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The Einstein Theory
of Relativity

A CONCISE STATEMENT

-VBY ,,

Prof. H. A. LORENTZ

of the University of Leyden

it'''-'

NEW YORK ^0^

BRENTANO'S
Publishers

I

QC

(o

Copyright, 1920, by
BRENTANO'S

Third Edition

NOTE

Whether it is true or not that not
more than twelve persons in all the
world are able to understand Ein-
stein's Theory, it is nevertheless a
fact that there is a constant de-
mand for information about this
much- debated topic of relativity.
The books published on the subject
are so technical that only a person
trained in pure physics and higher
mathemathics is able to fully under-
stand them. In order to make a
popular explanation of this far-
reaching theory available, the pres-
ent book is published.

Professor Lorentz is credited by
Einstein with sharing the develop-
ment of his theory. He is doubtless
[6]

better able than any other man —
except the author himself — to ex-
plain this scientific discovery.

The publishers wish to acknowl-
edge their indebtedness to the New
York Times J The Review of Reviews
and The Athenaeum for courteous
permission to reprint articles from
their pages. Professor Lorentz's
article appeared originally in The
Nieuwe Rotterdamsche Courant oi,
November 19, 1919.

[6]

INTRODUCTION

The action of the Royal Society at
its meeting in London on November
6, in recognizing Dr. Albert Ein-
stein's " theory of relativity " has
caused a great stir in scientific cir-
cles on both sides of the Atlantic.
Dr. Einstein propounded his theory
nearly fifteen years ago. The pres-
ent revival of interest in it is due to
the remarkable confirmation which
it received in the report of the ob-
servations made during the sun's
eclipse of last May to determine
whether rays of light passing close
to the sun are deflected from their
course.

The actual deflection of the rays
that was discovered by the astron-
[7]

THE EINSTEIN THEORY

omers was precisely what had been
predicted theoretically by Einstein
many years since. This striking
confirmation has led certain German
scientists to assert that no scientific
discovery of such importance has
been made since Newton's theory
of gravitation was promulgated.
This suggestion, however, was put
aside by Dr. Einstein himself when
he was interviewed by a correspond-
ent of the New York Times at his
home in Berlin. To this corre-
spondent he expressed the difference
between his conception and the law
of gravitation in the following
terms :

" Please imagine the earth re-
moved, and in its place suspended
a box as big as a room or a whole
house, and inside a man naturally
[81

THE EINSTEIN THEORY

floating in the center, there being
no force whatever pulling him. Im-
aginu, further, this box being, by a
rope or other contrivance, suddenly
jerked to one side, which is scien-
tifically termed * difform motion,' as
opposed to ' uniform motion.' The
person would then naturally reach
bottom on the opposite side. The
result would consequently be the
same as if he obeyed Newton's law
of gravitation, while, in fact, there
is no gravitation exerted whatever,
which proves that difform motion
will in every case produce the same
effects as gravitation.

" I have applied this new idea to
every kind of difform motion and
have thus developed mathematical
formulas which I am convinced give
more precise results than those

[9]

THE EINSTEIN THEORY

based on Newton's theory. New-
ton's formulas, however, are such
close approximations that it was dif-
ficult to find by observation any ob-
vious disagreement with experi-

ence."

Dr. Einstein, it must be remem-
bered, is a physicist and not an
astronomer. He developed his the-
ory as a mathematical formula.
The confirmation of it came from
the astronomers. As he himself
says, the crucial test was supplied
by the last total solar eclipse. Ob-
servations then proved that the rays
of fixed stars, having to pass close
to the sun to reach the earth, were
deflected the exact amount de-
manded by Einstein's formulas. The
deflection was also in the direction
predicted by him.
[101

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The question must have occurred
to many, what has all this to do
with relativity? When this query
was propounded by the Times cor-
respondent to Dr. Einstein he re-
plied as follows:

" The term relativity refers to
time and space. According to Gali-
leo and Newton, time and space
were absolute entities, and the mov-
ing systems of the universe were de-
pendent on this absolute time and
space. On this conception was built
the science of mechanics. The re-
sulting formulas sufficed for all mo-
tions of a slow nature; it was found,
however, that they would not con-
form to the rapid motions appar-
ent in electrodynamics.

"This led the Dutch professor,
Lorentz, and myself to develop the

THE EINSTEIN THEORY

theory of special relativity. Briefly,
it discards absolute time and space
and makes them in every instance
relative to moving systems. By this
theory all phenomena in electro-
dynamics, as well as mechanics,
hitherto irreducible by the old for-
mulae— and there are multitudes —
were satisfactorily explained.

" Till now it was believed that
time and space existed by them-
selves, even if there was nothing
else — ^no sun, no earth, no stars —
while now we know that time and
space are not the vessel for the uni-
verse, but could not exist at all if
there were no contents, namely, no
sun, earth and other celestial bodies.

" This special relativity, forming
the first part of my theory, relates
to all systems moving with uniform

[12]

THE EINSTEIN THEORY

motion; that is, moving in a straight
line with equal velocity.

" Gradually I was led to the idea,
seeming a very paradox in science,
that it might apply equally to all
moving systems, even of difform
motion, and thus I developed the
conception of general relativity
which forms the second part of my
theory."

As summarized by an American
astronomer, Professor Henry Nor-
ris Russell, of Princeton, in the
Scientific American for November
29, Einstein's contribution amounts
to this:

" The central fact which has been
proved — and which is of great inter-
est and importance — is that the na-
tural phenomena involving gravita-
tion and inertia (such as the mo-

[13]

THE EINSTEIN THEORY

tions of the planets) and the phe-
nomena involving electricity and
magnetism (including the motion of
light) are not independent of one
another, but are intimately related,
so that both sets of phenomena
should be regarded as parts of one
vast system, embracing all Nature.
The relation of the two is, however,
of such a character that it is per-
ceptible only in a very few in-
stances, and then only to refined
observations."

Already before the war, Einstein
had inmiense fame among physicists,
and among all who are interested in
the philosophy of science, because of
his principle of relativity.

Clerk Maxwell had shown that
light is electromagnetic, and had re-
duced the whole theory of electro-

[14]

THE EINSTEIN THEORY

magnetism to a small number of
equations, which are fundamental in
all subsequent work. But these equa-
tions were entangled with the hypo-
thesis of the ether, and with the no-
tion of motion relative to the ether.
Since the ether was supposed to be
at rest, such motion was indistin-
guishable from absolute motion.
The motion of the earth relatively to
the ether should have been different
at different points of its orbit, and
measurable phenomena should have
resulted from this difference. But
none did, and all attempts to detect
effects of motions relative to the
ether failed. The theory of relativ-
ity succeeded in accounting for this
fact. But it was necessary incident-
ally to throw over the one universal
time, and substitute local times at-

[15]

THE EINSTEIN THEORY

tached to moving bodies and varying
according to their motion. The
equations on which the theory of re-
lativity is based are due to Lorentz,
but Einstein connected them with his
general principle, namely, that there
must be nothing, in observable phe-
nomena, which could be attributed to
absolute motion of the observer.

In orthodox Newtonian dynamics
the principle of relativity had a sim-
pler form, which did not require the
substitution of local time for general
time. But it now appeared that
Newtonian dynamics is only valid
when we confine ourselves to veloci-
ties much less than that of light.
The whole Galileo-Newton system
thus sank to the level of a first ap-
proximation, becoming progressively
less exact as the velocities concerned
approached that of light.

[16]

THE EINSTEIN THEORY

Einstein's extension of his prin-
ciple so as to account for gravitation
was made during the war, and for a
considerable period our astronomers
were unable to become acquainted
with it, owing to the difficulty of ob-
taining German printed matter.
However, copies of his work ulti-
mately reached the outside world and
enabled people to learn more about
it. Gravitation, ever since Newton,
had remained isolated from other
forces in nature ; various attempts had
been made to account for it, but with-
out success. The immense unifica-
tion effected by electromagnetism ap-
parently left gravitation out of its
scope. It seemed that nature had
presented a challenge to the physi-
cists which none of them were able
to meet.

[17]

THE EINSTEIN THEORY

At this point Einstein intervened
with a hypothesis which, apart alto-
gether from subsequent verification,
deserves to rank as one of the great
monuments of human genius. After
correcting Newton, it remained to
correct Euclid, and it was in terms
of non-Euclidean geometry that he
stated his new theory. Non-Eucli-
dean geometry is a study of which
the primary motive was logical and
philosophical; few of its promoters
ever dreamed that it would come to
be applied in physics. Some of
Euclid's axioms were felt to be not
" necessary truths," but mere empiri-
cal laws; in order to establish this
view, self-consistent geometries were
constructed upon assumptions other
than those of Euclid. In these
geometries the sum of the angles of

ri8i

THE EINSTEIN THEORY

a triangle is not two right angles, and
the departure from two right angles
increases as the size of the triangle
increases. It is often said that in
non-Euclidean geometry space has a
curvature, but this way of stating the
matter is misleading, since it seems
to imply a fourth dimension, which
is not implied by these systems.

Einstein supposes that space is
Euclidean where it is sufficiently re-
mote from matter, but that the pres-
ence of matter causes it to become
slightly non-Euclidean — the more
matter there is in the neighborhood,
the more space will depart from
Euclid. By the help of this hypo-
thesis, together with his previous
theory of relativity, he deduces gravi-
tation— very approximately, but not
exactly, according to the Newtonian
law of the inverse square.

[19]

THE EINSTEIN THEORY

The minute differences between
the effects deduced from his theory
and those deduced from Newton are
measurable in certain cases. There
are, so far, three crucial tests of the
relative accuracy of the new theory
and the old.

(1) The perihelion of Mercury
shows a discrepancy which has long
puzzled astronomers. This discrep-
ancy is fully accounted for by Ein-
stein. At the time when he pub-
lished his theory, this was its only
experimental verification.

(2) Modem physicists were will-
ing to suppose that light might be
subject to gravitation — i,e., that a
ray of light passing near a great mass
like the sun might be deflected to the
extent to which a particle moving
with the same velocity would be de-

[20]

THE EINSTEIN THEORY

fleeted according to the orthodox
theory of gravitation. But Ein-
stein's theory required that the light
should be deflected just twice as much
as this. The matter could only be
tested during an eclipse among a
number of bright stars. Fortimately
a peculiarly favourable eclipse oc-
curred last year. The results of the
observations have now been pub-
lished, and are found to verify Ein-
stein's prediction. The verification
is not, of course, quite exact; with
such delicate observations that was
not to be expected. In some cases
the departure is considerable. But
taking the average of the best series
of observations, the deflection at the
sun's limb is found to be 1.98", with
a probable error of about 6 per cent.,
whereas the deflection calculated by

[21]

THE EINSTEIN THEORY

Einstein's theory should be 1.75". It
will be noticed that Einstein's theory-
gave a deflection twice as large as
that predicted by the orthodox the-
ory, and that the observed deflection
is slightly larger than Einstein pre-
dicted. The discrepancy is well with-
in what might be expected in view
of the minuteness of the measure-
ments. It is therefore generally ac-
knowledged by astronomers that the
outcome is a triumph for Einstein.
(3) In the excitement of this sen-
sational verification, there has been
a tendency to overlook the third ex-
perimental test to which Einstein's
theory was to be subjected. If his
theory is correct as it stands, there
ought, in a gravitational field, to be
a displacement of the lines of the
spectrum towards the red. No such

[22]

THE EINSTEIN THEORY

effect has been discovered. Spec-
troscopists maintain that, so far as
can be seen at present, there is no
way of accounting for this failure if
Einstein's theory in its present form
is assumed. They admit that some
compensating cause may be discov-
ered to explain the discrepancy, but
they think it far more probable that
Einstein's theory requires some es-
sential modification. Meanwhile, a
certain suspense of judgment is
called for. The new law has been
so amazingly successful in two of the
three tests that there must be some
thing valid about it, even if it is not
exactly right as yet.

Einstein's theory has the very
highest degree of aesthetic merit:
every lover of the beautiful must
wish it to be true. It gives a vast

[23]

THE EINSTEIN THEORY

unified survey of the operations of
nature, with a technical simplicity in
the critical assumptions which makes
the wealth of deductions astonishing.
It is a case of an advance arrived at
by pure theory: the whole effect of
Einstein's work is to make physics
more philosophical (in a good sense) ,
and to restore some of that intellec-
tual unity which belonged to the
great scientific systems of the seven-
teenth and eighteenth centuries, but
which was lost through increasing
specialization and the overwhelming
mass of detailed knowledge. In
some ways our age is not a good one
to live in, but for those who are in-
terested in physics there are great
compensations.

[24]

THE EINSTEIN THEORY
OF RELATIVITY

A Concise Statement by Prof. H. A,
Lorentz, of the University of Leyden

The total eclipse of the sun of
May 29, resulted in a striking con-
firmation of the new theory of the
universal attractive power of gravi-
tation developed by Albert Ein-
stein, and thus reinforced the con-
viction that the defining of this the-
ory is one of the most important
steps ever taken in the domain of
natural science. In response to a
request by the editor, I will at-
tempt to contribute something to its

[«5]

THE EINSTEIN THEORY

general appreciation in the follow-
ing lines.

For centuries Newton's doctrine
of the attraction of gravitation has
been the most prominent example
of a theory of natural science.
Through the simplicity of its basic
idea, an attraction between two
bodies proportionate to their mass
and also proportionate to the square
of the distance; through the com-
' pleteness with which it explained so
many of the peculiarities in the
movement of the bodies making up
the solar system; and, finally,
through its universal validity, even
in the case of the far-distant plan-
etary systems, it compelled the ad-
miration of all.

But, while the skill of the math-
ematicians was devoted to making

[26]

THE EINSTEIN THEORY

more exact calculations of the con-
sequences to which it led, no real
progress was made in the science of
gravitation. It is true that the in-
quiry -was transferred to the field of
physics, following Cavendish's suc-
cess in demonstrating the common
attraction between bodies with which
laboratory work can be done, but it
always was evident that natural
philosophy had no grip on the uni-
versal power of attraction. While
in electric effects an influence exer-
cised by the matter placed between
bodies was speedily observed — ^the
starting-point of a new and fertile
doctrine of electricity — in the case
of gravitation not a trace of an in-
fluence exercised by intermediate
matter could ever be discovered. It
was, and remained, inaccessible and

[27]

THE EINSTEIN THEORY

unchangeable, without any connec-
tion, apparently, with other phe-
nomena of natural philosophy.

Einstein has put an end to this
isolation; it is now well established
that gravitation affects not only
matter, but also light. Thus
strengthened in the faith that his
theory already has inspired, we may
assume with him that there is not a
single physical or chemical phe-
nomenon— which does not feel, al-
though very probably in an unno-
ticeable degree, the influence of
gravitation, and that, on the other
side, the attraction exercised by a
body is limited in the first place by
the quantity of matter it contains
and also, to some degree, by motion
and by the physical and chemical
condition in which it moves.

[28]

THE EINSTEIN THEORY

It is comprehensible that a person
could not have arrived at such a far-
reaching change of view by continu-
ing to follow the old beaten paths,
but only by introducting some sort
of new idea. Indeed, Einstein ar-
rived at his theory through a train
of thought of great originality. Let
me try to restate it in concise terms.

[29]

THE EARTH AS A MOVING
CAR

Everyone knows that a person
may be sitting in any kind of a
vehicle without noticing its progress,
so long as the movement does not
vary in direction or speed; in a car
of a fast express train objects fall
in just the same way as in a coach
that is standing still. Only when
we look at objects outside the train,
or when the air can enter the car, do
we notice indications of the motion.

We may compare the earth with
such a moving vehicle, which in its
course around the sun has a remark-
able speed, of which the direction
and velocity during a considerable
period of time may be regarded as

[30]

THE EINSTEIN THEORY

constant. In place of the air now
comes, so it was reasoned formerly,
the (jether which fills the spaces of
the universe and is the carrier of
light and of electro-magnetic phe-
nomena; there were good reasons to
assmne that the earth was entirely
permeable for the ether and could
travel through it without setting it
in motion. So here was a case com-
parable with that of a railroad coach
open on all sides. There certainly
should have been a powerful " ether
wind " blowing through the earth
and all our instruments, and it was
to have been expected that some
signs of it would be noticed in con-
nection with some experiment or
other. Every attempt along that
line, however, has remained fruitless ;
all the phenomena examined were

[31]

THE EINSTEIN THEORY

evidently independent of the motion
of the earth. That this is the way they
do function was brought to the front
by Einstein in his first or " special "
theory of relativity. For him the
ether does not function and in the
sketch that he draws of natural
phenomena there is no mention of
that intermediate matter.

If the spaces of the universe are
filled with an ether, let us suppose
with a substance, in which, aside
from eventual vibrations and other
slight movements, there is never any
crowding or flowing of one part
alongside of another, then we can
imagine fixed points existing in it;
for example, points in a straight
line, located one meter apart, points
in a level plain, like the angles or
squares on a chess board extend-

[32]

THE EINSTEIN THEORY

ing out into infinity, and finally,
points in space as they are obtained
by repeatedly shifting that level
spot a distance of a meter in the
direction perpendicular to it. If,
consequently, one of the points is
chosen as an " original point " we
can, proceeding from that point,
reach any other point through three
steps in the common perpendicular
directions in which the points are
arranged. The figures showing how
many meters are comprized in each
of the steps may serve to indicate
the place reached and to distinguish
it from any other ; these are, as is
said, the " co-ordinates " of these
places, comparable, for example,
with the numbers on a map giving
the longitude and latitude. Let us
imagine that each point has noted

[33]

THE EINSTEIN THEORY

upon it the three numbers that give
its position, then we have something
comparable with a measure with
numbered subdivisions ; only we now
have to do, one might say, with a
good many imaginary measures in
three common perpendicular direc-
tions. In this " system of co-ordi-
nates " the numbers that fix the po-
sition of one or the other of the
bodies may now be read off at any
moment.

This is the means which the as-
tronomers and their mathematical
assistants have always used in deal-
ing with the movement of the heav-
enly bodies. At a determined mo-
ment the position of each body is
fixed by its three co-ordinates. If
these are given, then one knows also
the common distances, as well as the

[84]

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angles formed by the connecting
lines, and the movement of a planet
is to be known as soon as one knows
how its co-ordinates are changing
from one moment to the other. Thus
the picture that one forms of the
phenomena stands there as if it were
sketched on the canvas of the mo-
tionless ether.

[36]

EINSTEIN'S DEPARTURE

Since Einstein has cut loose from
the ether, he lacks this canvas, and
therewith, at the first glance, also
loses the possibility of fixing the
positions of the heavenly bodies and
mathematically describing their
movement — i.e., by giving compari-
sons that define the positions at
every moment. How Einstein has
overcome this difficulty may be
somewhat elucidated through a sim-
ple illustration.

On the surface of the earth the
attraction of gravitation causes all
bodies to fall along vertical lines,
and, indeed, when one omits the re-
sistance of the air, with an equally

[36]

THE EINSTEIN THEORY

accelerated movement; the velocity
increases in equal degrees in equal
consecutive divisions of time at a
rate that in this country gives the
velocity attained at the end of a sec-
ond as 981 centimeters (32.2 feet)
per second. The number 981 de-
fines the " acceleration in the field
of gravitation," and this field is ful-
ly characterized by that single num-
ber; with its help we can also cal-
culate the movement of an object
hurled out in an arbitrary direction.
In order to measure the accelera-
tion we let the body drop alongside
of a vertical measure set solidly on
the ground; on this scale we read at
every moment the figure that indi-
cates the height, the only co-ordi-
nate that is of importance in this
rectilinear movement. Now we ask

[87]

THE EINSTEIN THEORY

what would we be able to see if the
measure were not bound solidly to
the earth, if it, let us suppose,
moved down or up with the place
where it is located and where we are
ourselves. If in this case the speed
Avere constant, then, and this is in
accord with the special theory of re-
lativity, there would be no motion
observed at all ; we should again find
an acceleration of 981 for a falling
body. It would be different if the
measure moved with changeable
velocity.

If it went down with a constant
acceleration of 981 itself, then an
object could remain permanently at
the same point on the measure, or
could move up or down itself along-
.side of it, with constant speed. The
relative movement of the body with
[38]

THE EINSTEIN THEORY

regard to the measure should be
without acceleration, and if we had
to judge only by what we observed
in the spot where we were and
which was falling itself, then we
should get the impression that there
was no gravitation at all. If the
measure goes down with an accele-
ration equal to a half or a third of
what it just was, then the relative
motion of the body will, of course,
be accelerated, but we should find
the increase in velocity per second
one-half or two-thirds of 981. If,
finally, we let the measure rise with
a uniformly accelerated movement,
then we shall find a greater accele-
ration than 981 for the body itself.
Thus we see that we, also when
the measure is not attached to the
earth, disregarding its displacement,

[89]

THE EINSTEIN THEORY

may describe the motion of the body
in respect to the measure always
in the same way — i.e., as one uni-
formly accelerated, as we ascribe
now and again a fixed value to the
acceleration of the sphere of gravi-
tation, in a particular case the value
of zero.

Of course, in the case here under
consideration the use of a measure
fixed immovably upon the earth
should merit all recommendation.
But in the spaces of the solar sys-
tem we have, now that we have
abandoned the ether, no such sup-
port. We can no longer establish
a system of co-ordinates, like the one
just mentioned, in a universal inter-
mediate matter, and if we were to
arrive in one way or another at a
definite system of lines crossing each

[40]

THE EINSTEIN THEORY

other in three directions, then we
should be able to use just as well
another similar system that in re-
spect to the first moves this or that
way. We should also be able to re-
model the system of co-ordinates in
all kinds of ways, for example by
extension or compression. That in
all these cases for fixed bodies that
do not participate in the movement
or the remodelling of the system
other co-ordinates will be read off
again and again is clear.

[41]

NEW SYSTEM OR CO-ORDI-
NATES

What way Einstein had to follow
is now apparent. He must — this
hardly needs to be said — in calculat-
ing definite, particular cases make
use of a chosen system of co-ordi-
nates, but as he had no means of
limiting his choice beforehand and
in general, he had to reserve full
liberty of action in this respect.
Therefore he made it his aim so to
arrange the theory that, no matter
how the choice was made, the phe-
nomena of gravitation, so far as its
effects and its stimulation by the at-
tracting bodies are concerned, may
always be described in the same way
[42]

THE EINSTEIN THEORY.

— i.e., through comparisons of the
same general form, as we again and
again give certain values to the num-
bers that mark the sphere of gravi-
tation. (For the sake of simplifica-
tion I here disregard the fact that
Einstein desires that also the way
in which time is measured and rep-
resented by figures shall have no
influence upon the central value of
the comparisons.)

Whether this aim could be at-
tained was a question of mathemati-
cal inquiry. It really was attained,
remarkably enough, and, we may
say, to the surprise of Einstein him-
self, although at the cost of consid-
erable simplicity in the mathemati-
cal form; it appeared necessary for
the fixation of the field of gravita-
tion in one or the other point in

[43]

THE EINSTEIN THEORY

space to introduce no fewer than
ten quantities in the place of the
one that occurred in the example
mentioned above.

In this connection it is of import-
ance to note that when we exclude
certain possibilities that would give
rise to still greater intricacy, the
form of comparison used by Ein-
stein to present the theory is the
only possible one; the principle of
the freedom of choice in co-ordi-
nates was the only one by which he
needed to allow himself to be guided.
Although thus there was no special
effort made to reach a connection
with the theory of Newton, it was
evident, fortunately, at the end of
the experiment that the connection
existed. If we avail ourselves of
the simplifying circumstance that

[44]

THE EINSTEIN THEORY

the velocities of the heavenly bodies
are slight in comparison with that
of light, then we can deduce the the-
ory of Newton from the new the-
ory, the "universal" relativity the-
ory, as it is called by Einstein.
Thus all the conclusions based upon
the Newtonian theory hold good, as
must naturally be required. But
now we have got further along.
The Newtonian theory can no
longer be regarded as absolutely
correct in all cases; there are slight
deviations from it, which, although
as a rule unnoticeable, once in a
while fall within the range of ob-
servation.

Now, there was a difficulty in
the movement of the planet Mer-
cury which could not be solved.
Even after all the disturbances

[45]

THE EINSTEIN THEORY
caused by the attraction of other
planets had been taken into account,
there remained an inexplicable
phenomenon — i.e,, an extremely-
slow turning of the ellipsis described
by Mercury on its own plane; Le-
verrier had found that it amounted
to forty-three seconds a century.
Einstein found that, according to
his formulas, this movement must
really amount to just that much.
Thus with a single blow he solved
one of the greatest puzzles of
astronomy.

Still more remarkable, because it
has a bearing upon a phenomenon
which formerly could not be imag-
ined, is the confirmation of Ein-
stein's prediction regarding the in-
fluence of gravitation upon the
[46]

THE EINSTEIN THEORY
course of the rays of light. That
such an influence must exist is
taught by a simple examination; we
have only to turn back for a moment
to the following comparison in which
we were just imagining ourselves to
make our observations. It was noted
that when the compartment is fall-
ing with the acceleration of 981 the
phenomena therein will occur just
as if there were no attraction of
gravitation. We caii then see an
object, A, stand still somewhere in
open space. A projectile, B, can
travel with constant speed along a
horizontal line, without varying
from it in the slightest.

A ray of light can do the same;
everybody will admit that in each
case, if there is no gravitation, light

[47]

THE EINSTEIN THEORY

will certainly extend itself in a rec-
tilinear way. If we limit the light
to a flicker of the slightest duration,
so that only a little bit, C, of a ray
of light arises, or if we fix our at-
tention upon a single vibration of
light, C, while we on the other hand
give to the projectile, B, a speed
equal to that of light, then we can
conclude that B and C in their con-
tinued motion can always remain
next to each other. Now if we
watch all this, not from the movable
compartment, but from a place on
the earth, then we shall note the
usual falling movement of object A,
which shows us that we have to deal
with a sphere of gravitation. The
projectile B will, in a bent path,
vary more and more from a hori-
zontal straight line, and the light

[4.8]

THE EINSTEIN THEORY

will do the same, because if we ob-
serve the movements from another
standpoint this can have no effect
upon the remaining next to each
other of B and C,

[49]

DEFLECTION OF LIGHT

The bending of a ray of light thus
described is much too light on the
surface of the earth to be observed.
But the attraction of gravitation ex-
ercised by the sun on its surface is,
because of its great mass, more than
twenty-seven times stronger, and a
ray of light that goes close by the
superficies of the sun must surely be
noticeably bent. The rays of a star
that are seen at a short distance from
the edge of the sun will, going along
the sun, deviate so much from the
original direction that they strike
the eye of an observer as if they
came in a straight line from a point
somewhat further removed than the
real position of the star from the
sun. It is at that point that we

[50]

THE EINSTEIN THEORY

think we see the star; so here is a
seeming displacement from the sun,
which increases in the measure in
which the star is observed closer to
the sun. The Einstein theory
teaches that the displacement is in
inverse proportion to the apparent
distance of the star from the centre
of the sun, and that for a star just
on its edge it will amount to 1\75
(1.75 seconds). This is approxi-
mately the thousandth part of the
apparent diameter of the sun.

Naturally, the phenomenon can
only be observed when there is a
total eclipse of the sun; then one
can take photographs of neighbor-
ing stars and through comparing
the plate with a picture of the same
part of the heavens taken at a time
when the sun was far removed from

[61]

THE EINSTEIN THEORY

that point the sought-for movement
to one side may become apparent.

Thus to put the Einstein theory
to the test was the principal aim of
the English expeditions sent out to
observe the eclipse of May 29, one
to Prince's Island, off the coast of
Guinea, and the other to Sobral,
Brazil. The first-named expedi-
tion's observers were Eddington and
Cottingham, those of the second,
Crommelin and Davidson. The con-
ditions were especially favorable, for
a very large number of bright stars
were shown on the photographic
plate; the observers at Sobral be-
ing particularly lucky in having
good weather.

The total eclipse lasted five min-
utes, during four of which it was
perfectly clear, so that good photo-

[62]

THE EINSTEIN THEORY

graphs could be taken. In the re-
port issued regarding the results the
following figures, which are the
average of the measurements made
from the seven plates, are given for
the displacements of seven stars:

1".02, 0".92, 0".84, 0".58, 0".54,
0".36, 0".24, whereas, according to
the theory, the displacements should
have amounted to: 0".88, 0".80,
0".75, 0".40, 0".52, 0".33, 0".20.

If we consider that, according to
the theory the displacements must
be in inverse ratio to the distance
from the centre of the sun, then we
may deduce from each observed dis-
placement how great the sideways
movement for a star at the edge of
the sun should have been. As the
most probable result, therefore, the
number 1".98 was found from all

[63]

THE EINSTEIN THEORY

the observations together. As the
last of the displacements given
above — i.e., 0".24 is about one-
eighth of this, we may say that the
influence of the attraction of the
sun upon light made itself felt upon
the ray at a distance eight times re-
moved from its centre.

The displacements calculated ac-
cording to the theory are, just be-
cause of the way in which they are
calculated, in inverse proportion to
the distance to the centre. Now
that the observed deviations also ac-
cord with the same rule, it follows
that they are surely proportionate
with the calculated displacements.
The proportion of the first and the
last observed sidewise movements is
4.2, and that of the two most ex-
treme of the calculated numbers is
4.4.

[64]

THE EINSTEIN THEORY

This result is of importance, be-^
cause thereby the theory is excluded,
or at least made extremely improb-
able, that the phenomenon of re-
fraction is to be ascribed to a ring
of vapor surrounding the sim for a
great distance. Indeed, such a re-
fraction should cause a deviation in
the observed direction, and, in or-
der to produce the displacement of
one of the stars under observation
itself a slight proximity of the vapor
ring should be sufficient, but we
have every reason to expect that if
it were merely a question of ^a mass
of gas around the sun the diminish-
ing effect accompanying a removal
from the sun should manifest itself
much faster than is really the case.
We cannot speak with perfect cer-
tainty here, as all the factors that

[66]

THE EINSTEIN THEORY

might be of influence upon the dis-
tribution of density in a sun at-
mosphere are not well enough
kno\^Ti, but we can surely demon-
strate that in case one of the gasses
with which we are acquainted were
held in equilibrium solely by the in-
fluence of attraction of the sun the
phenomenon should become much
less as soon as we got somewhat fur-
ther from the edge of the sun. If
the displacement of the first star,
which amounts to 1.02-seconds were
to be ascribed to such a mass of gas,
then the displacement of the second
must already be entirely inappreci-
able.

So far as the absolute extent of

the displacements is concerned, it

was found somewhat too great, as

has been shown by the figures given

[66]

THE EINSTEIN THEORY

above; it also appears from the final
result to be 1.98 for the edge of the
sun — i.e,, 13 per cent, greater than
the theoretical value of 1.75. It
indeed seems that the discrepancies
may be ascribed to faults in observa-
tions, which supposition is supported
by the fact that the observations at
Prince's Island, which, it is true,
did not turn out quite as well as
those mentioned above, gave the re-
sult, of 1.64, somewhat lower than
Einstein's figure.

(The cobservations made with a
second instrument at Sobral gave a
result of 0.93, but the observers are
of the opinion that because of the
shifting of the mirror which re-
flected the rays no value is to be
attached to it.)

[67]

DIFFICULTY EXAG-
GERATED

During a discussion of the results
obtained at a joint meeting of the
Royal Society and the Royal As-
tronomical Society held especially
for that purpose recently in Lon-
don, it was the general opinion that
Einstein's prediction might be re-
garded as justified, and warm tri-
butes to his genius were made on
all sides. Nevertheless, I cannot re-
frain, while I am mentioning it,
from expressing my surprise that,
according to the report in The
Times, there should be so much com-
plaint about the difficulty of under-
standing the new theory. It is evi-
dent that Einstein's little book

[58]

THE EINSTEIN THEORY

" About the Special and the Gen-
eral Theory of Relativity in Plain
Terms," did not find its way into
England during wartime. Any one
reading it will, in my opinion, come
to the conclusion that the basic ideas
of the theory are really clear and
simple; it is only to be regretted
that it was impossible to avoid cloth-
ing them in pretty involved mathe-
matical terms, but we must not wor-
ry about that.

I allow myself to add that, as
we follow Einstein, we may retain
much of what has been formerly
gained. The Newtonian theory re-
mains in its full value as the first
great step, without which one can-
not imagine the development of as-
tronomy and without which the sec-
ond step, that has now been made,

[69]

THE EINSTEIN THEORY

would hardly have been possible. It
remains, moreover, as the first, and
in most cases, sufficient, approxi-
mation. It is true that, according
to Einstein's theory, because it
leaves us entirely free as to the way
in which we wish to represent the
phenomena, we can imagine an idea
of the solar system in which the
planets follow paths of peculiar
form and the rays of light shine
along sharply bent lines — think of
a twisted and distorted planetarium
— ^but in every case where we apply
it to concrete questions we shall so
arrange it that the planets describe
almost exact ellipses and the rays of
light almost straight lines.

It is not necessary to give up en-
tirely even the ether. Many natural
philosophers find satisfaction in the

[60]

THE EINSTEIN THEORY

idea of a material intermediate sub-
stance in which the vibrations of
light take place, and they will very
probably be all the more inclined
to imagine such a medium when
they learn that, according to the
Einstein theory, gravitation itself
does not spread instantaneously, but
with a velocity that at the first es-
timate may be compared with that
of light. Especially in former years
were such interpretations current
and repeated attempts were made
by speculations about the nature of
the ether and about the mutations
and movements that might take
place in it to arrive at a clear pre-
sentation of electro-magnetic phe-
nomena, and also of the functioning
of gravitation. In my opinion it
is not impossible that in the future

[61]

THE EINSTEIN THEORY

this road, indeed abandoned at pres-
ent, will once more be followed with
good results, if only because it can
lead to the thinking out of new ex-
perimental tests. Einstein's theory-
need not keep us from so doing;
only the ideas about the ether must
accord with it.

Nevertheless, even without the
color and clearness that the ether
theories and the other models may
be able to give, and even, we can
feel it this way, just because of the
soberness induced by their absence,
Einstein's work, we may now posi-
tively expect, will remain a monu-
ment of science; his theory entirely
fulfills the first and principal de-
mand that we may make, that of
deducing the course of phenomena
from certain principles exactly and

[62]

THE EINSTEIN THEORY

to the smallest details. It was cer-
tainly fortunate that he himself put
the ether in the background; if he
had not done so, he probably would
never have come upon the idea that
has been the foundation of all his
examinations.

Thanks to his indefatigable exer-
tions and perseverance, for he had
great difficulties to overcome in his
attempts, Einstein has attained the
results, which I have tried to sketch,
while still young ; he is now 45 years
old. He completed his first inves-
tigations in Switzerland, where he
first was engaged in the Patent Bu-
reau at Berne and later as a pro-
fessor at the Polytechnic in Zurich.
After having been a professor for
a short time at the University of
Prague, he settled in Berlin, where

[63]

THE EINSTEIN THEORY

the Kaiser Wilhelm Institute af-
forded him the opportunity to de-
vote himself exckisively to his scien-
tific work. He repeatedly visited
our country and made his Nether-
land colleagues, among whom he
counts many good friends, part-
ners in his studies and his results.
He attended the last meeting of the
department of natural philosophy
of the Royal Academy of Sciences,
and the members then* had the priv-
ilege of hearing him explain, in his
own fascinating, clear and simple
way, his interpretations of the fun-
damental questions to which his
theory gives rise.

[64]

^r)

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