We apply Dickes 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.
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