# Towards a Definition of Locality in a Manifoldlike Causal Set

@article{Glaser2013TowardsAD, title={Towards a Definition of Locality in a Manifoldlike Causal Set}, author={Lisa Glaser and Sumati Surya}, journal={Physical Review D}, year={2013}, volume={88}, pages={124026} }

It is a common misconception that spacetime discreteness necessarily implies a violation of local Lorentz invariance. In fact, in the causal set approach to quantum gravity, Lorentz invariance follows from the specific implementation of the discreteness hypothesis. However, this comes at the cost of locality. In particular, it is difficult to define a "local" region in a manifoldlike causal set, i.e., one that corresponds to an approximately flat spacetime region. Following up on suggestions…

## Figures and Tables from this paper

## 30 Citations

Steps towards Lorentzian quantum gravity with causal sets

- PhysicsJournal of Physics: Conference Series
- 2019

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…

Manifoldlike Causal Sets

- Mathematics
- 2019

The content of this dissertation is written in a way to answer the important question of manifoldlikeness of causal sets. This problem has importance in the sense that in the continuum limit and in…

The causal set approach to quantum gravity

- PhysicsLiving Reviews in Relativity
- 2019

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…

Entanglement Entropy of Scalar Fields in Causal Set Theory

- Mathematics
- 2017

Entanglement entropy is now widely accepted as having deep connections with quantum gravity. It is therefore desirable to understand it in the context of causal sets, especially since they provide…

Spectral dimension on spatial hypersurfaces in causal set quantum gravity

- PhysicsClassical and Quantum Gravity
- 2019

An important probe of quantum geometry is its spectral dimension, defined via a spatial diffusion process. In this work we study the spectral dimension of a ``spatial hypersurface'' in a manifoldlike…

Endeavours in Discrete Lorentzian Geometry : A thesis in five papers

- Physics
- 2014

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…

Recovering General Relativity from a Planck scale discrete theory of quantum gravity

- Physics
- 2021

An argument is presented that if a theory of quantum gravity is physically discrete at the Planck scale and the theory recovers General Relativity as an approximation, then, at the current stage of…

Dimensionally restricted causal set quantum gravity: examples in two and three dimensions

- Physics
- 2019

We study dimensionally restricted non-perturbative causal set quantum dynamics in $2$ and $3$ spacetime
dimensions with non-trivial global spatial topology. The causal set sample space is generated…

Echoes of Asymptotic Silence in Causal Set Quantum Gravity

- Physics
- 2017

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…

Non Relativistic Quantum Mechanics and Classical Mechanics as Special Cases of the Same Theory.

- Physics
- 2015

We start by rewriting classical mechanics in a quantum mechanical fashion and point out that the only diﬀerence with quantum theory re- sides at one point. There is a classical analogon of the…

## References

SHOWING 1-10 OF 29 REFERENCES

Spacelike distance from discrete causal order

- Physics
- 2009

Any discrete approach to quantum gravity must provide some prescription as to how to deduce continuum properties from the discrete substructure. In the causal set approach it is straightforward to…

Directions in Causal Set Quantum Gravity

- Physics
- 2011

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…

On Recovering continuum topology from a causal set

- Mathematics, Physics
- 2007

An important question that discrete approaches to quantum gravity must address is how continuum features of space-time can be recovered from the discrete substructure. Here, we examine this question…

Space-time as a causal set.

- Physics, MedicinePhysical review letters
- 1987

We propose that space-time at the smallest scales is in reality a causal set: a locally finite set of elements endowed with a partial order corresponding to the macroscopic relation that defines past…

Ideal points in space-time

- MathematicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1972

A prescription is given for attaching to a space-time M, subject only to a causality condition, a collection of additional ‘ideal points’. Some of these represent ‘points at infinity’, others…

Discrete geometry of a small causal diamond

- Physics
- 2013

We study the discrete causal set geometry of a small causal diamond in a curved spacetime using the average abundance hCkiof k-element chains or total orders in the underlying causal set C. We begin…

Scalar curvature of a causal set.

- Mathematics, MedicinePhysical review letters
- 2010

A one parameter family of retarded linear operators on scalar fields on causal sets is introduced that approximate square-(1/2)R where R is the Ricci scalar curvature and can be used to define an approximately local action functional for causal sets.

DISCRETENESS WITHOUT SYMMETRY BREAKING: A THEOREM

- Physics
- 2009

This paper concerns random sprinklings of points into Minkowski spacetime (Poisson processes). It proves that there exists no equivariant measurable map from sprinklings to spacetime directions (even…

Boundary Term Contribution to the Volume of a Small Causal Diamond

- Physics
- 2012

In his calculation of the spacetime volume of a small Alexandrov interval in 4 dimensions Myrheim introduced a term which he referred to as a surface integral [1]. The evaluation of this term has…

Classical sequential growth dynamics for causal sets

- Physics
- 1999

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…