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.

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.

scholarly journals On the Semiclassical Approach of the Heisenberg Uncertainty Relation in the Strong Gravitational Field of Static Blackhole

2020 ◽  
Vol 22 (2) ◽  
pp. 15
Author(s):  
Fima Ardianto Putra
Keyword(s):  
Gravitational Field ◽  
Uncertainty Principle ◽  
Equivalence Principle ◽  
Uncertainty Relation ◽  
Fundamental Aspect ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty Relation ◽  
Strong Gravitational Field ◽  
Heisenberg Uncertainty ◽  
The Impact

Heisenberg Uncertainty and Equivalence Principle are the fundamental aspect respectively in Quantum Mechanic and General Relativity. Combination of these principles can be stated in the expression of Heisenberg uncertainty relation near the strong gravitational field i.e. pr   and Et  . While for the weak gravitational field, both relations revert to pr and Et. It means that globally, uncertanty principle does not invariant. This work also shows local stationary observation between two nearby points along the radial direction of blackhole. The result shows that the lower point has larger uncertainty limit than that of the upper point, i.e. . Hence locally, uncertainty principle does not invariant also. Through Equivalence Principle, we can see that gravitation can affect Heisenberg Uncertainty relation. This gives the impact to our’s viewpoint about quantum phenomena in the presence of gravitation. Key words: Heisenberg Uncertainty Principle , Equivalence Principle, and gravitational field 

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.

SPACE–TIME ENERGY–MOMENTUM, THE OBSERVER AND UNCERTAINTY IN GENERAL RELATIVITY

2010 ◽  
Vol 19 (14) ◽  
pp. 2353-2359 ◽  
Author(s):  
F. I. COOPERSTOCK ◽  
M. J. DUPRE
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Uncertainty Principle ◽  
Ricci Tensor ◽  
Space Time ◽  
Energy Integral ◽  
New Approach ◽  
Extended Space ◽  
Energy And Momentum

In this essay, we introduce a new approach to energy–momentum in general relativity. Space–time, as opposed to space, is recognized as the necessary arena for its examination, leading us to define new extended space–time energy and momentum constructs. From local and global considerations, we conclude that the Ricci tensor is the required element for a localized expression of energy–momentum to include the gravitational field. We present and rationalize a fully invariant extended expression for space–time energy, guided by Tolman's well-known energy integral for an arbitrary bounded stationary system. This raises fundamental issues which we discuss. The role of the observer emerges naturally and we are led to an extension of the uncertainty principle to general relativity, of particular relevance to ultra-strong gravity.

3. Extrasolar tests of gravity

2017 ◽  
pp. 35-45
Author(s):  
Timothy Clifton
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Field ◽  
Solar System ◽  
Neutron Stars ◽  
Event Horizon ◽  
Gravitational Fields ◽  
Binary Pulsars ◽  
Tests Of Gravity ◽  
Triple Star

By studying objects outside our Solar System, we can observe star systems with far greater gravitational fields. ‘Extrasolar tests of gravity’ considers stars of different sizes that have undergone gravitational collapse, including white dwarfs, neutron stars, and black holes. A black hole consists of a region of space-time enclosed by a surface called an event horizon. The gravitational field of a black hole is so strong that anything that finds its way inside the event horizon can never escape. Other star systems considered are binary pulsars and triple star systems. With the invention of even more powerful telescopes, there will be more tantalizing possibilities for testing gravity in the future.

2. Navigating through spacetime

2015 ◽  
Author(s):  
Katherine Blundell
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Event Horizon ◽  
Light Cone ◽  
Mathematical Language ◽  
Theory Of Relativity ◽  
Left Behind ◽  
Physical Universe

Mathematics is the perfect language needed for describing how the theory of relativity applies to the physical Universe and all of spacetime, and that description includes the strange behaviour that occurs near black holes. ‘Navigating through spacetime’ explains some of the complicated mathematical language using spacetime diagrams. It describes world-lines—the path left behind as an object journeys through spacetime—and light cones. Black holes profoundly affect the orientations of the light cones. As a particle approaches a black hole, its future light cone tilts more and more towards the black hole. When the particle crosses the event horizon, all of its possible future trajectories end inside the black hole.

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.

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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