Related papers: Spectral dimension in causal set quantum gravity
As a phenomenon encompassing measurement incompatibility and Bell nonlocality, quantum contextuality is not only central to our understanding of quantum mechanics, but also an essential resource in many quantum information processing tasks.…
We search for a continuum limit in the causal dynamical triangulation (CDT) approach to quantum gravity by determining the change in lattice spacing using two independent methods. The two methods yield similar results that may indicate how…
This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
Getting signatures of quantum gravity is one of the topical lines of research in modern theoretical physics and cosmology. This short review faces this challenge under a novel perspective. Instead of separating quantum-gravity effects of a…
In this paper we consider tests for nonlinear time series, which are motivated by the notion of serial dependence. The proposed tests are based on comparisons with the quantile spectral density, which can be considered as a quantile version…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
Quantum field theory (QFT) in classical spacetime has revealed interesting and puzzling aspects about gravitational systems, in particular black hole thermodynamics and its information processing. Although quantum gravitational effects may…
A satisfactory theory of quantum gravity may necessitate a drastic modification of our perception of space-time, by giving it a foamy structure at distances comparable to the Planck length. It is argued in this essay that the experimental…
We propose a new method to characterize the different phases observed in the non-perturbative numerical approach to quantum gravity known as Causal Dynamical Triangulation. The method is based on the analysis of the eigenvalues and the…
The notion of a spectral geometry on a compact metric space X is introduced. This notion serves as a discrete approximation of X motivated by the notion of a spectral triple from non-commutative geometry. A set of axioms charaterising…
We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. We define causaltopes, our chosen portmanteau of "causal polytopes", for…
After sketching a context in which to seek observable signals of spatio-temporal discreteness, I briefly review the status of the causal set program for quantum gravity, concluding with a simple model for the field produced by a moving…
We introduce a generalized version of the Causal Dynamical Triangulations (CDT) formulation of quantum gravity, in which the regularized, triangulated path integral histories retain their causal properties, but do not have a preferred…
An important task faced by all approaches of quantum gravity is to incorporate superpositions and quantify quantum uncertainties of spacetime causal relations. We address this task in 2D. By identifying a global $Z_2$ symmetry of 1+1D…
The field of quantum sensing explores the use of quantum phenomena to measure a broad range of physical quantities, of both static and time-dependent types. An important figure of merit for sensing time dependent signals is the spectral…
We compute the intrinsic Hausdorff dimension of spacetime at the infrared fixed point of the quantum conformal factor in 4D gravity. The fractal dimension is defined by the appropriate covariant diffusion equation in four dimensions and is…
It has been recently claimed [arXiv:1102.3434] that quantum gravity models where the number of dimensions reduces at the ultraviolet exhibit a potentially observable cutoff in the primordial gravitational wave spectrum, and that this is a…
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…
We propose that large quantum fluctuations of the conformal factor drastically modify classical general relativity at cosmological distance scales, resulting in a scale invariant phase of quantum gravity in the far infrared. We derive…