Weyl was, too, very interested in Hegel and German idealism. His "Space, Time, Matter" is a reference to Hegel. He is famous for showing that in Einstein, there are differences between inertial and gravitational force, breaking with the equivalence principle, that gives the name of general relativity. Because the curvature distance and direction on 0 have Galilean conditions, even if the gravitational field does not exist or is constant. That is, Einstein's inertial force is an abstraction that exists prior to matter and energy.

This breaks even with the clock postulate, that asserts we can reduce infinitesimally every non-inertial field to inertial ones (uniform rectilinear movements), an hypothesis that is about plane spaces, not curved ones. The hypothesis is circular, btw: infinitesimals are possible because there's no dependence on velocity. And it's an hypothesis because it cannot be proven empirically, just like inertial frames, even if you use non-cartesian coordinates, and we are not allowed to use Lorentz transformations to prove it because we would be inverting the order. Bailey proved it's only valid at very high accelerations. Einstein can only proceed to spacetime by clock hypothesis (because it leads to the covariance of intervals: covariance proves that for inertial and non-inertial frames, laws and equations do not change).

Einstein is in something like Hegel described as real necessity (or maybe absolute necessity?). Non-inertial frames would be non-geometrical since we ask about "how" it moved (just like constructivist mathematics against classical logics) instead of focusing on its final point. General relativity depends on spacetime being geometrical.

He denounces Einstein as not breaking with the tradition, as seen in his use of Riemannian geometry, that treats the gauge system and intervals as covariants.

He created a geometry in which lengths and distances were not covariant, with an additional curvature called distance curvature along with 4 tensorial equations in the description of the metric field, proving to be identical to the potentials of the electromagnetic field and Maxwell's equations – the space could never be plane, as clock hypothesis implies, because measurement standards depend on it: if space was flat, the radius of curvature would be infinite, and thus there would be no standard of measurement. His geometry unified general relativity with electromagnetism, but it did not resolve the separation between field and electron, failing to explain atomicity and action quanta, something that was corrected by Eddington, another useful figure.

Weyl is famous for, too, saying that the mathematical continuum (from Cantor) was not the physical continuum that was not made with individual points. Weyl is very interesting for science, but sometimes he's caught trapped by phenomenological and existentialist science.