Related papers: Constructing an interval of Minkowski space from a…

The Causal Set Theory (CST) approach to quantum gravity is motivated by the observation that, associated with any causal spacetime (M,g) is a poset (M,<), with the order relation < corresponding to the spacetime causal relation. Spacetime…

We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to…

Short distance scaling limits of a class of integrable models on two-dimensional Minkowski space are considered in the algebraic framework of quantum field theory. Making use of the wedge-local quantum fields generating these models, it is…

A quantum gravity computer is one for which the particular effects of quantum gravity are relevant. In general relativity, causal structure is non-fixed. In quantum theory non-fixed quantities are subject to quantum uncertainty. It is…

This paper studies the distribution of chain and maximal chain lengths in a causal set. We first provide a new derivation for these distributions for a causal set uniformly embedded in Minkowski space, for various dimensionalities, which…

We explore the idea of asymptotic silence in causal set theory and find that causal sets approximated by continuum spacetimes exhibit behaviour akin to asymptotic silence. We make use of an intrinsic definition of spatial distance between…

We survey indications from different branches of Physics that the fine scale structure of spacetime is not adequately described by a manifold. Based on the hints we accumulate, we propose a new structure, which we call a quantum topos. In…

We describe numerical and analytical investigations of causal sets sprinkled into spacetime manifolds. The first part of the paper is a numerical study of finite causal sets sprinkled into Alexandrov subsets of Minkowski spacetime of…

The quantum equivalence principle says that, for any given point, it is possible to find a quantum coordinate system with respect to which we have definite causal structure in the vicinity of that point. It is conjectured that this…

The embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a…

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…

In the causal set approach, spacetime is a continuous approximation of a faithful embedded causal set. But the faithful embedded causal set describes the empty spacetime and cannot describe matter. Only faithful embedding of coarse grained…

We address the "inverse problem" for discrete geometry, which consists in determining whether, given a discrete structure of a type that does not in general imply geometrical information or even a topology, one can associate with it a…

An important question that discrete approaches to quantum gravity must address is how continuum features of spacetime can be recovered from the discrete substructure. Here, we examine this question within the causal set approach to quantum…

The complex Minkowski phase space has the physical interpretation of the phase space of the scalar massive conformal particle. The aim of the paper is the construction and investigation of the quantum complex Minkowski space.

In causal set theory, there are three ambiguous concepts that this article tries to provide a solution to resolve these ambiguities. These three ambiguities in Planck's scale are: the causal relationship between events, the position of the…

After sketching a context in which to seek observable signals of spatio-temporal discreteness, I briefly review the status of the causal set program for quantum gravity, concluding with a simple model for the field produced by a moving…

Suppose the usual description of spacetime as a 4-dimensional manifold with a Lorentzian metric breaks down at Planck energies. Can we still construct sensible theoretical models of the universe? Are they testable? Do they lead to a…

Geometric approaches to network analysis combine simply defined models with great descriptive power. In this work we provide a method for embedding directed acyclic graphs into Minkowski spacetime using Multidimensional scaling (MDS). First…

The "problem of time" in canonical quantum gravity refers to the difficulties involved in defining a Hilbert space structure on states -- and local observables on this Hilbert space -- for a theory in which the spacetime metric is treated…