Related papers: Elementary Quantum Geometry
We investigate the geometry of a quantum universe with the topology of the four-torus. The study of non-contractible geodesic loops reveals that a typical quantum geometry consists of a small semi-classical toroidal bulk part, dressed with…
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces…
It is argued that (a) In the quantum realm test-particle masses have non-trivial observability which induces a non-geometric element in gravity, (b) Any theory of quantum gravity, on fundamental grounds, must contain an element of…
We study classical limit for quantum mechanics with two times and temperature, which describes a generalized dynamics of relativistic point mass. In this theory, thermodynamic time means a parameter of evolution, whereas geometric time is…
A key challenge for many quantum gravity approaches is to construct states that describe smooth geometries on large scales. Here we define a family of $(2+1)$-dimensional quantum gravity states which arise from curvature excitations…
We show how the quantization of two-dimensional gravity leads to an (Euclidean) quantum space-time where the average geometry is that of constant negative curvature and where the Hartle-Hawking boundary condition arises naturally.
Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured over the past fifteen years to a mathematically rigorous candidate quantum field theory of the gravitational field. The features that distinguish it from…
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…
With the two most profound conceptual revolutions of XXth century physics, quantum mechanics and relativity, which have culminated into relativistic spacetime geometry and quantum gauge field theory as the principles for gravity and the…
We propose three core ideas: 1. the wave-particle duality of the qudit quantum space; 2. the classification of all elementary quantum gates by ordered pairs of qudit functionals; 3. a new type of quantum gates called the "quantum wave…
The main obstacle in attempts to construct a consistent quantum gravity is the absence of independent flat time. This can in principle be cured by going out to higher dimensions. The modern paradigm assumes that the fundamental theory of…
This article introduces Universal Quantum Relativity which is a simple Theory of Everything. It relies on an ultimate doctrine that is the absence of absolute existence. This generalizes relativity principles up to a mother quantum theory.…
In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…
We provide a non-perturbative geometrical characterization of the partition function of $n$-dimensional quantum gravity based on a coarse classification of riemannian geometries. We show that, under natural geometrical constraints, the…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
We describe a theory amalgamating quantum theory and general relativity through the identification of a continuous 4-dimensional spacetime arena constructed from the substructures of a generalised multi-dimensional form for proper time. In…
Quantum gravity places entirely new challenges on the formulation of a consistent theory as well as on an extraction of potentially observable effects. Quantum corrections due to the gravitational field are commonly expected to be tiny…
Physical spacetime geometry follows from some effective thermodynamics of quantum states of all fields and particles described in frames of General Relativity. In the sense of pure field theoretical Einstein's point of view on gravitation…
The appearance of infinity together with collapsing quantum state due to the observation or interaction, which are two challenging features of quantum field theory, become very serious problems in quantum gravity as well as in quantum…
We consider functional-integral quantisation of the moduli of all quantum metrics defined as square-lengths $a$ on the edges of a Lorentzian square graph. We determine correlation functions and find a fixed relative uncertainty $\Delta…