Related papers: Detecting Causality with Symplectic Quandles
By relating and ordering events, causality constitutes a pivotal feature of our world. On the one hand, there are information-theoretic notions of causality defined in terms of the information processing ability of agents and on the other…
For a banded link $L$ in a surface times a circle, the Witten-Reshetikhin-Turaev invariants are topological invariants depending on a sequence of complex $2p$-th roots of unity $(A_p)_{p\in 2\mathbb{N}}$. We show that there exists a…
Recent results on the maximization of the charged-particle action I in a globally hyperbolic spacetime are discussed and generalized. We focus on the maximization of I over a given causal homotopy class C of curves connecting two causally…
We propose a discrete analogue of null geodesics in causal sets that are approximated by a region of 2d Minkowski spacetime, in the spirit of Kronheimer and Penrose's "grids" and "beams" for an abstract causal space. The causal set…
The discovery of causal relationships is a fundamental problem in science and medicine. In recent years, many elegant approaches to discovering causal relationships between two variables from observational data have been proposed. However,…
We describe a method that infers whether statistical dependences between two observed variables X and Y are due to a "direct" causal link or only due to a connecting causal path that contains an unobserved variable of low complexity, e.g.,…
A polynomial invariant of virtual links, arising from an invariant of links in thickened surfaces introduced by Jaeger, Kauffman, and Saleur, is defined and its properties are investigated. Examples are given that the invariant can detect…
For a smooth spacetime $X$, based on the timelike homotopy classes of its timelike paths, we define a topology on $X$ that refines the Alexandrov topology and always coincides with the manifold topology. The space of timelike or causal…
Causal discovery problems use a set of observations to deduce causality between variables in the real world, typically to answer questions about biological or physical systems. These observations are often recorded at regular time…
This paper is a continuation of the work done in \cite{sal-yas} and \cite{may-pat-rob}. We deal with the Vietoris hyperspace of all nontrivial convergent sequences $\mathcal{S}_c(X)$ of a space $X$. We answer some questions in…
We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities of angles less than $2\pi$ along a time-like graph $\Gamma$. To each such space we associate a graph and a finite family of…
In this work, we prove a synthetic splitting theorem for globally hyperbolic Lorentzian length spaces with global non-negative timelike curvature containing a complete timelike line. Just like in the case of smooth spacetimes, we construct…
The problems connected with a causality of space-time universe and with the paradox of Einstein, Podolsky, and Rosen are considered. A main philosophical problem and its possible solutions are briefly discussed. A concept of unified local…
We canonically quantize $(2+1)$-dimensional electrodynamics including a higher-derivative Chern-Simons term. The effective theory describes a standard photon and an additional degree of freedom associated with a massive ghost. We find the…
We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. This provides an abstract mathematical setting in which one can study causality independent…
I explain a simple definition of causality in widespread use, and indicate how it links to the Kramers Kronig relations. The specification of causality in terms of temporal differential eqations then shows us the way to write down dynamical…
In this paper we provide asymptotic upper bounds on the complexity in two (closely related) situations. We confirm for the total doubling coverings and not only for the chains the expected bounds of the form $$ \kappa({\mathcal U}) \le…
It is shown that the warped product spacetime P=M *_f H, where H is a complete Riemannian manifold, and the original spacetime M share necessarily the same causality properties, the only exceptions being the properties of causal continuity…
Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfactuals. In this paper, we prove that this assumption fails…
The quandle homology theory is generalized to the case when the coefficient groups admit the structure of Alexander quandles, by including an action of the infinite cyclic group in the boundary operator. Theories of Alexander extensions of…