Transcriber’s Notes:
Underscores “_” before and after a word or phrase indicate _italics_
in the original text.
Equal signs “=” before and after a word or phrase indicate =bold=
in the original text.
Small capitals have been converted to SOLID capitals.
Typographical and punctuation errors have been silently corrected.
EINSTEIN AND THE UNIVERSE
_A Popular Exposition of the Famous Theory_
_By_ CHARLES NORDMANN
_Astronomer to the Paris Observatory._
_Translated by_ JOSEPH McCABE
_With a Preface by the Rt. Hon._
THE VISCOUNT HALDANE, O.M.
T. FISHER UNWIN LTD.
LONDON: ADELPHI TERRACE
_First published in English April 1922_
_Second Impression June 1922_
_All rights reserved_
PREFACE
A distinguished German authority on mathematical physics, writing
recently on the theory of Relativity, declared that if his publishers
had been willing to allow him sufficient paper and print he could have
explained what he wished to convey without using a single mathematical
formula. Such success is conceivable. Mathematical methods present,
however, two advantages. Their terminology is precise and concentrated,
in a fashion which ordinary language cannot afford to adopt. Further,
the symbols which result from their employment have implications
which, when brought to light, yield new knowledge. This is deductively
reached, but it is none the less new knowledge. With greater precision
than is usual, ordinary language may be made to do some, if not a great
deal, of this work for which mathematical methods are alone quite
appropriate. If ordinary language can do part of it an advantage may
be gained. The difficulty that attends mathematical symbolism is the
accompanying tendency to take the symbol as exhaustively descriptive
of reality. Now it is not so descriptive. It always embodies an
abstraction. It accordingly leads to the use of metaphors which
are inadequate and generally untrue. It is only qualification by
descriptive language of a wider range that can keep this tendency in
check. A new school of mathematical physicists, still, however, small
in number, is beginning to appreciate this.
But for English and German writers the new task is very difficult.
Neither Anglo-Saxon nor Saxon genius lends itself readily in this
direction. Nor has the task as yet been taken in hand completely, so
far as I am aware, in France. Still, in France there is a spirit and a
gift of expression which makes the approach to it easier than either
for us or for the Germans. Lucidity in expression is an endowment which
the best French writers possess in a higher degree than we do. Some of
us have accordingly awaited with deep interest French renderings of the
difficult doctrine of Einstein.
M. Nordmann, in addition to being a highly qualified astronomer and
mathematical-physicist, possesses the gift of his race. The Latin
capacity for eliminating abstractness from the description of facts is
everywhere apparent in his writing. Individual facts take the places
of general conceptions, of _Begriffe_. The language is that of
the _Vorstellung_, in a way that would hardly be practicable in
German. Nor is our own language equal to that of France in delicacy of
distinctive description. This book could hardly have been written by an
Englishman. But the difficulty in his way would have been one as much
of spirit as of letter. It is the lucidity of the French author, in
combination with his own gift of expression, that has made it possible
for the translator to succeed so well in overcoming the obstacles
to giving the exposition in our own tongue this book contains. The
rendering seems to me, after reading the book both in French and in
English, admirable.
M. Nordmann has presented Einstein’s principle in words which lift
the average reader over many of the difficulties he must encounter in
trying to take it in. Remembering Goethe’s maxim that he who would
accomplish anything must limit himself, he has not aimed at covering
the full field to which Einstein’s teaching is directed. But he
succeeds in making many abstruse things intelligible to the layman.
Perhaps the most brilliant of his efforts in this direction are
Chapters V and VI, in which he explains with extraordinary lucidity
the new theory of gravitation and of its relation to inertia. I think
that M. Nordmann is perhaps less successful in the courageous attack he
makes in his third chapter on the obscurity which attends the notion
of the “Interval.” But that is because the four-dimensional world,
which is the basis of experience of space and time for Einstein and
Minkowski, is in itself an obscure conception. Mathematicians talk
about it gaily and throw its qualities into equations, despite the
essential exclusion from it of the measurement and shape which actual
experience always in some form involves. They lapse on that account
into unconscious metaphysics of a dubious character. This does not
destroy the practical value of their equations, but it does make them
very unreliable as guides to the character of reality in the meaning
which the plain man attaches to it. Here, accordingly, we find the
author of this little treatise to be a good man struggling with
adversity. If he could make the topic clear he would. But then no one
has made it clear excepting as an abstraction which works, but which,
despite suggestions made to the contrary, cannot be clothed for us in
images.
This, however, is the fault, not of M. Nordmann himself, but of a phase
of the subject. With the subject in its other aspects he deals with the
incomparable lucidity of a Frenchman. I know no book better adapted
than the one now translated to give the average English reader some
understanding of a principle, still in its infancy, but destined, as I
believe, to transform opinion in more regions of knowledge than those
merely of mathematical physics.
_Haldane_
CONTENTS
PREFACE BY THE RT. HON. VISCOUNT HALDANE, O.M. pp. 5-8
INTRODUCTION pp. 13-15
CHAPTER I
THE METAMORPHOSES OF SPACE AND TIME
_Removing the mathematical difficulties—The pillars
of knowledge—Absolute time and space, from
Aristotle to Newton—Relative time and space,
from Epicurus to Poincaré and Einstein—Classical
Relativity—Antinomy of stellar aberration and the
Michelson experiment_ pp. 17-31
CHAPTER II
SCIENCE IN A NO-THOROUGHFARE
_Scientific truth and mathematics—The precise function
of Einstein—Michelson’s experiment, the Gordian knot
of science—The hesitations of Poincaré—The strange,
but necessary, Fitzgerald-Lorentz hypothesis—The
contraction of moving bodies—Philosophical and
physical difficulties_ pp. 32-52
CHAPTER III
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_ pp. 53-72
CHAPTER IV
EINSTEIN’S MECHANICS
_The mechanical foundation of all the
sciences—Ascending the stream of time—The speed of
light an impassable limit—The addition of speeds
and Fizeau’s experiment—Variability of mass—The
ballistics of electrons—Gravitation and light as
atomic microcosms—Matter and energy—The death of
the sun_ pp. 73-100
CHAPTER V
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_ pp. 101-123
CHAPTER VI
THE NEW CONCEPTION OF GRAVITATION
_Geometry and reality—Euclid’s geometry and
others—Contingency of Poincaré’s criterion—The
real universe is not Euclidean but Riemannian—The
avatars of the number π—The point of view of the
drunken man—Straight and geodetic lines—The new
law of universal attraction—Explanation of the
anomaly of the planet Mercury—Einstein’s theory of
gravitation_ pp. 124-147
CHAPTER VII
IS THE UNIVERSE INFINITE?
_Kant and the number of the stars—Extinct stars and
dark nebulæ—Extent and aspect of the astronomical
universe—Different kinds of universes—Poincaré’s
calculation—Physical definition of the infinite—The
infinite and the unlimited—Stability and
curvature of cosmic space-time—Real and virtual
stars—Diameter of the Einsteinian universe—The
hypothesis of globes of ether_ pp. 148-159
CHAPTER VIII
SCIENCE AND REALITY
_The Einsteinian absolute—Revelation by
science—Discussion of the experimental bases of
Relativity—Other possible explanations—Arguments in
favour of Lorentz’s real contraction—Newtonian space
may be distinct from absolute space—The real is a
privileged form of the possible—Two attitudes in
face of the unknown_ pp. 160-172
CHAPTER IX
EINSTEIN OR NEWTON?
_Recent discussion of Relativism at the Academy
of Sciences—Traces of the privileged space
of Newton—The principle of causality,
the basis of science—Examination of M.
Painlevé’s objections—Newtonian arguments and
Relativist replies—M. Painlevé’s formulas of
gravitation—Fecundity of Einstein’s theory—Two
conceptions of the world—Conclusion_ pp. 173-185
INTRODUCTION
This book is not a romance. Nevertheless.... If love is, as Plato says,
a soaring toward the infinite, where shall we find more love than in
the impassioned curiosity which impels us, with bowed heads and beating
hearts, against the wall of mystery that environs our material world?
Behind that wall, we feel, there is something sublime. What is it?
Science is the outcome of the search for that mysterious something.
A giant blow has recently been struck, by a man of consummate ability,
Albert Einstein, upon this wall which conceals reality from us. A
little of the light from beyond now comes to us through the breach he
has made, and our eyes are enchanted, almost dazzled, by the rays. I
propose here to give, as simply and clearly as is possible, some faint
reflex of the impression it has made upon us.
Einstein’s theories have brought about a profound revolution in
science. In their light the world seems simpler, more co-ordinated,
more in unison. We shall henceforward realise better how grandiose and
coherent it is, how it is ruled by an inflexible harmony. A little of
the ineffable will become clearer to us.
Men, as they pass through the universe, are like those specks of dust
which dance for a moment in the golden rays of the sun, then sink into
the darkness. Is there a finer or nobler way of spending this life than
to fill one’s eyes, one’s mind, one’s heart with the immortal, yet so
elusive, rays? What higher pleasure can there be than to contemplate,
to seek, to understand, the magnificent and astounding spectacle of the
universe?
There is in reality more of the marvellous and the romantic than there
is in all our poor dreams. In the thirst for knowledge, in the mystic
impulse which urges us toward the deep heart of the Unknown, there is
more passion and more sweetness than in all the trivialities which
sustain so many literatures. I may be wrong, after all, in saying that
this book is not a romance.
I will endeavour in these pages to make the reader understand,
accurately, yet without the aid of the esoteric apparatus of the
technical writer, the revolution brought about by Einstein. I will try
also to fix its limits; to state precisely what, at the most, we can
really know to-day about the external world when we regard it through
the translucent screen of science.
Every revolution is followed by a reaction, in virtue of the rhythm
which seems to be an inherent and eternal law of the mind of man.
Einstein is at once the Sieyès, the Mirabeau, and the Danton of the
new revolution. But the revolution has already produced its fanatical
Marats, who would say to science: “Thus far and no farther.”
Hence we find some resistance to the pretensions of over-zealous
apostles of the new scientific gospel. In the Academy of Sciences M.
Paul Painlevé takes his place, with all the strength of a vigorous
mathematical genius, between Newton, who was supposed to be overthrown,
and Einstein. In my final pages I will examine the penetrating
criticisms of the great French geometrician. They will help me to fix
the precise position, in the evolution of our ideas, of Einstein’s
magnificent synthesis. But I would first expound the synthesis itself
with all the affection which one must bestow upon things that one would
understand.
Science has not completed its task with the work of Einstein. There
remains many a depth that is for us unfathomable, waiting for some
genius of to-morrow to throw light into it. It is the very essence
of the august and lofty grandeur of science that it is perpetually
advancing. It is like a torch in the sombre forest of mystery. Man
enlarges every day the circle of light which spreads round him, but
at the same time, and in virtue of his very advance, he finds himself
confronting, at an increasing number of points, the darkness of the
Unknown. Few men have borne the shaft of light so deeply into the
forest as has Einstein. In spite of the sordid cares which harass us
to-day, amid so many grave contingencies, his system reveals to us an
element of grandeur.
Our age is like the noisy and unsubstantial froth that crowns, and
hides for a moment, the gold of some generous wine. When all the
transitory murmur that now fills our ears is over, Einstein’s theory
will rise before us as the great lighthouse on the brink of this sad
and petty twentieth century of ours.
CHARLES NORDMANN.
EINSTEIN AND THE UNIVERSE
CHAPTER I
THE METAMORPHOSES OF SPACE AND TIME
_Removing the mathematical difficulties—The pillars
of knowledge—Absolute time and space, from
Aristotle to Newton—Relative time and space,
from Epicurus to Poincaré and Einstein—Classical
Relativity—Antinomy of stellar aberration and the
Michelson experiment._
“Have you read Baruch?” La Fontaine used to cry, enthusiastically.
To-day he would have troubled his friends with the question “Have you
read Einstein?”
But, whereas one needs only a little Latin to gain access to Spinoza,
frightful monsters keep guard before Einstein, and their horrible
grimaces seem to forbid us to approach him. They stand behind strange
moving bars, sometimes rectangular and sometimes curvilinear,
which are known as “co-ordinates.” They bear names as frightful as
themselves—“contravariant and covariant vectors, tensors, scalars,
determinants, orthogonal vectors, generalised symbols of three signs,”
and so on.
These strange beings, brought from the wildest depths of the
mathematical jungle, join together or part from each other with a
remarkable promiscuity, by means of some astonishing surgery which is
called _integration_ and _differentiation_.
In a word, Einstein may be a treasure, but there is a fearsome troop
of mathematical reptiles keeping inquisitive folk away from it; though
there can be no doubt that they have, like our Gothic gargoyles, a
hidden beauty of their own. Let us, however, drive them off with the
whip of simple terminology, and approach the splendour of Einstein’s
theory.
Who is this physicist Einstein? That is a question of no importance
here. It is enough to know that he refused to sign the infamous
manifesto of the professors, and thus brought upon himself persecution
from the Pan-Germanists.[1] Mathematical truths and scientific
discoveries have an intrinsic value, and this must be judged and
appreciated impartially, whoever their author may chance to be. Had
Pythagoras been the lowest of criminals, the fact would not in the
least detract from the validity of the square of the hypotenuse. A
theory is either true or false, whether the nose of its author has the
aquiline contour of the nose of the children of Sem, or the flattened
shape of that of the children of Cham, or the straightness of that of
the children of Japhet. Do we feel that humanity is perfect when we
hear it said occasionally: “Tell me what church you frequent, and I
will tell you if your geometry is sound.” Truth has no need of a civil
status. Let us get on.
[1] Albert Einstein, born in 1879, is a German Jew of Würtemberg.
He studied in Switzerland, and was an engineer there until 1909,
when he became professor at Zurich University. In 1911 he passed to
Prague University, in 1912 to the Zurich Polytechnic, and in 1914 to
the Prussian Academy of Science. He refused to give his name to the
manifesto in which ninety-three professors of Germany and Austria
defended Germany’s war-action.—Trans.
* * * * *
All our ideas, all science, and even the whole of our practical life,
are based upon the way in which we picture to ourselves the successive
aspects of things. Our mind, with the aid of our senses, chiefly
ranges these under the headings of time and space, which thus become
the two frames in which we dispose all that is apparent to us of the
material world. When we write a letter, we put at the head of it the
name of the place and the date. When we open a newspaper, we find the
same indications at the beginning of each piece of telegraphic news.
It is the same in everything and for everything. Time and space, the
situation and the period of things, are thus seen to be the twin
pillars of all knowledge, the two columns which sustain the edifice of
men’s understanding.
So felt Leconte de Lisle when, addressing himself to “divine death,” he
wrote, in his profound, philosophic way:
Free us from time, number, and space:
Grant us the rest that life hath spoiled.
He inserts the word “number” only in order to define time and space
quantitatively. What he has finely expressed in these famous and superb
lines is the fact that all that there is for us in this vast universe,
all that we know and see, all the ineffable and agitated flow of
phenomena, presents to us no definite aspect, no precise form, until it
has passed through those two filters which are interposed by the mind,
time and space.
The work of Einstein derives its importance from the fact that he has
shown, as we shall see, that we have entirely to revise our ideas
of time and space. If that is so, the whole of science, including
psychology, will have to be reconstructed. That is the first part of
Einstein’s work, but it goes further. If that were the whole of his
work it would be merely negative.
Once he had removed from the structure of human knowledge what had been
regarded as an indispensable wall of it, though it was really only a
frail scaffolding that hid the harmony of its proportions, he began to
reconstruct. He made in the structure large windows which allow us now
to see the treasures it contains. In a word, Einstein showed, on the
one hand, with astonishing acuteness and depth, that the foundation of
our knowledge seems to be different from what we had thought, and that
it needs repairing with a new kind of cement. On the other hand, he has
reconstructed the edifice on this new basis, and he has given it a bold
and remarkably beautiful and harmonious form.
I have now to show in detail, concretely, and as accurately as
possible, the meaning of these generalities. But I must first insist on
a point which is of considerable importance: if Einstein had confined
himself to the first part of his work, as I have described it, the part
which shatters the classical ideas of time and space, he would never
have attained the fame which now makes his name great in the world of
thought.
The point is important because most of those—apart from experts—who
have written on Einstein have chiefly, often exclusively, emphasised
this more or less “destructive” side of his work. But, as we shall
see, from this point of view Einstein was not the first, and he is not
alone. All that he has done is to sharpen, and press a little deeper
between the badly joined stones of classical science, a chisel which
others, especially the great Henri Poincaré, had used long before him.
My next point is to explain, if I can, the real, the immortal, title of
Einstein to the gratitude of men: to show how he has by his own powers
rebuilt the structure in a new and magnificent form after his critical
work. In this he shares his glory with none.
* * * * *
The whole of science, from the days of Aristotle until our own, has
been based upon the hypothesis—properly speaking, the hypotheses—that
there is an absolute time and an absolute space. In other words, our
ideas rested upon the supposition that an interval of time and an
interval of space between two given phenomena are always the same, for
every observer whatsoever, and whatever the conditions of observation
may be. For instance, it would never have occurred to anybody as long
as classical science was predominant, that the interval of time, the
number of seconds, which lies between two successive eclipses of the
sun, may not be the fixed and identically same number of seconds for an
observer on the earth as for an observer in Sirius (assuming that the
second is defined for both by the same chronometer). Similarly, no one
would have imagined that the distance in metres between two objects,
for instance the distance of the earth from the sun at a given moment,
measured by trigonometry, may not be the same for an observer on the
earth as for an observer in Sirius (the metre being defined for both by
the same rule).
“There is,” says Aristotle, “one single and invariable time, which
flows in two movements in an identical and simultaneous manner; and if
these two sorts of time were not simultaneous, they would nevertheless
be of the same nature.... Thus, in regard to movements which take place
simultaneously, there is one and the same time, whether or no the
movements are equal in rapidity; and this is true even if one of them is
a local movement and the other an alteration.... It follows that even
if the movements differ from each other, and arise independently, the
time is absolutely the same for both.”[2] This Aristotelic definition
of physical time is more than two thousand years old, yet it clearly
represents the idea of time which has been used in classic science,
especially in the mechanics of Galileo and Newton, until quite recent
years.
It seems, however, that in spite of Aristotle, Epicurus outlined the
position which Einstein would later adopt in antagonism to Newton. To
translate liberally the words in which Lucretius expounds the teaching
of Epicurus:
“Time has no existence of itself, but only in material objects, from
which we get the idea of past, present, and future. It is impossible
to conceive time in itself independently of the movement or rest of
things.”[3]
[2] _Physics_, bk. iv, ch. xiv.
[3] _De Natura Rerum_, bk. i, vv. 460 ff.
Both space and time have been regarded by science ever since Aristotle
as invariable, fixed, rigid, absolute data. Newton thought that he was
saying something obvious, a platitude, when he wrote in his celebrated
Scholion: “Absolute, true, and mathematical time, taken in itself and
without relation to any material object, flows uniformly of its own
nature.... Absolute space, on the other hand, independent by its own
nature of any relation to external objects, remains always unchangeable
and immovable.”
The whole of science, the whole of physics and mechanics, as they are
still taught in our colleges and in most of our universities, are based
entirely upon these propositions, these ideas of an absolute time and
space, taken by themselves and without any reference to an external
object, independent by their very nature.
In a word—if I may venture to use this figure—time in classical
science was like a river bearing phenomena as a stream bears boats,
flowing on just the same whether there were phenomena or not. Space,
similarly, was rather like the bank of the river, indifferent to the
ships that passed.
From the time of Newton, however, if not from the time of Aristotle,
any thoughtful metaphysician might have noticed that there was
something wrong in these definitions. Absolute time and absolute
space are “things in themselves,” and these the human mind has always
regarded as not directly accessible to it. The specifications of space
and time, those numbered labels which we attach to objects of the
material world, as we put labels on parcels at the station so that
they may not be lost (a precaution that does not always suffice), are
given us by our senses, whether aided by instruments or not, only when
we receive concrete impressions. Should we have any idea of them if
there were no bodies attached to them, or rather to which we attach the
labels? To answer this in the affirmative, as Aristotle, Newton, and
classical science do, is to make a very bold assumption, and one that
is not obviously justified.
The only time of which we have any idea apart from all objects is the
psychological time so luminously studied by M. Bergson: a time which
has nothing except the name in common with the time of physicists, of
science.
It is really to Henri Poincaré, the great Frenchman whose death has
left a void that will never be filled, that we must accord the merit of
having first proved, with the greatest lucidity and the most prudent
audacity, that time and space, as we know them, can only be relative. A
few quotations from his works will not be out of place. They will show
that the credit for most of the things which are currently attributed
to Einstein is, in reality, due to Poincaré. To prove this is not in
any way to detract from the merit of Einstein, for that is, as we shall
see, in other fields.
This is how Poincaré, whose ideas still dominate the minds of
thoughtful men, though his mortal frame perished years ago, expressed
himself, the triumphant sweep of his wings reaching further every day:
“One cannot form any idea of empty space.... From that follows the
undeniable relativity of space. Any man who talks of absolute space
uses words which have no meaning. I am at a particular spot in
Paris—the Place du Panthéon, let us suppose—and I say: ‘I will come
back _here_ to-morrow.’ If anyone asks me whether I mean that I
will return to the same point in space, I am tempted to reply, ‘Yes.’ I
should, however, be wrong, because between this and to-morrow the earth
will have travelled, taking the Place du Panthéon with it, so that
to-morrow the square will be more than 2,000,000 kilometres away from
where it is now. And it would be no use my attempting to use precise
language, because these 2,000,000 kilometres are part of our earth’s
journey round the sun, but the sun itself has moved in relation to the
Milky Way, and the Milky Way in turn is doubtless moving at a speed
which we cannot learn. Thus we are entirely ignorant, and always will
be ignorant, how far the Place du Panthéon shifts its position in space
in a single day. What I really meant to say was: ‘To-morrow I shall
again see the dome and façade of the Panthéon.’ If there were no
Panthéon, there would be no meaning in my words, and space would
disappear.”
Poincaré works out his idea in this way:
“Suppose all the dimensions of the universe were
increased a thousandfold in a night. The world would
remain the same, giving the word ‘same’ the meaning
it has in the third book of geometry. Nevertheless,
an object that had measured a metre in length will
henceforward be a kilometre in length; a thing that
had measured a millimetre will now measure a metre.
The bed on which I lie and the body which lies on it
will increase in size to exactly the same extent. What
sort of feelings will I have when I awake in the morning,
in face of such an amazing transformation? Well,
I shall know nothing about it. The most precise
measurements would tell me nothing about the revolution,
because the tape I use for measuring will have
changed to the same extent as the objects I wish to
measure. As a matter of fact, there would be no
revolution except in the mind of those who reason as
if space were absolute. If I have argued for a moment
as they do, it was only in order to show more clearly
that their position is contradictory.”
It would be easy to develop Poincaré’s argument. If all the objects in
the universe were to become, for instance, a thousand times taller, a
thousand times broader, we should be quite unable to detect it, because
we ourselves—our retina and our measuring rod—would be transformed
to the same extent at the same time. Indeed, if all the things in
the universe were to experience an absolutely irregular spatial
deformation—if some invisible and all-powerful spirit were to distort
the universe in any fashion, drawing it out as if it were rubber—we
should have no means of knowing the fact. There could be no better
proof that space is relative, and that we cannot conceive space apart
from the things which we use to measure it. When there is no measuring
rod, there is no space.
Poincaré pushed his reasoning on this subject so far that he came to
say that even the revolution of the earth round the sun is merely a
more convenient hypothesis than the contrary supposition, but not a
truer hypothesis, unless we imply the existence of absolute space.
It may be remembered that certain unwary controversialists have tried
to infer from Poincaré’s argument that the condemnation of Galileo was
justified. Nothing could be more amusing than the way in which the
distinguished mathematician-philosopher defended himself against this
interpretation, though one must admit that his defence was not wholly
convincing. He did not take sufficiently into account the agnostic
element.
Poincaré, in any case, is the leader of those who regard space as a
mere property which we ascribe to objects. In this view our idea of
it is only, so to say, the hereditary outcome of those efforts of our
senses by means of which we strive to embrace the material world at a
given moment.
It is the same with time. Here again the objections of philosophic
Relativists were raised long ago, but it was Poincaré who gave them
their definitive shape. His luminous demonstrations are, however, well
known, and we need not reproduce them here. It is enough to observe
that, in regard to time as well as space, it is possible to imagine
either a contraction or an enlargement of the scale which would be
completely imperceptible to us; and this seems to show that man
cannot conceive an absolute time. If some malicious spirit were to
amuse itself some night by making all the phenomena of the universe a
thousand times slower, we should not, when we awake, have any means of
detecting the change. The world would seem to us unchanged. Yet every
hour recorded by our watches would be a thousand times longer than
hours had previously been. Men would live a thousand times as long, yet
they would be unaware of the fact, as their sensations would be slower
in the same proportion.
When Lamartine appealed to time to “suspend its flight,” he said a
very charming, but perhaps meaningless, thing. If time had obeyed his
passionate appeal, neither Lamartine nor Elvire would have known and
rejoiced over the fact. The boatman who conducted the lovers on the Lac
du Bourget would not have asked payment for a single additional hour;
yet he would have dipped his oars into the pleasant waters for a far
longer time.
I venture to sum up all this in a sentence which will at first sight
seem a paradox: in the opinion of the Relativists it is the measuring
rods which create space, the clocks which create time. All this was
maintained by Poincaré and others long before the time of Einstein, and
one does injustice to truth in ascribing the discovery to him. I am
quite aware that one lends only to the rich, but one does an injustice
to the wealthy themselves in attributing to them what does not belong
to them, and what they need not in order to be rich.
There is, moreover, one point at which Galileo and Newton, for all
their belief in the existence of absolute space and time, admitted
a certain relativity. They recognised that it is impossible to
distinguish between uniform movements of translation. They thus
admitted the equivalence of all such movements, and therefore the
impossibility of proving an absolute movement of translation.
That is what is called the Principle of Classic Relativity.
* * * * *
An unexpected fact served to bring these questions upon a new plane,
and led Einstein to give a remarkable extension to the Principle
of Relativity of classic mechanics. This was the issue of a famous
experiment by Michelson, of which we must give a brief description.
It is well known that rays of light travel across empty space from
star to star, otherwise we should be unable to see the stars. From
this physicists long ago concluded that the rays travelled in a medium
that is devoid of mass and inertia, is infinitely elastic, and offers
no resistance to the movement of material bodies, into which it
penetrates. This medium has been named ether. Light travels through it
as waves spread over the surface of water at a speed of something like
186,000 miles a second: a velocity which we will express by the letter
=V=.
The earth revolves round the sun in a veritable ocean of ether, at a
speed of about 18 miles a second. In this respect the rotation of the
earth on its axis need not be noticed, as it pushes the surface of the
globe through the ether at a speed of less than two miles a second.
Now the question had often been asked: Does the earth, in its orbital
movement round the sun, take with it the ether which is in contact with
it, as a sponge thrown out of a window takes with it the water which it
has absorbed? Experiment—or rather, experiments, for many have been
tried with the same result—has shown that the question must be
answered in the negative.
This was first established by astronomical observation. There is in
astronomy a well-known phenomenon discovered by Bradley which is
called aberration. It consists in this: when we observe a star with a
telescope, the image of the star is not precisely in the direct line of
vision. The reason is that, while the luminous rays of the star which
have entered the telescope are passing down the length of the tube,
the instrument has been slightly displaced, as it shares the movement
of the earth. On the other hand, the luminous ray in the tube does
not share the earth’s motion, and this gives rise to the very slight
deviation which we call aberration. This proves that the medium in
which light travels, the ether which fills the instrument and surrounds
the earth, does not share the earth’s motion.
Many other experiments have settled beyond question that the ether,
which is the vehicle of the waves of light, is not borne along by the
earth as it travels. Now, since the earth moves through the ether as a
ship moves over a stationary lake (not like one floating on a moving
stream), it ought to be possible to detect some evidence of this speed
of the earth in relation to the ether.
One of the devices that may be imagined for the purpose is the
following. We know that the earth turns on itself from west to east,
and travels round the sun in the same way. It follows that in the
middle of the night the revolution of the earth round the sun means
that Paris will be displaced, in the direction from Auteuil toward
Charenton, at a speed of about thirty kilometres a second. During the
day, of course, it is precisely the opposite. Paris changes its place
round the sun in the direction from Charenton toward Auteuil. Well, let
us suppose that at midnight a physicist at Auteuil sends a luminous
signal. A physicist receiving this ray of light at Charenton, and
measuring its velocity, ought to find that the latter is =V= + 30
kilometres. We know that, as a result of the earth’s motion, Charenton
recedes before the ray of light. Consequently, since light travels
in a medium, the ether, which does not share the earth’s motion, the
observer at Charenton ought to find that the ray reaches him at a less
speed than it would if the earth were stationary. It is much the same
as if an observer were travelling on a bicycle in front of an express
train. If the express travels at thirty metres a second and the cyclist
at three metres a second, the speed of the train in relation to the
cyclist will be 30-3 = 27 metres a second. It would be _nil_ if
the train and the cyclist were travelling at the same rate.
On the other hand, if the cyclist were going toward the train, the
speed of the train in relation to him would be 30 + 3 = 33 metres a
second. Similarly, when the physicist at Charenton sends out a luminous
message at midnight, and the physicist of Auteuil receives it, the
latter ought to find that the ray of light has a velocity of =V= +
30 kilometres.
All this may be put in a different way. Suppose the distance between
the observer at Auteuil and the man at Charenton were exactly twelve
kilometres. While the ray of light emitted at Auteuil speeds toward
Charenton, that town is receding before it to a small extent. It
follows that the ray will have to travel a little more than twelve
kilometres before it reaches the man of science at Charenton. It will
travel a little less than that distance if we imagine it proceeding in
the opposite direction.
Now the American physicist Michelson, borrowing an ingenious idea
from the French physicist Fizeau, succeeded, with a high degree of
accuracy, in measuring distances by means of the interference-bands of
light. Every variation in the distance measured betrays itself by the
displacement of a certain number of these bands, and this may easily be
detected by a microscope.
Let us next suppose that our two physicists work in a laboratory
instead of between Charenton and Auteuil. Let us suppose that they
are, by means of the interference-bands, measuring the space traversed
by a ray of light produced in the laboratory, according as it travels
in the same direction as the earth or in the opposite direction. That
is Michelson’s famous experiment, reduced to its essential elements
and simplified for the purpose of this essay. In those circumstances
Michelson’s delicate apparatus ought to reveal a distinctly measurable
difference according as the light travels with the earth or in the
opposite direction.
But no such difference was found. Contrary to all expectation, and
to the profound astonishment of physicists, it was found that light
travels at precisely the same speed whether the man who receives it is
receding before it with the velocity of the earth or is approaching
it at the same velocity. It is an undeniable consequence of this that
_the ether shares the motion of the earth_. We have, however, seen
that other experiments, not less precise, had settled that _the ether
does not share the motion of the earth_.
Out of this contradiction, this conflict of two irreconcilable yet
indubitable facts, Einstein’s splendid synthesis, like a spark of light
issuing from the clash of flint and steel, came into being.