Related papers: Causal Sets and an Emerging Continuum

General Relativity is contaminated with non-trivial geometries which generate closed timelike curves. These apparently violate causality, producing time-travel paradoxes. We shall briefly discuss these geometries and analyze some of their…

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…

In all our well-established theories, it is assumed that events are embedded in a global causal structure such that, for every pair of events, the causal order between them is always fixed. However, the possible interplay between quantum…

We consider a very general class of theories, process theories, which capture the underlying structure common to most theories of physics as we understand them today (be they established, toy or speculative theories). Amongst these…

The causal structure of a unitary transformation is the set of relations of possible influence between any input subsystem and any output subsystem. We study whether such causal structure can be understood in terms of compositional…

By definition a spacetime is stably causal if it is possible to widen the light cones all over the spacetime without spoiling causality. We prove that if the spacetime is at least non-total imprisoning then it is stably causal provided the…

Theories of quantum gravity generically presuppose or predict that the reality underlying relativistic spacetimes they are describing is significantly non-spatiotemporal. On pain of empirical incoherence, approaches to quantum gravity must…

We formulate the Hauptvermutung of Causal Set Theory in two mathematically well-defined but different ways one of which turns out to be wrong and the other one turns out to be true. A further result is that the Hauptvermutung is true if we…

Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is…

In this article we set out to understand the significance of the process matrix formalism and the quantum causal modelling programme for ongoing disputes about the role of causation in fundamental physics. We argue that the process matrix…

Quantum theory is a mathematical formalism to compute probabilities for outcomes happenning in physical experiments. These outcomes constitute events happening in space-time. One of these events represents the fact that a system located in…

Causal spaces have recently been introduced as a measure-theoretic framework to encode the notion of causality. While it has some advantages over established frameworks, such as structural causal models, the theory is so far only developed…

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…

This proceeding is based on a talk prepared for the XIV Marcel Grossmann meeting. We review some results on causal set inspired non-local theories as well as work in progress concerning their phenomenology.

We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…

The paper considers causal smoothing of the real sequences, i.e.,discrete time processes in a deterministic setting. A family of causal linear time-invariant filters is suggested. These filters approximate the gain decay for some non-causal…

A classical precursor to a full quantum dynamics for causal sets has been forumlated in terms of a stochastic sequential growth process in which the elements of the causal set arise in a sort of accretion process. The transition…

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…

There is growing interest in the study of causal methods in the Earth sciences. However, most applications have focused on causal discovery, i.e. inferring the causal relationships and causal structure from data. This paper instead examines…

It is shown that causally simple inextendible spacetimes are hole-free, thus confirming the expectation that causal simplicity removes holes from spacetime. This result is optimal in the sense that causal simplicity cannot be weakened to…