Editorial note to: H. Weyl, On the general relativity theory

On the general relativity theory

In Appendix III of the fifth edition of his book Space, Time, Matter [15] henceforth cited as W (which has not been translated into English), Hermann Weyl derived for the first time, motivated by cosmological considerations, the general frequency shift formula for sources and observers moving arbitrarily in a general spacetime. In his discussion of cosmology (W, 39) he argued for a non-stationa...

Eigenvalues of the Weyl Operator as Observables of General Relativity

We consider the eigenvalues of the three-dimensional Weyl operator defined in terms of the (Euclidean) Ashtekar variables, and we study their dependence on the gravitational field. We notice that these eigenvalues can be used as gravitational variables, and derive explicit formulas for their Poisson brackets and their time evolution. P.A.C.S. number:+04.20,04.90 On leave from Dipartimento di Fi...

Some Remarks on Mathematical General Relativity Theory

This paper gives a brief survey of the development of general relativity theory starting from Newtonian theory and Euclidean geometry and proceeding through to special relativity and finally to general relativity and relativistic cosmology.

Einstein’s General Theory of Relativity

Measurement Theory and General Relativity

The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational and rotational) scales characteristic of the motion of the observer. Thus general relativity is a consistent theory of coincidences so long as these involve...