Beyond the Planck Length

1991 ◽  
pp. 285-314
Author(s):  
Michio Kaku
Keyword(s):  
Planck Length

scholarly journals Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1309
Author(s):  
Jerzy Lukierski
Keyword(s):  
Phase Space ◽  
Hopf Algebras ◽  
Deformation Parameter ◽  
Heisenberg Algebra ◽  
Planck Length ◽  
Covariant Quantum ◽  
Drinfeld Twist ◽  
Quantum Deformations ◽  
Heisenberg Double ◽  
Conformal Symmetries

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed D=4 quantum inhomogeneous conformal Hopf algebras Uθ(su(2,2)⋉T4) and Uθ¯(su(2,2)⋉T¯4), where T4 describes complex twistor coordinates and T¯4 the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently, we introduce the quantum deformations of D=4 Heisenberg-conformal algebra (HCA) su(2,2)⋉Hℏ4,4 (Hℏ4,4=T¯4⋉ℏT4 is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length λp, is called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and the quantization map in Hℏ4,4. We also introduce generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra Uθ(su(2,2)⋉T4).

scholarly journals PROPOSAL OF A SECOND GENERATION OF QUANTUM-GRAVITY-MOTIVATED LORENTZ-SYMMETRY TESTS: SENSITIVITY TO EFFECTS SUPPRESSED QUADRATICALLY BY THE PLANCK SCALE

2003 ◽  
Vol 12 (09) ◽  
pp. 1633-1639 ◽  
Author(s):  
GIOVANNI AMELINO-CAMELIA
Keyword(s):  
Quantum Gravity ◽  
Second Generation ◽  
Loop Quantum Gravity ◽  
Planck Scale ◽  
Cosmic Ray ◽  
Lorentz Symmetry ◽  
Planck Length ◽  
Satisfactory Description ◽  
Symmetry Tests ◽  
Quantum Spacetime

Over the last few years the study of possible Planck-scale departures from classical Lorentz symmetry has been one of the most active areas of quantum-gravity research. We now have a satisfactory description of the fate of Lorentz symmetry in the most popular noncommutative spacetimes and several studies have been devoted to the fate of Lorentz symmetry in loop quantum gravity. Remarkably there are planned experiments with enough sensitivity to reveal these quantum-spacetime effects, if their magnitude is only linearly suppressed by the Planck length. Unfortunately, in some quantum-gravity scenarios even the strongest quantum-spacetime effects are suppressed by at least two powers of the Planck length, and many authors have argued that it would be impossible to test these quadratically-suppressed effects. I here observe that advanced cosmic-ray observatories and neutrino observatories can provide the first elements of an experimental programme testing the possibility of departures from Lorentz symmetry that are quadratically Planck-length suppressed.

scholarly journals Rainbow Gravity Corrections to the Entropic Force

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong-Wen Feng ◽  
Shu-Zheng Yang
Keyword(s):  
Black Hole ◽  
Field Equation ◽  
Quantum Gravity ◽  
Gravity Model ◽  
Einstein Field Equation ◽  
Friedmann Equation ◽  
Quantum Corrections ◽  
Entropic Force ◽  
Planck Length ◽  
Multifunctional Properties

The entropic force attracts a lot of interest for its multifunctional properties. For instance, Einstein’s field equation, Newton’s law of gravitation, and the Friedmann equation can be derived from the entropic force. In this paper, utilizing a new kind of rainbow gravity model that was proposed by Magueijo and Smolin, we explore the quantum gravity corrections to the entropic force. First, we derive the modified thermodynamics of a rainbow black hole via its surface gravity. Then, according to Verlinde’s theory, the quantum corrections to the entropic force are obtained. The result shows that the modified entropic force is related not only to the properties of the black hole but also to the Planck length lp and the rainbow parameter γ. Furthermore, based on the rainbow gravity corrected entropic force, the modified Einstein field equation and the modified Friedmann equation are also derived.

The “Planckonions”

2019 ◽  
Vol 34 (33) ◽  
pp. 1950268
Author(s):  
Mofazzal Azam ◽  
Farook Rahaman ◽  
M. Sami ◽  
Jitesh R. Bhatt
Keyword(s):  
Mass Formula ◽  
Energy Conditions ◽  
Generalized Function ◽  
Spherically Symmetric ◽  
Planck Length ◽  
Spherical Shells ◽  
Central Singularity ◽  
Time Component ◽  
Stellar Configuration ◽  
Central Sphere

We consider a spherically symmetric stellar configuration with a density profile [Formula: see text]. This configuration satisfies the Schwarzchild black hole condition [Formula: see text] for every [Formula: see text]. We refer to it as “Planckonion”. The interesting thing about the Planckonion is that it has an onion-like structure. The central sphere with radius of the Planck-length [Formula: see text] has one unit of the Planck-mass [Formula: see text]. Subsequent spherical shells of radial width [Formula: see text] contain exactly one unit of [Formula: see text]. We study this stellar configuration using Tolman–Oppenheimer–Volkoff equation and show that the equation is satisfied if pressure [Formula: see text]. On the geometrical side, the space component of the metric blows up at every point. The time component of the metric is zero inside the star but only in the sense of a distribution (generalized function). The Planckonions mimic some features of black holes but avoid appearance of central singularity because of the violation of null energy conditions.

scholarly journals Can the Planck Length Be Found Independent of Big G?

2017 ◽  
Vol 9 (6) ◽  
pp. 58 ◽  
Author(s):  
Espen Gaarder Haug
Keyword(s):  
Measurement Error ◽  
Particle Accelerators ◽  
Relative Measurement ◽  
Planck Length ◽  
Relative Measurement Error ◽  
Set Up

In this paper we show how it is possible to measure the Planck length through a series of different methods. One of these measurements is totally independent of big G, but moving from the theoretical realm to the empirical realm would require particle accelerators far more powerful than the ones that we have today. However, a Cavendish-style experiment can also be performed to find the Planck length with no knowledge of the value of big G. Furthermore, the Cavendish style set-up gives half of the relative measurement error in the Planck length compared to the measurement error in big G.

Properties of a Set of Symmetric Maxwellian Equations

1988 ◽  
Vol 43 (7) ◽  
pp. 684-686
Author(s):  
Pierre Guéret
Keyword(s):  
Magnetic Monopole ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Quantum Mechanical ◽  
Planck Length ◽  
Coupling Term ◽  
Mechanical Coupling ◽  
Radial Limits ◽  
Relativistic Transformation ◽  
Dirac Electron

Abstract A set of fully symmetric maxwellian equations is proposed, with a quantum mechanical coupling term between matter and fields. Its relativistic transformation properties and conservation laws are presented. Dual, monopole-like solutions are described, which have properties consistent with those of the Dirac electron and magnetic monopole. The spatial extent of the monopole fields is proposed to be bound within two extreme radial limits rp and R0 such that α In (R0/rp) ≡ 1, where α ≃ 1/137 is the electromagnetic fine structure constant, yielding for the ratio R0/rp a very large number in the order of the ratio of the so-called universe radius to the Planck length.

Physical significance of planck length

1985 ◽  
Vol 165 (1) ◽  
pp. 38-58 ◽  
Author(s):  
T. Padmanabhan
Keyword(s):  
Physical Significance ◽  
Planck Length

Statistical Entropy of the G-H-S Black Hole to All Orders in Planck Length

2011 ◽  
Vol 51 (2) ◽  
pp. 554-557
Author(s):  
HangBin Sun ◽  
Feng He ◽  
Hai Huang
Keyword(s):  
Black Hole ◽  
Statistical Entropy ◽  
Planck Length
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