"This is the most important result obtained in connection with the
theory of gravitation since Newton's day. Einstein's reasoning is
the result of one of the highest achievements of human thought."
These words were uttered by Sir J. J. Thomson, the president of the
Royal Society, at a meeting of that body held on November 6, 1919,
to discuss the results of the Eclipse Expedition.
Einstein another Newton--and this from the lips of J. J. Thomson,
England's most illustrious physicist! If ever man weighed words
carefully it is this Cambridge professor, whose own researches have
assured him immortality for all time.
What has this Albert Einstein done to merit such extraordinary
praise? With the world in turmoil, with classes and races in a death
struggle, with millions suffering and starving, why do we find time
to turn our attention to this Jew? His ideas have no bearing on
Europe's calamity. They will not add one bushel of wheat to starving
populations.
The answer is not hard to find. Men come and men go, but the mystery of
the universe remains. It is Einstein's glory to have given us a deeper
insight into the universe. Our scientists are Huxley's agnostics:
they do not deny activities beyond our planet; they merely center
their attention on the knowable on this earth. Our philosophers,
on the other hand, go far afield. Some of them soar so high that,
like one poet's opinion of Shelley, the bubble bursts. Einstein,
using the tools of the scientist--the experimentalist--builded a
skyscraper which ultimately reached the philosophical school. His rôle
is the rôle of alcohol in causing water and ether (the anæsthetic)
to mix. Ether and water will mix no better than oil and water, without
the presence of alcohol; in its presence a uniform mixture is obtained.
The Object of the Eclipse Expedition. Einstein prophesied that a
ray of light passing near the sun would be pulled out of its course,
due to the action of gravity. He went even further. He predicted how
much out of its course the ray would be deflected. This prediction
was based on a theory of gravitation which Einstein had developed in
great mathematical detail. The object of the British Eclipse Expedition
was either to prove or disprove Einstein's assumption.
The Result of the Expedition. Einstein's prophecy was fulfilled almost
to the letter.
The Significance of the Result. Since Einstein's theory of gravitation
is intimately associated with certain revolutionary ideas concerning
time and space, and, therefore, with Fundamentals of the Universe,
the net result of the expedition was to strengthen our belief in the
validity of his new view of the universe.
It is our intention in the following pages to discuss the expedition
and the larger aspects of Einstein's theory that follow from it. But
before we do so we must have a clear idea of our solar system.
Our Solar System. In the center of our system is the sun, a flaming
mass of fire, much bigger than our own earth, and very, very far
away. The sun has its family of eight planets--of which the earth is
one--which travel around the sun; and around some of the planets there
travel satellites, or moons. The earth has such a satellite, the moon.
Now we have good reasons for believing that every star which twinkles
in the sky is a sun comparable to our own, having also its own planets
and its own moons. These stars, or suns, are so much further away
from us than our own sun, that but a speck of their light reaches us,
and then only at night, when, as the poets would say, our sun has
gone to its resting place.
The distances between bodies in the solar system is so immense that,
like the number of dollars spent in the Great War, the number of miles
conveys little, or no impression. But picture yourself in an express
train going at the average rate of 30 miles an hour. If you start
from New York and travel continuously you would reach San Francisco
in 4 days. If you could continue your journey around the earth at
the same rate you would complete it in 35 days. If now you could
travel into space and to the moon, still with the same velocity,
you would reach it in 350 days. Having reached the moon, you could
circumscribe it with the same express train in 8 days, as compared to
the 35 days it would take you to circumscribe the earth. If instead
of travelling to the moon you would book your passage for the sun
you, or rather your descendants, would get there in 350 years, and
it would then take them 10 additional years to travel around the sun.
Immense as these distances are, they are small as compared to the
distances that separate us from the stars. It takes light which,
instead of travelling 30 miles an hour, travels 186,000 miles a second,
about 8 minutes to get to us from the sun, and a little over 4 years
to reach us from the nearest star. The light from some of the other
stars do not reach us for several hundred years.
The Eclipse of the Sun. Now to return to an infinitesimal part of
the universe--our solar system. We have seen that the earth travels
around the sun, and the moon around the earth. At some time in the
course of these revolutions the moon must come directly between the
earth and the sun. Then we get the eclipse of the sun. As the moon
is smaller than the earth, only a portion of the earth's surface
will be cut off from the sun's rays. That portion which is so cut
off suffers a total eclipse. This explains why the eclipse of May,
1919, which was a total one for Brazil, was but a partial one for us.
Einstein's Assertion Re-stated. Einstein claimed that a ray of light
from one of the stars, if passing near enough to the surface of the
sun, would be appreciably deflected from its course; and he calculated
the exact amount of this deflection. To begin with, why should Einstein
suppose that the path of a ray of light would be affected by the son?
Newton's law of gravitation made it clear that bodies which have
mass attract one another. If light has mass--and very recent work
tends to show that it has--there is no reason why light should not be
attracted by the sun, or any other planetary body. The question that
agitated scientists was not so much whether a ray of light would be
deviated from its path, but to what extent this deviation would take
place. Would Einstein's figures be confirmed?
Of the bodies within our solar system the sun is by far the largest,
and therefore it would exert a far greater pull than any of the planets
on light rays coming from the stars. Under ordinary conditions,
however, the sun itself shines with such brilliancy, that objects
around it, including rays of light passing near its surface, are wholly
dimmed. Hence the necessity of putting our theory to the test only when
the moon covers up the sun--when there is a total eclipse of the sun.
A Graphical Representation. Imagine a star A, so selected that as
its light comes to us the ray just grazes the sun. If the path of
the ray is straight--if the sun has no influence on it--then the path
can be represented by the line AB. If, however, the sun does exert a
gravitational pull, then its real path will be AB', and to an observer
on the earth the star will have appeared to shift from A to A'.
What the Eclipse Expedition Set Out to Do. Photographs of stars
around the sun were to be taken during the eclipse, and these
photographs compared with others of the same region taken at night,
with the sun absent. Any apparent shifting of the stars could be
determined by measuring the distances between the stars as shown on
the photographic plates.
Three Possibilities Anticipated. According to Newton's assumption,
light consists of corpuscles, or minute particles, emitted from
the source of light. If this be true these particles, having mass,
should be affected by the gravitational pull of the sun. If we apply
Newton's theory of gravitation and make use of his formula, it can be
shown that such a gravitational pull would displace the ray of light
by an average amount equal to 0.75 (seconds of angular distance.) [4]
On the other hand, where light is regarded as waves set in motion in
the "ether" of space (the wave theory of light), and where weight is
denied light altogether, no deviation need be expected. Finally there
is a third alternative: Einstein's. Light, says Einstein, has mass,
and therefore probably weight. Mass is the matter light contains;
weight represents pull by gravity. Light rays will be attracted by
the sun, but according to Einstein's theory of gravitation the sun's
gravitational pull will displace the rays by an average amount equal
to 1.75 (seconds of angular distance).
The Expeditions. That science is highly international, despite many
recent examples to the contrary, is evidenced by this British Eclipse
Expedition. Here was a theory propounded by one who had accepted a
chair of physics in the university of Berlin, and across the English
Channel were Germany's mortal enemies making elaborate preparations
to test the validity of the Berlin professor's theory.
The British Astronomical Society began to plan the eclipse expedition
even before the outbreak of the Great War. During the years that
followed, despite the destinies of nations which hung on threads from
day to day, despite the darkest hours in the history of the British
people, our English astronomers continued to give attention to the
details of the proposed expedition. When the day of the eclipse came
all was in readiness.
One expedition under Dr. Crommelin was sent to Sobral, Brazil; another,
under Prof. Eddington, to Principe, an island off the west coast of
Africa. In both these places a total eclipse was anticipated.
The eclipse occurred on May 29, 1919. It lasted for six to eight
minutes. Some 15 photographs, with an average exposure of five to six
seconds, were taken. Two months later another series of photographs
of the same region were taken, but this time the sun was no longer
in the midst of these stars.
The photographs were brought to the famous Greenwich Observatory,
near London, and the astronomers and mathematicians began their
laborious measurements and calculations.
On November 6, at the meeting of the Royal Society, the result
was announced. The Sobral expedition reported 1.98; the Principe
expedition 1.62. The average was 1.8. Einstein had predicted 1.75,
Newton might have predicted 0.75, and the orthodox scientists would
have predicted 0. There could now no longer be any question as to which
of the three theories rested on a sure foundation. To quote Sir Frank
Dyson, the Astronomer Royal: "After a careful study of the plates I am
prepared to say that there can be no doubt that they confirm Einstein's
prediction. A very definite result has been obtained that light is
deflected in accordance with Einstein's law of gravitation." [5]
Where Did Einstein Get His Idea of Gravitation? In 1905 Einstein
published the first of a series of papers supporting and extending a
theory of time and space to which the name "the theory of relativity"
had been given. These views as expounded by Einstein came into direct
conflict with Newton's ideas of time and space, and also with Newton's
law of gravitation. Since Einstein had more faith in his theory of
relativity than in Newton's theory of gravitation, Einstein so changed
the latter as to make it harmonize with the former. More will be said
on this subject.
Let not the reader misunderstand. Newton was not wholly in the wrong;
he was only approximately right. With the knowledge existing in
Newton's day Newton could have done no more than he did; no mortal
could have done more. But since Newton's day physics--and science in
general--has advanced in great strides, and Einstein can interpret
present-day knowledge in the same masterful fashion that Newton
could in his day. With more facts to build upon, Einstein's law
of gravitation is more universal than Newton's; it really includes
Newton's.
But now we must turn our attention very briefly to the theory of
relativity--the theory that led up to Einstein's law of gravitation.
The Theory of Relativity. The story goes that Einstein was led to
his ideas by watching a man fall from a roof. This story bears a
striking similarity to Newton and the apple. Perhaps one is as true
as the other. [6]
However that may be, the principle of relativity is as old as
philosophical thought, for it denies the possibility of measuring
absolute time, or absolute space. All things are relative. We say
that it takes a "long time" to get from New York to Albany; long as
compared to what? long, perhaps, as compared to the time it takes to
go from New York City to Brooklyn. We say the White House is "large";
large when compared to a room in an apartment. But we can just as
well reverse our ideas of time and distance. The time it takes to go
from New York to Albany is "short" when compared to the time it takes
to go from New York to San Francisco. The size of the White House is
"small" when compared to the size of the city of Washington.
Let us take another illustration. Every time the earth turns on its
axis we mark down as a day. With this as a basis, we say that it
takes a little over 365 days for the earth to complete its revolution
around the sun, and our 365 days we call a year. But now consider some
of our other planets. With our time as a basis, it takes Jupiter or
Saturn 10 hours to turn on its axis, as compared to the 24 hours it
takes the earth to turn. Saturn's day is less than one-half our day,
and our day is more than twice Saturn's--that is, according to the
calculations of the inhabitants of the earth. Mercury completes her
circuit around the sun in 88 days; Neptune, in 164 years. Mercury's
year is but one-fourth ours, Neptune's, 164 times ours. And observers
at Mercury and Neptune would regard us from their standard of time,
which differs from our standard.
You may say, why not take our standard of time as the standard,
and measure everything by it? But why should you? Such a selection
would be quite arbitrary. It would not be based on anything absolute,
but would merely depend on our velocity around the sun.
These ideas are old enough in metaphysics. Einstein's improvement
of them consists not merely in speculating about them, but in giving
them mathematical form.
The Origin of the Theory of Relativity. A train moves with reference
to the earth. The earth moves with reference to the sun. We say the
sun is stationary and the earth moves around the sun. But how do we
know that the sun itself does not move with reference to some other
body? How do we know that our planetary system, and the stars, and
the cosmos as a whole is not in motion?
There is no way of answering such a question unless we could get a
point of reference which is fixed--fixed absolutely in space.
We have already alluded to our view of the nature of light, known as
the wave theory of light. This theory postulates the existence of an
all-pervading "ether" in space. Light sets up wave disturbances in
this ether, and is thus propagated. If the ocean were the ether, the
waves of the ocean would compare with the waves set up by the ether.
But what is this ether? It cannot be seen. It defies weight. It
permeates all space. It permeates all matter. So say the exponents of
this ether. To the layman this sounds very much like another name
for the Deity. To Sir Oliver Lodge it represents the spirits of
the departed.
To us, of importance is the conception that this ether is absolutely
stationary. Such a conception is logical if the various developments in
optics and electricity are considered. But if absolutely stationary,
then the ether is the long-sought-for point of reference, the guide
to determine the motion of all bodies in the universe.
The Famous Experiment Performed by Prof. Michelson. If there is an
ether, and a stationary ether, and if the earth moves with reference to
this ether, the earth, in moving, must set up ether "currents"--just
as when a train moves it sets up air currents. So reasoned Michelson,
a young Annapolis graduate at the time. And forthwith he devised a
crucial experiment the explanation of which we can simplify by the
following analogy:
Which is the quicker, to swim up stream a certain length, say a
hundred yards, and back again, or across stream the same length and
back again? The swimmer will answer that the up-and-down journey is
longer. [7]
Our river is the ether. The earth, if moving in this ether, will
set up an ether stream, the up stream being parallel to the earth's
motion. Now suppose we send a beam of light a certain distance up
this ether stream and back, and note the time; and then turn the
beam of light at right angles and send it an equal distance across
the stream and back, and note the time. How will the time taken for
light to travel in these two directions compare? Reasoning by analogy,
the up-and-down stream should take longer.
Michelson's results did not accord with analogy. No difference in time
could be detected between the beam of light travelling up-and-down,
and across-and-back.
But this was contrary to all reason if the postulate of an ether was
sound. Must we then revise our ideas of an ether? Perhaps after all
there is no ether.
But if no ether, how are we to explain the propagation of light in
space, and various electrical phenomena connected with it, such as
the Hertzian, or wireless waves?
There was another alternative, one suggested by Larmor in England
and Lorentz in Holland,--that matter is contracted in the direction
of its motion through the ether current. To say that bodies are
actually shortened in the direction of their motion--by an amount
which increases as the velocity of these bodies approaches that of
light--is so revolutionary an idea that Larmor and Lorentz would
hardly have adopted such a viewpoint but for the fact that recent
investigations into the nature of matter gave basis for such belief.
Matter, it has been shown, is electrical in nature. The forces which
hold the particles together are electrical. Lorentz showed that
mathematical formulas for electrical forces could be developed which
would inevitably lead to the view that material bodies contract in
the direction of their motion. [8]
"But this is ridiculous," you say; "if I am shorter in one direction
than in another I would notice it." You would if some things were
shortened and others were not. But if all things pointing in a certain
direction are shortened to an equal extent, how are you going to notice
it? Will you apply the yard stick? That has been shortened. Will you
pass judgment with the help of your eyes? But your retina has also
contracted. In brief, if all things contract to the same amount it
is as if there were no contraction at all.
Lorentz's Plausible Explanation Really Deepens the Mystery. The
startling ideas just outlined have opened up several new vistas,
but they have left unanswered the two problems we set out to solve:
whether there is an ether, and if so, what is the velocity of the earth
in reference to this ether? Lorentz maintains that there is an ether,
but the velocities of bodies relative to it must forever remain a
mystery. As you change your position your distances change; you change;
everything about you changes accordingly; and all basis for comparison
is lost. Nature has entered into a conspiracy to keep you ignorant.
Einstein Comes upon the Scene. Einstein starts with the assumption
that there is no possible way of identifying this ether. Suppose we
ignore the ether altogether, what then? [9]
If we do ignore the ether we no longer have any absolute point of
reference; for if the ether is considered stationary the velocity of
all bodies within the ether may be referred to it; any point in space
may be considered a fixed point. If, however, there is no ether, or if
we are to ignore it, how are we to get the velocity of bodies in space?
The Principle of Relativity. If we are to believe in the "causal
relationship between only such things as lie within the realm of
observation," then observation teaches us that bodies move only
relative to one another, and that the idea of absolute motion of a
body in space is meaningless. Einstein, therefore, postulates that
there is no such thing as absolute motion, and that all we can discuss
is the relative motion of one body with respect to another. This
is just as logical a deduction from Michelson's experiment as the
attempt to explain Michelson's anomalous results in the light of an
all-pervading ether.
Consider for a moment Newton's scheme. This great pioneer pictured
an absolute standard of position in space relative to which all
velocities are measured. Velocities were measured by noting the
distance covered and dividing the result by the time taken to cover
the distance. Space was a definite entity; and so was time. "Time,"
said Newton, "flows evenly on," independent of aught else. To Newton
time and space were entirely different, in no way to be confounded.
Just as Newton conceived of absolute space, so he conceived of absolute
time. From the latter standard of reference the idea of a "simultaneity
of events" at different places arose. But now if there is no standard
of reference, if the ether does not exist or does not function, if
two points A and B cannot be referred to a third, and fixed point C,
how can we talk of "simultaneity of events" at A and B? [10]
In fact, Einstein shows that if all you can speak about is relative
motion, then one event which takes say one minute on one planet would
not take one minute on another. For consider two bodies in space,
say the planets Venus and the earth, with an observer B on Venus
and another A on the earth. B notes the time taken for a ray of
light to travel from B to the distance M. A on the earth has means
of observing the same event. B records one minute. A is puzzled,
for his watch records a little more than one minute. What is the
explanation? Granting that the two clocks register the same time
to start with, and assuming further Einstein's hypothesis that the
velocity of light is independent of its source, the difference in
time is due to the fact that the planet Venus moves with reference to
the observer on the earth; so that A in reality does not measure the
path BM and MB, but BM' and M'B', where BB' represents the distance
Venus itself has moved in the interval. And if you put yourself in B's
position on Venus the situation is exactly reversed. All of which is
simply another way of saying that what is a certain time on one body
in space is another time on another body in space. There is nothing
definite in time.
Prof. Cohen's Illustration. Further bewildering possibilities are
clearly outlined in this apt illustration: "If when you are going away
on a long and continuous journey you write home at regular intervals,
you should not be surprised that with the best possible mail service
your letters will reach home at progressively longer intervals,
since each letter will have a greater distance to travel than its
predecessor. If you were armed with instruments to hear the home
clock ticking, you would find that as your distance from home keeps
on increasing, the intervals between the successive ticks (that is,
its seconds) grow longer, so that if you travelled with the velocity
of sound the home clock would seem to slow down to a standstill--you
would never hear the next tick.
"Precisely the same is true if you substitute light rays for sound
waves. If with the naked eye or with a telescope you watch a clock
moving away from you, you will find that its minute hand takes a longer
time to cover its five-minute intervals than does the chronometer in
your hand, and if the clock travelled with the velocity of light you
would forever see the minute hand at precisely the same point. That
which is true of the clock is, of course, also true of all time
intervals which it measures, so that if you moved away from the earth
with the velocity of light everything on it would appear as still as
on a painted canvas."
Your time has apparently come to a standstill in one position and
is moving in another! All this seems absurd enough, but it does show
that time alone has little meaning.
Minkowski's Conclusion. The relativity theory requires that we
thoroughly reorganise our method of measuring time. But this is
intimately associated with our method of measuring space, the distance
between two points. As we proceed we find that space without time has
little meaning, and vice versa. This leads Minkowski to the conclusion
that "time by itself and space by itself are mere shadows; they are
only two aspects of a single and indivisible manner of coordinating
the facts of the physical world." Einstein incorporated this time-space
idea in his theory of relativity.
How We Measure a Point in Space. Suppose I say to you that the chemical
laboratory of Columbia University faces Broadway; would that locate
the laboratory? Hardly, for any building along Broadway would face
Broadway. But suppose I add that it is situated at Broadway and 117th
Street, south-east? there could be little doubt then. But if, further,
this laboratory would occupy but part of the building, say the third
floor; then the situation would be specified by naming Broadway,
117th Street S. E., third floor. If Broadway represents length, 117th
Street width, and third floor height, we can see what is meant when we
say that three dimensions are required to locate a position in space.
The Fourth Dimension. A point on a line may be located by one
dimension; a point on a wall requires two dimensions; a point in the
room, like the chemical laboratory above ground, needs three. The
layman cannot grasp the meaning of a fourth dimension; yet the
mathematician does imagine it, and plays with it in mathematical
terms. Minkowski and Einstein picture time as the fourth dimension. To
them time occupies no more important position than length, breadth,
or thickness, and is as intimately related to these three as the three
are to one another. H. G. Wells, the novelist, has beautifully caught
this spirit when in his novel, "The Time Machine," he makes his hero
travel backwards and forwards along time just as a man might go north
or south. When the man with his time machine goes forward he is in
the future; when he goes backwards he is in the past.
In reality, if we stop to think a minute, there is no valid
reason for the non-existence of a fourth dimension. If one, two
and three dimensions, why not four--and five and six, for that
matter? Theoretically at least there is no reason why the limit
should be set at three. However, our minds become sluggish when we
attempt to picture dimensions beyond three; just as an extraordinary
effort on our part is needed to follow Einstein when he "juggles"
with space and time.
Our difficulty in imagining four dimensions may be likened to the
difficulty two-dimensioned beings would experience in imagining
us, beings of the conventional three dimensions. Suppose these
two-dimensional beings were living on the surface of the earth;
what could they see? They could see nothing below and nothing above
the surface. They would see shifting surfaces as we walked about,
but being sensitive to length and breadth only, and not to height,
they could gain no notion whatsoever of what we really look like. It
is thus with us when we attempt to picture four-dimensional space.
Perhaps the analogy of the motion picture may help us somewhat. As
everybody knows, these motion pictures consist of a series of
photographs which are shown in rapid succession on the screen. Each
photograph by itself conveys a sensation of space, that is, of three
dimensions; but one photograph rapidly following another conveys
the sensation of space and time--four dimensions. Space and time
are interlinked.
The Time-space Idea Further Developed. We have already alluded to the
fact that objects in space moving with different velocities build up
different time intervals. Thus the velocity of the star Arcturus, if
compared with reference to the earth, moves at the rate of 200 miles a
second. Its motion through space is different from ours. Objects which,
according to Lorentz, contract in the direction of their motion to an
extent proportional to their velocity, will contract differently on
the surface of Arcturus than on the earth. Our space is not Arcturus'
space; neither is Arcturus' time our time. And what is true of the
discrepancies existing between the space and time conceptions of the
earth and Arcturus is true of any other two bodies in space moving
at different velocities.
But is there no relationship existing between the space and time
of one body in the universe as compared to the space and time of
another? Can we not find something which holds good for all bodies
in the universe? We can. We can express it mathematically. It is the
concept of time and space interlinked; of time as the fourth dimension,
length, breadth and thickness being the other three; of time as
one of four co-ordinates and at right angles to the other three
(a situation which requires a terrific stretch of the imagination
to visualize). The four dimensions are sufficient to co-ordinate
the time-space relationships of all bodies in the cosmos, and hence
have a universality which is totally lacking when time and space
are used independently of one another. The four components of our
time-space are up-and-down, right-and-left, backwards-and-forwards,
and sooner-and-later.
"Strain" and "Distortion" in Space. The four-dimensional unit has been
given the name "world-line," for the "world-line" of any particle in
space is in reality a complete history of that particle as it moves
about in space. Particles, we know, attract one another. If each
particle is represented by a world-line these world-lines will be
deflected from their course owing to such attraction.
Imagine a bladder representing the universe, with lines on it
representing world-lines. Now squeeze the bladder. The world-lines are
bent in various directions; they are "distorted." This illustrates the
influence of gravity on these world-lines; it is the "strain" brought
about due to the force of attraction. The distorted bladder illustrates
even more, for it is a true representation of the real world.
How Einstein's Conception of Time and Space Led to a New View of
Gravitation. In our conventional language we speak of the sun as
exerting a "force" on the earth. We have seen, however, that this
force brings about a "distortion" or "strain" in world-lines; or,
what amounts to the same thing, a "distortion" or "strain" of time
and space. The sun's "force," the "force" of any body in space, is the
"force" due to gravity; and these "forces" may now be treated in terms
of the laws of time and space. "The earth," Prof. Eddington tells us,
"moves in a curved orbit, not because the sun exerts any direct pull,
but because the earth is trying to find the shortest way through a
space and time which have been tangled up by an influence radiating
from the sun." [11]
At this point Newton's conceptions fail, for his views and his laws
do not include "strains" in space. Newton's law of gravitation must
be supplanted by one which does include such distortions. It is
Einstein's great glory to have supplied us with this new law.
Einstein's Law of Gravitation. This appears to be the only law
which meets all requirements. It includes Newton's law, and cannot be
distinguished from it if our experiments are confined to the earth and
deal with relatively small velocities. But when we betake ourselves
to some orbits in space, with a gravitational pull much greater than
the earth's, and when we deal with velocities comparable to that of
light, the differences become marked.
Einstein's Theory Scores Its First Great Victory. In the beginning
of this chapter we referred to the elaborate eclipse expedition sent
by the British to test the validity of Einstein's new theory of
gravitation. The British scientists would hardly have expended so
much time and energy on this theory of Einstein's but for the fact
that Einstein had already scored one great victory. What was it?
Imagine but a single planet revolving about the sun. According to
Newton's law of gravitation, the planet's path would be that of an
ellipse--that is, oval--and the planet would travel indefinitely along
this path. According to Einstein the path would also be elliptical,
but before a revolution would be quite completed, the planet would
start along a slightly advanced line, forming a new ellipse slightly in
advance of the first. The elliptic orbit slowly turns in the direction
in which the planet is moving. After many years--centuries--the orbit
will be in a different direction.
The rapidity of the orbit's change of direction depends on the velocity
of the planet. Mercury moving at the rate of 30 miles a second is the
fastest among the planets. It has the further advantage over Venus or
the earth in that its orbit, as we have said, is an ellipse, whereas
the orbits of Venus and the earth are nearly circular; and how are
you going to tell in which direction a circle is pointing?
Observation tells us that the orbit of Mercury is advancing at the
rate of 574 seconds (of arc) per century. We can calculate how much
of this is due to the gravitational influence of other planets. It
amounts to 532 seconds per century. What of the remaining 42 seconds?
You might be inclined to attribute this shortcoming to experimental
error. But when all such possibilities are allowed for our
mathematicians assure us that the discrepancy is 30 times greater
than any possible experimental error.
This discrepancy between theory and observation remained one
of the great puzzles in astronomy until Einstein cleared up the
mystery. According to Einstein's theory the mathematics of the
situation is simply this: in one revolution of the planet the orbit
will advance by a fraction of a revolution equal to three times the
square of the ratio of the velocity of the planet to the velocity
of light. When we allow mathematicians to work this out we get the
figure 43, which is certainly close enough to 42 to be called identical
with it.
Still Another Victory? Einstein's third prediction--the shifting of
spectral lines toward the red end of the spectrum in the case of light
coming to us from the stars of appreciable mass--seems to have been
confirmed recently (March, 1920). "The young physicists in Bonn,"
writes Prof. Einstein to a friend, "have now as good as certainty
(so gut wie sicher) proved the red displacement of the spectral lines
and have cleared up the grounds of a previous disappointment."
Summary. Velocity, or movement in space, is at the basis of Einstein's
work, as it was at the basis of Newton's. But time and space no
longer have the distinct meanings that they had when examined with
the help of Newton's equations. Time and space are not independent but
interdependent. They are meaningless when treated as separate entities,
giving results which may hold for one body in the universe but do not
hold for any other body. To get general laws which are applicable to
the cosmos as a whole the Fundamentals of Mechanics must be united.
Einstein's great achievement consists in applying this
revised conception of space and time to elucidate cosmical
problems. "World-lines," representing the progress of particles in
space, consisting of space-time combinations (the four dimensions),
are "strained" or "distorted" in space due to the attraction that
bodies exhibit for one another (the force of gravitation). On
the other hand, gravitation itself--more universal than anything
else in the universe--may be interpreted in terms of strains on
world-lines, or, what amounts to the same thing, strains of space-time
combinations. This brings gravitation within the field of Einstein's
conception of time and space.
That Einstein's conception of the universe is an improvement upon that
of Newton's is evidenced by the fact that Einstein's law explains all
that Newton's law does, and also other facts which Newton's law is
incapable of explaining. Among these may be mentioned the distortion
of the oval orbits of planets round the sun (confirmed in the case of
the planet Mercury), and the deviation of light rays in a gravitational
field (confirmed by the English Solar Eclipse Expedition).
Einstein's Theories and the Inferences to be Drawn from
Them. Einstein's theories, supported as they are by very convincing
experiments, will probably profoundly influence philosophic and
perhaps religious thought, but they can hardly be said to be of
immediate consequence to the man in the street. As I have said
elsewhere, Einstein's theories are not going to add one bushel of
wheat to war-torn and devastated Europe, but in their conception of
a cosmos decidedly at variance with anything yet conceived by any
school of philosophy, they will attract the universal attention of
thinking men in all countries. The scientist is immediately struck
by the way Einstein has utilized the various achievements in physics
and mathematics to build up a co-ordinated system showing connecting
links where heretofore none were perceived. The philosopher is equally
fascinated with a theory, which, in detail extremely complex, shows
a singular beauty of unity in design when viewed as a whole. The
revolutionary ideas propounded regarding time and space, the brilliant
way in which the most universal property of matter, gravitation,
is for the first time linked up with other properties of matter,
and, above all, the experimental confirmation of several of his
more startling predictions--always the finest test of scientific
merit--stamps Einstein as one of those super-men who from time to
time are sent to us to give us a peep into the beyond.
Some Facts about Einstein Himself. Albert Einstein was born in Germany
some 45 years ago. At first he was engaged at the Patent Bureau in
Berne, and later became professor at the Zürich Polytechnic. After
a short stay at Prague University he accepted one of those tempting
"Akademiker" professorships at the university of Berlin--professorships
which insure a comfortable income to the recipient of one of them,
little university work beyond, perhaps, one lecture a week, and
splendid facilities for research. A similar inducement enticed the
chemical philosopher, Van 't Hoff, to leave his Amsterdam, and the
Swedes came perilously near losing their most illustrious scientist,
Arrhenius.
Einstein published his first paper on relativity in 1905, when not
more than 30 years old. Of this paper Planck, the Nobel Laureate
in physics this year, has offered this opinion: "It surpasses in
boldness everything previously suggested in speculative natural
philosophy and even in the philosophical theories of knowledge. The
revolution introduced into the physical conceptions of the world is
only to be compared in extent and depth with that brought about by
the introduction of the Copernican system of the universe."
Einstein published a full exposition of the relativity theory in 1916.
During the momentous years of 1914-19, Einstein quietly pursued his
labors. There seems to be some foundation for the belief that the ways
of the German High Command found little favor in his eyes. At any
rate, he was not one of the forty professors who signed the famous
manifesto extolling Germany's aims. "We know for a fact," writes
Dr. O. A. Rankine, of the Imperial College of Science and Technology,
London, "that Einstein never was employed on war work. Whatever may
have been Germany's mistakes in other directions, she left her men
of science severely alone. In fact, they were encouraged to continue
in their normal occupations. Einstein undoubtedly received a large
measure of support from the Imperial Government, even when the German
armies were being driven back across Belgium."
Quite recently (June, 1920) the Barnard Medal of Columbia University
was conferred on him "in recognition of his highly original
and fruitful development of the fundamental concepts of physics
through application of mathematics." In acknowledging the honor,
Prof. Einstein wrote to President Butler that "... quite apart from
the personal satisfaction, I believe I may regard your decision [to
confer the medal upon him] as a harbinger of a better time in which
a sense of international solidarity will once more unite scholars of
the various countries."