Quantum gravity and minimum length

A fundamental length is introduced into physics in a way which respects the principles of relativity and quantum field theory. This improves the properties of quantum field theory: divergences are removed. How to quantize gravity is also indicated. When the fundamental length tends to zero the present version of quantum field theory is recovered.

The traditional formulation of the ultimate goal of physics (in the narrower sense of axiomatic theory) involves the derivation of physical laws from first principles. Though, such option doesn't make things easier since the task of the first principles finding is not less complicated versus to the original problem. The alternative path for understanding the world around us is to interpret the fundamental limit values as a factor determining the physical laws structure. A sig...

Theories of Quantum Gravity predict a minimum measurable length and a corresponding modification of the Heisenberg Uncertainty Principle to the so-called Generalized Uncertainty Principle (GUP). However, this modification is usually formulated in non-relativistic language, making it unclear whether the minimum length is Lorentz invariant. We have formulated a Relativistic Generalized Uncertainty Principle, resulting in a Lorentz invariant minimum measurable length and the res...

We reply to the comment "A note on the innocuous implications of a minimum length in quantum gravity" by P.H. Frampton [Class. Quantum Grav. 26 (2009) 018001, arXiv:arXiv:0808.0283] on our paper "Dangerous implications of a minimum length in quantum gravity" [Class. Quantum Grav. 25 (2008) 195013, arXiv:0803.0749].

It is argued that the quadruple gravitational constant 4G can be seen as a fundamental limit of nature. The limit holds across all gravitational systems and distinguishes bound from unbound systems. Including the maximum force c^4/4G allows extending the Bronshtein cube of physical theories to a cube of limits. Every theory of physics refining Galilean physics - universal gravitation, special relativity, general relativity, quantum theory and quantum field theory - is defined...

The existence of a minimal length is a common prediction of various theories of quantum gravity. This minimal length leads to a modification of the Heisenberg uncertainty principle to a Generalized Uncertainty Principle (GUP). Various studies showed that a GUP modifies the Hawking radiation of black holes. In this paper, we propose a modification of the Schwarzschild metric based on the modified Hawking temperature derived from the GUP. Based on this modified metric, we calcu...

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 holes and how modified dispersion relations affect the Hawking decay, both in four space-time dimensions and in models with extra spatial dimensions. In the latter case, we briefly discuss possible phenomenological signatures.

In this work, we point out an overlooked and subtle feature of the generalized uncertainty principle (GUP) approach to quantizing gravity: namely that different pairs of modified operators with the same modified commutator, $[\hat{X},\hat{P}] = i \hbar (1+\beta p^2)$, may have different physical consequences such as having no minimal length at all. These differences depend on how the position and/or momentum operators are modified rather than only on the resulting modified co...

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 seemed to bound the minimal length scale to distances smaller than the Planck length, implying that spacetime appeared continuous to distances below the Planck length. This poses a challenge for such minimal distance models. Here we propos...

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 and the consequent minimal measurable length have important consequences on the dynamics of quantum systems. In the present work, we show that such consequences go beyond dynamics, reaching the definition of quantities such as energy, mome...