Related papers: Spectral geometry of spacetime
A mathematical formalism for treating spacetime topology as a quantum observable is provided. We describe spacetime foam entirely in algebraic terms. To implement the correspondence principle we express the classical spacetime manifold of…
We develop the spectral point of view on geometry based on the formalism of quantum physics. We start from the simple physical question of specifying our position in space and explain how the spectral geometric point of view provides a new…
We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…
For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to…
Suppose we assume that (a) information about a black hole is encoded in its Hawking radiation and (b) causality is not violated to leading order in gently curved spacetime. Then we argue that spacetime cannot just be described as a manifold…
A set of data supposed to give possible axioms for spacetimes with a sufficient number of isometries in spectral geometry is given. These data are shown to be sufficient to obtain 1+1 dimensional de Sitter spacetime. The data rely at the…
Close to the Planck energy scale, the quantum nature of space-time reveals itself and all forces, including gravity, should be unified so that all interactions correspond to just one underlying symmetry. In the absence of a full quantum…
A set of data supposed to give possible axioms for spacetimes. It is hoped that such a proposal can serve to become a testing ground on the way to a general formulation. At the moment, the axioms are known to be sufficient for cases with a…
In usual quantum theory, the information available about a quantum system is defined in terms of the density matrix describing it on a spacelike surface. This definition must be generalized for extensions of quantum theory which do not have…
In this letter we discuss the possibility of treating the spacetime by itself as a kind of deformable body for which we can define an fundamental lattice, just like atoms in crystal lattices. We show three signs pointing in that direction.…
Spacetime foam is analyzed within the simplistic model of a set of scalar fields on a flat background. We suggest the formula for the path integral which allows to account for the all possible topologies of spacetime. We show that the…
In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…
We consider globally hyperbolic flat spacetimes in 2+1 and 3+1 dimensions, in which a uniform light signal is emitted on the $r$-level surface of the cosmological time for $r\to 0$. We show that the frequency of this signal, as perceived by…
Four-dimensional spacetime, together with a natural generalisation to extra dimensions, is obtained through an analysis of the structures and symmetries deriving from possible arithmetic expressions for one-dimensional time. On taking the…
A general framework is developed to investigate the properties of useful choices of stationary spacelike slicings of stationary spacetimes whose congruences of timelike orthogonal trajectories are interpreted as the world lines of an…
Probabilistic Spacetime is a simple generalization of the classical model of spacetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a…
In this paper, we calculate in a transparent way the spectral dimension of a quantum spacetime, considering a diffusion process propagating on a fluctuating manifold. To describe the erratic path of the diffusion, we implement a minimal…
In this two-part paper we propose an extension of Connes' notion of even spectral triple to the Lorentzian setting. This extension, which we call a spectral spacetime, is discussed in part II where several natural examples are given which…
The spectral dimension has proven to be a very informative observable to understand the properties of quantum geometries in approaches to quantum gravity. In loop quantum gravity and its spin foam description, it has not been possible so…
There are competing schools of thought about the question of whether spacetime is fundamentally either continuous or discrete. Here, we consider the possibility that spacetime could be simultaneously continuous and discrete, in the same…