Related papers: Discrete mechanics: a sequential growth dynamics f…

Causal set quantum gravity is a Lorentzian approach to quantum gravity, based on the causal structure of spacetime. It models each spacetime configuration as a discrete causal network of spacetime points. As such, key questions of the…

The classical sequential growth model for causal sets provides a template for the dynamics in the deep quantum regime. This growth dynamics is intrinsically temporal and causal, with each new element being added to the existing causal set…

In the causal set approach to discrete quantum gravity 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…

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…

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…

Causality among events is widely recognized as a most fundamental structure of spacetime, and causal sets have been proposed as discrete models of the latter in the context of quantum gravity theories, notably in the Causal Set Programme.…

In order to construct a quantum theory of gravity, we may have to abandon certain assumptions we were making. In particular, the concept of spacetime as a continuum substratum is questioned. Causal Sets is an attempt to construct a quantum…

The causal set approach to quantum gravity embodies the concepts of causality and discreteness. This article explores some foundational and conceptual issues within causal set theory.

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…

To solve the path integral for quantum gravity, one needs to regularise the space-times that are summed over. This regularisation usually is a discretisation, which makes it necessary to give up some paradigms or symmetries of continuum…

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…

A discrete quantum gravity model given by a quantum sequential growth process (QSGP) is considered. The QSGP describes the growth of causal sets (causets) one element at a time in discrete steps. It is shown that the set $\pscript$ of…

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 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…

This article presents a simplified version of the author's previous work. We first construct a causal growth process (CGP). We then form path Hilbert spaces using paths of varying lengths in the CGP. A sequence of positive operators on…

This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…

A first step towards implementing a notion of coarse graining in an intrinsically Lorentzian, discrete quantum- gravity approach, namely causal set quantum gravity is taken. It makes use of an abstract notion of scale, based on counting the…

This paper offers suggested improvements to the causal sets program in discrete gravity, which treats spacetime geometry as an emergent manifestation of causal structure at the fundamental scale. This viewpoint, which I refer to as the…

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…