  Recent experiments on blinking quantum dots and weak turbulence in liquid
crystals reveal the fundamental connection between $1/f$ noise and power law
intermittency. The non-stationarity of the process implies that the power
spectrum is random -- a manifestation of weak ergodicity breaking. Here we
obtain the universal distribution of the power spectrum, which can be used to
identify intermittency as the source of the noise. We solve an outstanding
paradox on the non integrability of $1/f$ noise and the violation of Parseval's
theorem. We explain why there is no physical low frequency cutoff and therefore
cannot be found in experiments.
