(The London Times, November 28)
I GLADLY accede to the request of your colleague to write something
for The Times on relativity. After the lamentable breakdown of the old active intercourse between men of learning, I welcome this opportunity of expressing my feelings of joy and gratitude toward the astronomers and physicists of England. It is thoroughly in keeping with the great and proud traditions of scientific work in your country that eminent scientists should have spent much time and trouble, and your scientific institutions have spared no expense, to test the
implications of a theory which was perfected and published during the
war in the land of your enemies. Even though the investigation of the
influence of the gravitational field of the sun on light rays is a
purely objective matter, I cannot forbear to express my personal
thanks to my English colleagues for their work; for without it I could
hardly have lived to see the most important implication of my theory
We can distinguish various kinds of theories in physics. Most of them
are constructive. They attempt to build up a picture of the more
complex phenomena out of the materials of a relatively simple formal scheme from which they start out. Thus the kinetic theory of gases seeks to reduce mechanical, thermal, and diffusional processes to movements of molecules — i.e., to build them up out of the hypothesis of molecular motion. When we say that we have succeeded in understanding a group of natural processes, we invariably mean that a constructive theory has been found which covers the processes in question.
Along with this most important class of theories there exists a second, which I will call “principle-theories.” These employ the analytic, not the synthetic, method. The elements which form their
basis and starting-point are not hypothetically constructed but empirically diseovered ones, general characteristics of natural processes, principles that give rise to mathematically formulated criteria which the separate processes or the theoretical representations of them have to satisfy. Thus the science of thermodynamics seeks by analytical means to deduce necessary
conditions, which separate events have to satisfy, from the universally experienced fact that perpetual motion is impossible.
The advantages of the constructive theory are completeness,
adaptability, and clearness, those of the principle theory are logical
perfection and security of the foundations.
The theory of relativity belongs to the latter class. In order to
grasp its nature, one needs first of all to become acquainted with the
principles on which it is based. Before I go into these, however, I
must observe that the theory of relativity resembles a building
consisting of two separate stories, the special theory and the general
theory. The special theory, on which the general theory rests, applies
to all physical phenomena with the exception of gravitation; the
general theory provides the law of gravitation and its relations to
the other forces of nature.
It has, of course, been known since the days of the ancient Greeks
that in order to describe the movement of a body, a second body is
needed to which the movement of the first is referred. The movement of a vehicle is considered in reference to the earth’s surface, that of a planet to the totality of the visible fixed stars. In physics the body to which events are spatially referred is called the coordinate system. The laws of the mechanics of Galileo and Newton, for instance, can only be formulated with the aid of a coordinate system.
The state of motion of the coordinate system may not, however, be
arbitrarily chosen, if the laws of mechanics are to be valid (it must
be free from rotation and acceleration). A coordinate system which is
admitted in mechanics is called an “inertial system.” The state of
motion of an inertial system is according to mechanics not one that is
determined uniquely by nature. On the contrary, the following
definition holds good: a coordinate system that is moved uniformly and in a straight line relative to an inertial system is likewise an
inertial system. By the “special principle of relativity” is meant the generalization of this definition to include any natural event whatever: thus, every universal law of nature which is valid in relation to a coordinate system C, must also be valid, as it stands, in relation to a coordinate system C’, which is in uniform translatory motion
relatively to C.
The second principle, on which the special theory of relativity rests,
is the “principle of the constant velocity of light in vacuo.” This
principle asserts that light in vacuo always has a definite velocity
of propagation (independent of the state of motion of thc observer or
of the source of the light). The confidence which physicists place in
this principle springs from the successes achieved by the
electrodynamics of Maxwell and Lorentz.
Both the above-mentioned principles are powerfully supported by
experience, but appear not to be logically reconcilable. The special
theory of relativity finally succeeded in reconciling them logically
by a modification of kinematics — i.e., of the doctrine of the laws
relating to space and time (from the point of view of physics). It
became clear that to speak of the simultaneity of two events had no
meaning except in relation to a given coordinate system, and that the
shape of measuring devices and the speed at which clocks move depend
on their state of motion with respect to the coordinate system.
But the old physics, including the laws of motion of Galileo and
Newton, did not fit in with the suggested relativist kinematics. From
the latter, general mathematical conditions issued, to which natural
laws had to conform, if the above-mentioned two principles were really
to apply. To these, physics had to be adapted. In particular,
scientists arrived at a new law of motion for (rapidly moving) mass
points, which was admirably confirmed in the case of electrically
charged particles. The most important upshot of the special theory of
relativity concerned the inert masses of corporeal systems. It turned
out that the inertia of a system necessarily depends on its
energy-content, and this led straight to the notion that inert mass is
simply latent energy. The principle of the conservation of mass lost
its independence and became fused with that of the conservation of
The special theory of relativity, which was simply a systematic
development of the electrodynamics of Maxwell and Lorentz, pointed
beyond itself, however. Should the independence of physical laws of
the state of motion of the coordinate system be restricted to the
uniform translatory motion of coordinate systems in respect to each
other? What has nature to do with our coordinate systems and their
state of motion? If it is nccessary for the purpose of describing
nature, to make use of a coordinate system arbitrarily introduced by
us, then the choice of its state of motion ought to be subject to no
restriction; the laws ought to be entirely independent of this choice
(general principle of relativity).
The establishment of this general principle of relativity is made
easier by a fact of experience that has long been known, namely, that the weight and the inertia of a body are controlled by the same
constant (equality of inertial and gravitational mass). Imagine a
coordinate system which is rotating uniformly with respect to an
inertial system in the Newtonian manner. The centrifugal forces which manifest themselves in relation to this system must, according to Newton’s teaching, be regarded as effects of inertia. But these centrifugal forces are, exactly like the forces of gravity, proportional to the masses of the bodies. Ought it not to be possible in this case to regard the coordinate system as stationary and the centrifugal forces as gravitational forces? This seems the obvious view, but classical mechanics forbid it.
This hasty consideration suggests that a general theory of relativity
must supply the laws of gravitation, and the consistent following up
of the idea has justified our hopes.
But the path was thornier than one might suppose, because it demanded the abandonment of Euclidean geometry. This is to say, the laws according to which solid bodies may be arranged in space do not completely accord with the spatial laws attributed to bodies by
Euclidean geometry. This is what we mean when we talk of the
“curvature of space.” The fundamental concepts of the “straight line,”
the “plane,” etc., thereby lose their precise significance in physics.
In the general theory of relativity the doctrine of space and time, or
kinematics, no longer figures as a fundamental independent of the rest of physics. The geometrical behaviour of bodies and the motion of clocks rather depend on gravitational fields, which in their turn are
produced by matter.
The new theory of gravitation diverges considerably, as regards
principles, from Newton’s theory. But its practical results agree so
nearly with those of Newton’s theory that it is difficult to find criteria for distinguishing them which are accessible to experience.
Such have been discovered so far:
1. In the revolution of the ellipses of the planetary orbits round
the sun (confirmed in the case of Mercury).
2. In the curving of light rays by the action of gravitational fields
(confirmed by the English photography of eclipses).
3. In a displacement of the spectral lines toward the red end of the
spectrum in the case of light transmitted to us from stars of
considerable magnitude (unconfirmed so far). *
The chief attraction of the theory lies in its logical completeness.
If a single one of the conclusions drawn from it proves wrong, it must
be given up; to modify it without destroying the whole structure seems to be impossible.
Let no one suppose, however, that the mighty work of Newton can really be superseded by this or any other theory. His great and lucid ideas will retain their unique significance for all time as the foundation of our whole modern conceptual structure in the sphere of natural philosophy.
Note: Some of the statements in your paper concerning my life and
person owe their origin to the lively imagination of the writer. Here
is yet another application of the principle of relativity for the
delectation of the reader: today I am described in Germany as a
“German savant,” and in England as a “Swiss Jew.” Should it ever be my fate to be represented as a bête noire, I should, on the contrary,
become a “Swiss Jew” for the Germans and a “German savant” for the English.
* this criterion has since been confirmed