Exploring the causal Minkowski-like spaces of observer ensembles and their relational event universes

Abstract

This paper is devoted to 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 the representation of events. The novelty of our approach is in using a new mathematical picture of events universe. The events observed by an observer are described by a dendrogram, a finite tree. The event dynamics are 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 a statistical nature. Each dendrogram represents an ensemble of observers with the same relational tree representation of the events they measured/collected. Technically the essence of causal modelling is in encoding dendrograms by real parameters and in this way transitioning 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. This is a step towards the development of DHT-analog special relativity.