D O C . 7 5 N O B E L L E C T U R E 7 9
able by measuring rods and clocks. These quantities , however, also describe
the gravitational field with respect to the Gaussian coordinate system, whose essen-
tial unity with the physical cause of the metric we have established earlier. The case
as to the validity of the special theory of relativity for finite regions is characterized
by the ’s being independent of the ’s for finite regions, given a suitable
choice of coordinate system.
According to the general theory of relativity, the law of point motion within a
pure gravitational field is expressed by the equation for the geodesic line. In fact,
the geodesic line is the mathematically simplest line, and turns into a straight line
in the special case of constant ’s. Here we thus have before us the translation
of Galileo’s law of inertia into the general theory of relativity.
Mathematically, the search for the field equations comes down to the question
of the simplest generally covariant differential equations to which the gravitational
potentials can be subjected. These equations are determined by the demand
for them not to contain derivatives of the with respect to the beyond second
order, and to depend on them only linearly. This condition makes these equations
appear to be a coherent translation of the Poisson field equation of Newtonian grav-
itation theory into the general theory of relativity.
The indicated considerations led to the theory of gravitation, which yields New-
tonian theory to first approximation and, furthermore, yields the motion of Mercu-
ry’s perihelion, light deflection by the Sun, and the redshift of spectral lines in
agreement with
experience.2)
In order to complete the basis of the general theory of relativity, the electromag-
netic field still has to be introduced, which according to our present views also pro-
vides the material from which we have to construct the elementary structure of mat-
ter. It is also easily possible to translate the Maxwell field equations into the general
theory of relativity. This translation is an entirely unambiguous one if one merely
assumes that the equations do not contain differential quotients of the ’s of
higher than first order. and that they take the usual Maxwellian form in the local
inertial frame. It is also easy to supplement the gravitational field equations with
electromagnetic terms in a manner prescribed by the Maxwell equations so that
they contain the gravitating effect of the electromagnetic field.
These field equations did not deliver a theory of matter. In order to incorporate
into the theory the field-producing effect of ponderable masses, it was therefore
necessary (as in classical physics) to introduce matter into the theory in an approx-
imative, phenomenological representation.
2)
As regards redshift, however, the agreement with experience is not yet entirely
secured.[5]
gμν
gμν xν
[p. 7]
gμν
gμν
gμν xν
gμν