The behaviour of coherent structures emerging as outcome of a phase transition can beruled by classical or by quantum laws. The latter circumstance depends in a critical wayon the relative importance of quantum fluctuations which, in turn, depends on thenumerical value of Planck's constant. In this paper we explore the consequences of thehypothesis according to which there are different kinds of Planck's constant, each onerelated to the kind of interaction entering into play in the specific phase transition. Withinthis paper we dealt with the simplest case, in which we have only two Planck's constants:the usual one, interpreted as related to electromagnetic interactions, and another, relatedto gravitational interactions. We feel this framework should be useful to describecosmological phase transitions, such as galaxy and star formation, as well as the birth ofblack holes. According to our hypotheses, these emerging coherent structures should beruled by suitable quantum laws (expressed, for instance, by a suitable kind ofSchrodinger equation), including a "gravitational" Planck's constant. Even if the presentpaper deals with the particular case of gravitational interactions, it seems that itsmethodology could be useful even to study other kinds of emergent phenomena.
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