scholarly journals Thermodynamics of Ideal Gas at Planck Scale with Strong Quantum Gravity Measurement

2021 ◽  
Author(s):  
Latevi Mohamed Lawson
Keyword(s):  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Free Particle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Ideal Gas ◽  
Minimal Length ◽  
Maximal Length ◽  
Gravity Measurement ◽  
Thermodynamic Quantities

Abstract More recently in J. Phys. A: Math. Theor. 53, 115303 (2020), we have introduced a set of noncommutative algebra that describes the space-time at the Planck scale. The interesting significant result we found is that the generalized uncertainty principle induced a maximal length of quantum gravity which has different physical implications to the one of generalized uncertainty principle with minimal length. The emergence of a maximal length in this theory revealed strong quantum gravitational effects at this scale and predicted the detection of gravity particles with low energies. To make evidence of these predictions, we study the dynamics of a free particle confined in an infinite square well potential in one dimension of this space. Since the effects of quantum gravity are strong in this space, we show that the energy spectrum of this system is weakly proportional to the ordinary one of quantum mechanics free of the theory of gravity. The states of this particle exhibit proprieties similar to the standard coherent states which are consequences of quantum fluctuation at this scale. Then, with the spectrum of this system at hand, we analyze the thermodynamic quantities within the canonical and micro-canonical ensembles of an ideal gas made up of N indistinguishable particles at the Planck scale. The results show a complete consistency between both statistical descriptions. Furthermore, a comparison with the results obtained in the context of minimal length scenarios and black hole theories indicates that the maximal length in this theory induces logarithmic corrections of deformed parameters which are consequences of a strong quantum gravitational effect.

scholarly journals Exotic fermionic fields and minimal length

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
J. M. Hoff da Silva ◽  
D. Beghetto ◽  
R. T. Cavalcanti ◽  
R. da Rocha
Keyword(s):  
Dirac Equation ◽  
Quantum Gravity ◽  
Dirac Operator ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Dynamical Equations ◽  
Spacetime Manifold ◽  
Fermionic Fields

Abstract We investigate the effective Dirac equation, corrected by merging two scenarios that are expected to emerge towards the quantum gravity scale. Namely, the existence of a minimal length, implemented by the generalized uncertainty principle, and exotic spinors, associated with any non-trivial topology equipping the spacetime manifold. We show that the free fermionic dynamical equations, within the context of a minimal length, just allow for trivial solutions, a feature that is not shared by dynamical equations for exotic spinors. In fact, in this coalescing setup, the exoticity is shown to prevent the Dirac operator to be injective, allowing the existence of non-trivial solutions.

scholarly journals Towards Thermodynamics with Generalized Uncertainty Principle

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ahmed Farag Ali ◽  
Mohamed Moussa
Keyword(s):  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Ideal Gas ◽  
Considerable Change ◽  
Heisenberg Uncertainty Principle ◽  
Ideal Gases ◽  
Quantum Gravity Effect ◽  
Photon Gas ◽  
Heisenberg Uncertainty

Various frameworks of quantum gravity predict a modification in the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP). Introducing quantum gravity effect makes a considerable change in the density of states inside the volume of the phase space which changes the statistical and thermodynamical properties of any physical system. In this paper we investigate the modification in thermodynamic properties of ideal gases and photon gas. The partition function is calculated and using it we calculated a considerable growth in the thermodynamical functions for these considered systems. The growth may happen due to an additional repulsive force between constitutes of gases which may be due to the existence of GUP, hence predicting a considerable increase in the entropy of the system. Besides, by applying GUP on an ideal gas in a trapped potential, it is found that GUP assumes a minimum measurable value of thermal wavelength of particles which agrees with discrete nature of the space that has been derived in previous studies from the GUP.

scholarly journals Maximally Localized States and Quantum Corrections of Black Hole Thermodynamics in the Framework of a New Generalized Uncertainty Principle

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Yan-Gang Miao ◽  
Ying-Jie Zhao ◽  
Shao-Jun Zhang
Keyword(s):  
Black Hole ◽  
Uncertainty Principle ◽  
Decay Time ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Localized States ◽  
Quantum Corrections ◽  
Thermodynamic Quantities ◽  
Mixing Effect ◽  
Significant Difference

As a generalized uncertainty principle (GUP) leads to the effects of the minimal length of the order of the Planck scale and UV/IR mixing, some significant physical concepts and quantities are modified or corrected correspondingly. On the one hand, we derive the maximally localized states—the physical states displaying the minimal length uncertainty associated with a new GUP proposed in our previous work. On the other hand, in the framework of this new GUP we calculate quantum corrections to the thermodynamic quantities of the Schwardzschild black hole, such as the Hawking temperature, the entropy, and the heat capacity, and give a remnant mass of the black hole at the end of the evaporation process. Moreover, we compare our results with that obtained in the frameworks of several other GUPs. In particular, we observe a significant difference between the situations with and without the consideration of the UV/IR mixing effect in the quantum corrections to the evaporation rate and the decay time. That is, the decay time can greatly be prolonged in the former case, which implies that the quantum correction from the UV/IR mixing effect may give rise to a radical rather than a tiny influence to the Hawking radiation.

scholarly journals Primordial big bang nucleosynthesis and generalized uncertainty principle

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Giuseppe Gaetano Luciano
Keyword(s):  
Uncertainty Principle ◽  
Deformation Parameter ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Big Bang ◽  
Minimal Length ◽  
Gravity Models ◽  
Light Elements ◽  
Semiclassical Approach ◽  
Big Bang Nucleosynthesis

AbstractThe Generalized Uncertainty Principle (GUP) naturally emerges in several quantum gravity models, predicting the existence of a minimal length at Planck scale. Here, we consider the quadratic GUP as a semiclassical approach to thermodynamic gravity and constrain the deformation parameter by using observational bounds from Big Bang Nucleosynthesis and primordial abundances of the light elements $${}^4 He, D, {}^7 Li$$ 4 H e , D , 7 L i . We show that our result fits with most of existing bounds on $$\beta $$ β derived from other cosmological studies.

scholarly journals Minimal length and the flow of entropy from black holes

2018 ◽  
Vol 27 (14) ◽  
pp. 1847028 ◽  
Author(s):  
Ana Alonso-Serrano ◽  
Mariusz P. Da̧browski ◽  
Hussain Gohar
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Hawking Radiation ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Evaporation Process ◽  
Black Hole Evaporation ◽  
The Impact

The existence of a minimal length, predicted by different theories of quantum gravity, can be phenomenologically described in terms of a generalized uncertainty principle. We consider the impact of this quantum gravity motivated effect onto the information budget of a black hole and the sparsity of Hawking radiation during the black hole evaporation process. We show that the information is not transmitted at the same rate during the final stages of the evaporation, and that the Hawking radiation is not sparse anymore when the black hole approaches the Planck mass.

scholarly journals Effect of Generalized Uncertainty Principle on Main-Sequence Stars and White Dwarfs

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed Moussa
Keyword(s):  
Quantum Gravity ◽  
Uncertainty Principle ◽  
White Dwarfs ◽  
Main Sequence ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Main Sequence Stars ◽  
Emden Equation ◽  
Astrophysical Objects ◽  
Applicable Range

This paper addresses the effect of generalized uncertainty principle, emerged from different approaches of quantum gravity within Planck scale, on thermodynamic properties of photon, nonrelativistic ideal gases, and degenerate fermions. A modification in pressure, particle number, and energy density are calculated. Astrophysical objects such as main-sequence stars and white dwarfs are examined and discussed as an application. A modification in Lane-Emden equation due to a change in a polytropic relation caused by the presence of quantum gravity is investigated. The applicable range of quantum gravity parameters is estimated. The bounds in the perturbed parameters are relatively large but they may be considered reasonable values in the astrophysical regime.

scholarly journals A novel mechanism for probing the Planck scale

2021 ◽  
Author(s):  
Saurya Das ◽  
Sujoy Modak
Keyword(s):  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Relativistic Correction ◽  
Leading Order ◽  
Mean Velocity ◽  
Important Improvement ◽  
Gravity Effects ◽  
Time Required

Abstract The Planck or the quantum gravity scale, being $16$ orders of magnitude greater than the electroweak scale, is often considered inaccessible by current experimental techniques. However, it was shown recently by one of the current authors that quantum gravity effects via the Generalized Uncertainty Principle affects the time required for free wavepackets to double their size, and this difference in time is at or near current experimental accuracies [1,2]. In this work, we make an important improvement over the earlier study, by taking into account the leading order relativistic correction, which naturally appears in the sytems under consideration, due to the significant mean velocity of the travelling wavepackets. Our analysis shows that although the relativistic correction adds nontrivial modifications to the results of [1,2], the earlier claims remain intact and are in fact strengthened. We explore the potential for these results being tested in the laboratory.

scholarly journals ENTROPY OF THE FRW UNIVERSE BASED ON THE GENERALIZED UNCERTAINTY PRINCIPLE

2010 ◽  
Vol 25 (15) ◽  
pp. 1267-1274 ◽  
Author(s):  
WONTAE KIM ◽  
YOUNG-JAI PARK ◽  
MYUNGSEOK YOON
Keyword(s):  
Uncertainty Principle ◽  
Apparent Horizon ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Minimal Length ◽  
Time Dependent ◽  
Brick Wall ◽  
Statistical Entropy ◽  
Frw Universe ◽  
Wall Method

The statistical entropy of the FRW universe described by time-dependent metric is newly calculated using the brick wall method based on the general uncertainty principle with the minimal length. We can determine the minimal length with the Planck scale to obtain the entropy proportional to the area of the cosmological apparent horizon.

scholarly journals EFFECT OF THE GENERALIZED UNCERTAINTY PRINCIPLE ON COMPACT STARS

2013 ◽  
Vol 22 (05) ◽  
pp. 1350020 ◽  
Author(s):  
AHMED FARAG ALI ◽  
ABDEL NASSER TAWFIK
Keyword(s):  
String Theory ◽  
Thermodynamic Properties ◽  
Quantum Gravity ◽  
Special Relativity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Compact Stars ◽  
Doubly Special Relativity ◽  
Heisenberg Principle

Based on the generalized uncertainty principle (GUP), proposed by some approaches to quantum gravity such as string theory and doubly special relativity theories, we investigate the effect of GUP on the thermodynamic properties of compact stars with two different components. We note that the existence of quantum gravity correction tends to resist the collapse of stars if the GUP parameter α is taking values between Planck scale and electroweak scale. Comparing with approaches, it is found that the radii of compact stars become smaller relative to the cases utilizing standard Heisenberg principle. Increasing energy almost exponentially decreases the radii of compact stars.

scholarly journals MINIMAL LENGTH AND GENERALIZED DIRAC EQUATION

2005 ◽  
Vol 20 (40) ◽  
pp. 3095-3103 ◽  
Author(s):  
KOUROSH NOZARI ◽  
MOJDEH KARAMI
Keyword(s):  
Dirac Equation ◽  
String Theory ◽  
Eigenvalue Problem ◽  
Quantum Gravity ◽  
Free Particle ◽  
Planck Scale ◽  
Minimal Length ◽  
Generalized Dirac Equation ◽  
Modified Dirac Equation

Existence of a minimal observable length which has been indicated by string theory and quantum gravity, leads to a modification of Dirac equation. In this letter we find this modified Dirac equation and solve its eigenvalue problem for a free particle. We will show that due to background spacetime fluctuation, it is impossible to have free particle in Planck scale.

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