Does the radioactive decay obey the Poisson statistics ?

It is shown that a nontrivial quantum structure of our space at macroscopic scales, which may exist as a relic of quantum gravity processes in the early universe, gives rise to a new fundamental phenomenon: spontaneous origin of an interference picture in every physical process. This explains why statistical distributions in radioactivity measurements may be different from the Poisson distribution. In this letter I would like to draw attention to the strange phenomenon which was claimed to be observed in radioactivity measurements [1]. The phenomenon pointed out represents the fact that an instant shape of the probability density distribution for the number of fissions, which should obey the conventional Poisson distribution, apparently exhibits the existence of a fine structure. Presumably, this structure evolves and disappears after averaging over some period of time. The last fact would explain why it is difficult to observe this structure in consecutive measurements (as in the case of radioactive decay) and why in Ref. [1] it was used a rather nonstandard procedure to analyze measurement data. The oddity (from the modern physics standpoint) of such a phenomenon causes strong doubts in the existence of the effect itself and makes people 1 The claims of Ref. [1] are more ambitious. However, from our point of view the most important fact, which can be extracted from this work, is the possible violation of the Poisson statistics.