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):
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]
gμνdxμdxν 0 = =
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