Discrete mechanics: a sequential growth dynamics for causal sets that is based on binary alternatives

TL;DR

This paper introduces a stochastic sequential growth model for causal sets in discrete pregeometry, where new elements are added based on binary alternatives, providing a novel approach to quantum gravity modeling.

Contribution

It presents a new discrete pregeometry model using causal sets with a growth dynamics based on binary alternatives, advancing quantum gravity theories.

Findings

Probabilistic growth depends on existing causal set structure

Binary alternatives determine the sequential addition of elements

Quadratic dependence of growth probabilities on binary paths

Abstract

One of approaches to quantum gravity is different models of a discrete pregeometry. An example of a discrete pregeometry on a microscopic scale is introduced. This is the particular case of a causal set. The causal set is a locally finite partially ordered set. The dynamics of this model is a stochastic sequential growth dynamics. New elements of causal set are added one by one. The probability of this addition of a new element depends on the structure of existed causal set. The particular case of the dynamics is considered. This dynamics is based on binary alternatives. Each directed path is considered as a sequence of outcomes of binary alternatives. The probabilities of a stochastic sequential growth have quadratic dependence on these paths.