D O C . 3 1 I D E A S A N D M E T H O D S 1 3 9

attribute to space any 〈independent〉 mechanically distinct properties but rather, in

principle, accepted all coordinate systems as equal. According to this interpreta-

tion, inertia also was an interaction between bodies just as is the case in Newtonian

gravitation. It is true that this idea did not yet point to a rigorous (quantitative) treat-

ment of the problem, and in essence the natural equality between inertia and grav-

itation—as laid out earlier (hypothesis of

equivalence)[41]—remained

hidden to

Mach. But he was (after Newton) the first to vividly feel and clearly illuminate the

epistemological weakness of classical mechanics.

It should by no means be claimed that the basically unsubstantiated preference

of inertial systems over other coordinate systems constitutes an error of classical

mechanics. The preference of certain sates of motion (namely, of inertial systems)

in nature could be a final fact that we have to accept without being able to explain

it (or reduce it to some cause). However, a theory in which all states of motion of

coordinate systems are—in principle—equal has to be appreciated from an episte-

mological point of view as being far more satisfying. For the following consider-

ation we want to use this equivalence as a basis under the name of “general

〈postulate〉 principle of

relativity.”[42]

17. Some Consequences of the Equivalence Hypothesis

We consider a space-time domain in which, under suitable choice of the coordinate

system , there is no gravitational field (relative to ); thus, is an inertial sys-

tem in the sense of classical mechanics. The laws valid in reference to , e.g., the

law of the propagation of light, can then be viewed as known. Now we introduce

besides a second coordinate system that is accelerated relative to . There

then is a gravitational field relative to due to the equivalence hypothesis. Since

it is possible to establish the course of natural processes in reference to by a

mere transformation from to , one learns from this procedure what type of

effect the gravitational field relative to has upon the natural processes under

consideration.

A vacuum light ray proceeds rectilinearly and uniformly relative to with ve-

locity . A simple, geometric consideration shows that this same light ray has a

curvature relative to as soon as the light ray forms an angle with the direction

of acceleration of the system. The gravitational force bends the light ray as if light

were a catapulted heavy body.

This consequence is of great significance in a twofold way. First, it provides a

criterion for the theory that is accessible to observation. Because , a simple calcu-

[p. 24]

K K K

K

K K′ K

K′

K′

K K′

K′

K

c

K′

[p. 25]