Related papers: The minimal length is physical
We review our work on the minimal length uncertainty relation as suggested by perturbative string theory. We discuss simple phenomenological implications of the minimal length uncertainty relation and then argue that the combination of the…
The effects of noncommutativity and of the existence of a minimal length on the phase space of a dilatonic cosmological model are investigated. The existence of a minimum length, results in the Generalized Uncertainty Principle (GUP), which…
There have been many papers suggesting that the parameter of the generalized uncertainty principle should be negative rather than positive in some specific scenarios, and the negative parameter can remove the minimum length. However, the…
Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of…
The canonical approach to quantizing quantum gravity is understood to suffer from pathological non-renomalizability. Nevertheless in the context of effective field theory, a viable perturbative approach to calculating elementary processes…
Modifications of Heisenberg's uncertainty relations have been proposed in the literature which imply a minimum position uncertainty. We study the low energy effects of the new physics responsible for this by examining the consequent change…
The existence of a minimum measurable length could deform not only the standard quantum mechanics but also classical physics. The effects of the minimal length on classical orbits of particles in a gravitation field have been investigated…
The full algebra of relativistic quantum mechanics (Lorentz plus Heisenberg) is unstable. Stabilization by deformation leads to a new deformation parameter $\epsilon \ell ^{2}$, $\ell $ being a length and $\epsilon$ a $\pm$ sign. The…
According to a number of arguments in quantum gravity, both model-dependent and model-independent, Heisenberg's uncertainty principle is modified when approaching the Planck scale. This deformation is attributed to the existence of a…
Based on quantum mechanical framework for the minimal length uncertainty, we demonstrate that the generalized uncertainty principle (GUP) parameter could be best constrained by recent gravitational waves observations on one hand. On other…
Many theories that attempt to formulate a quantum description of gravity suggest the existence of a fundamental minimum length scale. A popular method for incorporating this minimum length is through a modification of the Heisenberg…
We show that a deformation of the Heisenberg algebra which depends on a dimensionful parameter $\kappa$ is the algebraic structure which underlies the generalized uncertainty principle in quantum gravity. The deformed algebra and therefore…
We study the thermodynamics of various physical systems in the framework of the Generalized Uncertainty Principle that implies a minimal length uncertainty proportional to the Planck length. We present a general scheme to analytically…
In this article we examine a Generalized Uncertainty Principle which differs from the Heisenberg Uncertainty Principle by terms linear and quadratic in particle momenta, as proposed by the authors in an earlier paper. We show that this…
Theories of emergent gravity have established a deep connection between entropy and the geometry of spacetime by looking at the latter through a thermodynamic lens. In this framework, the macroscopic properties of gravity arise in a…
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position…
The Heisenberg Uncertainty Principle (HUP) limits the accuracy in the simultaneous measurements of the position and momentum variables of any quantum system. This is known to be true in the context of non-relativistic quantum mechanics.…
In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The…
A one-dimensional deformed Heisenberg algebra $[X,P]=if(P)$ is studied. We answer the question: For what function of deformation $f(P)$ there exists a nonzero minimal uncertainty in position (minimal length). We also find an explicit…
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…