scholarly journals On the Generalized Uncertainty Principle

2021 ◽  
Author(s):  
Ming-Cheng Chen ◽  
Chao-Yang Lu ◽  
Jian-Wei Pan
Keyword(s):  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Thought Experiment ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Physical Systems ◽  
New Directions ◽  
Quantum Version ◽  
Coupling Principle

Generalized Uncertainty Principle (GUP), which manifests a minimal Planck length in quantum spacetime, is central in various quantum gravity theories and has been widely used to describe the Planck-scale phenomenon. Here, we propose a thought experiment based on GUP – as a quantum version of Galileo's falling bodies experiment – to show that the experimental results cannot be consistently described in quantum mechanics. This paradox arises from the interaction of two quantum systems in an interferometer, a photon and a mirror, with different effective Planck constants. Our thought experiment rules out the widely used GUP, and establishes a Quantum Coupling Principle that two physical systems of different effective Planck constants cannot be consistently coupled in quantum mechanics. Our results point new directions to quantum gravity.

scholarly journals A CLASS OF GUP SOLUTIONS IN DEFORMED QUANTUM MECHANICS

2010 ◽  
Vol 19 (12) ◽  
pp. 2003-2009 ◽  
Author(s):  
POURIA PEDRAM
Keyword(s):  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Loop Quantum Gravity ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Uncertainty Principle ◽  
Deformed Algebra ◽  
Heisenberg Uncertainty

Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to the so-called generalized uncertainty principle (GUP). This approach results from the modification of the commutation relations and changes all Hamiltonians in quantum mechanics. In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrödinger equations. These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum. We show that this procedure prevents us from doing equivalent but lengthy calculations.

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 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 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 Discreteness of Curved Spacetime from GUP

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Ahmad Adel Abutaleb
Keyword(s):  
Dirac Equation ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Curved Spacetime ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Heisenberg's Uncertainty Principle ◽  
Area And Volume

Diverse theories of quantum gravity expect modifications of the Heisenberg's uncertainty principle near the Planck scale to a so-called Generalized uncertainty principle (GUP). It was shown by some authors that the GUP gives rise to corrections to the Schrodinger , Klein-Gordon, and Dirac equations. By solving the GUP corrected equations, the authors arrived at quantization not only of energy but also of box length, area, and volume. In this paper, we extend the above results to the case of curved spacetime (Schwarzschild metric). We showed that we arrived at the quantization of space by solving Dirac equation with GUP in this metric.

scholarly journals Position in Minimal Length Quantum Mechanics

Universe ◽  
2021 ◽  
Vol 8 (1) ◽  
pp. 17
Author(s):  
Pasquale Bosso
Keyword(s):  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Standard Theory ◽  
Heisenberg Uncertainty Principle ◽  
Simple Quantum ◽  
Heisenberg Uncertainty ◽  
Quantum Mechanical Systems

Several approaches to quantum gravity imply the presence of a minimal measurable length at high energies. This is in tension with the Heisenberg Uncertainty Principle. Such a contrast is then considered in phenomenological approaches to quantum gravity by introducing a minimal length in quantum mechanics via the Generalized Uncertainty Principle. Several features of the standard theory are affected by such a modification. For example, position eigenstates are no longer included in models of quantum mechanics with a minimal length. Furthermore, while the momentum-space description can still be realized in a relatively straightforward way, the (quasi-)position representation acquires numerous issues. Here, we will review such issues, clarifying aspects regarding models with a minimal length. Finally, we will consider the effects of such models on simple quantum mechanical systems.

scholarly journals Prediction for the cosmological constant and constraints on SUSY GUTs in resummed quantum gravity

2018 ◽  
Vol 33 (29) ◽  
pp. 1830028
Author(s):  
B. F. L. Ward
Keyword(s):  
General Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Planck Scale ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty

Working in the context of the Planck scale cosmology formulation of Bonanno and Reuter, we use our resummed quantum gravity approach to Einstein’s general theory of relativity to estimate the value of the cosmological constant as [Formula: see text]. We show that SUSY GUT models are constrained by the closeness of this estimate to experiment. We also address various consistency checks on the calculation. In particular, we use the Heisenberg uncertainty principle to remove a large part of the remaining uncertainty in our estimate of [Formula: see text].

scholarly journals Remarks on Remnants by Fermions’ Tunnelling from Black Strings

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Deyou Chen ◽  
Zhonghua Li
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Final Stage ◽  
Generalized Uncertainty Principle ◽  
Black Hole Evaporation ◽  
Quantum Numbers ◽  
Black Strings

Hawking’s calculation is unable to predict the final stage of the black hole evaporation. When effects of quantum gravity are taken into account, there is a minimal observable length. In this paper, we investigate fermions’ tunnelling from the charged and rotating black strings. With the influence of the generalized uncertainty principle, the Hawking temperatures are not only determined by the rings, but also affected by the quantum numbers of the emitted fermions. Quantum gravity corrections slow down the increases of the temperatures, which naturally leads to remnants left in the evaporation.

Sign in / Sign up

Export Citation Format

Share Document