  Riemann’s ideas were brought to a concrete realization fifty years  later in Einstein’s general theory of relativity. The basic idea  underlying the general theory of relativity was Einstein’s  recognition that the metric field, which has such powerful real  effects on matter, cannot be a rigid once and for all given geometric structure of the spacetime, but must itself be something real, that  not only has effects on matter, but is in turn also affected by  matter. Riemann had already suggested that analogous to the  electromagnetic field, the metric field reciprocally interacts with  matter. Einstein came to this idea of reciprocity between matter and  field independently of Riemann, and in the context of his theory of  general relativity, applied this principle of reciprocity to four  dimensional spacetime. Thus Einstein could adopt Riemann’s  infinitesimal geometry with the important difference: given the  causal requirements of Einstein’s theory of special relativity,  Riemann’s quadratic form is not positive definite but indefinite; it  has signature   1.[37]  Weyl (1922a) says: 