Related papers: A general solution for classical sequential growth…

Starting from certain causality conditions and a discrete form of general covariance, we derive a very general family of classically stochastic, sequential growth dynamics for causal sets. The resulting theories provide a relatively…

The ``generic'' family of classical sequential growth dynamics for causal sets provides cosmological models of causal sets which are a testing ground for ideas about the, as yet unknown, quantum theory. In particular we can investigate how…

We study a collection of discrete Markov chains related to the causal set approach to modeling discrete theories of quantum gravity. The transition probabilities of these chains satisfy a general covariance principle, a causality principle,…

The spacetime discreteness of causal set theory has enabled the formulation of novel spacetime dynamics. In these so-called "growth" dynamics, a causal set spacetime is generated probabilistically by means of a random walk on certain tree…

The Causal Set approach to quantum gravity asserts that spacetime, at its smallest length scale, has a discrete structure. This discrete structure takes the form of a locally finite order relation, where the order, corresponding with the…

We explore whether the growth dynamics paradigm of Causal Set Theory is compatible with past-infinite causal sets. We modify the Classical Sequential Growth dynamics of Rideout and Sorkin to accommodate growth "into the past" and discuss…

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…

A large class of the dynamical laws for causal sets described by a classical process of sequential growth yield a cyclic universe, whose cycles of expansion and contraction are punctuated by single `origin elements' of the causal set. We…

We discuss the causal set approach to discrete quantum gravity. We begin by describing a classical sequential growth process in which the universe grows one element at a time in discrete steps. At each step the process has the form of a…

This article presents the most interesting philosophical issues as they arise in causal set theory. The first concerns the apparent disappearance of spacetime at the fundamental level. It shows how the looming empirical incoherence is…

Classical sequential growth models for causal sets provide an important step towards the formulation of a quantum causal set dynamics. The covariant observables in a class of these models known as generalised percolation have been…

We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes.…

We present a categorical construction for modelling causal structures within a general class of process theories that include the theory of classical probabilistic processes as well as quantum theory. Unlike prior constructions within…

We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of…

Semi-Markov processes represent a well known and widely used class of random processes in classical probability theory. Here, we develop an extension of this type of non-Markovian dynamics to the quantum regime. This extension is…

Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad…

Within the context of a recently proposed family of stochastic dynamical laws for causal sets, one can ask whether the universe might have emerged from the quantum-gravity era with a large enough size and with sufficient homogeneity to…

Spatial birth-and-death processes with a finite number of particles are obtained as unique solutions to certain stochastic equations. Conditions are given for existence and uniqueness of such solutions, as well as for continuous dependence…

By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose…

We develop a new formalism for constructing probabilities associated to the causal ordering of events in quantum theory, where by an event we mean the emergence of a measurement record on a detector. We start with constructing probabilities…