Related papers: The mathematics of causal sets
It was recently suggested that causal structures are both dynamical, because of general relativity, and indefinite, due to quantum theory. The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal…
Recently, it was shown that the quantum effects of the matter, could be used to determine the conformal degree of freedom of the space-time metric. So both gravity and quantum are geometrical features. Gravity determines the causal…
This thesis is situated within the context of quantum gravity, broadly understood as any effort to explore the interplay between gravitation and the quantum realm, without necessarily requiring the quantization of the gravitational field…
Causal modelling provides a powerful set of tools for identifying causal structure from observed correlations. It is well known that such techniques fail for quantum systems, unless one introduces `spooky' hidden mechanisms. Whether one can…
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…
A potentially powerful approach to quantum gravity has been developed over the last few years under the name of Causal Dynamical Triangulations. Numerical simulations have given very interesting results in the cases of two, three and four…
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…
One of the main technical obstacles in constructing a consistent theory of quantum gravity is that the metric itself defines the causal structure required for quantization. This motivates implementing quantum aspects of gravity through an…
The finiteness of black hole entropy suggest that spacetime is fundamentally discrete, and hints at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered, but should…
We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This viewpoint can…
The causality principle for the Relativistic Theory of Gravitation (RTG) is presented. It is a straightforward consequence of the RTG basic postulates. The necessary conditions for physical solutions of the gravitational field equations to…
The literature on quantum-gravity-inspired scenarios for the quantization of spacetime has so far focused on particle-physics-like studies. This is partly justified by the present limitations of our understanding of quantum-gravity…
A first step towards implementing a notion of coarse graining in an intrinsically Lorentzian, discrete quantum- gravity approach, namely causal set quantum gravity is taken. It makes use of an abstract notion of scale, based on counting the…
The problem of causality is analyzed in the context of Local Quantum Field Theory. Contrary to recent claims, it is shown that apparent noncausal behaviour is due to a lack of the notion of sharp localizability for a relativistic quantum…
There has been a body of works deriving the complex Hilbert space structure of quantum theory from axioms/principles/postulates to deepen our understanding about quantum theory and to reveal ways to go beyond it to resolve foundational…
We discuss the notion of causality in Quantum Gravity in the context of sum-over-histories approaches, in the absence therefore of any background time parameter. In the spin foam formulation of Quantum Gravity, we identify the appropriate…
It is well-known that if one assumes quantum theory to hold locally, then processes with indefinite causal order and cyclic causal structures become feasible. Here, we study qualitative limitations on causal structures and correlations…
We propose a mathematically concrete way of modelling the suggestion that in quantum gravity the spacetime disappears, replacing it with a discrete approximation to the causal path space described as an object in a model category. One of…
Most of the approaches to the construction of a theory of quantum gravity share some principles which do not have specific experimental support up to date. Two of these principles are relevant for our discussion: (i) the gravitational field…
Existing work on quantum causal structure assumes that one can perform arbitrary operations on the systems of interest. But this condition is often not met. Here, we extend the framework for quantum causal modelling to situations where a…