EMERGENCE AND GRAVITATIONAL CONJECTURES

The behaviour of coherent structures emerging as outcome of a phase transition can be ruled by classical or by quantum laws. The latter circumstance depends in a critical way on the relative importance of quantum fluctuations which, in turn, depends on the numerical value of Planck's constant. In this paper we explore the consequences of the hypothesis according to which there are different kinds of Planck's constant, each one related to the kind of interaction entering into play in the specific phase transition. Within this 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, related to gravitational interactions. We feel this framework should be useful to describe cosmological phase transitions, such as galaxy and star formation, as well as the birth of black holes. According to our hypotheses, these emerging coherent structures should be ruled by suitable quantum laws (expressed, for instance, by a suitable kind of Schrödinger equation), including a "gravitational" Planck's constant. Even if the present paper deals with the particular case of gravitational interactions, it seems that its methodology could be useful even to study other kinds of emergent phenomena.