scholarly journals A Solution to the Soccer Ball Problem for Generalized Uncertainty Relations

2019 ◽  
Vol 64 (11) ◽  
pp. 1036 ◽  
Author(s):  
M. J. Lake
Keyword(s):  
Uncertainty Principle ◽  
Equivalence Principle ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Total Momentum ◽  
Uncertainty Relations ◽  
Relativistic Limit ◽  
Soccer Ball ◽  
Ball Problem ◽  
Extended Uncertainty

We propose a new method for generating generalized uncertainty relations (GURs) including the generalized uncertainty principle (GUP), extended uncertainty principle (EUP), and extended generalized uncertainty principle (EGUP), previously proposed in the quantum gravity literature, without modifying the Heisenberg algebra. Our approach is compatible with the equivalence principle, and with local Poincar´e invariance in the relativistic limit, thus circumventing many of the problems associated with GURs derived from modified commutation relations. In particular, it does not require the existence of a nonlinear additional law for momenta. This allows sensible multi-particle states to be constructed in which the total momentum is macroscopic, even if the momentum of an individual particle is bounded by the Planck momentum, thus providing a resolution of the “soccer ball problem” that plagues current approaches to GURs.

scholarly journals The generalized and extended uncertainty principles and their implications on the Jeans mass

2019 ◽  
Vol 488 (1) ◽  
pp. L69-L74 ◽  
Author(s):  
H Moradpour ◽  
A H Ziaie ◽  
S Ghaffari ◽  
F Feleppa
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Ideal Gas ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Newtonian Gravity ◽  
Uncertainty Principles ◽  
Temperature Relation ◽  
Heisenberg Uncertainty Principle ◽  
Extended Uncertainty

ABSTRACT The generalized and extended uncertainty principles affect the Newtonian gravity and also the geometry of the thermodynamic phase space. Under the influence of the latter, the energy–temperature relation of ideal gas may change. Moreover, it seems that the Newtonian gravity is modified in the framework of the Rényi entropy formalism motivated by both the long-range nature of gravity and the extended uncertainty principle. Here, the consequences of employing the generalized and extended uncertainty principles, instead of the Heisenberg uncertainty principle, on the Jeans mass are studied. The results of working in the Rényi entropy formalism are also addressed. It is shown that unlike the extended uncertainty principle and the Rényi entropy formalism that lead to the same increase in the Jeans mass, the generalized uncertainty principle can decrease it. The latter means that a cloud with mass smaller than the standard Jeans mass, obtained in the framework of the Newtonian gravity, may also undergo the gravitational collapse process.

scholarly journals Heisenberg Algebra in the Bargmann-Fock Space with Natural Cutoffs

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Maryam Roushan ◽  
Kourosh Nozari
Keyword(s):  
Uncertainty Principle ◽  
Fock Space ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Maximal Momentum

We construct a Heisenberg algebra in Bargmann-Fock space in the presence of natural cutoffs encoded as minimal length, minimal momentum, and maximal momentum through a generalized uncertainty principle.

COVARIANT DEFORMATION OF THE POINCARÉ–HEISENBERG ALGEBRA

1998 ◽  
Vol 13 (20) ◽  
pp. 1587-1595
Author(s):  
CLEMENS HEUSON
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Lorentz Transformations ◽  
Deformation Function

Starting from deformed coordinates a covariant deformation of the Poincaré and Heisenberg algebra is derived. The deformation function is determined uniquely by the Jacobi identities leading to noncommutative coordinates, a generalized uncertainty principle and deformed Lorentz transformations.

scholarly journals Kinetic energy properties and weak equivalence principle in a space with generalized uncertainty principle

2020 ◽  
Vol 35 (13) ◽  
pp. 2050096
Author(s):  
Kh. P. Gnatenko ◽  
V. M. Tkachuk
Keyword(s):  
Kinetic Energy ◽  
Energy Dependence ◽  
Uncertainty Principle ◽  
Equivalence Principle ◽  
Generalized Uncertainty Principle ◽  
Weak Equivalence ◽  
Weak Equivalence Principle ◽  
Deformation Function ◽  
Commutation Relations ◽  
Deformed Commutation Relations

A space with deformed commutation relations for coordinates and momenta leading to generalized uncertainty principle (GUP) is studied. We show that GUP causes great violation of the weak equivalence principle for macroscopic bodies, violation of additivity property of the kinetic energy, dependence of the kinetic energy on composition, great corrections to the kinetic energy of macroscopic bodies. We find that all these problems can be solved in the case of arbitrary deformation function depending on momentum if parameter of deformation is proportional inversely to squared mass.

scholarly journals EXTENDED UNCERTAINTY PRINCIPLE AND THE GEOMETRY OF (ANTI)-DE SITTER SPACE

2010 ◽  
Vol 25 (20) ◽  
pp. 1697-1703 ◽  
Author(s):  
S. MIGNEMI
Keyword(s):  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Sitter Spacetime ◽  
Heisenberg Uncertainty ◽  
Sitter Background ◽  
Extended Uncertainty

It has been proposed that on (anti)-de Sitter background, the Heisenberg uncertainty principle should be modified by the introduction of a term proportional to the cosmological constant. We show that this modification of the uncertainty principle can be derived straightforwardly from the geometric properties of (anti)-de Sitter spacetime. We also discuss the connection between the so-called extended generalized uncertainty principle and triply special relativity.

scholarly journals COSMOLOGY WITH MINIMAL LENGTH UNCERTAINTY RELATIONS

2009 ◽  
Vol 18 (07) ◽  
pp. 1059-1071 ◽  
Author(s):  
BABAK VAKILI
Keyword(s):  
Quantum Cosmology ◽  
Generalized Uncertainty Principle ◽  
Poisson Algebra ◽  
Heisenberg Algebra ◽  
Small Scale ◽  
Minimum Length ◽  
Uncertainty Relations ◽  
Inflationary Universe ◽  
De Sitter ◽  
Approximate Analytical Solutions

We study the effects of the existence of a minimal observable length in the phase space of classical and quantum de Sitter (dS) and anti-de Sitter (AdS) cosmology. Since this length has been suggested in quantum gravity and string theory, its effects in the early universe might be expected. Adopting the existence of such a minimum length results in the generalized uncertainty principle (GUP), which is a deformed Heisenberg algebra between minisuperspace variables and their momenta operators. We extend these deformed commutating relations to the corresponding deformed Poisson algebra in the classical limit. Using the resulting Poisson and Heisenberg relations, we then construct the classical and quantum cosmology of dS and AdS models in a canonical framework. We show that in classical dS cosmology this effect yields an inflationary universe in which the rate of expansion is larger than that of the usual dS universe. Also, for the AdS model it is shown that the GUP might change the oscillatory nature of the corresponding cosmology. We also study the effects of the GUP in quantized models through approximate analytical solutions to the Wheeler–DeWitt (WD) equation, in the limit of a small scale factor for the universe, and compare the results with the ordinary quantum cosmology in each case.

scholarly journals Asymptotic generalized extended uncertainty principle

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Mariusz P. Da̧browski ◽  
Fabian Wagner
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Ricci Scalar ◽  
Position Operator ◽  
Spatial Curvature ◽  
Curved Space ◽  
Extended Uncertainty ◽  
Curvature Tensors ◽  
Cartan Invariant ◽  
Expected Position

Abstract We present a formalism which allows for the perturbative derivation of the Extended Uncertainty Principle (EUP) for arbitrary spatial curvature models and observers. Entering the realm of small position uncertainties, we derive a general asymptotic EUP. The leading 2nd order curvature induced correction is proportional to the Ricci scalar, while the 4th order correction features the 0th order Cartan invariant $$\Psi _2$$Ψ2 (a scalar quadratic in curvature tensors) and the curved space Laplacian of the Ricci scalar all of which are evaluated at the expectation value of the position operator i.e. the expected position when performing a measurement. This result is first verified for previously derived homogeneous space models and then applied to other non-trivial curvature related effects such as inhomogeneities, rotation and an anisotropic stress fluid leading to black hole “hair”. Our main achievement combines the method we introduce with the Generalized Uncertainty Principle (GUP) by virtue of deformed commutators to formulate a generic form of what we call the Asymptotic Generalized Extended Uncertainty Principle (AGEUP).

scholarly journals Hawking temperature for various kinds of black holes from Heisenberg uncertainty principle

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040004 ◽  
Author(s):  
Fabio Scardigli
Keyword(s):  
Black Holes ◽  
Large Class ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Hawking Temperature ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Classical Physics ◽  
Heisenberg Uncertainty ◽  
Extended Uncertainty

Hawking temperature for a large class of black holes (Schwarzschild, Reissner–Nordström, (Anti) de Sitter, with spherical, toroidal and hyperboloidal topologies) is computed using only laws of classical physics plus the “classical” Heisenberg Uncertainty Principle. This principle is shown to be fully sufficient to get the result, and there is no need to this scope of a Generalized Uncertainty Principle or an Extended Uncertainty Principle.

scholarly journals QUANTIZATION OF FIELDS BASED ON GENERALIZED UNCERTAINTY PRINCIPLE

2006 ◽  
Vol 21 (16) ◽  
pp. 1285-1296 ◽  
Author(s):  
TOSHIHIRO MATSUO ◽  
YUUICHIROU SHIBUSA
Keyword(s):  
Quantum Theory ◽  
Scalar Field ◽  
Path Integral ◽  
Uncertainty Principle ◽  
Deformation Parameter ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Integral Formalism ◽  
Higher Dimensional ◽  
Free Scalar

We construct a quantum theory of free scalar field in (1+1) dimensions based on the deformed Heisenberg algebra [Formula: see text] where β is a deformation parameter. Both canonical and path integral formalisms are employed. A higher dimensional extension is easily performed in the path integral formalism.

scholarly journals The most general form of deformation of the Heisenberg algebra from the generalized uncertainty principle

2016 ◽  
Vol 763 ◽  
pp. 218-227 ◽  
Author(s):  
Syed Masood ◽  
Mir Faizal ◽  
Zaid Zaz ◽  
Ahmed Farag Ali ◽  
Jamil Raza ◽  
...  
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra
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