UNCERTAINTY PRINCIPLE AND THE QUANTUM FLUCTUATIONS OF THE LIGHT CONES IN THE STATIC SPACE-TIMES

1986 ◽  
Vol 01 (03) ◽  
pp. 731-737 ◽  
Author(s):  
VARSHA DAFTARDAR ◽  
NARESH DADHICH
Keyword(s):  
Uncertainty Principle ◽  
Light Cone ◽  
Uncertainty Relation ◽  
Quantum Fluctuations ◽  
Surface Gravity ◽  
Asymptotically Flat ◽  
Cone Structure ◽  
Source Point ◽  
Static Space

The application of the uncertainty relation to position and velocity of a source point represented by a general asymptotically flat static metric leads to fluctuations of the metric and the light cone structure. The fluctations in the coordinate photon velocity are given by the formula [Formula: see text] where k is the surface gravity and m is the mass of the source point.

UNCERTAINTY PRINCIPLE AND THE QUANTUM FLUCTUATIONS OF THE SCHWARZSCHILD LIGHT CONES

1986 ◽  
Vol 01 (02) ◽  
pp. 491-498 ◽  
Author(s):  
T. PADMANABHAN ◽  
T.R. SESHADRI ◽  
T.P. SINGH
Keyword(s):  
Gravitational Field ◽  
Event Horizon ◽  
Uncertainty Principle ◽  
Light Cone ◽  
Uncertainty Relation ◽  
Quantum Fluctuations ◽  
Point Mass ◽  
Conjugate Momentum

We consider the gravitational field of a point mass and show that the application of the uncertainty principle leads to (i) an uncertainty relation for the metric and its conjugate momentum and (ii) finite fluctuations of the light-cone at the event horizon.

THE GENERALIZED GEOMETRIC UNCERTAINTY PRINCIPLE FOR SPIN 1/2 SYSTEM`

2021 ◽  
Vol 10 (9) ◽  
pp. 3253-3262
Author(s):  
H. Umair ◽  
H. Zainuddin ◽  
K.T. Chan ◽  
Sh.K. Said Husein
Keyword(s):  
Uncertainty Principle ◽  
Symplectic Form ◽  
Uncertainty Relation ◽  
Riemannian Metric ◽  
Hamiltonian Flow ◽  
Geometric Uncertainty ◽  
Projective Hilbert Space ◽  
Space Dynamics ◽  
Geometric Quantum Mechanics ◽  
Complex Projective

Geometric Quantum Mechanics is a version of quantum theory that has been formulated in terms of Hamiltonian phase-space dynamics. The states in this framework belong to points in complex projective Hilbert space, the observables are real valued functions on the space, and the Hamiltonian flow is described by the Schr{\"o}dinger equation. Besides, one has demonstrated that the stronger version of the uncertainty relation, namely the Robertson-Schr{\"o}dinger uncertainty relation, may be stated using symplectic form and Riemannian metric. In this research, the generalized Robertson-Schr{\"o}dinger uncertainty principle for spin $\frac{1}{2}$ system has been constructed by considering the operators corresponding to arbitrary direction.

Quantum fluctuations and the Casimir effect

2020 ◽  
Vol 29 (08) ◽  
pp. 2050059 ◽  
Author(s):  
Daniel Chemisana ◽  
Jaume Giné ◽  
Jaime Madrid
Keyword(s):  
Spherical Shell ◽  
Uncertainty Principle ◽  
Casimir Effect ◽  
Quantum Fluctuations ◽  
Casimir Energy ◽  
Effective Radius ◽  
Vacuum Fluctuations ◽  
Effective Distance ◽  
Observable Consequence

The most important observable consequence of the vacuum fluctuations is the Casimir effect. Its classical manifestation is a force between two uncharged conductive plates placed a few nanometers apart. In this work, we improve the deduction of the Casimir effect from the uncertainty principle by using an effective radius for the quantum fluctuations. Moreover, the existence of this effective distance is discussed. Finally, a heuristic derivation of the Casimir energy for a spherical shell and a sphere-plate cases is given.

Induced Quantum Fluctuations in the Spherically Symmetric Space–Time

1997 ◽  
Vol 12 (18) ◽  
pp. 3171-3180 ◽  
Author(s):  
Kamal K. Nandi ◽  
Anwarul Islam ◽  
James Evans
Keyword(s):  
Symmetric Space ◽  
Light Cone ◽  
Quantum Fluctuation ◽  
Quantum Fluctuations ◽  
Dynamical Variable ◽  
Nonrelativistic Limit ◽  
Space Time ◽  
Spherically Symmetric ◽  
Speed Of Light

In the Schwarzschild field due to a mass moving with velocity v → c0, where c0 is the speed of light in vacuum, the source-induced quantum fluctuation in the light cone exhibits consistency with the Aichelburg–Sexl solution while that in the metric dynamical variable does not. At the horizon, none of the fluctuations is proportional to anything finite. However, in the nonrelativistic limit (v → 0), known expressions follow.

scholarly journals CONFORMAL GENERATORS AND DOUBLY SPECIAL RELATIVITY THEORIES

2005 ◽  
Vol 20 (11) ◽  
pp. 861-867 ◽  
Author(s):  
CARLOS LEIVA
Keyword(s):  
Special Relativity ◽  
Linear Combination ◽  
Dimensional Reduction ◽  
Light Cone ◽  
Massless Particle ◽  
Conformal Group ◽  
Cone Structure ◽  
Doubly Special Relativity

In this paper, the relation between the modified Lorenz boosts, proposed in the doubly relativity theories and a linear combination of Conformal Group generators in R1,d-1 is investigated. The introduction of a new generator is proposed in order to deform the Conformal Group to achieve the connection conjectured. The new generator is obtained through a formal dimensional reduction from a free massless particle living in a R2,d space. Due to this treatment it is possible to say that even DSR theories modify light-cone structure in R1,d-1, it could remains, in some cases, untouched in R2,d.

Light-Cone Structure of Current Commutators in the Gluon-Quark Model

1971 ◽  
Vol 4 (4) ◽  
pp. 1059-1072 ◽  
Author(s):  
David J. Gross ◽  
S. B. Treiman
Keyword(s):  
Quark Model ◽  
Light Cone ◽  
Cone Structure

On the attractive force of the gravitational field in static space times

1970 ◽  
Vol 68 (1) ◽  
pp. 187-197 ◽  
Author(s):  
H. Müller zum Hagen
Keyword(s):  
Gravitational Field ◽  
Test Particle ◽  
Gravitational Force ◽  
Killing Vector ◽  
Attractive Force ◽  
Potential Surfaces ◽  
Asymptotically Flat ◽  
Definition Of ◽  
Meaningful Definition ◽  
Static Space

AbstractA static metric is considered. A meaningful definition of gravitational force is given and the potential, which is the norm of the Killing vector ξa, is studied. For the case that the metric is asymptotically flat, the following is shown: The equi-potential surfaces are closed 2-dimensional surfacesSlying in the rest space V3, which is the hypersurface orthogonal to ξa. All the surfacesSenclose matter, and the gravitational force points intoStowards the enclosed matter. A test particle starting atSwill be pulled into the domain bounded bySand will never leave this domain.

Is the Uncertainty Relation at the Root of all Mutual Exclusiveness?

1997 ◽  
Vol 52 (5) ◽  
pp. 398-402 ◽  
Author(s):  
D. Sen ◽  
A. N. Basu ◽  
S. Sengupta
Keyword(s):  
Interference Pattern ◽  
Uncertainty Principle ◽  
Uncertainty Relation ◽  
Quantum Mechanical ◽  
Complementarity Principle ◽  
Conventional Analysis ◽  
Double Slit Experiment ◽  
Slit Experiment ◽  
Double Slit

Abstract It is argued that two distinct types of complementarity are implied in Bohr's complementarity principle. While in the case of complementary variables it is the quantum mechanical uncertainty relation which is at work, the collapse hypothesis ensures this exclusiveness in the so-called wave-particle complementarity experiments. In particular it is shown that the conventional analysis of the double slit experiment which invokes the uncertainty principle to explain the absence of the simultaneous knowledge of the which-slit information and the interference pattern is incorrect and implies consequences that are quantum mechanically inconsistent.

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