Electromagnetic and gravitational radiation from massless particles

We demonstrate that full description of both electromagnetic and gravitational radiation from massless particles lies outside the scope of classical theory. Synchrotron radiation from the hypothetical massless charge in quantum electrodynamics in external magnetic field has finite total power while the corresponding classical formula diverges in the massless limit. We argue that in both cases classical theory describes correctly only the low-frequency part of the spectra, while the total power diverges because of absence of the UV frequency cutoff. Failure of description of gravitational radiation from massless particles by classical General Relativity may be considered as another appeal for quantization of gravity apart from the problem of singularities.