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I have been asked to write brief, gentle introduction to the basic idea behind the field of "quantum gravity" in 1500 words or less. Doing so appears to be almost as great a challenge as coming up with a consistent theory of quantum…

Generic arguments lead to the idea that quantum gravity has a minimal length scale. A possible observational signal of such a minimal length scale is that photons should exhibit dispersion. In 2009 the observation of a short gamma ray burst…

The narrow and subtle difference between the Hilbert spaces of operators corresponding to the purely quantum mechanical momentum and the generalized momentum that includes minimal length effects is polished. Additionally, the existence of…

This note presents two ideas. The first one is that quantum theory has a fundamentally perturbative basis but leads to nonperturbative states which it would seem natural to take into account in the foundation of a theory of quantum…

Phenomenological studies of quantum gravity have proposed a modification of the commutator between position and momentum in quantum mechanics so to introduce a minimal uncertainty in position in quantum mechanics. Such a minimal uncertainty…

In this work it is demonstrated that, provided a theory involves a minimal length, this theory must be free from such infinitesimal quantities as infinitely small variations in surface of the holographic screen, its volume, and entropy. The…

The existence of a minimum length in quantum gravity is investigated by computing the in-in expectation value of the proper distance in the Schwinger-Keldysh formalism. No minimum geometrical length is found for arbitrary gravitational…

It has been proposed that the incorporation of an observer independent minimal length scale into the quantum field theories of the standard model effectively describes phenomenological aspects of quantum gravity. The aim of this paper is to…

This paper is a set of notes that we wrote concerning the first version of Emergent Gravity [gr-qc/0602022]. It is our version of an exercise that we proposed to some of our students. The idea was to find mathematical errors and…

After revival of the concept of minimal length, many investigations have been devoted, in literature, to estimate upper-bound on minimal length for systems like hydrogen atom, deuteron etc. We report here a possible origin of minimal length…

The present work is a continuation of the previous papers written by the author on the subject. In terms of the measurability (or measurable quantities) notion introduced in a minimal length theory, first the consideration is given to a…

In this Chapter we would like to review a "~phenomenological~" approach taking into account the most fundamental feature of string theory or, more in general, of quantum gravity, whatever its origin, which is the existence of a minimal…

Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards…

A modification to the time-energy uncertainty relation in quantum gravity has been interpreted as increasing the duration of fluctuations producing virtual black holes with masses greater than the Planck mass. I point out that such virtual…

We discuss the generic phenomenology of quantum gravity and, in particular, argue that the observable effects of quantum gravity, associated with new, extended, non-local, non-particle-like quanta, and accompanied by a dynamical…

This is a comment on articles Phys. Rev. Lett. 119, 240401 (2017) [arXiv:1707.06050] and Phys. Rev. Lett. 119, 240402 (2017) [arXiv:1707.06036]. We argue that gravity-induced entanglement by Newtonian forces is agnostic to the quantum or…

These lecture notes introduce the basic ideas of the Asymptotic Safety approach to Quantum Einstein Gravity (QEG). In particular they provide the background for recent work on the possibly multifractal structure of the QEG space-times.…

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…

We review the main consequences of the possible existence of a minimum measurable length, of the order of the Planck scale, on quantum effects occurring in black hole physics. In particular, we focus on the ensuing minimum mass for black…

Quantum gravitational corrections to black holes are studied in four and higher dimensions using a renormalisation group improvement of the metric. The quantum effects are worked out in detail for asymptotically safe gravity, where the…