  We apply Dicke's theory of superradiance introduced in 1954 to the methanol
6.7 GHz and water 22 GHz spectral lines, often detected in molecular clouds as
signposts for the early stages of the star formation process. We suggest that
superradiance, characterized by burst-like features taking place over a wide
range of time-scales, may provide a natural explanation for the recent
observations of periodic and seemingly alternating methanol and water maser
flares in G107.298+5.639. Although these observations would be very difficult
to explain within the context of maser theory, we show that these flares may
result from simultaneously initiated 6.7-GHz methanol and 22-GHz water
superradiant bursts operating on different time-scales, thus providing a
natural mechanism for their observed durations and time ordering. The evidence
of superradiance in this source further suggests the existence of entangled
quantum mechanical states, involving a very large number of molecules, over
distances up to a few kilometres in the interstellar medium.
