Attempts to formulate a quantum theory of gravitation are collectively known as quantum gravity. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special relativity theories predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-...

This paper provides a brief introduction to Loop Quantum Gravity which is the main competitor of String Theory for a quantized theory of gravity. It is formulated on the basis of a Hamiltonian formalism of General Relativity with quantization performed in a non-perturbative and background independent manner. Coupling to matter fields as they appear in the Standard Model is also considered. Cano...

Until the middle of the 1990’s, string theory had a reputation for being a rather ambitious formalism that, while being the most promising candidate for unifying gravity with the Standard Model, had provided few concrete, testable predictions or applications. This changed following Maldacena’s proposal, the AdS/CFT correspondence or gauge/gravity duality [36, 2], in 1997; building on holographi...

Over the last few years the study of possible Planck-scale departures from classical Lorentz symmetry has been one of the most active areas of quantum-gravity research. We now have a satisfactory description of the fate of Lorentz symmetry in the most popular noncommutative spacetimes and several studies have been devoted to the fate of Lorentz symmetry in loop quantum gravity. Remarkably there...

Using the canonical formalism for spherically symmetric black hole inside the apparent horizon we investigate the mass inflation in the Reissner-Nordström black hole in the framework of quantum gravity. It is shown that like in classical gravity the combination of the effects of the influx coming from the past null infinity and the outflux backscattered by the black hole’s curvature causes the ...

2. Quantum gravity is an important and to great extent unsolved problem. There are many different approaches to the quantization of the metric field, both perturbative and non-perturbative. The current situation in the perturbative quantum gravity is characterized by a number of different models, some of them well elaborated but no one perfect nor mathematically neither phenomenologically, main...

Quantum gravity presents something of a unique puzzle for the philosophy of science. For in a very real sense, there is no such thing as quantum gravity. Despite near unanimous agreement among physicists that a quantum theory of gravitation is needed to reconcile the contradictions between general relativity and quantum mechanics, there are no pressing empirical issues that require this resolut...

Graviton pairing and destruction of these pairs under collisions with bodies may lead to the Newtonian attraction. It opens us a new way to a very-low-energy quantum gravity model. In the model by the author, cosmological redshifts are caused by interactions of photons with gravitons of the background. Non-forehead collisions with gravitons lead to an additional relaxation of any photonic flux....

A growing number of studies is being devoted to the identification of plausible quantum properties of spacetime which might give rise to observably large effects. The literature on this subject is now relatively large, including studies in string theory, loop quantum gravity and noncommutative geometry. It is useful to divide the various proposals into proposals involving a systematic quantum-g...