Related papers: Causal set approach to discrete quantum gravity
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…
A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal…
The causal set approach to the problem of quantum gravity is based on the hypothesis that spacetime is fundamentally discrete. Spacetime discreteness opens the door to novel types of dynamical law for cosmology and the Classical Sequential…
The proposed theory of causally structured discrete fields studies integer values on directed edges of a self-similar graph with a propagation rule, which we define as a set of valid combinations of integer values and edge directions around…
In this thesis we investigate the importance of causality in non-perturbative approaches to quantum gravity. Firstly, causal sets are introduced as a simple kinematical model for causal geometry. It is shown how causal sets could account…
This article presents a sequential growth model for the universe that acts like a quantum computer. The basic constituents of the model are a special type of causal set (causet) called a $c$-causet. A $c$-causet is defined to be a causet…
The basic framework for this article is the causal set approach to discrete quantum gravity (DQG). Let $Q_n$ be the collection of causal sets with cardinality not greater than $n$ and let $K_n$ be the standard Hilbert space of…
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,…
In a previous paper, the author introduced a covariant causet ($c$-causet) approach to discrete quantum gravity. A $c$-causet is a finite partially ordered set that is invariant under labeling. The invariant labeling of a $c$-causet $x$…
Quantum algorithms offer the potential for significant computational advantages; however, in many cases, it remains unclear how these advantages can be practically realized. Causal Set Theory is a discrete, Lorentz-invariant approach to…
A potentially powerful approach to quantum gravity has been developed over the last few years under the name of Causal Dynamical Triangulations. Numerical simulations have given very interesting results in the cases of two, three and four…
This article begins by reviewing the causal set approach in discrete quantum gravity. In our version of this approach a special role is played by covariant causal sets which we call $c$-causets. The importance of $c$-causets is that they…
The causal set theory (CST) approach to quantum gravity postulates that at the most fundamental level, spacetime is discrete, with the spacetime continuum replaced by locally finite posets or "causal sets". The partial order on a causal set…
There are several indications (from different approaches) that Spacetime at the Plank Scale could be discrete. One approach to Quantum Gravity that takes this most seriously is the Causal Sets Approach. In this approach spacetime is…
A model of a discrete pregeometry on a microscopic scale is introduced. This model is a finite network of finite elementary processes. The mathematical description is a d-graph that is a generalization of a graph. This is the particular…
Causal set theory provides a model of discrete spacetime in which spacetime events are represented by elements of a causal set---a locally finite, partially ordered set in which the partial order represents the causal relationships between…
The causal set approach to quantum gravity is based on the hypothesis that the underlying structure of spacetime is that of a random partial order. We survey some of the interesting mathematics that has arisen in connection with the causal…
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…
There are numerous indications that a discrete substratum underlies continuum spacetime. Any fundamentally discrete approach to quantum gravity must provide some prescription for how continuum properties emerge from the underlying…
We point out that labeled causets have a much simpler structure than unlabeled causets. For example, labeled causets can be uniquely specified by a sequence of integers. Moreover, each labeled causet processes a unique predecessor and hence…