Related papers: Proper time is stochastic time in 2d quantum gravi…
We review recent developments in the understanding of the fractal properties of quantum spacetime of 2d gravity coupled to c>0 conformal matter. In particular we discuss bounds put by numerical simulations using dynamical triangulations on…
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…
Causal Dynamical Triangulations (CDT) is a proposal for a theory of quantum gravity, which implements a path-integral quantization of gravity as the continuum limit of a sum over piecewise flat spacetime geometries. We use Monte Carlo…
I propose the Langevin equation for 3-geometries in the Ashtekar's formalism to describe 4D Euclidean quantum gravity, in the sense that the corresponding Fokker-Planck hamiltonian recovers the hamiltonian in 4D quantum gravity exactly. The…
Time in quantum gravity is not a well-defined notion, despite its central role in the very definition of dynamics. Using the formalism of quantum geometrodynamics, we shortly review the problem and illustrate it with two proposed solutions.…
Curvature is a key notion in General Relativity, characterizing the local physical properties of spacetime. By contrast, the concept of curvature has received scant attention in nonperturbative quantum gravity. One may even wonder whether…
We study the geometries generated by two-dimensional causal dynamical triangulations (CDT) coupled to $d$ massless scalar fields. Using methods similar to those used to study four-dimensional CDT we show that there exists a $c=1$ "barrier",…
Causal Dynamical Triangulations (CDT) is a lattice approach to quantum gravity. CDT has rich phase structure, including a semiclassical phase consistent with Einstein's general relativity. Some of the observed phase transitions are second…
We introduced with coauthors some years ago a solution to the problem of time in quantum gravity which consists in formulating the quantum theory in terms of real clocks. It combines Page and Wootters' relational proposal with Rovelli's…
The formalism of Causal Dynamical Triangulations (CDT) attempts to provide a non-perturbative regularization of quantum gravity, viewed as an ordinary quantum field theory. In two dimensions one can solve the lattice theory analytically and…
A practical way to deal with the problem of time in quantum cosmology and quantum gravity is proposed. The main tool is effective equations, which mainly restrict explicit considerations to semiclassical regimes but have the crucial…
In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…
I suggest that measurement in quantum theory should be regarded as a sense of time (of things happening), which is as important as the conventional relativistic notion of time. A key question -- of basic physical interest whether one…
A modification of the homogeneous isotropic model of the Friedman universe with a scalar field is proposed, in which the proper time of the universe is added to the dynamic variables under the additional condition of its classical dynamics.…
It is widely hoped that quantum gravity will shed light on the question of the origin of time in physics. The currently dominant approaches to a candidate quantum theory of gravity have naturally evolved from general relativity, on the one…
The role of topology change in a fundamental theory of quantum gravity is still a matter of debate. However, when regarding string theory as two-dimensional quantum gravity, topological fluctuations are essential. Here we present a third…
We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical…
Some recent studies of the properties of D-particles suggest that in string theory a rather conventional description of spacetime might be available up to scales that are significantly smaller than the Planck length. We test this…
We describe the motivation behind the recent formulation of a nonperturbative path integral for Lorentzian quantum gravity defined through Causal Dynamical Triangulations (CDT). In the case of two dimensions the model is analytically…
We construct a duality between several simple physical systems by showing that they are different aspects of the same quantum theory. Examples include the free relativistic massless particle and the hydrogen atom in any number of…