8 0 D O C . 7 5 N O B E L L E C T U R E

And that exhausts the direct consequences of the relativity principle. I now turn

to the problems attached to the development sketched. Already Newton recognized

that the law of inertia was unsatisfactory in a way as yet unmentioned in this expo-

sition, namely it offers no real cause for the special place physics of the states of

motion of inertial frames as compared to all other states of motion. It makes ob-

servable material bodies responsible for the gravitational behavior of a material

point, yet it does not indicate any material cause for the inertial behavior of the ma-

terial point, but offers only a fictitious cause for it (absolute space, resp., the inertial

ether). This is not logically inadmissible, but it is unsatisfactory. For this reason E.

Mach called for a modification of the law of inertia so that inertia would be con-

ceived as resistance to acceleration by bodies against one another and not against

“space.”[6]

This interpretation brings about the expectation that accelerated bodies

have concordant accelerating action on other bodies (acceleration induction).

This interpretation is even more plausible according to general relativity, which

eliminates the separation between inertial and gravitational effects. It boils down to

the stipulation that, apart from the arbitrariness due to the free choice of coordi-

nates, the -field be completely determined by matter. Yet another factor speak-

ing in favor of the Machian stipulation in general relativity is that acceleration in-

duction does indeed exist according to the gravitational field equations; even

though the effect is so small that direct detection by mechanical experiments is out

of the question.

One can do justice to the Machian stipulation in the general theory of relativity

by considering the universe as spatially finite and closed. This hypothesis also

makes it possible to assume the mean density of matter in the universe as finite,

whereas it would have to vanish in a spatially infinite (quasi-Euclidean) world. It

must not be left unsaid, though, that for the suggested fulfillment of the Machian

postulate, a term must be introduced into the field equations that is not based on

any experience; nor is it logically called for in any way by the other terms of the

equations. For this reason the suggested solution to the “cosmological problem” is

not entirely satisfactory at

present.[7]

A second problem that currently preoccupies minds particularly keenly is the es-

sential unity of the gravitational field and the electromagnetic field. A mind seek-

ing unity within the theory cannot be content with the existence of two, in essence

entirely independent fields. A mathematically unitary field theory is sought in

which the gravitational field and the electromagnetic field are conceived as merely

different components or forms of appearance of the same unitary field, and where

the field equations may not consist of logically independent summands anymore.

The theory of gravitation—that is, viewed from the standpoint of mathematical

formalism, Riemannian geometry—shall be generalized in such a way as to include

[p. 8]

gμν

[p. 9]