  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 the metric uniquely determines the symmetric linear connection, the homogeneous metric field (rest field) determines an integrable affine structure. Therefore, a flat Minkowski spacetime consistent with the complete absence of matter is endowed with an integrable connection and thus determines all (hypothetical) free motions. According to Weyl, there exists in the absence of matter a homogeneous metric field, a structural field (Strukturfeld), which has the character of a rest field, and which constitutes an all pervasive background that cannot be eliminated. The structure of this rest field determines the extension of the spacetime congruence relations and determines Lorentz invariance. The rest field possesses no net energy and makes no contribution to  curvature. 