The causal set approach to quantum gravity

Abstract

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 represents a proto-causality relation while local finiteness encodes an intrinsic discreteness. In the continuum approximation the former corresponds to the spacetime causality relation and the latter to a fundamental spacetime atomicity, so that finite volume regions in the continuum contain only a finite number of causal set elements. CST is deeply rooted in the Lorentzian character of spacetime, where a primary role is played by the causal structure poset. Importantly, the assumption of a fundamental discreteness in CST does not violate local Lorentz invariance in the continuum approximation. On the other hand, the combination of discreteness and Lorentz invariance gives rise to a characteristic non-locality which distinguishes CST from most other approaches to quantum gravity.In this review we give a broad, semi-pedagogical introduction to CST, highlighting key results as well as some of the key open questions. This review is intended both for the beginner student in quantum gravity as well as more seasoned researchers in the field.

Universal critical behavior in tensor models for four-dimensional quantum gravity

“…Thus, we aim at an implementation of the path integral without auxiliary geometric background structures 1 . A promising route to construct a background independent path integral consists of making a transition to discrete building blocks, as in dynamical triangulations [5], Regge calculus [6], matrix/tensor models [7][8][9], spin foams [10] and causal sets [11]. This allows to construct a discrete approximation of all random geometries (and potentially additional configurations with no interpreta- * eichhorn@cp3.sdu.dk † j.lumma@thphys.uni-heidelberg.de ‡ adpjunior@id.uff.br § a.sikandar@thphys.uni-heidelberg.de 1 An alternative route makes use of an auxiliary background structure at the technical level while ensuring the independence of physical results from this background structure, see, e.g., [4].…”

As below, so before: ‘synchronic’ and ‘diachronic’ conceptions of spacetime emergence

“…23 This step leads to the appearance of spin network states in the theory. These are eigenstates of the so-called 'area' and 'volume' operators, and form the basis for a 'kinematical' 22 For more on causal set theory accessible for philosophers, see Dowker (2005); Henson (2009); Sorkin (2005); Wüthrich (2012); for a review, see Surya (2019). 23 Thanks to a referee for emphasising this point.…”

Horizon molecules in causal set theory

“…We have everything we need to evaluate the first order correction to I (d) n (q; l, τ ). In d = 2 we must match the first order correction to a term of the form b (2) n K(q) l , (5.35) in order to determine the constant b (2) n (we must also use the fact that K(q) = −2a). We find b (2) n = − 2Γ n + 5 2 6nΓ(n + 2) + 3Γ(n + 2)…”

“…Following similar steps to above, we can evaluate the first order correction to I 1 ), and we have determined the constants b (2) n and b (4) i,n that appear at first order in l. In this section we will discuss how to use the explicit expressions for these constants to extract continuum geometry from the causal set.…”