Related papers: A background independent notion of causality
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 causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
To a significant extent, the metrical and topological properties of spacetime can be described purely order-theoretically. The $K^+$ relation has proven to be useful for this purpose, and one could wonder whether it could serve as the…
The causal set approach to quantum gravity is based on the hypothesis that the underlying structure of spacetime is that of a random partial order. We survey some of the interesting mathematics that has arisen in connection with the causal…
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…
We introduce a very natural topology on the set of total orderings of monomials of any algebra having a countable basis over a field. This topological space and some notable subspaces are compact. This topological framework allows us to…
Prior work has shown that causal structure can be uniquely identified from observational data when these follow a structural equation model whose error terms have equal variances. We show that this fact is implied by an ordering among…
This paper frames causal structure estimation as a machine learning task. The idea is to treat indicators of causal relationships between variables as `labels' and to exploit available data on the variables of interest to provide features…
Causal sets are locally finite, partially ordered sets (posets), which are considered as discrete models of spacetimes. On the one hand, causal sets corresponding to a spacetime manifold are commonly generated with a random process called…
A causal set is a countably infinite poset in which every element is above finitely many others; causal sets are exactly the posets that have a linear extension with the order-type of the natural numbers -- we call such a linear extension a…
The ideas of spacetime discreteness and causality are important in several of the popular approaches to quantum gravity. But if discreteness is accepted as an initial assumption, conflict with Lorentz invariance can be a consequence. The…
In this work, we give rigorous operational meaning to superposition of causal orders. This fits within a recent effort to understand how the standard operational perspective on quantum theory could be extended to include indefinite…
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 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.
The causal structure of space-time offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non time-like related with it. We show that for a general space-time the…
We present a categorical framework for relating causal models that represent the same system at different levels of abstraction. We define a causal abstraction as natural transformations between appropriate Markov functors, which concisely…
We propose an algebraic formulation of the notion of causality for spectral triples corresponding to globally hyperbolic manifolds with a well defined noncommutative generalization. The causality is given by a specific cone of Hermitian…
Following on from the notion of (first-order) causality, which generalises the notion of being tracepreserving from CP-maps to abstract processes, we give a characterization for the most general kind of map which sends causal processes to…
We investigate the position that foundational theories should be modelled on ordinary computability. In this context, we investigate the metamathematics of $\Sigma$ formulas. We consider theories whose axioms are implications between…
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…