EINSTEIN’S SOLUTION
_Provisional rejection of ether—Relativist
interpretation of Michelson’s experiment—New aspect
of the speed of light—Explanation of the contraction
of moving bodies—Time and the four dimensions of
space—Einstein’s “Interval” the only material reality._
Einstein’s first act of intelligent audacity was that, without
relegating the ether to the category of those obsolete fluids, such as
phlogiston and animal spirits, which obstructed the avenues of science
until Lavoisier appeared—without denying all reality to ether, for
there must be some sort of support for the rays which reach us from the
sun—he observed that, in all that we have as yet seen, there is always
question of velocities relatively to the ether.
We have no means whatever of establishing such velocities, and perhaps
it would be simpler to leave out of our arguments this entity, real
or otherwise, which is inaccessible and merely plays the futile and
troublesome part of fifth wheel to the electro-magnetic chariot in the
progress of physicists along the ruts of their difficulties.
The first point is then: Einstein begins, provisionally, by omitting
the ether from his line of reasoning. He neither denies nor affirms its
existence. He begins by ignoring it.
We will now follow his example. We shall no longer, in the course of
our demonstration, speak about the medium in which light travels. We
shall consider light only in relation to the beings or material objects
which emit or receive it. We shall find that our progress becomes at
once much easier. For the moment we will relegate the ether of the
physicists to the store of useless accessories, along with the suave,
formless, vague—but so precious artistically—ether of the poets.
* * * * *
Shortly, what does Michelson’s experiment prove? Only that a ray of
light travels at the surface of the earth from west to east at exactly
the same speed as from east to west. Let us imagine two similar guns in
the middle of a plain, both firing at the same moment, in calm weather,
and discharging their shells with the same initial velocity, but one
toward the west and the other toward the east. It is clear that the two
shells will take the same time to traverse an equal amount of space,
one going toward the west and the other toward the east. The rays of
light which we produce on the earth behave in this respect, as regards
their progress, exactly as the shells do. There would therefore be
nothing surprising in the result of the Michelson experiment, if we
knew only what experience tells us about the luminous rays.
But let us push the comparison further. Let us consider the shell fired
by one of the guns, and imagine that it hits a target at a certain
spot, and that, when it reaches the target, the residual velocity of
the shell is, let us say, fifty metres a second. I imagine the target
mounted on a motor tractor. If the latter is stationary the velocity of
the shell in relation to the target will be, as we said, fifty metres a
second at the point of impact. But let us suppose that the tractor and
the target are moving at a speed of, for instance, ten metres a second
toward the gun, so that the target passes to its preceding position
exactly at the moment when the shell strikes it. It is clear that the
velocity of the shell relatively to the target at the moment of impact
will not now be fifty metres, but 50 + 10 = 60 metres a second. It
is equally evident that the speed will fall to 50-10 = 40 metres a
second if (other things being equal) the target is travelling away from
the gun, instead of toward it. If, in the latter case, the velocity
of the target were equal to that of the shell, it is clear that the
relative velocity of the shell would now be _nil_.
So much is clear enough. That is how jugglers in the music-halls can
catch eggs falling from a height on plates without breaking them. It is
enough to give the plate, at the moment of contact, a slight downward
velocity, which lessens by so much the velocity of the shock. That is
also how skilled boxers make a movement backward before a blow, and
thus lessen its effective force, whereas the blow is all the harder if
they advance to meet it.
If the luminous rays behaved in all respects like the shells, as they
do in the Michelson experiment, what would be the result? When one
advances very rapidly to meet a ray of light, one ought to find its
velocity increased relatively to the observer, and lessened if the
observer recedes before it. If this were the case, all would be simple;
the laws of optics would be the same as those of mechanics; there
would be no contradiction to sow discord in the peaceful army of our
physicists, and Einstein would have had to spend the resources of his
genius on other matters.
Unfortunately—perhaps we ought to say fortunately, because, after all,
it is the unforeseen and the mysterious that lend some charm to the
way of the world—this is not the case. Both physical and astronomical
observation show that, under all conditions, when an observer advances
rapidly toward luminous waves or recedes rapidly from them, they still
show always the same velocity relatively to him. To take a particular
case, there are in the heavens stars which recede from us and stars
which approach us; that is to say, stars from which we recede, or which
we approach, at a speed of tens, and in some cases hundreds, of miles a
second. But an astronomer, de Sitter, has proved that the velocity of
the light which reaches us is, for us, always exactly the same.
Thus, up to the present it has proved quite impossible for us, by any
device or movement, to add to or lessen in the least the velocity with
which a ray of light reaches us. The observer finds that the rate of
speed of the light is always exactly the same relatively to himself,
whether the light comes from a source which rapidly approaches or
recedes from him, whether he is advancing toward it or retreating
before it. The observer can always increase or lessen, relatively to
himself, the speed of a shell, a wave of sound, or any moving object,
by pushing toward or moving away from the object. When the moving
object is a ray of light, he can do nothing of the kind. The speed of a
vehicle cannot in any case be added to that of the light it receives or
emits, or be subtracted from it.
This fixed speed of about 186,000 miles a second, which we find always
in the case of light, is in many respects analogous to the temperature
of 273° below zero which is known as “absolute zero.” This also is, in
nature, an impassable limit.
All this proves that the laws which govern optical phenomena are not
the same as the classic laws of mechanical phenomena. It was for
the purpose of reconciling these apparently contradictory laws that
Lorentz, following Fitzgerald, gave us the strange hypothesis of
contraction.
* * * * *
But we shall now find Einstein showing us, in luminous fashion, that
this contraction is seen to be perfectly natural when we abandon
certain conceptions—perhaps erroneous, though classical—which ruled
our habitual and traditional way of estimating lengths of space and
periods of time.
Take any object—a measuring rod, for instance. What is it that settles
for us the apparent length of the rod? It is the image made upon our
retina by the two rays that come from the two ends of the rod, and
which reach our eye _simultaneously_.
I italicise the word, because it is the key of the whole matter. If the
rod is stationary before us, the case is simple. But if it is moved
while we are looking at it, the case is less simple. It is so much
less simple that before the work of Einstein most of our learned men
and the whole of classic science thought that the instantaneous image
of an object that was not subject to change of shape was necessarily
and always identical, and independent of the velocities of the object
and the observer. The whole of classical science argued as if the
spread of light was itself instantaneous—as if it had an infinite
velocity—which is not the case.
I stand on the bank by the side of a railway. On the line is a handsome
Pullman car, in which it is so pleasant to think that space is
relative, in the Galileian sense of the word. Close to the line I have
two pegs fixed, one blue, the other red, and they exactly mark the
ends of the coach and indicate its length. Then, without leaving my
observation-post on the bank, my face turned towards the middle of
the coach, I give orders for the coach to be drawn back and coupled
to a locomotive of unheard-of power, which is to carry the coach past
me at a fantastic speed, millions of times faster than the speed any
mere engineer could provide. Such is the potential superiority of
the imagination over sober reality! I assume further that my retina
is perfect, and is so constituted that the visual impressions will
remain on it only as long as the light which causes them. These
somewhat arbitrary suppositions count for nothing in the essence of the
demonstration. They are only for the sake of convenience.
Now for the question. Will the coach (which I assume to be of some
rigid metal), as it passes before me at full speed, seem to me to
be exactly the same length as it did when it was at rest? To put it
differently, at the moment when I see its front end coincide with the
blue peg I had planted, shall I see its back end coincide at the same
time with the red peg? To this question Galileo, Newton, and all the
supporters of classic science would reply _yes_. Yet according to
Einstein the answer is _no_.
Here is the simple proof, as we deduce it from Einstein’s general idea.
I am, recollect, on the edge of the track, at an equal distance from
both pegs. When the front end of the coach coincides with the blue peg,
it sends toward my eye a certain ray of light (which, for convenience,
we will call the front ray), and this coincides with the luminous ray
coming to me from the blue peg. This front ray reaches my eye _at
the same time_ as a certain ray that comes from the back end of the
coach (which we will call the back ray). Does the back ray coincide
with the ray which comes to me from the red peg? Clearly not. The front
ray leaves the front end of the coach at the same speed as the back ray
leaves the back end; as any observer in the coach would find who cared
to try the Michelson experiment on them. But the front end of the coach
is receding from me while the back end is approaching me. Hence the
front ray travels toward my eye more slowly than the back ray, though
I cannot perceive this, as, when they reach me, I find that they both
have the same velocity. Hence the back ray, which reaches my eye at the
same time as the front ray, must have left the back end of the coach
later than the front ray left the front end of the coach. Therefore,
when I see the front end of the coach coincide with the blue peg, I
at the same time see the back end of the carriage _after_ it has
passed the red peg. Therefore the length of a coach travelling at full
speed, and such as it appears to me, is shorter than the distance
between the two pegs, which indicated the length of the coach at rest.
Q.E.D.
Very little attention is needed for any person to understand this
argument, though its elementary simplicity has not been attained
without difficulty. It is part of Einstein’s mathematical argument and
of his conception of simultaneity.
* * * * *
It follows that the coach, or, in general, any object, seems to
be contracted in virtue of its velocity, and in the direction of
that velocity, relatively to the spectator. The same thing happens,
obviously, if the observer moves in relation to the object, because we
can know only relative velocities, in virtue of the Classical Principle
of Relativity of Newton and Galileo.
In this new light the Lorentz-Fitzgerald contraction becomes
intelligible, or at least admissible. The contraction, thus considered,
is not the cause of the negative result of the Michelson experiment: it
is an effect of it. It is now quite clear, and we see that there was
something wrong with the classical way of estimating the instantaneous
dimension of objects.
Certainly the fact that luminous rays, starting out from their sources
at different speeds, should have the same speed when they reach our
eye, is strange. It upsets our habitual way of looking at things. If
I may venture to use a comparison simply for the purpose of provoking
reflection, not at all in the way of explanation, we have here
something analogous to what happens with the bombs of aviators. Bombs
of a given type, whether released at a height of 5,000 or of 10,000
metres, which therefore have very different downward velocities at
5,000 metres from the ground, have always the same residual velocity
when they reach the ground. This is due to the moderating and
equalising influence of the atmospheric resistance, which prevents the
speed from increasing indefinitely, and makes it constant when it has
attained a certain value.
Must we suppose that there is round our eye and round objects a sort of
field of resistance which sets a similar limit to the light? Who knows?
But perhaps such questions have no meaning for the physicist. He can
know nothing about the behaviour of light except when it leaves its
source or when it reaches the eye, whether armed with instruments or no.
He cannot learn how it behaves during its passage across the
intermediate space, in which there is no matter.
Indeed, the more deeply we study the new physics, the more we see that
it derives almost all its strength from its systematic disdain of all
that is beyond phenomena, all that cannot fall under experimental
observation. It is because it is solely based upon facts (however
contradictory they may be) that our proof of the necessary contraction
of objects owing to their velocity relatively to the observer is so
strong.
* * * * *
We must understand the profound significance of the Fitzgerald-Lorentz
contraction. This apparent contraction is by no means due to the
movement of objects relatively to the ether. It is essentially the
effect of the movements of objects and observers relatively to each
other, or relative movements in the sense of the older mechanics.
The greatest relative velocities to which we are accustomed in our
daily life are less than a few kilometres a second. The initial
velocity of the shell fired by “Bertha” was only about 1,300 metres
a second. For movements so slow as this the Relativist contraction
is entirely negligible. Hence, as the classical mechanics had never
observed such contraction, it regarded the shapes and dimensions of
rigid objects as independent of systems of reference.
It was very nearly true; and that makes all the difference between
true and false. To say that 999,990 + 9 = 1,000,000, is to say
something that is very nearly true, and is therefore false. When it
was discovered that the earth was round no change was made in their
procedure by architects. They continued to build as if the direction
indicated by the plumb-line was always parallel to itself. In the same
way those who make our locomotives and aeroplanes will not have to
consider the forms of the machines as dependent on their velocities.
What does it matter? The practical point of view is not, and cannot be,
that of science except indirectly. So much the worse if there is no
indirect influence, or if it is slow in coming.
Some years ago, however, we discovered things which move at speeds,
relatively to us, of tens or hundreds of thousands of kilometres a
second; the projectiles of the cathode rays and of radium. In this case
the Relativist contraction is very considerable. We shall see how it
has been observed.
But let us first recapitulate what we have seen. Objects seem to alter
their shape in the direction of their movement and not in the direction
perpendicular to this. Therefore their forms, even if they be composed
of an ideal and perfectly rigid material, depend on their velocity
relatively to the observer. This is the essentially new point of view
which Einstein’s “Special Relativity” superimposes upon the Relativity
of classical mechanics and philosophers. For these the absolute
dimensions of a rigid object or a geometrical figure were not absolute;
it was only the _relations_ of these dimensions which were real.
The new point of view is that these relations are themselves relative,
because they are a function of the velocity of the observer. It is
a sort of Relativity in the second degree, of which neither the
philosophers nor the classic physicists had dreamed.
Spatial relations themselves are relative, in a space which is already
relative.
In the case of our Pullman car and the two pegs which mark its length
when it is stationary, an observer situated in the carriage would find
the distance between the two pegs shortened as he passes them. The
coach would seem to him longer than the distance between the pegs. I
who remain beside the pegs observe the contrary. Yet I have no means of
proving to the passenger that he is wrong. I see quite plainly that the
ray of light which comes from the back peg runs behind the coach, and
has therefore, relatively to it, a speed of less than 186,000 miles a
second. I know that this is the reason for the passenger’s error, but I
have no means of convincing him that he is wrong. He will always say,
and rightly: “I have measured the speed at which this ray reaches me,
and I have found it 186,000 miles a second.” Each of us is really right.
In very rapid motion a square would seem to the observer a rectangle;
a circle would appear to be an ellipse. If the earth travelled some
thousands of times faster round the sun, we should see it elongated,
like a giant lemon suspended in the heavens. If an aviator could fly
at a fantastic speed over Trafalgar Square, in the direction of the
Strand—and if the impressions on his retina were instantaneous—he
would see the Square as a very flattened rectangle. If he flew in a
diagonal line about it, he would find it shaped like a lozenge. If the
same aviator flew across a road on which fat cattle were being driven
to the slaughter-house, he would be astonished, for the beasts would
seem to him extraordinarily lean, while there would be no change in
their length.
The fact that these alterations of shape owing to velocity are
reciprocal is one of the most curious consequences of all this. A man
who could pass in every direction amongst his fellows at the fantastic
speed of one of Shakespeare’s spirits—let us put it at about 170,000
miles an hour, though there would be no limit—would find that his
fellows had become dwarfs only half as large as himself. Would he have
become a giant, a sort of Gulliver amongst the Lilliputians? Not in
the least. Such is the justice of the scheme of earthly things that he
himself would seem a dwarf to the people whom he thought smaller than
himself, and who are quite sure of the contrary.
Which is right, and which wrong? Both. Each point of view is accurate,
but there are only personal points of view.
Again, any observer whatever will only see things that are not
connected with him as smaller—never larger—than the things which are
connected with his movement. If I might venture to relieve this sober
exposition by a reflexion rather less austere than is usual in physics,
I would say that the new system affords a supreme justification of
egoism, or, rather, of egocentricism.
It is the same with time as with space. By similar reasoning to that
which has shown us how the distance of things in space is connected
with their velocity relatively to the observer, it can be shown that
their distance in time likewise depends upon this.
It would be useless to reproduce here the whole of the Einsteinian
argument as to duration. It is analogous to that which we have used
in regard to length, and even simpler. The result is as follows. The
time expressed in seconds which a train takes to pass from one station
to another is shorter for the passengers on the train than for us who
watch it pass, though our watches may be just the same as theirs.[5]
Similarly, all the gestures of men who are on moving vehicles will seem
to a stationary observer slowed down, and therefore prolonged, and vice
versa. But the velocity would, as in the case of variation in length,
have to be fantastic to make these variations in time perceptible.
[5] The best definition of the second that can be given is the
following: it is the time which light takes to cover 186,000 miles
in empty space and far from any strong gravitational field. This
definition, the only strict definition, is further justified by the
fact that there is no better means of regulating clocks than luminous
or Hertzian (which have the same speed) signals.
It is not less true that the time between the birth and the death of
any creature, its life, will seem longer if the creature moves rapidly
and fantastically relatively to the observer. In this world, where
appearance is almost everything, this is not without importance, and it
follows that, philosophically speaking, to move on is to last longer;
but for others, not for oneself; just as others may seem to me to last
longer. A striking, a profound, an unforeseen justification of the
words of the sage: immobility is death!
* * * * *
Formerly, before the Einsteinian _hegira_, before the Relativist
Era opened, everybody was convinced that the portion of _space_
occupied by an object was sufficiently and explicitly defined by its
dimensions—length, breadth, and height. These are what are called
the three _dimensions_ of an object; just as we speak, to use a
different expression, of the longitude, latitude, and altitude of each
of its points, or as we speak in astronomy of its right ascension,
declination, and distance.
It was quite understood that we had, in addition, to indicate the
epoch, the moment, to which these data correspond. If I define the
position of an aeroplane by its longitude, latitude, and altitude,
these indications are only correct for a certain moment, because the
aeroplane is moving relatively to the observer, and the moment also
must be indicated. In this sense it has long been known that space
depends upon time.
But the Relativist theory shows that it depends upon time in a much
more intimate and deeper manner, and that time and space are as closely
connected as those twin monsters which the surgeon cannot separate
without killing both.
The dimensions of an object, its shape, the apparent _space_
occupied by it, depend upon its velocity: that is to say, upon the
_time_ which the observer takes to traverse a certain distance
relatively to the object. Here we have _space_ already depending
upon _time_. In addition, the observer measures the time with
a chronometer, the seconds of which are more or less accelerated
according to his velocity.
Hence it is impossible to define space without time. That is why we
now say that time is the fourth dimension of space, or that the space
in which we live has four dimensions. It is remarkable that there were
able men in the past who had a more or less clear intuition of this.
Thus we find Diderot, in 1777, writing in the _Encyclopédie_, in
the article “Dimension”:
“I have already said that it is impossible to conceive more than three
dimensions. A learned man of my acquaintance, however, believes that
one might regard duration as a fourth dimension, and that the product
of time by solidity would be, in a sense, a product of four dimensions.
The idea may not be admitted, but it seems to be not without merit, if
it be only the merit of originality.”
It was algebra, undoubtedly, that gave rise to the idea of a space with
more than three dimensions. Since, in point of fact, lines or spaces of
one dimension are represented by algebraical expressions of the first
degree, surfaces or spaces of two dimensions by formulæ of the second
degree, and volumes or spaces of three dimensions by expressions of the
third degree, it was natural to ask oneself if formulæ of the fourth
and higher degrees are not also the algebraical representation of some
form of space with four or more dimensions.
The four-dimensional space of the Relativists is, however, not quite
what Diderot imagined. It is not the product of time by extension, for
a diminution of time is not compensated in it by an increase of space.
Quite the contrary. Take two events, such as the successive passage
of our Pullman car through two stations. For a passenger in the car
the distance between the two stations, measured by the length of the
track covered, is, as we saw, shorter than for a person who is standing
stationary beside the line. The time between passing through the two
stations is likewise less for the first observer. The number of seconds
and fractions of seconds marked by his chronometer is smaller for him,
as we saw.
In a word, distance in time and distance in space diminish
simultaneously when the velocity of the observer increases, and both
increase when the velocity of the observer lessens.
Thus velocity (velocity relatively to the things observed, we must
always remember) acts in a sense as a double brake lessening durations
and shortening lengths. If a different illustration be preferred,
velocity enables us to see both spaces and times more obliquely, at an
increasingly sharp angle. Space and time are therefore only changing
effects of perspective.
Can we conceive space of four dimensions? That is to say, can we
imagine or visualise it? Even if we cannot, it proves nothing as
regards the reality of such space. During ages no one conceived such
a thing as the Hertzian waves, and even to-day we have no direct
sense-impression of them. They exist none the less. As a matter of
fact, we find it difficult to conceive space of three dimensions. If it
were not for our muscular changes, we should know nothing about it. A
paralysed and one-eyed man, that is to say, a man without the sensation
of relief which we get from binocular vision—and even this is, in the
first place, a muscular sensation—would, with his single eye, see all
objects on the same plane, as on the drop-scene of a theatre. He could
have no perception of three-dimensional space.
I believe there are people who can form an idea of four-dimensional
space. The successive appearances of a flower in its various phases of
growth, from the day when it is but a frail green bud until the time
when its exhausted petals fall sadly to the ground, and the successive
changes of its corolla under the influence of the wind, give us a
globular image of the flower in four-dimensional space.
Are there any who can see all this together? I believe that there are,
especially amongst good chess-players. When a skilful player plays
well, it is because he can take in with a single glance of his mental
eye the whole chronological and spatial series of moves that may follow
the first move, with all their effects on the board. He _sees the
whole series simultaneously_.
The words I have italicised look contradictory. That is because we are
in a province where it is all but impossible to express the fine shades
of things in words. One might just as well attempt to define verbally
all that there is in a symphony of Beethoven. “The translator is a
traitor.” If there is any truth in the proverb, it is because words are
the organ of translation.
* * * * *
We have reached a point in our gradual progress into Relativist physics
where we have before our eyes merely a battlefield strewn with corpses
and ruins.
We had regarded time and space as hooks solidly fastened to the wall
behind which lurks reality, and on these we hang our floating ideas of
the material world, just as we hang our coats on the rack. Now they
lie, torn down and crumpled, amongst the rubbish of ancient theories,
victims of the hammer-blows of the new physics.
We knew quite well, of course, that the souls of men were inscrutable
to us, but we did think that we saw their faces. Now, as we approach
them, we find that it is only masks we saw. The material world, as
Einstein shows it to us, is a sort of masked ball, and, by a deceptive
irony, it is we ourselves who have made the black velvet masks and the
gay costumes.
Instead of revealing reality to us, space and time are, according to
Einstein, only moving veils, woven by ourselves, which hide it from us.
Yet—strange and melancholy reflection—we can no more conceive the
world without space and time than we can observe certain microbes under
the microscope without first injecting colouring matter into them.
Are time and space, then, merely hallucinations? And, if so, what
_is_ real?
No. Once the Relativist has thrown down the tottering ruins, he begins
to reconstruct. Behind the veils, now torn down and trodden under foot,
a new and more subtle reality is about to appear.
If we describe the universe in the usual way, in separate categories
of space and time, we see that its aspect depends upon the observer.
Happily, it is not the same when we describe it in the unique category
of the four-dimensional continuum in which Einstein locates phenomena,
and in which space and time are inseparably united.
If I may venture to use this illustration, time and space are like
two mirrors, one convex, the other concave, the curvature of which
is accentuated in proportion to the velocity of the observer. Each
of these mirrors gives us, separately, a distorted picture of the
succession of things. But this is fortunately compensated for by the
fact that, when we combine the two mirrors so that one reflects the
rays received by the other, the picture of the succession of things is
restored in its unaltered reality.
The distance in time and the distance in space of two given events
which are close to each other both increase or decrease when the
velocity of the observer decreases or increases. We have shown
that. But an easy calculation—easy on account of the formula given
previously to express the Lorentz-Fitzgerald contraction—shows that
there is a constant relation between these concomitant variations of
time and space. To be precise, the distance in time and the distance in
space between two contiguous events are numerically to each other as
the hypotenuse and another side of a rectangular triangle are to the
third side, which remains invariable.[6]
[6] In the geometrical calculus or representation that may be
substituted for this the hypotenuse of the triangle is the distance in
time, each second being represented by 300,000 kilometres.
Taking this third side for base, the other two will describe, above
it, a triangle more or less elevated according as the velocity of the
observer is more or less reduced. This fixed base of the triangle, of
which the other two sides—the spatial distance and the chronological
distance—vary simultaneously with the velocity of the observer, is,
therefore, a quantity independent of the velocity.
It is this quantity which Einstein has called the _Interval_
of events. This “Interval” of things in four-dimensional space-time
is a sort of conglomerate of space and time, an amalgam of the two.
Its components may vary, but it remains itself invariable. It is the
constant resultant of two changing vectors. The “Interval” of events,
thus defined, gives us for the first time, according to Relativist
physics, an impersonal representation of the universe. In the striking
words of Minkowski, “space and time are mere phantoms. All that exists
in reality is a sort of intimate union of these entities.”
The sole reality accessible to man in the external world, the one
really objective and impersonal thing which is comprehensible, is the
Einsteinian _Interval_ as we have defined it. The _Interval_
of events is to Relativists the sole perceptible part of the real.
Apart from that there is something, perhaps, but nothing that we can
know.
Strange destiny of human thought! The principle of relativity has, in
virtue of the discoveries of modern physics, spread its wings much
farther than it did before, and has reached summits which were thought
beyond the range of its soaring flight. Yet it is to this we owe,
perhaps, our first real perception of our weakness in regard to the
world of sense, in regard to reality.
Einstein’s system, of which we have now to see the constructive
part, will disappear some day like the others, for in science there
are merely theories with “provisional titles,” never theories with
“definitive titles.” Possibly that is the reason of its many victories.
The idea of the _Interval_ of things will, no doubt, survive all
these changes. The science of the future must be built upon it. The
bold structure of the science of our time rises upon it daily.
It must, in fine, be clearly understood that the _Einsteinian
Interval_ tells us nothing about the absolute, about things in
themselves. It, like all others, shows us only relations between
things. But the relations which it discloses seem to be real and
unvarying. They share the degree of objective truth which classic
science attributed, with, perhaps, unfounded assurance, to the
chronological and spatial relations of phenomena. In the view of the
new physics these were but false scales. The Einsteinian Interval alone
shows us what can be known of reality.
Einstein’s system, therefore, takes pride in having lifted for all
future time a corner of the veil which conceals from us the sacred
nudity of nature.