Quantum field is overwhelmed by its phase factors as local gauge invariance. On the other hand, general relativity worries about what to do with its tetrads of tangent vector bundles inherited from local coordinate patches which main utility is to avoid breaking global symmetry (extremely difficult to verify by the homogeneity and isotropy of cosmological observations). Both do describe certain local rotational symmetries of gauge invariance. In the case of quantum field a complete circuit takes no time at all, and it’s clocking or timing is done by space-time parametrization of its relative phases. However, for gravitational field a cycle takes infinite time to complete, and its timing is done by constancy of light’s speed.
Although quantum mechanics successfully describes the quantized energy field (e.g. photon field), there is no theory that describes a quantized matter field even though, historically, the atomic structure of macroscopic matter came first (relative to microscopic elementary particles of high energy physics). As far as empirical verifications go, the quanta (bosons) of all interaction fields: graviton, photon, W±, Z0, and gluon are pure space-time points, so are the quanta of matter fields: the three fermions’ families of quarks and leptons.


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