Related papers: Causal Sets and an Emerging Continuum

These notes present some elements of causality theory. While they are not as complete as other treatments of the topic, there is some originality in that the whole approach is based on a definition of causal curves which allows to simplify…

In fundamental theories that accounts for quantum gravitational effects, the spacetime causal structure is expected to be quantum uncertain. Previous studies of quantum causal structure focused on finite-dimensional systems. Here we present…

Within the causal set approach to quantum gravity, a discrete analog of a spacelike region is a set of unrelated elements, or an antichain. In the continuum approximation of the theory, a moment-of-time hypersurface is well represented by…

Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad…

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 propose an approach to quantum theory based on the energetic causal sets, introduced in Cort\^{e}s and Smolin (2013). Fundamental processes are causal sets whose events carry momentum and energy, which are transmitted along causal links…

Models of particle propagation in causal set theory are investigated through simulations. For the swerves model the simulations are shown to agree with the expected continuum diffusion behaviour. Given the limitations on the simulated…

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…

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…

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…

Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…

Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of…

A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual "near future" macroscopic phenomena is attributed to a cosmological asymmetry and to rules…

We show a general theorem of existence of temporal foliations in a general causal set, under mild constraints. Then we study automorphisms of infinite causal sets (which satisfy further requirements) and show that they fall under one of two…

Causality is one of the most fundamental -- and yet elusive -- concepts in physics. From its intuitive role in everyday experience to its formal and often implicit role in scientific theories, causality has challenged philosophers and…

Some physical consequences of the negation of the continuum hypothesis are considered. It is shown that quantum and classical mechanics are component parts of the multicomponent description of the set of variable infinite cardinality.…

We give an up-to-date perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of causal…

Discovery of causal relations is fundamental for understanding the dynamics of complex systems. While causal interactions are well defined for acyclic systems that can be separated into causally effective subsystems, a mathematical…

In causal set theory, cycles of cosmic expansion and collapse are modelled by causal sets with "breaks" and "posts" and a special role is played by cyclic dynamics in which the universe goes through perpetual cycles. We identify and…

We study a collection of discrete Markov chains related to the causal set approach to modeling discrete theories of quantum gravity. The transition probabilities of these chains satisfy a general covariance principle, a causality principle,…