Related papers: Some Aspects of Minimal Length Quantum Mechanics
Recently, the authors presented a covariant extension of the Generalized Uncertainty Principle (GUP) with a Lorentz invariant minimum length. This opens the way for constructing and exploring the observable consequences of minimum length in…
The minimal-length paradigm, a possible implication of quantum gravity at low energies, is commonly understood as a phenomenological modification of Heisenberg's uncertainty relation. We show that this modification is equivalent to a…
When minimal length uncertainty emerging from generalized uncertainty principle (GUP) is thoughtfully implemented, it is of great interest to consider its impacts on {\it "gravitational} Einstein field equations (gEFE) and to try to find…
The fundamental physical description of Nature is based on two mutually incompatible theories: Quantum Mechanics and General Relativity. Their unification in a theory of Quantum Gravity (QG) remains one of the main challenges of theoretical…
In this paper, we clarify a foundational loose end affecting the phenomenological approach to quantum gravity centered around the generalization of Heisenberg uncertainty principle. This misconception stems from a series of recently…
We discuss a Gedanken experiment for the measurement of the area of the apparent horizon of a black hole in quantum gravity. Using rather general and model-independent considerations we find a generalized uncertainty principle which agrees…
In this paper we study the effects of the Generalized Uncertainty Principle (GUP) on the spectrum of a particle that is bouncing vertically and elastically on a smooth reflecting floor in the Earth's gravitational field (a quantum bouncer).…
A maximun acceleration analysis by Pati dating back to 1992 is here improved by replacing the traditional Heisenberg Uncertainty Principle (HUP) with the Generalized Uncertainty Principle (GUP), which predicts the existence of a minimum…
The generalized uncertainty principle (GUP) is a gravitational correction of Heisenberg's uncertainty principle, which allows us to probe some features of quantum gravity even without the full theory. We are used to working with metric…
The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for…
The effects of the generalized uncertainty principle (GUP) on the low-energy stationary states of a particle moving in a cavity with no sharp boundaries are determined by means of the perturbation expansion in the framework of…
Different candidates of quantum gravity proposal such as string theory, noncommutative geometry, loop quantum gravity and doubly special relativity, all predict the existence of a minimum observable length and/or a maximal momentum which…
The concept of minimum length, widely accepted as a low-energy effect of quantum gravity, manifests itself in quantum mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at the heart of similar…
The possibility of finding the measurable maximal energy and the minimal time interval is discussed in different quantum aspects. It is found that the linear generalized uncertainty principle (GUP) approach gives a non-physical result.…
We extend significantly previous works on the Hilbert space representations of the Generalized Uncertainty Principle (GUP) in 3+1 dimensions of the form $[X_i,P_j] = i F_{ij}$ where $ F_{ij} = f(P^2) \delta_{ij} + g(P^2) P_i P_j $ for any…
Several theories that attempt to unify quantum theory and gravitational theory assume that space has an observable limiting resolution related to the Planck length, denoted by $\sqrt{\beta_0}L_p$. Quantum mechanically, this concept derives…
The cosmological particle horizon is the maximum measurable length in the Universe. The existence of such a maximum observable length scale implies a modification of the quantum uncertainty principle. Thus due to non-locality of quantum…
There are several theoretical indications that the quantum gravity approaches may have predictions for a minimal measurable length, and a maximal observable momentum and throughout a generalization for Heisenberg uncertainty principle. The…
The existence of a minimal observable length has long been suggested, in quantum gravity, as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal…
The existence of a minimum length and a generalization of the Heisenberg uncertainty principle seem to be two fundamental ingredients required in any consistent theory of quantum gravity. In this letter we show that they would predict…