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

motion[6]

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.

[p. 3]

[p. 4]