A Classical Sequential Growth Dynamics for Causal Sets

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 macroscopic notion of spacetime causality, is taken to be a fundamental aspect of nature. After an introduction to the Causal Set approach, this thesis considers a simple toy dynamics for causal sets. Numerical simulations of the model prov...

A classical precursor to a full quantum dynamics for causal sets has been forumlated in terms of a stochastic sequential growth process in which the elements of the causal set arise in a sort of accretion process. The transition probabilities of the Markov growth process satisfy certain physical requirements of causality and general covariance, and the generic solution with all transition probabilities non-zero has been found. Here we remove the assumption of non-zero probabi...

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 causal set and the "completed" universe is given by a path through a discretely growing chain of causal sets. We then introduce a method for quantizing this classical formalism to obtain a quantum sequential growth process which may lead to a ...

We begin by describing a sequential growth model in which the universe grows one element at a time in discrete time steps. At each step, the process has the form of a causal set and the "completed" universe is given by a path consisting of a discretely growing chain of causal sets. We then introduce a quantum dynamics to obtain a quantum sequential growth process (QSGP) which may lead to a viable model for discrete quantum gravity. A discrete version of Einstein's field equat...

In the causal set approach to quantum gravity the spacetime continuum arises as an approximation to a fundamentally discrete substructure, the causal set, which is a locally finite partially ordered set. The causal set paradigm was elucidated in a classic paper by Bombelli, Lee, Meyer and Sorkin in 1987. While early kinematical results already showed promise, the program received a substantial impetus about a decade ago with the work of Rideout and Sorkin on a classical stoch...

This paper is based on the causal set approach to discrete quantum gravity. We first describe a classical sequential growth process (CSGP) in which the universe grows one element at a time in discrete steps. At each step the process has the form of a causal set (causet) and the "completed" universe is given by a path through a discretely growing chain of causets. We then quantize the CSGP by forming a Hilbert space $H$ on the set of paths. The quantum dynamics is governed by ...

We consider a covariant causal set approach to discrete quantum gravity. We first review the microscopic picture of this approach. In this picture a universe grows one element at a time and its geometry is determined by a sequence of integers called the shell sequence. We next present the macroscopic picture which is described by a sequential growth process. We introduce a model in which the dynamics is governed by a quantum transition amplitude. The amplitude satisfies a sto...

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 general covariance manifests itself and address the problem of identifying and interpreting covariant ``observables'' in quantum gravity. The problem becomes, in this setting, that of identifying measurable covariant collections of causal s...

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. ...

This paper provides a thorough introduction to the causal set hypothesis aimed at students, and other interested persons, with some knowledge of general relativity and nonrelativistic quantum mechanics. I elucidate the arguments for why the causal set structure might be the appropriate structure for a theory of quantum gravity. The logical and formal development of a causal set theory as well as a few illuminating examples are also provided.