An intuitive picture of the Casimir effect (original) (raw)
Related papers
The Casimir effect: some aspects
Brazilian Journal of Physics, 2006
We start this paper with a historical survey of the Casimir effect, showing that its origin is related to experiments on colloidal chemistry. We present two methods of computing Casimir forces, namely: the global method introduced by Casimir, based on the idea of zero-point energy of the quantum electromagnetic field, and a local one, which requires the computation of the energy-momentum stress tensor of the corresponding field. As explicit examples, we calculate the (standard) Casimir forces between two parallel and perfectly conducting plates and discuss the more involved problem of a scalar field submitted to Robin boundary conditions at two parallel plates. A few comments are made about recent experiments that undoubtedly confirm the existence of this effect. Finally, we briefly discuss a few topics which are either elaborations of the Casimir effect or topics that are related in some way to this effect as, for example, the influence of a magnetic field on the Casimir effect of charged fields, magnetic properties of a confined vacuum and radiation reaction forces on non-relativistic moving boundaries.
The Scattering Approach to the Casimir Force
International Journal of Modern Physics A, 2010
We present the scattering approach which is nowadays the best tool for describing the Casimir force in realistic experimental configurations. After reminders on the simple geometries of 1d space and specular scatterers in 3d space, we discuss the case of stationary arbitrarily shaped mirrors in electromagnetic vacuum. We then review specific calculations based on the scattering approach, dealing for example with the forces or torques between nanostructured surfaces and with the force between a plane and a sphere. In these various cases, we account for the material dependence of the forces, and show that the geometry dependence goes beyond the trivial Proximity Force Approximation often used for discussing experiments.
Light-front analysis of the Casimir effect
Physical Review D, 2013
The Casimir force between conducting plates at rest in an inertial frame is usually computed in equal-time quantization, the natural choice for the given boundary conditions. We show that the well-known result obtained in this way can also be obtained in light-front quantization. This differs from a light-front analysis where the plates are at "rest" in an infinite momentum frame, rather than an inertial frame; in that case, as shown by Lenz and Steinbacher, the result does not agree with the standard result. As is usually done, the analysis is simplified by working with a scalar field and periodic boundary conditions, in place of the complexity of quantum electrodynamics. The two key ingredients are a careful implementation of the boundary conditions, following the work of Almeida et al. on oblique light-front coordinates, and computation of the ordinary energy density, rather than the light-front energy density. The analysis demonstrates that the physics of the effect is independent of the coordinate choice, as it must be.
Casimir force and the quantum theory of lossy optical cavities
Physical Review A, 2003
We present a new derivation of the Casimir force between two parallel plane mirrors at zero temperature. The two mirrors and the cavity they enclose are treated as quantum optical networks. They are in general lossy and characterized by frequency dependent reflection amplitudes. The additional fluctuations accompanying losses are deduced from expressions of the optical theorem. A general proof is given for the theorem relating the spectral density inside the cavity to the reflection amplitudes seen by the inner fields. This density determines the vacuum radiation pressure and, therefore, the Casimir force. The force is obtained as an integral over the real frequencies, including the contribution of evanescent waves besides that of ordinary waves, and, then, as an integral over imaginary frequencies. The demonstration relies only on general properties obeyed by real mirrors which also enforce general constraints for the variation of the Casimir force.
Non-Local Effects in the Casimir Force
AIP Conference Proceedings, 2005
Although the Casimir force, i.e., the force between the walls of a cavity due to the zero point and the thermal fluctuations of its electromagnetic field, was predicted half a century ago, it has only been measured with precision in the last decade. The possibility of comparing theory to experiment and the importance that Casimir forces might have on micro and nano machines has stimulated a renewed interest in their precise calculation for real materials. We show that the character of the cavity field is completely determined by the optical reflection amplitudes of the wall materials. Thus, we obtained an expression for the Casimir force which requires no assumption and no particular model for its walls. Thus, our results constitute a generalization of Lifshitz formula, applicable to a wide class of materials, which could be semi-infinite or finite, local or spatially dispersive, homogeneous or layered, dissipative or dissipationless, isotropic or anisotropic, etc. As an application, we evaluate the force between two metallic slabs accounting for the spatial dispersion of the dynamical response of their conduction electrons. A self-consistent jellium theory predicts a force that is significantly larger than that of a local theory at nanometric distances due to the fact that most of the screening charge at a metallic surface lies outside the nominal surface of the conductor and within vacuum.
Casimir force: an alternative treatment
2009
The Casimir force between two parallel uncharged closely spaced metallic plates is evaluated in ways alternatives to those usually considered in the literature. In a first approximation we take in account the suppressed quantum numbers of a cubic box, representing a cavity which was cut in a metallic block. We combine these ideas with those of the MIT bag model of hadrons, but adapted to nonrelativistic particles. In a second approximation we consider the particles occupying the energy levels of a Bohr atom, so that the Casimir force depends explicitly on the fine structure constant α. In both treatments, the mean energies which have explicit dependence on the particle mass and on the maximum occupied quantum number (related to the Fermi level of the system) at the beginning of the calculations, have these dependences mutually canceled at the end of them. Finally by comparing the averaged energies computed in both approximations, we are able to make an estimate of the value of the fine structure constant α.
Microscopic theory of the Casimir effect
2005
Based on the photon-exciton Hamiltonian a microscopic theory of the Casimir problem for dielectrics is developed. Using well-known many-body techniques we derive a perturbation expansion for the energy which is free from divergences. In the continuum limit we turn off the interaction at a distance smaller than a cut-off distance a to keep the energy finite. We will show that the macroscopic theory of the Casimir effect with hard boundary conditions is not well defined because it ignores the finite distance between the atoms, hence is including infinite self-energy contributions. Nevertheless for disconnected bodies the latter do not contribute to the force between the bodies. The Lorentz-Lorenz relation for the dielectric constant that enters the force is deduced in our microscopic theory without further assumptions. The photon Green’s function can be calculated from a Dyson type integral equation. The geometry of the problem only enters in this equation through the region of integration which is equal to the region occupied by the dielectric. The integral equation can be solved exactly for various plain and spherical geometries without using boundary conditions. This clearly shows that the Casimir force for dielectrics is due to the forces between the atoms. Convergence of the perturbation expansion and the metallic limit are discussed. We conclude that for any dielectric function the transverse electric (TE) mode does not contribute to the zerofrequency term of the Casimir force.
Scattering theory approach to electrodynamic Casimir forces
Physical Review D, 2009
We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by re-deriving the Lifshitz formula for infinite half spaces, by demonstrating the Casimir-Polder to van der Waals cross-over, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.
Physical Review A, 2007
The lateral Casimir force between two corrugated metallic plates makes possible a study of the nontrivial interplay of geometry and Casimir effect appearing beyond the regime of validity of the proximity-force approximation. Quantitative evaluations can be obtained by using scattering theory in a perturbative expansion valid when the corrugation amplitudes are smaller than the three other length scales: the mean separation distance L of the plates, the corrugation period λC , and the plasma wavelength λP . Within this perturbative expansion, evaluations are obtained for arbitrary relative values of L , λC , and λP while limiting cases, some of them already known, are recovered when these values obey some specific orderings. The consequence of these results for comparison with existing experiments is discussed at the end of the paper.