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 the preceding chapter we 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. I
mean 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 positions
_freely_ in 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’s
generalised mechanics has a strange affinity to this idea, and at the
same time to the curious declination, the _clinamen_, 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 circulate
_freely_; 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 a _petitio 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
principle _Hypotheses 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 is
_a priori_ easier 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 superb
synthesis, 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 is _a
priori_ evident 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 spatial
distances 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 his _Exposition 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 a previous chapter
in 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, if
they 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 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]
[8] _De Natura Rerum_, bk. ii, vv. 235-40.
Now if weight were a _force_ analogous 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 has
its 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.
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 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.
[9] It is obvious that we assume the projectile to be without rotation:
that is to say, the Columbia cannon must not, in our hypotheses, be
rifled. This is indispensable, for if the projectile turned, there
would be centrifugal effects which would greatly complicate both the
phenomena and our argument.
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 extraordinarily
light, 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 their
weight, 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 are
at 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 the preceding chapters that 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 an _invariant_,
as physicists say, or invariable, for the observers who move at
different speeds, this something must _naturally_ remain 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 was
fired 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 light
travels 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 his
head 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 the
sunlight 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 this _was_ proved, 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 at
night 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 possible
interpretation, 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.