There are several kinds of theory in physics. Most of them are
constructive. These attempt to build a picture of complex phenomena out
of some relatively simple proposition. The kinetic theory of gases,
for instance, attempts to refer to molecular movement the mechanical
thermal, and diffusional properties of gases. When we say that we
understand a group of natural phenomena, we mean that we have found
a constructive theory which embraces them.
Theories of Principle.--But in addition to this most weighty group of
theories, there is another group consisting of what I call theories of
principle. These employ the analytic, not the synthetic method. Their
starting-point and foundation are not hypothetical constituents, but
empirically observed general properties of phenomena, principles from
which mathematical formulæ are deduced of such a kind that they apply
to every case which presents itself. Thermodynamics, for instance,
starting from the fact that perpetual motion never occurs in ordinary
experience, attempts to deduce from this, by analytic processes,
a theory which will apply in every case. The merit of constructive
theories is their comprehensiveness, adaptability, and clarity,
that of the theories of principle, their logical perfection, and the
security of their foundation.
The theory of relativity is a theory of principle. To understand it,
the principles on which it rests must be grasped. But before stating
these it is necessary to point out that the theory of relativity is
like a house with two separate stories, the special relativity theory
and the general theory of relativity.
Since the time of the ancient Greeks it has been well known that in
describing the motion of a body we must refer to another body. The
motion of a railway train is described with reference to the ground,
of a planet with reference to the total assemblage of visible fixed
stars. In physics the bodies to which motions are spatially referred
are termed systems of coordinates. The laws of mechanics of Galileo
and Newton can be formulated only by using a system of coordinates.
The state of motion of a system of coordinates can not be chosen
arbitrarily if the laws of mechanics are to hold good (it must be
free from twisting and from acceleration). The system of coordinates
employed in mechanics is called an inertia-system. The state of
motion of an inertia-system, so far as mechanics are concerned,
is not restricted by nature to one condition. The condition in the
following proposition suffices; a system of coordinates moving in the
same direction and at the same rate as a system of inertia is itself
a system of inertia. The special relativity theory is therefore the
application of the following proposition to any natural process:
"Every law of nature which holds good with respect to a coordinate
system K must also hold good for any other system K' provided that
K and K' are in uniform movement of translation."
The second principle on which the special relativity theory rests is
that of the constancy of the velocity of light in a vacuum. Light
in a vacuum has a definite and constant velocity, independent of
the velocity of its source. Physicists owe their confidence in this
proposition to the Maxwell-Lorentz theory of electro-dynamics.
The two principles which I have mentioned have received strong
experimental confirmation, but do not seem to be logically
compatible. The special relativity theory achieved their logical
reconciliation by making a change in kinematics, that is to say,
in the doctrine of the physical laws of space and time. It became
evident that a statement of the coincidence of two events could have
a meaning only in connection with a system of coordinates, that the
mass of bodies and the rate of movement of clocks must depend on
their state of motion with regard to the coordinates.
The Older Physics.--But the older physics, including the laws of
motion of Galileo and Newton, clashed with the relativistic kinematics
that I have indicated. The latter gave origin to certain generalized
mathematical conditions with which the laws of nature would have to
conform if the two fundamental principles were compatible. Physics had
to be modified. The most notable change was a new law of motion for
(very rapidly) moving mass-points, and this soon came to be verified
in the case of electrically-laden particles. The most important result
of the special relativity system concerned the inert mass of a material
system. It became evident that the inertia of such a system must depend
on its energy-content, so that we were driven to the conception that
inert mass was nothing else than latent energy. The doctrine of the
conservation of mass lost its independence and became merged in the
doctrine of conservation of energy.
The special relativity theory which was simply a systematic extension
of the electro-dynamics of Maxwell and Lorentz, had consequences which
reached beyond itself. Must the independence of physical laws with
regard to a system of coordinates be limited to systems of coordinates
in uniform movement of translation with regard to one another? What has
nature to do with the coordinate systems that we propose and with their
motions? Although it may be necessary for our descriptions of nature
to employ systems of coordinates that we have selected arbitrarily,
the choice should not be limited in any way so far as their state of
motion is concerned. (General theory of relativity.) The application
of this general theory of relativity was found to be in conflict
with a well-known experiment, according to which it appeared that
the weight and the inertia of a body depended on the same constants
(identity of inert and heavy masses). Consider the case of a system of
coordinates which is conceived as being in stable rotation relative
to a system of inertia in the Newtonian sense. The forces which,
relatively to this system, are centrifugal must, in the Newtonian
sense, be attributed to inertia. But these centrifugal forces are,
like gravitation, proportional to the mass of the bodies. Is it not,
then, possible to regard the system of coordinates as at rest, and
the centrifugal forces as gravitational? The interpretation seemed
obvious, but classical mechanics forbade it.
This slight sketch indicates how a generalized theory of relativity
must include the laws of gravitation, and actual pursuit of the
conception has justified the hope. But the way was harder than
was expected, because it contradicted Euclidian geometry. In other
words, the laws according to which material bodies are arranged in
space do not exactly agree with the laws of space prescribed by the
Euclidian geometry of solids. This is what is meant by the phrase
"a warp in space." The fundamental concepts "straight," "plane,"
etc., accordingly lose their exact meaning in physics.
In the generalized theory of relativity, the doctrine of space and
time, kinematics, is no longer one of the absolute foundations of
general physics. The geometrical states of bodies and the rates
of clocks depend in the first place on their gravitational fields,
which again are produced by the material system concerned.
Thus the new theory of gravitation diverges widely from that of Newton
with respect to its basal principle. But in practical application
the two agree so closely that it has been difficult to find cases in
which the actual differences could be subjected to observation. As
yet only the following have been suggested:
1. The distortion of the oval orbits of planets round the sun
(confirmed in the case of the planet Mercury).
2. The deviation of light-rays in a gravitational field (confirmed
by the English Solar Eclipse expedition).
3. The shifting of spectral lines towards the red end of the spectrum
in the case of light coming to us from stars of appreciable mass
(not yet confirmed).
The great attraction of the theory is its logical consistency. If
any deduction from it should prove untenable, it must be given up. A
modification of it seems impossible without destruction of the whole.
No one must think that Newton's great creation can be overthrown in
any real sense by this or by any other theory. His clear and wide
ideas will for ever retain their significance as the foundation on
which our modern conceptions of physics have been built.