Motivated by the Immirzi ambiguity in loop quantum gravity and the near conformal invariance of the standard model of elementary particles, Charles Wang and co-workers have argued that the problem of time may be related to an underlying scale invariance of gravity-matter systems. Scale invariance has also been proposed to resolve the hierarchy problem of fundamental couplings. As a global continuous symmetry, scale invariance generates a conversed Weyl current according to Noether’s theorem. In scale-invariant cosmological models, this Weyl current naturally gives rise to a harmonic time. In the context of loop quantum gravity, Charles Wang et al. suggest that scale invariance may lead to the existence of a quantized time.