D O C . 5 8 K I N G ’ S C O L L E G E L E C T U R E 2 3 9
has upon the shape of bodies and upon the rate of clocks; also the equivalence of
energy and inertial mass.
The theory of general relativity owes its origin primarily to the experimental fact
of the numerical equality of inertial and gravitational mass of a body, a fundamental
fact for which classical mechanics has given no interpretation. Such interpretation
is obtained by extending the principle of relativity to inertial systems that are ac-
celerated relative to each other. The introduction of coordinate systems that are ac-
celerated relative to inertial systems causes the appearance of gravitational fields
relative to these coordinate systems. This is the reason why the theory of general
relativity, based upon the equality of inertia and gravity, also provides a theory of
the gravitational field.
The introduction of coordinate systems that are accelerated relative to each other
as equally admissible coordinate systems—as it is implied by the identity of inertia
and gravity—leads in combination with the results of the theory of special relativity
to the conclusion that the laws of positioning rigid bodies in the presence of gravi-
tational fields do not obey the laws of Euclidean geometry. An analogous result fol-
lows with respect to the rate of clocks. From this arises the need for a second gen-
eralization of the theory of space and time, because the immediate interpretation of
space and time coordinates as measurements with rods and clocks breaks down.
This generalization of metric—already worked out in the field of pure mathematics
by the researches of Gauss and Riemann—is essentially based upon the fact that
the metric of the theory of special relativity is still valid for the general case, pro-
vided it is confined to small domains.
The course of development that we described here deprives the space-time co-
ordinate system of all independent reality. Now the metric reality is only defined
when the space-time coordinates are combined with the mathematical quantities
that describe the gravitational field.
There is a second root to the basic ideas of the theory of general relativity. As
Ernst Mach has already emphasized, there is the following unsatisfying point in
Newton’s theory. When motion is not viewed from a causal but rather from a purely
descriptive point of view, then there is a relative
of things against each
other. But the acceleration in Newton’s laws of motion cannot be understood in the
concept of relative motion. This forced Newton to hypothetically imagine a physi-
cal space relative to which an acceleration should exist. This concept of absolute
space, introduced ad hoc, is admittedly logically correct, but it is not satisfying.
Therefore, Mach looks for a modification of the equations of mechanics such that
the inertia of bodies is not derived from their motion against absolute space but
rather against the totality of all the other gravitating bodies. Given the state of the
art as it existed then, his attempts had to fail.