the universe where there is weight—at the moon’s surface, for instance—there is a remarkable gun which can fire a ball that has and retains (along its whole path) the velocity of light.
The trajectory of this ball will be very extensive, on account of its great velocity, yet curved toward the surface of the moon on account of its weight. As we may make our choice in the field of hypotheses, there is nothing to prevent us from supposing that the ball is of such a nature as to disclose its path by a faint luminous trail. There were projectiles of this character during the Great War.
As the ball advances, it also falls every second toward the moon’s surface, to the same extent as any other projectile would which wasfired at any velocity whatever, or had no velocity. All objects near the surface of the ground (in a vacuum) fall at the same vertical velocity, and this is independent of their motion in the horizontal direction. That is, in fact, the reason why the paths of projectiles are the more curved the less initial speed they have.
Seen from the windows of Jules Verne’s projectile (which is itself falling toward the moon), the trajectory of the ball will seem to the passengers to be a straight line, because it falls with the same velocity as they.
Now let us suppose that a luminous ray, from the flame of the gun, starts at the same time and in the same direction as the ball. This luminous ray will obviously be rectilinear for the passengers in the projectile, because light travels in a straight line when there is no weight. Consequently, since it has the same form, direction, and velocity as the luminous ball, the passengers will see the ray of light coincide in its whole course with the trajectory of the ball.
It further follows that the “Interval” (both in time and space) of the luminous ray and of the ball is, and remains, zero. Now this “Interval” must remain the same, whatever be the velocity of the observer. Hence, if Jules Verne’s projectile ceases to fall, and is stopped at the moon’s surface, its passengers will continue to see the luminous ray coincide at every point with the trajectory of the ball. This trajectory is, as they now notice, curved on account of weight. Therefore, the luminous ray is similarly curved in its path on account of weight.
This shows that light does not travel in a straight line, but falls, under the influence of gravitation, like all other objects. The reason why this was never known before, and it was always thought that lighttravels in a straight line, is that on account of the enormous velocity of light its trajectory is only very slightly curved by weight.
That is easy to understand. At the earth’s surface, for instance, light must fall (like all other objects) with a velocity equal to 981 centimetres at the end of a second. Now by the end of a second a luminous ray has travelled 300,000 kilometres. Suppose we could observe a horizontal luminous ray 300 kilometres long near the earth’s surface—a very far-fetched supposition—during the thousandth part of a second, which it will take the ray to pass from one observer to the other, it will fall to the extent of only about the five-thousandth of a millimetre.
We can understand how it was that a luminous ray that deviates only to this imperceptible extent from its initial direction in the course of three hundred kilometres was always considered rectilinear.
Is there no means of verifying whether light is or is not bent out of its path by gravitation? There is such a means in astronomy, as we shall now see.
It is impossible to detect the curvature of a luminous ray travelling from one point to another on the earth’s surface, mainly because weight on the earth is too slight to bend the ray much. A further reason is that our planet is so ridiculously small that we cannot follow the light over a sufficient distance.
But what cannot be done on this little globule of ours, the entire diameter of which light can cover in the twenty-fifth of a second, may possibly be done in the gigantic laboratory of celestial space. We have, almost within our reach—a mere matter of 93,000,000 miles away,that is to say—a star on which weight is twenty-seven times greater than on the earth. We mean the sun. On the sun a body left to itself falls 132 metres in the first second. Its fall is twenty-seven times as rapid as on the earth.
Hence, near the sun, light will be much more bent out of its path by gravitation. The deviation will be all the greater from the fact that the sun is 800,000 miles in diameter, and a luminous ray needs a much longer time to cover this distance than to travel the length of the earth’s diameter. Hence gravitation acts upon the ray of light during a much longer time than upon a ray that reaches the earth, and it will be all the more curved.
Take a luminous ray that comes from a star at a great distance behind the sun. If it reaches us after passing near to the sun, it will behave like a projectile. Its path will no longer be rectilinear. It will be slightly curved toward the sun. In other words, the ray will deviate from a straight line, and the direction it has when our eyes receive it on the earth is a little different from the direction it had when it left the star. It has been diverted.
Calculation shows that this deviation, though very slight, can be measured. It is equal to an angle of a second and three-quarters: an angle which the delicate methods of our astronomers are able to measure.
Certainly such an angle is very far from considerable, for it takes 324,000 angles of one second to make a right angle. In other words, an angle of one second is that at which we should see the two ends of a rod, a metre in length, fixed in the ground, at a distance of 206 kilometres. If our eyes were sharp enough to see a man of normal height standing 200 kilometres away from us, our glance, in passing from hishead to his feet, would have a very small angle of deviation. Well, this angle accurately represents the deviation experienced by the light that comes to us from a star when it has passed close to the golden globe of the sun.
Minute as this angle is, the methods of the astronomer are so delicate and precise that he can determine it. The tiny measurement is by no means to be despised. Disdain of the men who devote themselves to such refined subtleties is very much out of place, because our modern science has been revolutionised by this measurement. Einstein is right, and Newton wrong, because we have been able to measure this minute angle and establish the curvature of light.
A great difficulty arose when we wished to verify this. How can we observe in full daylight a ray of light that comes to us from a star and passes close to the sun? It cannot be done. Even if we use the most powerful glasses the stars on the farther side of the sun are completely drowned in its blaze—to speak more correctly, in the light which is diffused by our atmosphere.
To say the truth—if we may venture upon a parenthetic remark at this juncture—night has taught us much more than day about the mysteries of the universe. In literary symbolism, in politics, the light of day is the very symbol of progress and knowledge: night is the symbol of ignorance. What folly! It is a blasphemy against night, the sweetness of which we ought rather to venerate. I do not refer to its romantic charm, but to the mighty progress in knowledge which it has enabled us to make.
Midnight is not merely the hour of crime. It is also the hour of prodigious flight toward remote worlds. During the day we see only one sun: by night we see millions of suns. The blinding veil which thesunlight draws across the heavens may be woven of the most brilliant rays, but it is none the less a veil, for it makes us as blind as the moths which, in a strong light, can see no further than the tips of their wings.
In order to solve our problem, therefore, we have to observe in complete darkness stars which are nevertheless near the edge of the sun’s disk. Is that impossible? No. Nature has met our need by providing total eclipses of the sun which may at times be seen from various stations on the earth. At those times the bright disk is hidden for a few minutes behind the disk of the moon. Midday is turned into midnight. We see stars shine out close to the masked face of the sun.
Fortunately, a total eclipse, visible in Africa and South America, was due on May 29, 1919, shortly after Einstein had, on the strength of an argument like that we have just expounded, announced the deviation of the light of the stars when it passed the sun.
Two expeditions were organised by the astronomers of Greenwich and Oxford. One proceeded to Sobral, in Brazil, the other to the small Portuguese island Principe, in the Gulf of Guinea. Some of the English astronomers were rather sceptical about the issue. How could we, until it was proved, admit that Newton was wrong, or had at least failed to formulate a perfect law? But thiswasproved, and very decisively, by the observations.
These observations consisted in taking a certain number of photographs during the few minutes of total eclipse of the stars near the sun. They had been photographed with the same instruments some weeks before, at a time when the region of the sky in which they shine was visible atnight and far from the sun. As everybody knows, the sun passes successively, in its annual course, through the different constellations of the zodiac.
If the light of the stars which were photographed were not bent out of its path in passing the sun, it is clear that their distances ought to be the same on the plates exposed during the eclipse as on the negatives taken during the night some time previously. But if the light from them were bent out of its course during the eclipse by the gravitational influence of the sun, it would be quite otherwise. The reason is as follows. When the moon rises on one of our plains, it is not round, as everybody will have noticed, but flattened at top and bottom, somewhat like a giant tangerine lifted above the horizon for some magic supper. The moon has, of course, not ceased to be round. It merely seems to be flattened because the rays which come from its lower edge, and have to pass through a thick stratum of the atmosphere before they reach us, are bent toward the ground by the refraction of the denser atmosphere much more than are the rays coming from the moon’s upper edge, which pass through a less dense mass of air. Our eyes see the edge of the moon in the direction from which its rays come to us, not in the direction from which they started. That is why the lower edge of the moon seems to us to be raised higher above the horizon than it really is. This deviation is due to refraction.
In the same way a star situated a little to the east of the sun (the rays in this case being curved by weight, not by refraction) will seem to us further away from it. It will look as if it were further east than it really is. Similarly, a star to the west of the sun will seem to us still further from the sun’s western edge.
Hence the stars on either side of the sun will, if Einstein is right, be more widely separated from each other in the negatives taken during the eclipse. In their normal position, on the photographs taken during the night, they will seem nearer to each other.
This is precisely what was found when the photographs taken at Sobral and Principe were studied with the aid of the micrometer. Not only was it thus proved that the light of the stars is bent out of its path by the sun, but it was found that the deviation had exactly the extent which had been predicted by Einstein. It amounts to an angle of one second and three-quarters (1″·75) in the case of a star that is quite close to the sun’s disk, and the angle decreases rapidly in proportion to the distance of stars from the sun. It was a great triumph for the theory of Einstein, and for the first time it gave us some connecting link between light and gravitation.
On the preceding page I compared the curvature of light owing to its weight with the deviation that is caused by atmospheric refraction. As a matter of fact, there were astronomers who wondered whether the agreement between Einstein’s theory and the results obtained during the eclipse was not merely a coincidence: whether the deviation that was recorded was not due to refractive action by the sun’s atmosphere.
It seems impossible to admit this. Sometimes we see comets passing quite close to the surface of the sun during their journey through space. Their movement would be considerably disturbed if the sun’s atmosphere were refractive enough to account for the deviations observed at Sobral and Principe. Perturbations of cometary orbits of this nature, near the sun, have never been recorded. The only possibleinterpretation, therefore, is that the phenomena are due to the effect of weight upon light.
Thus the light of the stars, weighed in a balance of the most exquisite delicacy, has given us a decisive confirmation of Einstein’s theoretical deductions. By its fruit we know the tree.