Related papers: Causal set as a discretized phase spacetime

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…

Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and…

The theory of causal fermion systems is a recent approach to fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. The dynamics is…

We present evidence for a phase transition in a theory of 2D causal set quantum gravity which contains a dimensionless non-locality parameter $\epsilon \in (0,1]$. The transition is between a continuum phase and a crystalline phase,…

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…

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 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…

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…

Although we lack complete understanding of quantum aspects of gravitation, it is usually agreed, using general arguments, that a final quantum gravity theory will endow space and time with some (fundamental or effective) notion of…

We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural "tangent 2-bundle," analogous to the tangent bundle…

Causal set theory is a discrete model of spacetime that retains a notion of causal structure. We understand how to construct causal sets that approximate a given spacetime, but most causal sets are not at all manifold-like, and must be…

It is difficult to extract reliable criteria for causal locality from the limited ingredients found in textbook quantum theory. In the end, Bell humbly warned that his eponymous theorem was based on criteria that "should be viewed with the…

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…

Causal set theory offers a simple and elegant picture of discrete physics. But the vast majority of causal sets look nothing at all like continuum spacetimes, and must be excluded in some way to obtain a realistic theory. I describe recent…

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…

A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated…

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…

We consider Lorentzian manifolds as examples of partially ordered measure spaces, sets endowed with compatible partial order relations and measures, in this case given by the causal structure and the volume element defined by each…

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…

In this paper we consider a claim that in the natural world there is no fact of the matter about the spatio-temporal separation of events. In order to make sense of such a notion and construct useful models of the world, it is proposed to…