The action of the Royal Society at its meeting in London on November
6, in recognizing Dr. Albert Einstein's "theory of relativity"
has caused a great stir in scientific circles on both sides of the
Atlantic. Dr. Einstein propounded his theory nearly fifteen years
ago. The present revival of interest in it is due to the remarkable
confirmation which it received in the report of the observations
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
astronomers 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 correspondent of the New York
Times at his home in Berlin. To this correspondent he expressed the
difference between his conception and the law of gravitation in the
following terms:
"Please imagine the earth removed, and in its place suspended a box as
big as a room or a whole house, and inside a man naturally floating
in the center, there being no force whatever pulling him. Imagine,
further, this box being, by a rope or other contrivance, suddenly
jerked to one side, which is scientifically 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 based on Newton's theory. Newton's
formulas, however, are such close approximations that it was difficult
to find by observation any obvious disagreement with experience."
Dr. Einstein, it must be remembered, is a physicist and not an
astronomer. He developed his theory 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. Observations
then proved that the rays of fixed stars, having to pass close to
the sun to reach the earth, were deflected the exact amount demanded
by Einstein's formulas. The deflection was also in the direction
predicted by him.
The question must have occurred to many, what has all this to do with
relativity? When this query was propounded by the Times correspondent
to Dr. Einstein he replied as follows:
"The term relativity refers to time and space. According to Galileo and
Newton, time and space were absolute entities, and the moving systems
of the universe were dependent on this absolute time and space. On
this conception was built the science of mechanics. The resulting
formulas sufficed for all motions of a slow nature; it was found,
however, that they would not conform to the rapid motions apparent
in electrodynamics.
"This led the Dutch professor, Lorentz, and myself to develop
the 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 electrodynamics, as well as
mechanics, hitherto irreducible by the old formulae--and there are
multitudes--were satisfactorily explained.
"Till now it was believed that time and space existed by themselves,
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 universe,
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 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 Norris
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 interest
and importance--is that the natural phenomena involving gravitation
and inertia (such as the motions of the planets) and the phenomena
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 perceptible only in a very few instances,
and then only to refined observations."
Already before the war, Einstein had immense 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 electro-magnetic, and had reduced
the whole theory of electro-magnetism to a small number of equations,
which are fundamental in all subsequent work. But these equations
were entangled with the hypothesis of the ether, and with the notion
of motion relative to the ether. Since the ether was supposed to be
at rest, such motion was indistinguishable 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
relativity succeeded in accounting for this fact. But it was necessary
incidentally to throw over the one universal time, and substitute
local times attached to moving bodies and varying according to their
motion. The equations on which the theory of relativity is based are
due to Lorentz, but Einstein connected them with his general principle,
namely, that there must be nothing, in observable phenomena, which
could be attributed to absolute motion of the observer.
In orthodox Newtonian dynamics the principle of relativity had a
simpler 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 velocities much less than that
of light. The whole Galileo-Newton system thus sank to the level
of a first approximation, becoming progressively less exact as the
velocities concerned approached that of light.
Einstein's extension of his principle 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 obtaining German printed matter. However, copies of his work
ultimately 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 without success. The immense unification effected by
electro-magnetism apparently left gravitation out of its scope. It
seemed that nature had presented a challenge to the physicists which
none of them were able to meet.
At this point Einstein intervened with a hypothesis which, apart
altogether 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-Euclidean 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 empirical 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
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
remote from matter, but that the presence 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 hypothesis, together with his previous theory of relativity, he
deduces gravitation--very approximately, but not exactly, according
to the Newtonian law of the inverse square. 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 discrepancy is fully accounted for by
Einstein. At the time when he published his theory, this was its only
experimental verification.
(2) Modern physicists were willing 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 deflected according
to the orthodox theory of gravitation. But Einstein'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. Fortunately a peculiarly favourable eclipse occurred
last year. The results of the observations have now been published,
and are found to verify Einstein'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 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 theory,
and that the observed deflection is slightly larger than Einstein
predicted. The discrepancy is well within what might be expected in
view of the minuteness of the measurements. It is therefore generally
acknowledged by astronomers that the outcome is a triumph for Einstein.
(3) In the excitement of this sensational verification, there has
been a tendency to overlook the third experimental 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 effect has
been discovered. Spectroscopists 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 discovered to explain the discrepancy, but
they think it far more probable that Einstein's theory requires some
essential 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 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
intellectual unity which belonged to the great scientific systems of
the seventeenth 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 interested in physics there are great compensations.