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French

ID: <

10670/1.o1zkh0

>

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Introduction to a relational approach to probability. Study of examples

Abstract

summary of a text in writing We propose a relational approach to the concept of probability: the probabilistic model built about such a series of events, which we describe as ‘apparent’, is built in opposition to, or in composition with, another probabilistic model, concerning a set of ‘hidden’ events; they serve as a gauge and their law is uniform (the probabilities of their different events are equal). Both views can be exchanged, based on the initial events of the non-uniform probability model to define the gauge: they are given a uniform law and, by comparison, new measures are defined for the initially uniform hidden model. We speak of the dual formulation of the problem, as opposed to its original original formulation. For random variables of normalised values between 0 and 1, the distribution functions of the two laws, corresponding to each of the two formulations, shall be symmetrical to each other in relation to the first bissector; this corresponds, in the continuous case, to inverted probability densities of each other. One of our reasons is to describe in probabilistic terms the physical phenomena showing quotations, in the sense of discontinuities or breaks in the quantities studied (the sauts correspond to very low probability intervals). We are interested in such phenomena when described by equations with partial derivatives in relation to space and time variables. By exchange with physical quantities, space and time variables can be quantified. In this way, we reread the probabilistic approach to quantum mechanics and show how quantifications of the spatial and temporal variables themselves can be identified (this is required to link general and quantum mechanics). At this stage of our work, we do not provide a rigorous or complete axiomatic of our proposals; we are presenting ideas, illustrated by small examples, for further work.

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