Emergent Minkowski-like spaces of many-observers relational event universes

Abstract

This paper is devoted to the event-observational modelling in physics and more generally natural science. The basic entities of such modelling are events and where space-time is the secondary structure for representation of events. The novelty of our approach is in using new mathematical picture for events universe. The events recorded by an observer are described by a dendrogram, a finite tree. The event dynamics is realized in the dendrogramic configuration space. In a dendrogram all events are intercoupled via the hierarchic relational structure of the tree. This approach is called Dendrogramic Holographic Theory (DHT). We introduce the causal structure on the dendrogramic space, like the causal structure on the Minkowski space-time. In contrast to the latter, DHT-emergent causality is of the statistical nature. Each dendrogram represents an ensemble of observers with same relational tree-representation of the events they measured/collected. Technically the essence of the causal modelling is in encoding dendrograms by real parameters and in this way transition to the real space-time. Then we proceed in the framework of information geometry corresponding to Hellinger distance and introduce a kind of light-cone in the space of dendrograms. The real parameter spaces discovered in our numerical analysis, while related to an ensemble of observers, primarily represent purely observer-subjective and observer-dependent knowledge of an observer about the universe. In that sense these spaces are inherently subjective. This is a step towards development of DHT-analog special relativity.