According to Weyl, the metric field does not cease to exist in a world devoid of matter but is in a state of rest: As a rest field it would possess the property of metric homogeneity; the mutual orientations of the orthogonal groups characterizing the Pythagorean-Riemannian nature of the metric everywhere would not differ from point to point. This means that in a matter-empty universe the metric is fixed. Consequently, the set of congruence relations on spacetime is uniquely determined. Since th