Fact-nets: towards a mathematical framework for relational quantum mechanics

Abstract

The relational interpretation of quantum mechanics (RQM) has received a growing interest since its first formulation in 1996. Usually presented as an interpretational layer over the usual quantum mechanics formalism, it is often seen as a philosophical perspective without proper mathematical counterparts. This state of affairs has direct consequences on the scientific debate on RQM which still suffers from misunderstandings and imprecise statements. In an attempt to clarify those debates, the present paper proposes a radical reformulation of the mathematical framework of quantum mechanics which is relational from the start: fact-nets. The core idea is that all statements about the world, facts, are binary entities involving two systems that can be symmetrically thought of as observed and observer. We initiate a study of the fact-nets formalism and outline how it can shed new relational light on some familiar quantum features.

A Testable Theory for the Emergence of the Classical World

“…The emergence of these ‘ever more stable facts’ drives the symmetry breaking toward one among the 2 N bases is chosen. Following the relational quantum mechanics framework (RQM) suggested first by Rovelli, and developed over decades [ 3 , 4 , 5 , 6 ], we are to consider unstable relative facts of one variable, which need to be labelled against at least one other variable in the system from whose perspective such facts are actualized. However, there are also stable facts, each of which does not require such labelling, and appear to some other variables in the systems (or ‘observers’) as an invariant fact.…”