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A particle theory of the Casimir effect

Patrick Suppes, San Sant'Adonai, A, De Barros, J A

Published Oct 10, 1995• 8 citations
OpenAlex

Abstract

In previous works Suppes and de Barros used a pure particle model to derive interference effects, where individual photons have well-defined trajectories, and hence no wave properties. In the present paper we extend that description to account for the Casimir effect. We consider that the linear momentum \\sum\\frac{1}{2}\\hbar {\\bf k} of the vacuum state in quantum electrodynamics corresponds to the linear momentum of virtual photons. The Casimir effect, in the cases of two parallel plates and the solid ball, is explained in terms of the pressure caused by the photons. Contrary to quantum electrodynamics, we assume a finite number of virtual photons.

Related papers

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Vacuum fluctuations in Rainbow space-time: Study of Casimir effect

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We investigate the Casimir effect in rainbow space-time, focusing on leading-order corrections to the Casimir energy and force. Starting with the scalar field Lagrangian in rainbow space-time, with parallel plates introduced through delta-function potentials, we find the corresponding energy-momentum tensor. We obtain the vacuum expectation value of this energy-momentum tensor by expressing it as a quadratic operator acting on the Green's function. By solving the Euler-Lagrange equation of a scalar field in rainbow space-time, we obtain the Green's function solutions. Employing these Green's function solutions in the vacuum expectation value of the energy-momentum tensor, we obtain the modified Casimir energy and Casimir force expressions in rainbow space-time. We study the variation of the deformed Casimir force and energy with the distance between the plates for different choices of rainbow functions. Our results show that for two choices of rainbow functions, the absolute value of the Casimir energy and force is decreasing or increasing, whereas for one specific choice of rainbow functions, it remains the same as the standard result in Minkowski space-time. Comparing our result with experimentally measured value of Casimir force, we obtain the bound on the rainbow parameter dependent terms to be of the order of 10^-24.

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Decoherence due to the Casimir effect?

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Open system dynamics of an electron is studied in the presence of radiation field, confined between two parallel conducting pates. It has been suggested in previous works that the quantized zero-point modes of this field lead to finite decoherence effects, possibly due to the Casimir force. However, in this work it is shown that the decoherence found in previous works is due to the sudden switching on of the system-environment interaction and due to the acceleration of the electron enforced by the background paths whose superposition was analyzed. The work discusses important theoretical aspects of the setup and shows that, while coherence might be lost due to bremsstrahlung induced by an external or the image potential, it cannot be lost due to the mere presence of the quantum vacuum fluctuations between the plates.

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Quantum mechanics predicts the occurrence of random electromagnetic field fluctuations, or virtual photons, in vacuum. The exchange of virtual photons between two bodies in relative motion could lead to non-contact quantum vacuum friction or Casimir friction. Despite its theoretical significance, the non-contact Casimir frictional force has not been observed and its theoretical predictions have varied widely. In this work, we report the first measurement of the non-contact Casimir frictional force between two moving bodies. By employing two mechanical oscillators with resonant frequencies far lower than those in Lorentz models of electrons in dielectric materials, we have amplified the Casimir frictional force at low relative velocities by several orders of magnitude. We directly measure the non-contact Casimir frictional force between the two oscillators and show its linear dependence on velocity, proving the dissipative nature of Casimir friction. This advancement marks a pivotal contribution to the field of dissipative quantum electrodynamics and enhances our understanding of friction at the nanoscale.

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Casimir forces in Bose-Einstein condensates: finite size effects in three-dimensional rectangular cavities

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Recently, the Casimir pressure was calculated for infinitely thin and infinitely repulsive parallel plates due to quantum fluctuations of the quasiparticle vacuum in a zero-temperature dilute Bose-Einstein condensate (BEC). We generalize this result and obtain an expression for the Casimir pressure in a three-dimensional rectangular cavity with Dirichlet boundary conditions and arbitrary lengths. We then calculate finite size corrections to the parallel plate scenario.

•Jan 1, 2005•14 citations

Photon Wave and Particle Concepts of an Extended Electromagnetic Theory

Bo Lehnert

Several important questions regarding the photon wave and particle concepts have so far not been fully settled by means of conventional theory which is based on Maxwell's equations. This concerns the problems of the angular momentum and the divergence of the obtained solutions in vacuum space. In attempts to tackle these and other unclear points, a number of extended non-Maxwellian theories have been elaborated. The present analysis is due to one of these approaches, as being based on a nonzero electric field divergence in the vacuum state, under the condition of Lorentz invariance. This theory leads to models for the individual photon being based on axisymmetric wave packet solutions with imposed relevant quantum conditions. Such solutions can be confined to a limited volume in vacuum space, thereby giving rise to a nonzero angular momentum, as required for a boson particle. Two wave packed modes are obtained which have limited characteristic diameters in the direction being perpendicular to that of the propagation. For one of the modes the diameter even becomes comparable to atomic dimensions. This provides the possibility for an efficient photon-electron interaction in the widely discussed but not fully understood photoionization effect. Both modes further have features in common with an earlier theory by de Broglie, where the photon is represented by a propagating pilot wave with a superimposed particle-like part having a very small rest mass. A proposal is finally made for the photon to appear in different quantum states, and where rapid transitions can take place between these states in the form of "photon oscillations".

Physica Scripta•Jan 1, 2002•7 citations
In previous works Suppes and de Barros used a pure particle model to derive interference effects, where individual photons have well-defined trajectories, and hence no wave properties. In the present paper we extend that description to account for the Casimir effect. We consider that the linear momentum \sum\frac{1}{2}\hbar {\bf k} of the vacuum state in quantum electrodynamics corresponds to the linear momentum of virtual photons. The Casimir effect, in the cases of two parallel plates and the solid ball, is explained in terms of the pressure caused by the photons. Contrary to quantum electrodynamics, we assume a finite number of virtual photons.
We investigate the Casimir effect in rainbow space-time, focusing on leading-order corrections to the Casimir energy and force. Starting with the scalar field Lagrangian in rainbow space-time, with parallel plates introduced through delta-function potentials, we find the corresponding energy-momentum tensor. We obtain the vacuum expectation value of this energy-momentum tensor by expressing it as a quadratic operator acting on the Green's function. By solving the Euler-Lagrange equation of a scalar field in rainbow space-time, we obtain the Green's function solutions. Employing these Green's function solutions in the vacuum expectation value of the energy-momentum tensor, we obtain the modified Casimir energy and Casimir force expressions in rainbow space-time. We study the variation of the deformed Casimir force and energy with the distance between the plates for different choices of rainbow functions. Our results show that for two choices of rainbow functions, the absolute value of the Casimir energy and force is decreasing or increasing, whereas for one specific choice of rainbow functions, it remains the same as the standard result in Minkowski space-time. Comparing our result with experimentally measured value of Casimir force, we obtain the bound on the rainbow parameter dependent terms to be of the order of 10^-24.
Open system dynamics of an electron is studied in the presence of radiation field, confined between two parallel conducting pates. It has been suggested in previous works that the quantized zero-point modes of this field lead to finite decoherence effects, possibly due to the Casimir force. However, in this work it is shown that the decoherence found in previous works is due to the sudden switching on of the system-environment interaction and due to the acceleration of the electron enforced by the background paths whose superposition was analyzed. The work discusses important theoretical aspects of the setup and shows that, while coherence might be lost due to bremsstrahlung induced by an external or the image potential, it cannot be lost due to the mere presence of the quantum vacuum fluctuations between the plates.
Quantum mechanics predicts the occurrence of random electromagnetic field fluctuations, or virtual photons, in vacuum. The exchange of virtual photons between two bodies in relative motion could lead to non-contact quantum vacuum friction or Casimir friction. Despite its theoretical significance, the non-contact Casimir frictional force has not been observed and its theoretical predictions have varied widely. In this work, we report the first measurement of the non-contact Casimir frictional force between two moving bodies. By employing two mechanical oscillators with resonant frequencies far lower than those in Lorentz models of electrons in dielectric materials, we have amplified the Casimir frictional force at low relative velocities by several orders of magnitude. We directly measure the non-contact Casimir frictional force between the two oscillators and show its linear dependence on velocity, proving the dissipative nature of Casimir friction. This advancement marks a pivotal contribution to the field of dissipative quantum electrodynamics and enhances our understanding of friction at the nanoscale.
Several important questions regarding the photon wave and particle concepts have so far not been fully settled by means of conventional theory which is based on Maxwell's equations. This concerns the problems of the angular momentum and the divergence of the obtained solutions in vacuum space. In attempts to tackle these and other unclear points, a number of extended non-Maxwellian theories have been elaborated. The present analysis is due to one of these approaches, as being based on a nonzero electric field divergence in the vacuum state, under the condition of Lorentz invariance. This theory leads to models for the individual photon being based on axisymmetric wave packet solutions with imposed relevant quantum conditions. Such solutions can be confined to a limited volume in vacuum space, thereby giving rise to a nonzero angular momentum, as required for a boson particle. Two wave packed modes are obtained which have limited characteristic diameters in the direction being perpendicular to that of the propagation. For one of the modes the diameter even becomes comparable to atomic dimensions. This provides the possibility for an efficient photon-electron interaction in the widely discussed but not fully understood photoionization effect. Both modes further have features in common with an earlier theory by de Broglie, where the photon is represented by a propagating pilot wave with a superimposed particle-like part having a very small rest mass. A proposal is finally made for the photon to appear in different quantum states, and where rapid transitions can take place between these states in the form of "photon oscillations".