Related papers: Fractal properties of quantum spacetime
General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like…
The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth…
This letter extends previous findings on the modified Schr\"odinger evolution inspired by quantum gravity phenomenology. By establishing a connection between this approach and fractional quantum mechanics, we provide insights into a…
Using a \emph{gedanken} experiment providing presumably a minimal inaccuracy the uncertainty contributions to the space-time measurement are precisely evaluated for clock and mirror respectively. The resulting expression of minimal…
We derive the cutoff length scale of the quadratic gravity in $d \geq 5$ dimensional spacetime by demanding that the quantum focusing conjecture for the smeared quantum expansion holds at the classical level. The cutoff scale has different…
We present the case for a fundamentally discrete quantum spacetime and for Group Field Theories as a candidate consistent description of it, briefly reviewing the key properties of the GFT formalism. We then argue that the outstanding…
Quantum-gravity renders the space-time dimension to depend on the size of region; it monotonically increases with the size of region and asymptotically approaches four for large distances. This effect was discovered in numerical simulations…
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…
Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-Planckian distances it predicts that spacetime is a fractal with an effective…
The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its…
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…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
Quantum gravity has become a fertile interface between gravitational physics and quantum many-body physics, with its double goal of identifying the microscopic constituents of the universe and their fundamental dynamics, and of…
We present results from a detailed numerical study of the small-scale and loop production properties of cosmic string networks, based on the largest and highest resolution string simulations to date. We investigate the non-trivial fractal…
The aim of this work is to review the concepts of time in quantum mechanics and general relativity to show their incompatibility. We show that the absolute character of Newtonian time is present in quantum mechanics and also partially in…
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…
We study a class of perturbative scalar quantum field theories where dynamics is characterized by Lorentz-invariant or Lorentz-breaking non-local operators of fractional order and the underlying spacetime has a varying spectral dimension.…
The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In this work we carry out a detailed renormalization group study of the spectral dimension $d_s$ and walk…
This review consists of two parts. The first part establishes certain astrophysical bounds on the smoothness of classical spacetime. Some of the best bounds to date are based on the absence of vacuum Cherenkov radiation in ultrahigh-energy…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…