Casimir effect and the uncertainty principle

2018 ◽  
Vol 33 (24) ◽  
pp. 1850140 ◽  
Author(s):  
Jaume Giné
Keyword(s):  
Uncertainty Principle ◽  
Casimir Effect ◽  
Vacuum Fluctuations

The Casimir effect is one of the observable consequences of the vacuum fluctuations. The Casimir effect manifests itself as a force between two uncharged conductive plates in a vacuum placed a few nanometers apart. In this work, we try to deduce the Casimir effect directly from the uncertainty principle.

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.

scholarly journals Effects of Quantum Fields Outside Cosmic Strings

1988 ◽  
Vol 130 ◽  
pp. 565-565
Author(s):  
D. A. Konkowski ◽  
T. M. Helliwell
Keyword(s):  
Cosmic String ◽  
Casimir Effect ◽  
Semiclassical Approximation ◽  
Mass Density ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Energy Tensor ◽  
Parallel Plates ◽  
Vacuum Fluctuations ◽  
Gravitational Influence

The space surrounding a long straight cosmic string is flat but conical. The conical topology implies that such a string focuses light rays or particles passing by opposite sides of the string, which can have important astrophysical effects. The flatness, however, implies that the string has no gravitational influence on matter at rest with respect to the string. The flatness is a consequence of the fact that the tension along a cosmic string is equal to its linear mass density μ. There may be physical effects, however, which destroy the equality of tension and mass density, so that straight strings might after all affect matter at rest. One such effect we and others have calculated is the vacuum fluctuations of fields near the strings induced by the conical topology. Such fluctuation s are physically observable but normally small, as in the Casimir effect between parallel plates. We find the vacuum expectation value of the stress - energy tensor of a conformally coupled scalar field around a cosmic string to be in cylindrical coordinates (t, r, θ, z). The equality of Ttt and Tzz means that the effective tension and mass density of the vacuum fluctuations are equal, so that at least in a semiclassical approximation a string dressed by such fields still has no gravitational influence on matter at rest, even though it has a substantial mass density.

scholarly journals Influence of quantized massive matter fields on the Casimir effect

2015 ◽  
Vol 30 (20) ◽  
pp. 1550099
Author(s):  
Yu. A. Sitenko
Keyword(s):  
Magnetic Field ◽  
Casimir Effect ◽  
Hamiltonian Operator ◽  
Matter Field ◽  
Parallel Plates ◽  
Vacuum Fluctuations ◽  
New Type ◽  
The Magnetic Field ◽  
External Uniform Magnetic Field ◽  
Matter Fields

Charged massive matter fields of spin-0 and spin-[Formula: see text] are quantized in the presence of an external uniform magnetic field in a spatial region bounded by two parallel plates. The most general set of boundary conditions at the plates, that is required by mathematical consistency and the self-adjointness of the Hamiltonian operator, is employed. The vacuum fluctuations of the matter field in the case of the magnetic field orthogonal to the plates are analyzed, and it is shown that the pressure from the vacuum onto the plates is positive and independent of the boundary condition, as well as of the distance between the plates. Possibilities of the detection of this new-type Casimir effect are discussed.

scholarly journals The Role of Vacuum Fluctuations and Symmetry in the Hydrogen Atom in Quantum Mechanics and Stochastic Electrodynamics

Atoms ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 39
Author(s):  
G. Maclay
Keyword(s):  
Electromagnetic Field ◽  
Hydrogen Atom ◽  
Casimir Effect ◽  
Classical Mechanics ◽  
Zero Point ◽  
Radiation Reaction ◽  
Quantum Mechanical ◽  
Vacuum Fluctuations ◽  
Stochastic Electrodynamics

Stochastic Electrodynamics (SED) has had success modeling black body radiation, the harmonic oscillator, the Casimir effect, van der Waals forces, diamagnetism, and uniform acceleration of electrodynamic systems using the stochastic zero-point fluctuations of the electromagnetic field with classical mechanics. However the hydrogen atom, with its 1/r potential remains a critical challenge. Numerical calculations have shown that the SED field prevents the electron orbit from collapsing into the proton, but, eventually the atom becames ionized. We look at the issues of the H atom and SED from the perspective of symmetry of the quantum mechanical Hamiltonian, used to obtain the quantum mechanical results, and the Abraham-Lorentz equation, which is a force equation that includes the effects of radiation reaction, and is used to obtain the SED simulations. We contrast the physical computed effects of the quantized electromagnetic vacuum fluctuations with the role of the real stochastic electromagnetic field.

scholarly journals Zeta Functions and the Cosmos—A Basic Brief Review

Universe ◽  
2020 ◽  
Vol 7 (1) ◽  
pp. 5
Author(s):  
Emilio Elizalde
Keyword(s):  
Large Scale ◽  
Casimir Effect ◽  
Zeta Functions ◽  
Harmonic Series ◽  
Quantum Vacuum ◽  
Vacuum Fluctuations ◽  
Dynamical Casimir Effect ◽  
Quantum Theories ◽  
Hard Problems ◽  
Physical Quantities

This is a very basic and pedagogical review of the concepts of zeta function and of the associated zeta regularization method, starting from the notions of harmonic series and of divergent sums in general. By way of very simple examples, it is shown how these powerful methods are used for the regularization of physical quantities, such as quantum vacuum fluctuations in various contexts. In special, in Casimir effect setups, with a note on the dynamical Casimir effect, and mainly concerning its application in quantum theories in curved spaces, subsequently used in gravity theories and cosmology. The second part of this work starts with an essential introduction to large scale cosmology, in search of the observational foundations of the Friedmann-Lemaître-Robertson-Walker (FLRW) model, and the cosmological constant issue, with the very hard problems associated with it. In short, a concise summary of all these interrelated subjects and applications, involving zeta functions and the cosmos, and an updated list of the pioneering and more influential works (according to Google Scholar citation counts) published on all these matters to date, are provided.

Recent progress in engineering the Casimir effect – applications to nanophotonics, nanomechanics, and chemistry

Nanophotonics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 523-536
Author(s):  
Tao Gong ◽  
Matthew R. Corrado ◽  
Ahmed R. Mahbub ◽  
Calum Shelden ◽  
Jeremy N. Munday
Keyword(s):  
Quantum Mechanics ◽  
Boundary Conditions ◽  
Recent Progress ◽  
Casimir Effect ◽  
Classical Electrodynamics ◽  
Quantum Vacuum ◽  
Vacuum Fluctuations ◽  
Future Directions ◽  
Recent Developments ◽  
Repulsive Forces

AbstractQuantum optics combines classical electrodynamics with quantum mechanics to describe how light interacts with material on the nanoscale, and many of the tricks and techniques used in nanophotonics can be extended to this quantum realm. Specifically, quantum vacuum fluctuations of electromagnetic fields experience boundary conditions that can be tailored by the nanoscopic geometry and dielectric properties of the involved materials. These quantum fluctuations give rise to a plethora of phenomena ranging from spontaneous emission to the Casimir effect, which can all be controlled and manipulated by changing the boundary conditions for the fields. Here, we focus on several recent developments in modifying the Casimir effect and related phenomena, including the generation of torques and repulsive forces, creation of photons from vacuum, modified chemistry, and engineered material functionality, as well as future directions and applications for nanotechnology.

scholarly journals Time Energy Uncertainty Principle and Vacuum Fluctuations

2019 ◽  
Author(s):  
Mirza Wasif BAig
Keyword(s):  
Differential Equation ◽  
Wave Function ◽  
Uncertainty Principle ◽  
High Energy Physics ◽  
Present Theory ◽  
High Energy ◽  
Vacuum Fluctuations ◽  
Third Order ◽  
Virtual Particles ◽  
Energy Physics

Phenomenon of vacuum fluctuations of virtual particles in high energy physics has been mathematically modeled by a third order differential equation. Aim of present theory is to unravel underlying mathematical equation capable of explaining microscopic phenomenon of vacuum fluctuations. Solution of such a differential equation after applying appropriate boundary conditions gives an acceptable wave function i.e. . Operation of energy and time operator on this wave function proves that these operators do not hold commutative property. Time energy uncertainty principle has been derived by calculating variance of energy and time for the same wave function.

scholarly journals Heuristic derivation of the Casimir effect from Generalized Uncertainty Principle

2019 ◽  
Vol 1275 ◽  
pp. 012024 ◽  
Author(s):  
M Blasone ◽  
G Lambiase ◽  
G G Luciano ◽  
L Petruzziello ◽  
F Scardigli
Keyword(s):  
Uncertainty Principle ◽  
Casimir Effect ◽  
Generalized Uncertainty Principle

scholarly journals The case for a Casimir cosmology

2020 ◽  
Vol 378 (2177) ◽  
pp. 20190229 ◽  
Author(s):  
Ulf Leonhardt
Keyword(s):  
New York ◽  
Cosmological Constant ◽  
Casimir Effect ◽  
Quantum Field ◽  
Vacuum Fluctuations ◽  
Correct Order ◽  
Dielectric Media ◽  
Analogue Gravity ◽  
Lifshitz Theory ◽  
Order Of Magnitude

The cosmological constant, also known as dark energy, was believed to be caused by vacuum fluctuations, but naive calculations give results in stark disagreement with fact. In the Casimir effect, vacuum fluctuations cause forces in dielectric media, which is very well described by Lifshitz theory. Recently, using the analogy between geometries and media, a cosmological constant of the correct order of magnitude was calculated with Lifshitz theory (Leonhardt 2019 Ann. Phys. ( New York ) 411 , 167973. ( doi:10.1016/j.aop.2019.167973 )). This paper discusses the empirical evidence and the ideas behind the Lifshitz theory of the cosmological constant without requiring prior knowledge of cosmology and quantum field theory. This article is part of a discussion meeting issue ‘The next generation of analogue gravity experiments’.

scholarly journals Difference between Hawking and Unruh radiation derived from studies about pair production by lasers in vacuum

2006 ◽  
Vol 24 (4) ◽  
pp. 579-603 ◽  
Author(s):  
TIMOTHY STAIT-GARDNER ◽  
REYNALDO CASTILLO
Keyword(s):  
Black Holes ◽  
Pair Production ◽  
Vacuum Polarization ◽  
Casimir Effect ◽  
Vacuum Fluctuations ◽  
Laser Fields ◽  
Laser Acceleration

Laser acceleration of electrons in laser fields of intensities above 1028 W/cm2 were found to be in the same range as acceleration at the surface of black holes, where the laser intensities are in the range of pair production in vacuum due to vacuum polarization. The results in connection with the black holes arrived at similarities to the Hawking and Unruh radiation. We present here results based on the thermodynamics of the vacuum fluctuations that there is a difference between Hawking and Unruh effects in connection with the Casimir effect in view of the vacuum properties for laser produced pairs in a vacuum.

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