Related papers: The Geometry of Small Causal Cones
For closed and oriented hyperbolic surfaces, a formula of Witten establishes an equality between two volume forms on the space of representations of the surface in a semisimple Lie group. One of the forms is a Reidemeister torsion, the…
Causality is pivotal to our understanding of the world, presenting itself in different forms: information-theoretic and relativistic, the former linked to the flow of information, the latter to the structure of space-time. Leveraging a…
We formulate a conjectural Lefschetz formula for locally symmetric spaces of finite volume. The formula can be verified in the compact case and for Riemann surfaces.
In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…
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…
A brief overview of some open questions in general relativity with important consequences for causality theory is presented, aiming to a better understanding of the causal structure of the spacetime. Special attention is accorded to the…
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding…
Motivated by the Hawking-King-McCarthy-Malament (HKMM) theorem and the associated reconstruction of spacetime geometry from its causal structure $(M,\prec)$ and local volume element $\epsilon$, we define a one-parameter family of spatial…
The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin-foam models for quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to…
The model is a particular case of causal set. This is a discrete model of spacetime in a microscopic level. In paper the most general properties of the model are investigated without any reference to a dynamics. The dynamics of the model is…
Quantum measurements often exhibit non-classical features, such as contextuality, which generalizes Bell's non-locality and serves as a resource in various quantum computation models. Existing frameworks have rigorously captured these…
For polyhedral convex cones in ${\mathbb R}^d$, we give a proof for the conic kinematic formula for conic curvature measures, which avoids the use of characterization theorems. For the random cones defined as typical cones of an isotropic…
Calculations are presented for creation of massive and massless scalar particles coupled to Gauss-Bonnet type curvature in Friedmann cosmological models. It has been shown that, for fields of mass~$m$, the effect of the coupling parameter…
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…
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…
The Newman-Penrose equations for spacetimes having one spacelike Killing vector are reduced -- in a geometrically defined "canonical frame'' -- to a minimal set, and its differential structure is studied. Expressions for the frame vectors…
This paper discusses how the transactional interpretation of quantum mechanics can provide for a natural account of the emergence of spacetime events from a quantum substratum. In this account, spacetime is not a substantive manifold that…
We compute the intrinsic volumes of the cone of positive semidefinite matrices over the real numbers, over the complex numbers, and over the quaternions, in terms of integrals related to Mehta's integral. Several applications for the…
We describe the interface between measure theoretic probability and causal inference by constructing causal models on probability spaces within the potential outcomes framework. We find that measure theory provides a precise and instructive…
A characterization of causal automorphism on Minkowski spacetime is given by use of wave equation. The result shows that causal analysis of spacetime may be replaced by studies of wave equation on manifolds.