Generalized Uncertainty Principle Research Articles

A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound

Motivated by the potential connection between metric-affine gravity and linear generalized uncertainty principle (GUP) in the phase space, we develop a covariant form of linear GUP and an associated modified Poincaré algebra, which exhibits distinctive behavior, nearing nullity at the minimal length scale proposed by linear GUP. We use three-torus geometry to visually represent linear GUP within a covariant framework. The three-torus area provides an exact geometric representation of Bekenstein’s universal bound. We depart from Bousso’s approach, which adapts Bekenstein’s bound by substituting the Schwarzschild radius ( rs ) with the radius (R) of the smallest sphere enclosing the physical system, thereby basing the covariant entropy bound on the sphere’s area. Instead, our revised covariant entropy bound is described by the area of a three-torus, determined by both the inner radius rs and outer radius R where rs⩽R due to gravitational stability. This approach results in a more precise geometric representation of Bekenstein’s bound, notably for larger systems where Bousso’s bound is typically much larger than Bekensetin’s universal bound. Furthermore, we derive an equation that turns the standard uncertainty inequality into an equation when considering the contribution of the three-torus covariant entropy bound, suggesting a new avenue of quantum gravity.

Relativistic generalised uncertainty and the corrected vacuum energy

Abstract In this short paper we make use of the recent covariant extension of the
generalised uncertainty principle to study the corrections to the vacuum energy
of the simplest scalar quantum field theory. We then calculate the modifications
to the Casimir effect that such a correction to the vacuum energy would bring
about. We emphasise that these corrections are indeed physical.

Casimir wormhole with GUP correction in extended symmetric teleparallel gravity

Quantum mechanical concept such as the Casimir effect is explored to model traversable wormholes in an extended symmetric teleparallel gravity theory. The minimal length concept leading to the generalized uncertainty principle (GUP) is used to obtain the Casimir energy density. The effect of the GUP correction in the geometrical and physical properties of traversable Casimir wormholes are investigated. It is noted that the GUP correction has a substantial effect on the wormhole geometry and it modifies the energy condition. From a detailed calculation of the exotic matter content of the GUP corrected Casimir wormhole, it is shown that, a minimal amount of exotic matter is sufficient to support the stability of the wormhole.

On some quantum correction to the Coulomb potential in generalized uncertainty principle approach

Taking into account the importance of the unified theory of quantum mechanics and gravity, and the existence of a minimal length of the order of the Planck scale, we consider a modified Schrödinger equation resulting from a generalized uncertainty principle, which finds applications from the realm of quantum information to large-scale physics, with a quantum mechanically corrected gravitational interaction proposed very recently. As the resulting equation cannot be solved by common exact approaches, we propose a Bethe ansatz approach, which will be applied and whose results we will discuss, commenting on the analogy of the present study with some other interesting physical problems.

Thermodynamics of harmonic oscillator with minimal length

Abstract The generalized uncertainty principle has been applied to the Schr"{o}dinger wave equation for a one-dimensional harmonic oscillator to generate a sixth-order generalized Schr"{o}dinger equation in the position representation. 
The energy eigenvalues and the eigenfunctions of the sixth-order equation have been obtained. The results show the approximate correction terms of the energies due to the modified uncertainty principle. The quantum partition functions derived from the energy eigenvalue have also been used to study the thermodynamic properties of the system. The results suggest a lower bound for the minimal length equivalent to the thermal wavelength of the oscillator at very high temperature.

First-order quantum correction of thermodynamics in a charged accelerating AdS black hole with gauge potential

In this paper, we study the tunneling radiation from a charged-accelerating AdS black hole with gauge potential under the impact of quantum gravity. Using the semi-classical phenomenon known as the Hamilton–Jacobi ansatz, it is studied that tunneling radiation occurs via the horizon of a black hole and also employs the Lagrangian equation using the generalized uncertainty principle. Furthermore, we investigate the impact of charge, gauge potential, and first order correction parameters on the temperature as well as the stable and unstable states of the black hole. We also compute thermodynamic properties such as entropy, internal energy, Helmholtz free energy, enthalpy, specific heat, and Gibbs free energy under the impact of the correction parameter for the black hole. We calculate the logarithmic modification terms for entropy around the equilibrium state to analyze the impacts of logarithmic correction. In the presence of the correction terms, we also check the validity of the thermodynamics. It examines the graphical representation of the influence of logarithmic correction on the thermodynamic properties of black hole stability as well as charged, accelerating, and gauge potential parameters.

Non-singular gravitational collapse through modified Heisenberg algebra

We study the effects of cut-off physics, in the form of a modified algebra inspired by Polymer Quantum Mechanics and by the Generalized Uncertainty Principle representation, on the collapse of a spherical dust cloud. We analyze both the Newtonian formulation, originally developed by Hunter, and the general relativistic formulation, that is the Oppenheimer–Snyder model; in both frameworks we find that the collapse is stabilized to an asymptotically static state above the horizon, and the singularity is removed. In the Newtonian case, by requiring the Newtonian approximation to be valid, we find lower bounds of the order of unity (in Planck units) for the deformation parameter of the modified algebra. We then study the behaviour of small perturbations on the non-singular collapsing backgrounds, and find that for certain range of the parameters (the polytropic index for the Newtonian case and the sound velocity in the relativistic setting) the collapse is stable to perturbations of all scales, and the non-singular super-Schwarzschild configurations have physical meaning.

Conditional Effects, Observables and Instruments

We begin with a study of operations and the effects they measure. We define the probability that an effect $a$ occurs when the system is in a state $\rho$ by $P_{\rho}(a)=\textrm{Tr}(\rho a)$. If $P_{\rho}(a)\ne0$ and $\mathcal{I}$ is an operation that measures $a$, we define the conditional probability of an effect $b$ given $a$ relative to $\mathcal{I}$ by $P_{\rho}(b\mid a)=\textrm{Tr}[\mathcal{I}(\rho)b]/P_{\rho}(a)$. We characterize when Bayes' quantum second rule $P_{\rho}(b\mid a)=\frac{P_{\rho}(b)}{P_{\rho}(a)}\,P_{\rho}(a\mid b)$ holds. We then consider Lüders and Holevo operations. We next discuss instruments and the observables they measure. If $A$ and $B$ are observables and an instrument $\mathcal{I}$ measures $A$, we define the observable $B$ conditioned on $A$ relative to $\mathcal{I}$ and denote it by $(B\mid A)$. Using these concepts, we introduce Bayes' quantum first rule. We observe that this is the same as the classical Bayes' first rule, except it depends on the instrument used to measure $A$. We then extend this to Bayes' quantum first rule for expectations. We show that two observables $B$ and $C$ are jointly commuting if and only if there exists an atomic observable $A$ such that $B=(B\mid A)$ and $C=(C\mid A)$. We next obtain a general uncertainty principle for conditioned observables. Finally, we discuss observable conditioned quantum entropies. The theory is illustrated with many examples.Quanta 2024; 13: 1–10.

Uncertainty principle from the noise of gravitons

The effect of the noise induced by gravitons in the case of a freely falling particle from the viewpoint of an external observer has been recently calculated in Phys. Rev. D 107, 066024 (2023). There the authors have calculated the quantum gravity modified Newton’s law of free fall where the spacetime has been considered to be weakly curved. In our work, we extend this work by calculating the variance in the velocity and eventually the momentum of the freely falling massive particle. From this simple calculation, we observe that the product of the standard deviation in the position with that of the standard deviation in momentum picks up a higher order correction which is proportional to the square of the standard deviation in momentum. We also find out that in the Planck limit (both Planck length and Planck mass), this uncertainty product gives the well-known form of the generalized uncertainty principle. We then calculate a similar uncertainty product when the graviton is in a squeezed state, and eventually, we get back the same uncertainty product. Finally, we extend our analysis for the gravitons being in a thermal state and obtain a temperature-dependent uncertainty product. If one replaces this temperature with the Planck temperature and the mass of the particle by the Planck mass, the usual uncertainty product appears once again. We also obtain an upper bound of the uncertainty product thereby giving a range of the product of the variances in position and momentum.

Black hole evaporation and its remnants with the generalized uncertainty principle including a linear term

In recent years, researchers have investigated the evaporation of Schwarzschild black holes using various forms of the generalized uncertainty principle (GUP), metric quantum correction, and non-commutative geometry, respectively. However, there are differences between the GUP correction and the other two methods in terms of describing the later stages of black hole evaporation. Furthermore, some studies argue that the GUP with a negative parameter cannot effectively correct black hole evaporation, while others contend that the positivity or negativity of the GUP parameters should not affect the correction results. Taking the above into consideration, we reconsider black hole evaporation with the generalized uncertainty principle including a linear term (LGUP), and examine the case of negative parameters. The results indicate that the evaporation behavior of both Schwarzschild black holes and Reissner–Nordström black holes, under LGUP correction, is consistent with the results of metric quantum correction and non-commutative geometry. Additionally, the negative parameter LGUP can also effectively correct for black hole evaporation.

Neutral current neutrino-electron scattering and generalized uncertainty principle

In this article, we study the effect of quantum gravitational corrections on neutrino electron scattering in electroweak theory SU(2) L × U(1) Y . We consider a neutrino that scatters off an electron by an exchange of a massive neutral gauge boson. In the minimal length formalism, starting from the equation of motion for a massive gauge field we obtain the propagator. And currents are obtained from the action for a massless Dirac fermion. Scattering amplitudes and differential cross sections as function of inelasticity variable y are obtained using expressions of the propagator and leptonic current. All usual expressions are recovered when the deformation parameter α tends to zero. We find that quantum gravitational effects become important only for a highly energetic process with a momentum transfer being much greater than the neutral gauge boson mass.

Effects of a generalized uncertainty principle on the MIT bag model equation of state

AbstractThe Generalized Uncertainty Principle (GUP) is motivated by the premise that spacetime fluctuations near the Planck scale impose a lower bound on the achievable resolution of distances, leading to a minimum length. Inspired by a semiclassical method that integrates the GUP into the partition function by deforming its phase space, we induce a modification on the thermodynamic quantities of the MIT bag model that we propose serves as an effective semiclassical description of deconfined quark matter in a space with minimal length. We investigate the consequences of this deformation on the zero‐temperature limit, revealing a saturation limit for the energy density, pressure, and baryon number density and an overall decrease of the thermodynamic quantities which suggests an enhanced stability against gravitational collapse. These findings extend existing research on GUP‐deformed Fermi gases. Ultimately, our description introduces the effects of quantum gravity in the equations of state for compact stars in a mathematically simple manner, suggesting the potential for extension to more complex systems.

Gravitational observations and LQGUP

Motivated by recent works, we employ the bounds on the dimensionless quantum-gravity parameter obtained from six solar system-based gravitational tests in order to obtain bounds on the dimensionless parameter of the generalized uncertainty principle with linear and quadratic terms in momentum. The bounds obtained here are much tighter than those obtained, from the same six solar system-based gravitational tests, for the dimensionless parameter of the uncertainty principle with only quadratic terms in momentum.

Unveiling phase space modifications: A clash of modified gravity and the generalized uncertainty principle

Unveiling phase space modifications: A clash of modified gravity and the generalized uncertainty principle

Thermodynamics in a quantum corrected Reissner–Nordström–AdS black hole and its GUP-corrections

We calculate the thermodynamic quantities in the quantum corrected Reissner–Nordström–AdS (RN-AdS) black hole, and examine their quantum corrections. By analyzing the mass and heat capacity, we give the critical state and the remnant state, respectively, and discuss their consistency. Then, we investigate the quantum tunneling from the event horizon of massless scalar particle by using the null geodesic method, and charged massive boson W ± and fermions by using the Hamilton–Jacob method. It is shown that the same Hawking temperature can be obtained from these tunneling processes of different particles and methods. Next, by using the generalized uncertainty principle (GUP), we study the quantum corrections to the tunneling and the temperature. Then the logarithmic correction to the black hole entropy is obtained.

Exploring the Implications of the Deformation Parameter and Minimal Length in the Generalized Uncertainty Principle

Exploring the Implications of the Deformation Parameter and Minimal Length in the Generalized Uncertainty Principle

Hawking radiation under generalized uncertainty principle

The generalized uncertainty relation is expected to be an essential element in a theory of quantum gravity. In this work, we examine its effect on the Hawking radiation of a Schwarzschild black hole formed from collapse by incorporating a minimal uncertainty length scale into the radial coordinate of the background. This is implemented in both the ingoing Vaidya coordinates and a family of freely falling coordinates. We find that, regardless of the choice of the coordinate system, Hawking radiation is turned off at around the scrambling time. Interestingly, this phenomenon occurs while the Hawking temperature remains largely unmodified.

Non-singular collapse scenario from generalized uncertainty principle

Non-singular collapse scenario from generalized uncertainty principle

Constraining Snyder and GUP models with low-mass stars

We investigate the application of an equation of state that incorporates corrections derived from the Snyder model (and the Generalized Uncertainty Principle) to describe the behaviour of matter in a low-mass star. Remarkably, the resulting equations exhibit striking similarities to those arising from modified Einstein gravity theories. By modeling matter with realistic considerations, we are able to more effectively constrain the theory parameters, surpassing the limitations of existing astrophysical bounds. The bound we obtain is β0≤4.5×1047\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _0 \\le 4.5 \ imes 10^{47}$$\\end{document}. We underline the significance of realistic matter modeling in order to enhance our understanding of effects arising in quantum gravity phenomenology and implications of quantum gravitational corrections in astrophysical systems.

Constraints via the Event Horizon Telescope for Black Hole Solutions with Dark Matter under the Generalized Uncertainty Principle Minimal Length Scale Effect

AbstractFour spherically symmetric but non‐asymptotically flat black hole solutions surrounded with spherical dark matter distribution perceived under the minimal length scale effect is derived via the generalized uncertainty principle. Here, the effect of this quantum correction, described by the parameter , is considered on a toy model galaxy with dark matter and the three well‐known dark matter distributions: the cold dark matter, scalar field dark matter, and the universal rotation curve. The aim is to find constraints to by applying these solutions to the known supermassive black holes: Sagittarius A (Sgr. A*) and Messier 87* (M87*), in conjunction with the available Event Horizon telescope. The effect of is then examined on the event horizon, photonsphere, and shadow radii, where unique deviations from the Schwarzschild case are observed. As for the shadow radii, bounds are obtained for the values of on each black hole solution at confidence level. The results revealed that under minimal length scale effect, black holes can give positive (larger shadow) and negative values (smaller shadow) of , which are supported indirectly by laboratory experiments and astrophysical or cosmological observations, respectively.