Related papers: Fuzzy spacetime from a null-surface version of GR
We define and discuss various quantum operators that describe the geometry of spacetime in quantum general relativity. These are obtained by combining the Null-Surface Formulation of general relativity, recently developed, with asymptotic…
We review certain emergent notions on the nature of spacetime from noncommutative geometry and their radical implications. These ideas of spacetime are suggested from developments in fuzzy physics, string theory, and deformation…
A quantum theory of asymptotically flat space-times is presented using the solutions of the Null Surface Formulation (NSF) field equations in a perturbative scheme. Free-field commutation relations are given for the null free data of NSF at…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
Quantum gravity (or quantum spacetime) is to unify general relativity and quantum mechanics into a single theoretical framework and presented as the most important open puzzle in fundamental physics. The development of a microscopic theory…
We consider fuzzy spacetime, quanta of area and related concepts in the context of latest approaches to Quantum Gravity and show its interface with usual non-Abelian gauge theory. We also discuss in this context a cosmology which correctly…
In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature…
In this paper we introduce a new general framework for the study of phenomenological quantum gravity theories (PQG). The key idea is the introduction of two different types of spacetime, an observer-independent spacetime (modeled by a…
The proper resolution of the so-called measurement problem requires a "top-down" conception of the quantum world that is opposed to the usual "bottom-up" conception, which builds on an intrinsically and maximally differentiated manifold.…
The Null Surface Formulation of General Relativity is developed for 2+1 dimensional gravity. The geometrical meaning of the metricity condition is analyzed and two approaches to the derivation of the field equations are presented. One…
Gravity is understood as a geometrization of spacetime. But spacetime is also the manifold of the boundary values of the spinless point particle in a variational approach. Since all known matter, baryons, leptons and gauge bosons are…
Flatly Foliated Relativity (FFR) is a new theory which conceptually lies between Special Relativity (SR) and General Relativity (GR), in which spacetime is foliated by flat Euclidean spaces. While GR is based on the idea that "matter curves…
The gauge theoretical formulation of general relativity is presented. We are only concerned with local intrinsic geometry, i.e. our space-time is an open subset of a four-dimensional real vector space. Then the gauge group is the set of…
In prior work, we have argued that spacetime functionalism provides tools for clarifying the conceptual difficulties specifically linked to the emergence of spacetime in certain approaches to quantum gravity. We argue in this article that…
We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
A review is made of recent efforts to define linear connections and their corresponding curvature within the context of noncommutative geometry. As an application it is suggested that it is possible to identify the gravitational field as a…
We present a quantum geometric framework for stochastic quantisation in the case of a free Klein-Gordon field on Euclidean space. In this approach the noise is part of the background space, spacetime is fuzzy. We extend the notion of sharp…
The geometric foundations of General Relativity are revisited, with particular attention to its gauge invariance, as a key to understanding the true nature of spacetime. Beyond the common image of spacetime as a deformable 'fabric' filling…
We propose an approach which, by combining insights from Loop Quantum Gravity (LQG), Topos theory, Non-commutative Geometry \`a la Connes, and spacetime relationalism, provides fertile ground for the search of an adequate spacetime picture…