EINSTEIN
THE SEARCHER
HIS WORK EXPLAINED FROM
DIALOGUES WITH EINSTEIN
BY
ALEXANDER MOSZKOWSKI
TRANSLATED BY
HENRY L. BROSE
METHUEN & CO. LTD.
36 ESSEX STREET W.C.
LONDON
EXTRACT FROM THE AUTHOR'S
PREFACE
THE book which is herewith presented to the public has few
contemporaries of a like nature; it deserves special attention inasmuch
as it is illuminated by the name _Albert Einstein_, and deals with a
personality whose achievements mark a turning-point in the development
of science.
Every investigator, who enlarges our vision by some permanent discovery,
becomes a milestone on the road to knowledge, and great would be the
array of those who have defined the stages of the long avenue of
research. One might endeavour, then, to decide to whom mankind owes the
greater debt, to Euclid or to Archimedes, to Plato or to Aristotle, to
Descartes or to Pascal, to Lagrange or to Gauss, to Kepler or to
Copernicus. One would have to investigate--as far as this is
possible--in how far each outstanding personality was in advance of his
time, whether some contemporary might not have had the equal good
fortune to stumble on the same discovery, and whether, indeed, the time
had not come when it must inevitably have been revealed. If we then
further selected only those who saw far beyond their own age into the
inimitable future of knowledge, this great number of celebrities would
be considerably diminished. We should glance away from the milestones,
and fix our gaze on the larger signs that denote the lines of
demarcation of the sciences, and among them we should find the name of
Albert Einstein. We may find it necessary to proceed to a still more
rigorous classification; Science, herself, may rearrange her
chronological table later, and reckon the time at which Einstein's
doctrine first appeared as the beginning of an important era.
This would in itself justify--nay, render imperative--the writing of
a book _about_ Einstein. But this need has already been satisfied on
several occasions, and there is even now a considerable amount of
literature about him. At the end of this generation we shall possess a
voluminous library composed entirely of books about Einstein. The
present book will differ from most of these, in that Einstein here
occurs not only objectively but also subjectively. We shall, of course,
speak of him here too, but we shall also hear him speak himself, and
there can be no doubt that all who are devoted to the world thought can
but gain by listening to him.
The title agrees with the circumstance to which this book owes its
birth. And in undertaking to address itself to the circle of readers as
to an audience, it promises much eloquence that came from Einstein's own
lips, during hours of social intercourse, far removed from academic
purposes and not based on any definite scheme intended for instruction.
It will, therefore, be neither a course of lectures nor anything similar
aiming at a systematic order and development. Nor is it a mere
phonographic record, for this is made impossible if for no other reason
than that whoever has the good fortune to converse with this man, finds
every minute far too precious to waste it in snatching moments to take
shorthand notes. What he has heard and discussed crystallizes itself in
subsequent notes, and to some extent he relies on his memory, which
would have to be extraordinarily lax if it managed to forget the
essentials of such conversations.
But these essentials could not be attained by clinging closely to the
exact terms of utterance. This would be a gain neither for the scheme of
the book nor for the reader who wishes to follow a great thinker in all
the ramifications of his ideas. It must be reiterated that this book is
intended neither as a textbook nor as a guide leading to a complete
system of thought; nor, above all, is it in any way due to Einstein, nor
desired by him. Any value and attraction of the book is rather to be
sought in its kaleidoscopic nature, its loose connexion, which expresses
a general meaning without being narrowed to pedantic limits by a
restriction to literal repetition. It is just this absence of the method
that is rightly demanded of a textbook, which may enable these
conversations to pass on to the world a little of the pleasure which
they originally gave me. Perhaps they will even be sufficient to furnish
the reader with a picture of the eminent scientist, sufficient to give
him a glimpse of his personality, without demanding a detailed study to
secure this end. Even here I should like to state that the range of
Einstein's genius extends much further than is generally surmised by
those who have busied themselves only with the actual physical theory.
It sends out rays in all directions, and brings into view wonderful
cosmic features under his stimulus--features which are, of course,
embedded in the very refractory mathematical shell of his physics which
embraces the whole world. But only minds of the distant future, perhaps,
will be in a position to realize that _all_ our mental knowledge is
illuminated by the light of his doctrine.
Einstein's mission is that of a king who is pursuing building operations
on a large scale; carters and workmen, each in their own line, receive
employment for decades ahead. But apart from the technical work, there
may still be room for non-technical account, which, without following a
definite programme, yet pursues a definite object, to offer Einsteiniana
in an easily intelligible and ever-changing form, to represent him, as
it were, wandering over fields and meadows, and every now and then
stooping to pluck some problem in the guise of a flower. Seeing that he
granted me the pleasure of accompanying him on these excursions, it was
not within my sphere to expect in addition that he would direct his
steps according to a preconceived plan. Often enough the goal vanished,
and there remained nothing but the pleasure of the rambles themselves
with the consciousness of their purpose. As Schopenhauer remarks, one
who walks for leisure can never be said to be making detours; and this
holds true independently of the nature of the country that happens to be
traversed at the moment. If I just now mentioned walks on meadowy
slopes, this is not to be understood literally. In Einstein's company
one encounters from moment to moment quite suddenly some adventure which
destroys our comparison with idyllic rambles. Abysmal depths appear, and
one has to pass along dangerous pathways. It is at these moments that
unexpected views present themselves, and many strips of landscape that,
according to our previous estimate, appeared to be situated on higher
slopes, are now discovered reposing far below. We are familiar with the
"Wanderer Fantasie" of Schubert; its tonal disposition is realistic,
conforming to Nature, yet its general expression is transcendental: so
is a ramble with Einstein; he remains firmly implanted in reality, but
the distant views that he points out stretch into transcendental
regions. He seems to me to be essentially as much an artist as a
discoverer, and if some sense of this heaven-sent combination of gifts
should be inspired by this book, it alone would justify the publication
of these talks.
TRANSLATOR'S NOTE
IT is scarcely necessary to enlarge on the scope and design of the
present book, which manifest themselves at a glance.
The author merits our thanks for making accessible to us material about
Einstein which, in the ordinary course of events, would ever remain
unknown. An account of Einstein's work would be incomplete without a
sketch of his personality. Mr. Moszkowski invites us to ramble with
Einstein into realms not confined to pure physics. Many subjects that
have a peculiar interest at the present critical stage of the world's
history receive illuminating attention. It is hoped that the appearance
of the book in English will stimulate further interest in the
thought-world of a great scientist.
Warm thanks are due to Mr. Raymond Kershaw, B.A., and to my sister, Miss
Hilda Brose, for help in reading the manuscript and the proofs.
HENRY L. BROSE
OXFORD, 1921
CONTENTS
CHAPTER
I. Phenomena in the Heavens
II. Beyond our Power
III. Valhalla
IV. Education
V. The Discoverer
VI. Of Different Worlds
VII. Problems
VIII. Highways and By-ways
IX. An Experimental Analogy
X. Disconnected Suggestions
XI. Einstein's Life and Personality
INDEX
EINSTEIN THE SEARCHER
CHAPTER I
PHENOMENA IN THE HEAVENS
Proclamation of the New Mechanics.--Verification of Theoretical
Results.--Parallels with Leverrier.--Neptune and Mercury.--Testing the
Theory of Relativity.--The Solar Eclipse of 1919.--The Programme of an
Expedition.--The Curved Ray of Light.--Refinement of Calculation and
Measurement.--Stellar Photography.--The Principle of Equivalence.--The
Sun Myth.
ON the 13th October 1910 a memorable event took place in the Berlin
Scientific Association: Henri Poincaré, the eminent physicist and
mathematician, had been announced to give a lecture in the rooms of the
institute "Urania"; an audience of rather meagre dimensions assembled. I
still see him before me in my mind's eye, a scholar who was snatched
away in the prime of his creative period, a man whose external
appearance did not suggest the light of genius, and whose carefully
trimmed beard reminded one rather of the type of a practising barrister.
He walked up and down the platform, accompanying his speech with
gestures marked by an easy elegance. There was no sign of an attempt to
force a doctrine. He developed his thesis, in spite of the foreign
language, in fluent and readily intelligible terms.
It was at this lecture that we heard the name Albert Einstein pronounced
for the first time.
Poincaré's address was on the New Mechanics, and was intended to make
us acquainted with the beginning of a tendency which, he himself
confessed, had violently disturbed the equilibrium of his former
fundamental views. He repeatedly broke the usually even flow of his
voice to indicate, with an emphatic gesture, that we had perhaps arrived
at a critical, nay epochal, point marking the commencement of a new era
of thought.
"Perhaps" was a word he never failed to emphasize. He persistently laid
stress on his doubts, differentiated between hardened facts and
hypotheses, still clinging to the hope that the new doctrine he was
expounding would yet admit of an avenue leading back to the older views.
This revolution, so he said, seemed to threaten things in science which
a short while ago were looked upon as absolutely certain, namely,
fundamental theorems of classical mechanics, for which we are indebted
to the genius of Newton. For the present this revolution is of course
only a threatening spectre, for it is quite possible that, sooner or
later, the old established dynamical principles of Newton will emerge
victoriously. Later in the course of his lecture he declared repeatedly
that he felt a diffidence akin to fear at the sight of the accumulating
number of hypotheses, and that it seemed to border on the impossible to
attempt to arrange them into a system.
It is a matter of complete indifference how the revelations of Poincaré
affected us individually; if I may infer from my own case, there is only
one word to express it--staggering! Oblivious of the doubts of the
lecturer, I was swept along under the impetus of this new and mighty
current of thought. This awakened two wishes in me: to become acquainted
with Einstein's researches as far as lay within my power, and, if
possible, to see him once in person. In me the abstract had become
inseparable from the concrete personal element. The presentiment of the
happy moment in the future hovered before my vision, whispering that I
should hear his doctrine from his own lips.
Several years later Einstein was appointed professor of the Academy of
Sciences with the right of lecturing at the University of Berlin. This
brought my personal wish within reach. Trusting to good fortune, I set
about materializing it. In conjunction with a colleague I wrote him a
letter asking him to honour with his presence one of the informal
evenings instituted by our Literary Society at the Hôtel Bristol. Here
he was my neighbour at table, and chatted with me for some hours.
Nowadays his appearance is known to every one through the innumerable
photos which have appeared in the papers. At that time I had never seen
his countenance before, and I became absorbed in studying his features,
which struck me as being those of a kindly, artistically inclined,
being, in nowise suggesting a professor. He seemed vivacious and
unrestrained in conversation, and, in response to our request, willingly
touched upon his own subject as far as the place and occasion allowed,
exemplifying Horace's saying, "Omne tulit punctum, qui miscuit utile
dulci, tironem delectando pariterque monendo." It was certainly most
delightful. Yet at moments I was reminded of a male sphinx, suggested by
his highly expressive enigmatic forehead. Even now, after a warm
acquaintanceship stretching over years, I cannot shake off this
impression. It often overcomes me in the midst of a pleasant
conversation interspersed with jests whilst enjoying a cigar after tea;
I suddenly feel the mysterious sway of a subtle intellect which
captivates and yet baffles the mind.
At that time, early in 1916, only a few members of the Literary Society
divined who it was that was enjoying their hospitality. In the eyes of
Berlin, Einstein's star was beginning its upward course, but was still
too near the horizon to be visible generally. My own vision, sharpened
by the French lecture and by a friend who was a physicist, anticipated
events, and already saw Einstein's star at its zenith, although I was
not even aware at that time that Poincaré had in the meantime overcome
his doubts and had fully recognized the lasting importance of Einstein's
researches. I had the instinctive feeling that I was sitting next to a
Galilei. The fanfares sounded in the following years as a sign of
appreciation by his contemporaries were only a fuller instrumentation of
the music of destiny which had vibrated in my ears ever since that time.
I recollect one little incident: one of these lovers of literature, who
was, however, totally ignorant of natural science, had accidentally seen
several learned articles dealing with Einstein's Reports for the
Academy, and had preserved the cuttings in his pocket-book. He
considered this a fitting opportunity for enlightenment. Surely a brief
question would suffice to guide one through these intricate channels.
"Professor, will you kindly tell me the meaning of potential, invariant,
contravariant, energy-tensor, scalar, relativity-postulate,
hyper-Euclidean, and inertial system? Can you explain them to me in a
few words?"--"Certainly," said Einstein, "those are merely technical
expressions!" That was the end of the little lesson.
Far into the night three of us sat in a café while Einstein gently
lifted the veil from his newest discovery for the benefit of my
journalist friend and myself. We gathered from his remarks that a
Special Theory of Relativity formed a prelude to a general theory which
embraced the problem of gravitation in its widest sense, and hence also
the physical constitution of the world. What interested me apart from
this theme, which was, of course, only touched upon lightly, was the
personal question in its psychological aspect.
"Professor," said I, "such investigations must involve enormous mental
excitement. I imagine that there lurks behind every solved problem ever
and again some new problem with a threatening or a fascinating aspect,
as the case may be, each one calling up a tumult of emotion in its
author. How do you succeed in mastering this difficulty? Are you not
continually tormented by restless thoughts that noisily invade your
dreams? Do you ever succeed at all in enjoying undisturbed slumber?"
The very tone in which the answer was given showed clearly how free he
felt himself of such nervous troubles which usually oppress even the
mediocre thinker. It is fortunate that such affections do not penetrate
to his high level. "I break off whenever I wish," he said, "and banish
all difficulties when the hour for sleep arrives. Thinking during
dreams, as in the case of artists, such as poets and composers, by which
they weave the thread of day on into the night, is quite foreign to me.
Nevertheless, I must confess that at the very beginning, when the
special theory of relativity began to germinate in me, I was visited by
all sorts of nervous conflicts. When young I used to go away for weeks
in a state of confusion, as one who at that time had yet to overcome the
stage of stupefaction in his first encounter with such questions. Things
have changed since then, and I can assure you that there is no need to
worry about my rest."
"Notwithstanding," I answered, "cases may arise in which a certain
result is to be verified by observation and experiment. This might
easily give rise to nerve-racking experiences. If, for instance, a
theory leads to a calculation which does not agree with reality, the
propounder must surely feel considerably oppressed by this mere
possibility. Let us take a particular event. I have heard that you have
made a new calculation of the path of the planet Mercury on the basis of
your doctrine. This must certainly have been a laborious and involved
piece of work. You were firmly convinced of the theory, perhaps you
alone. It had not yet been verified by an actual fact. In such cases
conditions of great psychological tension must surely assert themselves.
What in Heaven's name will happen if the expected result does not
appear? What if it contradicts the theory? The effect on the founder of
the theory cannot even be imagined!"
"Such questions," said Einstein, "did not lie in my path. That result
could not be otherwise than right. I was only concerned in putting the
result into a lucid form. I did not for one second doubt that it would
agree with observation. There was no sense in getting excited about what
was self-evident."
Let us now consider several facts of natural science, apart from this
chat, but suggested by it, which caused Einstein little excitement, but
the whole world generally, so much the more. By way of illustration we
shall link them up with the result of a forerunner who, like Einstein,
fixed on paper what should happen in the heavens.
Formerly, whenever one wished to play a particularly effective trump
card in favour of research work it was customary to quote the
achievement of the French astronomer Leverrier who, pen in hand,
established the material existence of a planet at that time quite
unknown and unnoticed. Certain disturbances in the orbit of the planet
Uranus, which was regarded as being the most distant of the wandering
stars, at that time had caused him to believe in the certainty of the
existence of a still more distant planet, and by using merely the
theoretical methods of celestial mechanics in connexion with the problem
of three bodies he succeeded in revealing what was hidden behind the
visible constellations. He reported the result of his calculations to
the Berlin Observatory about seventy-five years ago, as it was at that
time in possession of the best instruments. It was then that the amazing
event happened: on the very same evening an observer in Berlin,
Gottfried Galle, discovered the predicted new star almost exactly at the
point of the heavens for which it was prophesied, only half the moon's
diameter from it. The new planet Neptune, the farthest outpost of our
solar system, reposed as a prisoner in his telescope; the seemingly
undiscoverable star had capitulated in the face of mental efforts of a
mathematical scholar, who, in reasoning meditation, had sketched his
curves in the quiet atmosphere of his study.
This was certainly bewildering enough, but nevertheless this incredible
result which stirred the imagination so strongly was directly rooted in
reality, lay on the path of research, followed of necessity from the
laws of motion known at that time, and disclosed itself as a new proof
of the doctrines of astronomy which had long been recognized as supreme
and incontestable. Leverrier had not created these, but had found them
ready; he applied them with the mind of genius. Anyone who nowadays is
sufficiently trained to work through the highly complicated calculation
of Leverrier has every reason to marvel at a work which is entirely
mathematical throughout.
Our own times have been marked by an event of still greater
significance.
Irregularities had shown themselves in observation of the heavens that
could not be explained or grasped by the accepted methods of classical
mechanics. To interpret them, ideas of a revolutionary nature were
necessary. Man's view of the plan according to which the universe is
mapped out had to be radically reformed to bring within comprehension
the problems that presented themselves in macroscopic as well as in
microscopic regions, in the courses of the stars as well as in the
motions of the ultimate constituents of the atom of material bodies,
incapable of being directly observed. The goal consisted in bringing
those doctrines in which truth had been proclaimed in its essential
features, but not exhaustively, by the genius of Copernicus, Galilei,
Kepler, and Newton, to their conclusion by penetrating as far as
possible into the mysteries of the structure of the universe. This is
where Einstein comes forward.
Whereas the outermost planet Neptune had bowed to the accepted laws, by
merely disclosing his presence, Mercury, the innermost planet, preserved
an obstinate attitude even in the face of the most refined calculations.
These always led to an unaccountable remainder, a disagreement, which
seemed very small when expressed in numbers and words, and yet enclosed
a deep secret. Wherein did this disagreement consist? In a difference of
arc which had likewise been discovered by Leverrier and which defied
explanation. It was only a matter of about forty-five insignificant
quantities, seconds of arc, which seemed vanishingly small since this
deviation did not occur within a month or a year, but was spread over a
whole century. By just so much, or rather so little, the rotation of
Mercury's orbit differed from what might be termed the allowable
astronomical value. Observation was exact, calculation was exact; why,
then, the discrepancy?
It was thus inferred that there was still some hidden unexplored factor
which had to be taken into account in the fundamental principles of
celestial mechanics. The formerly invisible Neptune confirmed the old
rule by appearing. Mercury, which was visible, opposed the rule.
In 1910 Poincaré had touched upon this embarrassing question,
mentioning that here was a possibility of testing the new mechanics.
He declined the suggestion of some astronomers that this was again a
Leverrier problem and that there must exist another undiscovered planet
still nearer the sun and disturbing Mercury's orbit. He also refused to
accept the assumption that the disturbance might be caused by a ring of
cosmic matter distributed round the sun. Poincaré divined that the new
mechanics could supply the key to the enigma, but, obviously to be quite
conscientious, he expressed his presentiment in very cautious terms. On
that occasion he said that some special cause had yet to be found to
explain the anomaly of Mercury's behaviour; till that was discovered one
could only say that the new doctrine could not be regarded as in
contradiction to astronomical facts. But the true explanation was
gradually drawing near. Five years later, on 18th November 1915, Albert
Einstein presented to the Prussian Academy of Sciences a paper which
solved this riddle which, expressed in seconds, seemed so insignificant
and yet was of such enormous importance in its bearing on fundamental
questions. He proved the problem was solved quite accurately if the
general Theory of Relativity he had founded was accepted as the only
valid basis for the phenomena of cosmic motions.
Many would at this point express a wish to have the essence of the
doctrine of relativity explained in an easily intelligible manner.
Indeed, some would go even further in their desire, and would ask for a
simple description in a few succinct sentences. This, measured in terms
of difficulty and possibility, would be about equivalent to wishing to
learn the history of the world by reading several quarto pages of
manuscript or a novelette. But even if we start at long range and use
elaborate materials for our description, we should have to give up the
idea that this knowledge may be gained with playful ease. For this
doctrine, inasmuch as it discloses the relationship between mathematical
and physical events, emerges out of mathematics, which thus limits the
mode of its representation. Whoever undertakes to present it in a form
in which it is easily intelligible, that is quite unmathematical and yet
complete, is engaged in an impossible venture; he is like one who would
whistle Kepler's Laws on the flute or would elucidate Kant's Critique of
Pure Reason by means of coloured illustrations. In all frankness we must
confess once and for all that whenever popular accounts are attempted
they can be only in the nature of vague suggestions removed from the
domain of mathematics. But even such indications have a fruitful result
if they succeed in focusing the attention of the reader or the hearer so
that the connexions, the Leitmotivs, so to speak, of the doctrine, are
at least suggested.
It must therefore suffice if we place the conception of approximation in
the foreground here as in other parts of this book. Till quite recently
Newton's Equations of Motion were used as a foundation for verifying
astronomical occurrences. These are symbolical representations expressed
as formulæ that contain in an exceedingly simple form the law of mass
attraction. They express the comprehensive principle that the attraction
is directly proportional to the mass and inversely proportional to the
square of the distance; so that the moving force is doubled when the
mass is doubled, whereas if the distance is double, the force is only a
quarter as great, if the distance is trebled, the force becomes
one-ninth as great.
According to the Theory of Relativity this fundamental law is not wrong
or invalid, but no longer holds fully if pursued to its last inferences.
In applying corrections to it, new factors occur, such as the ratio of
given velocities to the velocity of light, and the new geometry which
operates with "world-lines" in space which, amalgamated with the
dimension of time, is regarded as a quadruply extended continuum.
Einstein has actually supplemented these fundamental equations for the
motion of masses so that the original form states the true condition of
affairs only approximately, whereas Einstein's equations give the motion
with very great accuracy.
The above-mentioned essay of Einstein is carried out as if the structure
bequeathed to us by Newton required the addition of a final, very
delicate pinnacle. For the mathematician this pinnacle is given as a
combination of signs, representing a so-called "Elliptic Interval." Such
an interval is a very weird construction, and the man who will make it
apprehended by the general reader is yet to be born. When Lord Byron
said:
"And Coleridge, too, has lately taken wing.
But like a hawk encumbered with his hood,--
Explaining Metaphysics to the nation--
_I wish he would explain his Explanation_."
(_Dedication to "Don Juan._")
he had still a sure footing in intelligibility, compared with the
non-mathematician, who demands an explanation for such a construction.
And what a complex of mathematical dangers must be overcome even before
the question of the meaning of this integral is crystallized out!
But now the explanation had arrived and could be evaluated, if only
approximately. Before we give the result, let us just describe at least
one technical term, namely, "Perihelion." It is that point of a
planetary orbit which lies nearest the sun. This orbit is an ellipse,
that is, an elongated curved fine in the interior of which one
distinguishes a major axis in the direction of elongation, and a minor
axis perpendicular to the former at its middle point. The perihelion of
a planetary orbit is at one of the end points of the major axis.
In time the perihelion alters its position in space, advancing in the
same sense as the orbit is traversed. It would naturally be assumed that
the amount of this advance as measured astronomically would agree with
the calculation resulting from Newton's theory. But this was not the
case. An unaccountable remainder was left over, which astronomers
ascertained to be 45 seconds (of arc) per 100 years, with a possible
fluctuation of plus or minus 5 seconds. Thus, if the new result were
found to be between 40 and 50 seconds, the new theory would henceforth
have to be regarded as the only valid one.
It happened just as Einstein predicted: calculation according to his
theory shows that for the planet Mercury the perihelion should advance
43 seconds per 100 years. This signifies full agreement with observation
and fully removes the former apparent difficulty. Whereas Leverrier in
his time had pointed out a new planet, Einstein brought to view
something far more important: a new truth.
It was a test of accuracy so dazzling that it alone would have sufficed
to prove the correctness of Einstein's Principles. Yet, a second test,
fraught with graver and more far-reaching consequences, presented
itself--a test which could be applied only several years later, and
which developed into a scientific event of the highest importance.
For at the same time that Einstein solved the problem of Mercury, he had
investigated the path of light-rays according to his revolutionary
method, and had arrived at the conclusion that every ray under the
influence of a gravitational field, as, for example, in the
neighbourhood of the sun, must become curved. This daring announcement
gave a new possibility of putting the theory to a practical test during
the total eclipse of the sun on 29th May 1919. For, when the disc of the
sun is obscured, the stars that are closest to it become visible (even
to the naked eye). They may be photographed, and the distances of the
points of light on the negative allow us to detect whether the rays from
the stars in passing the massive body of the sun have actually been
deflected by the amount prophesied by Einstein.
Once again current thought encountered a sharp corner, and "common
sense," which furnishes its own certificate of merit, threatened to
become rebellious. How now? A ray from a star could be curved? Does not
this contradict the elementary conception of the straight lines, that
is, the shortest lines, for which we have no better picture than just
these rays? Did not Leonardo da Vinci define the straight line by means
of the term _linea radiosa_.
But such supposedly self-evident facts have no longer a place in the
space-time world. The point was to test whether a physical anomaly which
had been predicted actually existed. If the deflection of the rays
really happened, it should manifest itself in the distances between the
stars on the photographic plate being greater than one would expect from
their actual position.
For the curvature has its concave side towards the sun, as is easy to
see, once the phenomenon is regarded as possible. It is as if the ray
were directly subject to gravitation. Let us take two stars, one on each
side of the sun. On account of the concavities the eye receives rays
from them under a greater visual angle than if the rays were straight,
and interprets this angle as denoting a greater distance between the
sources of light, that is, it sees the two stars farther apart than in
the case of rectilinear propagation.
By how much farther apart? The preceding calculation and the subsequent
direct observation demanded incredible delicacy of measurement. If we
suppose the whole arc of the heavens divided into easily picturable
units such as degrees, then the apparent width of the moon is about half
a degree. We may still easily imagine the thirtieth part of this,
namely, a minute of arc. But the sixtieth part of the latter, the second
of arc, vanishes almost out of the range of sense-perception. And it was
just this minute measure that came into question, for the theory which
had been developed from pure thought predicted a deflection of seconds
of arc. This corresponds to about a hairbreadth when seen at a distance
of 17 yards, or to the thickness of a match at a distance of over half a
mile.
One of the greatest problems of the most comprehensive science depended
on this unthinkably small measure.
In no sense did Einstein himself entertain a possibility of doubt.
On repeated occasions before May 1919 I had opportunities of questioning
him on this point. There was no shadow of a scruple, no ominous fears
clouded his anticipations. Yet great things were at stake.
Observation was to show "the correctness of Einstein's world system" by
a fact clearly intelligible to the whole world, one depending on a very
sensitive test of less than two seconds of arc.
"But, Professor," said I, on various occasions, "what if it turns out to
be more or less? These things are dependent on apparatus that may be
faulty, or on unforeseen imperfections of observation." A smile was
Einstein's only answer, and this smile expressed his unshakeable faith
in the instruments and the observers to whom this duty was to be
entrusted.
Moreover, it is to be remarked that no great lengths of time were
available for comfortable experimentation in taking this photographic
record. For the greatest possible duration of a total eclipse of the sun
viewed at a definite place amounts to less than eight minutes, so that
there was no room for mishaps in this short space of time, nor must any
intervening cloud appear. The kindly co-operation of the heavens was
indispensable--and was not refused. The sun, in this case the darkened
sun, brought this fact to light.
Two English expeditions had been equipped for the special occasion of
the eclipse--one to proceed to Sobral and the other to the Island of
Principe, off Portuguese Africa; they were sent officially with
equipment provided in the main by the time-honoured Royal Society.
Considering the times, it was regarded as the first symptom of the
revival of international science, a praiseworthy undertaking. A huge
apparatus was set into motion for a purely scientific object with not
the slightest relation to any purpose useful in practical life. It was a
highly technical investigation whose real significance could be grasped
by only very few minds. Yet interest was excited in circles reaching far
beyond that of the professional scientist. As the solar eclipse
approached, the consciousness of amateurs became stirred with indefinite
ideas of cosmic phenomena. And just as the navigator gazes at the Polar
Star, so men directed their attention to the constellation of Einstein,
which was not yet depicted in stellar maps, but, from which something
uncomprehended, but undoubtedly very important, was to blaze forth.
In June it was announced that the star photographs had been successful
in most cases, yet for weeks, nay for months, we had to exercise
patience. For the photographs, although they required little time to be
taken, took much longer to develop and, above all, to be measured; in
view of the order of smallness of the distances to be compared, this was
a difficult and troublesome task, for the points of light on the plate
did not answer immediately with Yes or No, but only after mechanical
devices of extreme delicacy had been carefully applied.
At the end of September they proclaimed their message. It was in the
affirmative, and this Yes out of far-distant transcendental regions
called forth a resounding echo in the world of everyday life. Genuinely
and truly the seconds of arc had come out, correct to the decimal point.
These points representing ciphers, as it were, had chanted of the
harmony of the spheres in their Pythagorean tongue. The transmission of
this message seemed to be accompanied by the echoing words of Goethe's
"Ariel":
"With a crash the Light draws near!
Pealing rays and trumpet-blazes,--
Eye is blinded, ear amazes."
Never before had anything like this happened. A wave of amazement swept
over the continents. Thousands of people who had never in their lives
troubled about vibrations of light and gravitation were seized by this
wave and carried on high, immersed in the wish for knowledge although
incapable of grasping it. This much all understood, that from the quiet
study of a scholar an illuminating gospel for exploring the universe had
been irradiated.
During that time no name was quoted so often as that of this man.
Everything sank away in face of this universal theme which had taken
possession of humanity. The converse of educated people circled about
this pole, could not escape from it, continually reverted to the same
theme when pressed aside by necessity or accident. Newspapers entered on
a chase for contributors who could furnish them with short or long,
technical or non-technical, notices about Einstein's theory. In all
nooks and corners social evenings of instruction sprang up, and
wandering universities appeared with errant professors that led people
out the three-dimensional misery of daily life into the more hospitable
Elysian fields of four-dimensionality. Women lost sight of domestic
worries and discussed co-ordinate systems, the principle of
simultaneity, and negatively-charged electrons. All contemporary
questions had gained a fixed centre from which threads could be spun to
each. Relativity had become the sovereign password. In spite of some
grotesque results that followed on this state of affairs it could not
fail to be recognized that we were watching symptoms of mental hunger
not less imperative in its demands than bodily hunger, and it was no
longer to be appeased by the former books by writers on popular science
and by misguided idealists.
And whilst leaders of the people, statesmen, and ministers made vain
efforts to steer in the fog, to arrive at results serviceable to the
nation, the multitude found what was expedient for it, what was
uplifting, what sounded like the distant hammering of reconstruction.
Here was a man who had stretched his hands towards the stars; to forget
earthly pains one had but to immerse oneself in his doctrine. It was the
first time for ages that a chord vibrated through the world invoking all
eyes towards something which, like music or religion, lay outside
political or material interests.
The mere thought that a living Copernicus was moving in our midst
elevated our feelings. Whoever paid him homage had a sensation of
soaring above Space and Time, and this homage was a happy augury in an
epoch so bare of brightness as the present.
* * * * * * * *
As already remarked, there was no lack of rare fruits among the
newspaper articles, and a chronicler would doubtless have been able to
make an attractive album of them. I brought Einstein several foreign
papers with large illustrations which must certainly have cost the
authors and publishers much effort and money. Among others there were
full-page beautifully coloured pictures intended to give the reader an
idea of the paths pursued by the rays from the stars during the total
eclipse of the sun. These afforded Einstein much amusement, namely, _e
contrario_, for from the physical point of view these pages contained
utter nonsense. They showed the exact opposite of the actual course of
the rays inasmuch as the author of the diagrams had turned the convex
side of the deflected ray towards the sun. He had not even a vague idea
of the character of the deflection, for his rays proceeded in a straight
line through the universe until they reached the sun, where they
underwent a sudden change of direction reminiscent of a stork's legs.
The din of journalistic homage was not unmixed with scattered voices of
dissent, even of hostility. Einstein combated these not only without
anger but with a certain satisfaction. For indeed the series of unbroken
ovations became discomfiting, and his feelings took up arms against what
seemed to be developing into a star-artist cult. It was like a breath of
fresh air when some column of a chance newspaper was devoted to a
polemic against his theory, no matter how unfounded or unreasoned it may
have been, merely because a dissonant tone broke the unceasing chorus of
praise. On one occasion he even said of a shrill disputant, "The man is
quite right!" And these words were uttered in the most natural manner
possible. One must know him personally if one is to understand these
excesses of toleration. So did Socrates defend his opponents.
In our conversation we returned to the original question, and I asked
whether there was no means of making the deflection of the ray
intelligible to an average person.
Einstein replied: "In a very superficial manner this is certainly
possible." And with a few strokes on the paper, which I shall here try
to describe in words, he gave his explanation in terms something like
the following:
This square is to denote the cross-section of a closed box which we
imagine to be situated somewhere in the universe. Inside it there lives
a physicist who makes observations and draws inferences from them. In
the course of time he perceives, what is familiar to all of us, that
every body not supported and left to itself, for example, a stone that
is released, drops to the floor with uniform acceleration, that is, with
a steady increase of velocity in going downwards. There are _two_ ways
open to him to explain this phenomenon.
_Firstly_, he might suspect--and this suspicion would be most likely to
occur to him--that his box was resting on some body in the heavens. For
if indeed the box were a cave in some part of the world, the falling of
the stone would suggest nothing unusual; it would be quite self-evident
to every occupant, and quite explicable to the physicist according to
Galilei's (or Newton's) Laws for Falling Bodies. He need not necessarily
restrict himself to the Earth, for if the box happened to be on some
other star, this phenomenon of falling would likewise occur, with
greater or less speed, and the body would certainly fall with uniform
acceleration. Thus the physicist could say: this is an effect of
gravitation, exhibiting the property of weight which I explain to myself
as usual, as due to the attraction of a heavenly body.
_Secondly_, another idea might strike him. For we stipulated nothing
about the position of the box, and assumed only that it was to exist
"somewhere in the universe." The physicist in the box might reason as
follows:
Supposing I am separated by incalculable distances from every attracting
heavenly body, and supposing gravitation existed neither for me nor for
the stone which I release from my hand, then it would still be possible
for me to give a complete explanation of the phenomena I observe. I
should only have to assume that the body is moving with uniform
acceleration "upwards." The motion previously interpreted by me as a
falling "downwards" need not take place at all. The stone, as an _inert_
body, could persist in its position (relative to the box or the
observer), and would, in spite of this, show exactly the same behaviour
when the box moves with acceleration upwards as if it were falling with
increasing velocity downwards.
Now since our physicist has no system which might serve for reference
and orientation, and since in his box which is shut off from the
universe he has no means at his disposal of determining whether he is in
the sphere of influence of an attracting heavenly body or not, both the
above explanations are feasible for him and both are equally valid, and
it is impossible for him to come to a decision in his choice. He can
interpret the acceleration in either way, as being upwards or downwards,
connected to one another by relativity; a fundamental reason for
preferring one interpretation to the other cannot be furnished, since
the phenomenon of falling is represented unchanged whether he assumes
the stone to be falling and the box to be at rest, or vice versa. This
may be generalized in these words:
At every point of the world the observed acceleration of a body left to
itself may be interpreted either as a gravitational _or_ as an inertial
effect--that is, from the point of view of physics we may assert with
equal right that the system (the box, the complex defining the
orientation) from which I observe the event is accelerated, or that the
event takes place in a gravitational field. The equal right to these two
views is called the "Principle of Equivalence" by Einstein. It asserts
the equivalence or the identity of inertial and gravitational mass. If
we familiarize ourselves with this identity, an exceedingly important
road to knowledge is opened up to our consciousness. We arrive at the
inevitable conclusion that every inertial effect that we perceive in
bodies, the most essential quality of it, itself so to speak in its
persistent nature, is to be traced back to the influence to which it is
subjected by other bodies. When this has become clear to us, we feel
impelled to inquire how a ray of light would behave under the influence
of gravitation. Hence we return to our physicist in the box, and we now
know that as a consequence of the Principle of Equivalence we are free
to assume either that an attracting heavenly body, such as the sun, is
situated somewhere below the box, or to refer the phenomena to the box
regarded as being accelerated upwards. In the box we distinguish the
floor, the ceiling, four walls, and among these again, according to the
position we take up, the wall on the left and its opposite one on the
right.
We now imagine a marksman to be outside the box and having no connexion
with us, being poised freely in space, and suppose him to fire out of a
horizontal gun at the box so that the bullet pierces both the wall on
the left and the wall on the right. Now, if everything else were to
remain at rest, the holes in both walls would be equally distant from
the floor, and the bullet would move in a straight line parallel to the
floor and to the ceiling. But, as we have seen, all events happen as if
the box itself moved with constant acceleration. The bullet that
requires time to pass from one wall to the other thus finds that when it
reaches the wall on the right the latter has advanced a little, so that
the resulting hole is a little lower than that on the left wall. This
means that the flight of the bullet, according to our observation in the
interior of the box, is no longer rectilinear. In fact, if we trace the
bullet from point to point, we should find that for us, situated in the
box, it would describe a line bent downwards, with its concave side to
the floor.
Exactly the same thing happens with a ray of light which is emitted by a
source outside in a horizontal direction and which traverses the space
between the walls (supposed transparent). Only the velocity would be
different. In the course of its flight the ray would move like a
projectile that is whizzing along at the rate of 180,000 miles per
second. But provided sufficiently delicate means of measurement are
applied, it should still be possible to prove the existence of an
infinitesimal deflection from the rectilinear horizontal path, an
insignificant concavity towards the floor.
Consequently this curvature of the light-ray (say, from a star) must
also be perceptible in places where it is subject to the influence of a
gravitational field. If we drop our imaginary picture of the box, the
argument is in nowise altered. A ray from a star which passes close by
the sun seems to our perception to be bent in towards the sun, and the
order of this deflection can be determined if sufficiently delicate
instruments be used. As above remarked, it is a question of detecting a
difference of 1.7 seconds of arc, which is to be manifested as a
distance on the photographic plate, and is actually found to be present.
The fact that scientists are able to detect this appears in itself a
marvel of technical precision far in advance of "splitting hairs," for
in comparison a single hair is, in this case, to be removed to a
considerable distance if we are to use it to give an idea of the size of
angle under consideration. Fortunately stellar photography has been
developed so wonderfully that in every single case extraordinarily
accurate results are got even from preliminary measurements.
In ordinary astronomical practice it is usually found that a millimetre
in linear measure on the plate corresponds to a minute of arc. This
means that the sun's disc itself has a diameter of 3 centimetres on the
photograph. The stars appear as tiny dots, which may be sharply
differentiated in an enlargement. Stars of the fourteenth order of
magnitude and beyond it become visible, whereas the naked eye cannot see
those of order higher than the sixth. A grating whose lines are
¹⁄₁₀₀ millimetre wide is copied on to the plate to make the
measurement more accurate, so that the positions of objects can be
ascertained with certainty to within a few tenths of a second of arc.
Thus the problem which was to be solved by the solar eclipse of 1919 lay
within the realm of possibility as regards our means of measurement.
A copy of this photograph had been sent to Einstein from England, and he
told me of it with evident pleasure. He continually reverted to the
delightful little picture of the heavens, quite fascinated by the thing
itself, without the slightest manifestation of a personal interest in
his own success. Indeed, I may go further and am certainly not mistaken
in saying his new mechanics did not even enter his head, nor the
verification of it by the plate; on the contrary, he displayed that
disposition of the mind which in the case of genius as well as in that
of children shows itself as _naïveté_. The prettiness of the
photograph charmed him, and the thought that the heavens had been drawn
up as for parade to be a model for it.
All things are repeated in the history of life. In these happenings,
which mark the 29th May 1919 as a red-letter day in the history of
science, we recognize a revival of the Sun Myth, unperceived by the
individual, but as an expression of the universal consciousness, just as
when Copernicus converted the geocentric picture of the universe into a
heliocentric one, the Sun Myth again sprang into life; the symbolization
of faith in the light-giving and heat-giving star. This time it has
arisen, purified of all dross, scarcely perceptible to our senses, like
an aureole spun about the sun by far-distant sources of light, in honour
of a principle, and even if most of us do not yet know what a "system of
reference" means, yet for many such a system has unconsciously evolved,
a thought-system serving as a reference for the development of their
knowledge when they thought or spoke of Einstein.