2 2 4 D O C . 5 4 A D D I T I O N T O G E N E R A L R E L A T I V I T Y

54. “On a Natural Addition to the Foundation

of the General Theory of Relativity”

[Einstein 1921e]

Submitted 3 March 1921

Published 17 March 1921

In: Königlich Preußische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1921):

261–264.

It is well known that H. Weyl tried to supplement the general theory of relativity

by adding a further condition of invariance. He arrived at a theory which deserves

high regard due to its consequential and daring mathematical structure. The theory

is essentially based on two ideas.

a. The ratios of components of the gravitational potential have a far more

fundamental physical meaning than the components themselves. The totality

of the world directions issuing from a world point in which light signals can be

emitted by it, i.e., the light cone, seems to be given directly with the space-time con-

tinuum. This light cone, however, is determined by the equation

into which only the ratios of the enter. Into the electromagnetic equations of

the vacuum too, only the ratios of the enter. In contrast, the quantity ds, which

is determined by the themselves, does not represent a property of the space-

time continuum because its quantitative measurement requires a material object

(clock). This suggests the question: Can the theory of relativity be modified by the

assumption that not the quantity ds itself, but only the equation has an in-

variant meaning?

b. Weyl’s second idea is related to the method of generalization of the

Riemannian metric and to the physical interpretation of the newly arising quantities

in it. The idea can be sketched as follows: metric requires the transfer of lengths

[p. 261]

[1]

gμν

gμν

ds2

gμνdxμdxν 0 = =

gμν

gμν

gμν

ds2=

0,

[2]

φν