The recently suggested modification of the transverse electric contribution to the Lifshitz formula (S. K. Lamoreaux, arXiv:0801.1283) is discussed. We show that this modification is inconsistent with the data of two precise experiments, and violates the Nernst heat theorem. The preprint's suggestion concerning the resolution of the "apparent violation of the Third Law of Thermodynamics" is shown to be incorrect.
By considering the effect of diffusion on the external electric field response of charge carriers in metals and semiconductors, it is shown that the finite temperature correction proposed Bostrom and Sernelius requires substantial modification, and there is no large correction as suggested for good conductors. The apparent violation of the Third Law of Thermodynamics of the various proposed temperature corrections to the Casimir force is also resolved. Finally, the effect of Debye screening on electrostatic calibrations between pure germanium surfaces is calculated
It is well known that, beginning in 2000, the behavior of the thermal correction to the Casimir force between real metals has been hotly debated. As was shown by several research groups, the Lifshitz theory, which provides the theoretical foundation for the calculation of both the van der Waals and Casimir forces, leads to different results depending on the model of metal conductivity used. To resolve these controversies, the theoretical considerations based on the principles of thermodynamics and new experimental tests were invoked. We analyze the present status of the problem (in particular,…
The phenomena implied by the existence of quantum vacuum fluctuations, grouped under the title of the Casimir effect, are reviewed, with emphasis on new results discovered in the past four years. The Casimir force between parallel plates is rederived as the strong-coupling limit of $δ$-function potential planes. The role of surface divergences is clarified. A summary of effects relevant to measurements of the Casimir force between real materials is given, starting from a geometrical optics derivation of the Lifshitz formula, and including a rederivation of the Casimir-Polder forces. A great de…
Linear in temperature correction to the Casimir force is discussed. The correction is important for small separations between bodies tested in the recent experiments and disappears in the case of perfect conductors.
We reply to the "Comment on 'The Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic mirrors'" [arXiv:1604.06432]. We believe the comment misrepresents our papers, and fails to provide a plausible resolution to the conflict between theory and experiment.
We show that the claims expressed in the Comment arXiv:0810.3244v1 by R.S. Decca et al against our paper, D.A.R. Dalvit and S.K. Lamoreaux, Phys. Rev. Lett. {\bf 101}, 163203 (2008), are wrong and manifestly inconsistent with basic principles of statistical physics.
We comment on a recently published measurement of the Casimir force for distances in the 0.6 to 6 micrometer range between two Au surfaces (Phys. Rev. Lett. 78, 5(1997)) and the net discrepancy reported for the comparison with theoretical predictions (Phys. Rev. Lett. 81, 5475 (1998)).
Recently D. A. R. Dalvit and S. K. Lamoreaux arXiv:0805.1676 [Phys. Rev. Lett. v.101, 163203 (2008)] suggested the modification of the reflection coefficients in the Lifshitz theory taking into account the screening effects and diffusion currents. We demonstrate that the suggested modification is thermodynamically and experimentally inconsistent.
We make remarks on Hoodbhoy's paper [J. Phys. A: Math. Gen. 38 (2005) 10253-10256] by pointing out the single plate considered could be elastic and there will be deformations once the net (one-sided) force being upon the plate which will change the position-dependent potential imposed by Hoodbhoy.
In a recent paper (M. Bostrom and Bo E. Sernelius, Phys. Rev. Lett. 84, 4757 (2000)) the combined effect of finite conductivity and finite temperature on the Casimir force is analyzed, and significant deviations from other theoretical results and a recent experiment are obtained. In this Comment, I show that the extrapolation to zero frequency is incorrect because the authors have neglected that the wavenumber and frequency of the electromagentic mode must simultaneously appraoch zero
A recent theoretical calculation shows that the Casimir force between two parallel plates can be repulsive for plates with nontrivial magnetic properties (O. Kenneth et al., Phys. Rev. Lett. 89, 033001 (2002)). According to the authors, the effect may be observed with known materials, such as ferrites and garnets, and it might be possible to engineer micro- or nanoelectromechanical systems (MEMS or NEMS) that could take advantage of a short range repulsive force. Here we show that on the contrary the Casimir force between two parallel plates in vacuum at micron and submicron distance is always…
In a recent paper [C. Raabe and D.-G. Welsch, Phys. Rev. A 71, 013814 (2005)] an electromagnetic energy-momentum tensor is suggested as an alternative to the Abraham-Minkowski tensor and is applied to calculations of Casimir forces in planar geometries. We argue that the universality of the suggested tensor is doubtful; application of the Raabe-Welsch theory to a simple example in classical electrodynamics shows that their proposed tensor is unable to describe the situation in a simple way. We also show that modified Casimir forces acting on the cavity medium as prescribed by these authors suf…
Recently J.S. Hoye, I.Brevik, J.B. Aarseth, and K.A. Milton [Phys. Rev. E v.67, 056116 (2003); quant-ph/0212125] proposed that if the Lifshitz formula is combined with the Drude model, the transverse electric zero mode does not contribute to the result for real metals and there arises a linear temperature correction to the Casimir force at small temperatures. The authors claim that in spite of the fact that the Casimir entropy in their approach is negative, the Nernst heat theorem is satisfied. In the present Comment we show that the authors' conclusion regarding the Nernst heat theorem is in …
Recently Guerout et al. [Phys. Rev. E, v.93, 022108 (2016)] advocated that the lossless plasma model has to be redefined as the limit of the Drude model when the relaxation parameter goes to zero. It was claimed that the previously used plasma model cannot correctly describe the Casimir pressure between two plates made of both nonmagnetic and magnetic metals and has to be replaced with the redefined one. We show that the suggested redefinition does not satisfy necessary physical requirements imposed on the dielectric permittivity. We also present a plausible explanation to the fact that the lo…
In a recent paper, Geyer, Klimchitskaya, and Mostepanenko [Phys. Rev. A 67, 062102 (2003); quant-ph/0306038] proposed the final solution of the problem of temperature correction to the Casimir force between real metals. The basic idea was that one cannot use the dielectric permittivity in the frequency region where a real current may arise leading to Joule heating of the metal. Instead, the surface impedance approach is proposed as a solution of all contradictions. The purpose of this comment is to show that (i) the main idea contradicts to the fluctuation dissipation theorem, (ii) the propose…
We have reviewed the Comment of Geyer et al. [arXiv:0708.1548] concerning our recent work [Phys. Rev. A 75, 060102 (R) (2007)], and while we disagree with their criticisms, we acknowledge them for giving us the opportunity to add interesting addition material and a more detailed description of our experiment. We describe further our calculation and explain why a more sophisticated model is not warranted. We also present detailed experiments on the effects of electrostatic forces in our measurements and show that the contribution due to work function differences is small and that the residual e…
It is shown that recent criticism by C. R. Hagen (hep-th/9902057) questioning the validity of stress tensor treatments of the Casimir energy for space divided into two parts by a spherical boundary is without foundation.
Recently W. J. Kim, M. Brown-Hayes, D. A. R. Dalvit, J. H. Brownell, and R. Onofrio [Phys. Rev. A, v.78, 036102(R) (2008)] performed electrostatic calibrations for a plane plate above a centimeter-size spherical lens at separations down to 20-30 nm and observed "anomalous behavior". It was found that the gradient of the electrostatic force does not depend on separation as predicted on the basis of a pure Coulombian contribution. Some hypotheses which could potentially explain the deviation from the expected behavior were considered, and qualitative arguments in favor of the influence of patch …
Recently D. Garcia-Sanches, K. Y. Fong, H. Bhaskaran, S. Lamoreaux, and H. X. Tang [Phys. Rev. Lett. v.109, 027202 (2012)] claimed that the frequency shift of an oscillator under the influence of the residual electric and Casimir forces is best described by the Drude model approach to the Casimir force and excludes the plasma model approach. We demonstrate that calculations in support of this claim are performed incorrectly and that the measured data are in strong disagreement with both theoretical approaches to the Casimir force, thus, suggesting the presence of an unaccounted systematic erro…
We demonstrate that the approach by Rodrigues et al. (PRL, v.96, 100402, 2006) to the description of the lateral Casimir force between corrugated surfaces is in disagreement with a path-integral theory by Emig et al. (PRA, v.67, 022114, 2003), and the approximations used are not appropriate for comparison to experiment.
I show that reflection positivity implies that the force between any mirror pair of charge-conjugate probes of the quantum vacuum is attractive. This generalizes a recent theorem of Kenneth and Klich to interacting quantum fields, to arbitrary semiclassical bodies, and to quantized probes with non-overlapping wavefunctions. I also prove that the torques on charge-conjugate probes tend always to rotate them into a mirror-symmetric position.
Recently Yampol'skii et al. [Phys. Rev. A v.82, 032511 (2010)] advocated that Lifshitz theory is not applicable when the characteristic wavelength of the fluctuating electromagnetic field, responsible for the thermal correction to the Casimir force, is larger than the size of the metal test bodies. It was claimed that this is the case in experiments which exclude Lifshitz theory combined with the Drude model. We calculate the wavelengths of the evanescent waves giving the dominant contribution to the thermal correction and we find that they are much smaller than the sizes of the test bodies. T…
In a recent letter [Phys. Rev. Lett. 91, 220801 (2003)], V. Mkrtchian and co-workers calculated the radiation pressure force on a moving body, assuming the electromagnetic field to be at temperature $T,$ and the velocity to be much smaller than $c.$ They considered both dielectrics and conductors, and related the effect to Casimir dissipative forces. Here we claim that their approach may only apply in the Rayleigh-Ganz scattering regime, which corresponds to very small particles and/or electromagnetically rarefied media. Moreover, we argue that their interpretation in terms of the Casimir effe…
Recently V. A. Yampol'skii, S. Savel'ev, Z. A. Mayselis, S. S. Apostolov, and F. Nori [Phys. Rev. Lett., v.101, 096803 (2008),arXiv:0712.1395] claimed that the Casimir force between a thin metal film described by the Drude model and an ideal metal semispace can decrease with temperature whereas for bulk samples the Casimir force increases with temperature. On this basis the experimental observation of the decreasing temperature dependence of the Casimir force magnitude between a film and a bulk ideal metal was proposed. We demonstrate that, contrary to what is claimed by the authors, the magni…
In Phys. Rev. {\bf E 70}, 047102 (2004), J.R. Torgerson and S.K. Lamoreaux investigated for the first time the real-frequency spectrum of finite temperature correction to the Casimir force, for metallic plates of finite conductivity. The very interesting result of this study is that the correction from the TE mode is dominated by low frequencies, for which the dielectric description of the metal is invalid. However, their analysis of the problem, based on more appropriate low-frequency metallic boundary conditions, uses an incorrect form of boundary conditions for TE modes. We repeat their ana…
In a recent Comment, Decca et al. [Phys. Rev. A 79, 026101 (2009); arXiv:0809.3576] discussed the origin of the anomalies recently reported by us in Phys. Rev. A 78, 036102(R) (2008); arXiv:0812.0028 . Here we restate our view, corroborated by their considerations, that quantitative geometrical and electrostatic characterizations of the conducting surfaces (a topic not discussed explicitly in the literature until very recently) are critical for the assessment of precision and accuracy of the demonstration of the Casimir force and for deriving meaningful limits on the existence of Yukawian comp…
Recently, Brevik et al. [Phys. Rev. E 71, 056101 (2005)] adduced arguments against the traditional approach to the thermal Casimir force between real metals and in favor of one of the alternative approaches. The latter assumes zero contribution from the transverse electric mode at zero frequency in qualitative disagreement with unity as given by the thermal quantum field theory for ideal metals. Those authors claim that their approach is consistent with experiments as well as with thermodynamics. We demonstrate that these conclusions are incorrect. We show specifically that their results are c…
We present the status of an experimental test for gravitational strength forces below 1 mm. Our experiment uses small 1 kilohertz oscillators as test masses, with a stiff counducting shield between them to suppress backgrounds. At the present sensitivity of approximately 1000 times gravitational strength, we see no evidence for new forces with interaction ranges between 75 microns and 1 mm. While the Casimir background is not expected to be significant at this range, an extension of the shielding technique we employ may be useful for reducing this background in experiments below a few microns.…
Recently J.N. Munday and F. Capasso [Phys. Rev. A {\bf 75}, 060102(R) (2007); arXiv:0705.3793] claimed that they have performed a precision measurement of the Casimir force between a sphere and a plate coated with Au, both immersed in ethanol. The measurement results were claimed to be consistent with the Lifshitz theory. We demonstrate that the calculation of the Casimir force between the smooth bodies following the authors prescription has a discrepancy up to 25% with respect to authors result. We show also that the attractive electrostatic force only due to the surface potential differences…
Here we reply to the comment of Li et al. (arXiv:2009.09377) on the preprint (arXiv:2003.00760) of our publication (Z. Naturforsch. A 75, 803-807; DOI:10.1515/zna-2020-0204).
From energy considerations there is reason to expect that the work done by Casimir forces during a slow displacement of the parallel plates reflects the free energy of the surface tension of the adjacent surfaces. We show this explicitly, for a one-component ionic fluid or plasma with $q_c$ as ionic charge, where the particles are neutralized by a uniform continuous oppositely charged background. For two equal half-planes, the surface-associated free energy for one half-plane turns out to be just one half of the total Casimir energy for the conventional Casimir setup. We also comment, from a w…
Recently Bo E. Sernelius [Phys. Rev. B {\bf 71}, 235114 (2005)] investigated the effects of spatial dispersion on the thermal Casimir force between two metal half spaces. He claims that incorporating spatial dispersion results in a negligible contribution from the transverse electric mode at zero frequency as compared to the transverse magnetic mode. We demonstrate that this conclusion is not reliable because, when applied to the Casimir effect, the approximate description of spatial dispersion used is unjustified.
The finite temperature Casimir effect for a scalar field in the bulk region of the two Randall-Sundrum models, RSI and RSII, is studied. We calculate the Casimir energy and the Casimir force for two parallel plates with separation $a$ on the visible brane in the RSI model. High-temperature and low-temperature cases are covered. Attractiveness versus repulsiveness of the temperature correction to the force is discussed in the typical special cases of Dirichlet-Dirichlet, Neumann-Neumann, and Dirichlet-Neumann boundary conditions at low temperature. The Abel-Plana summation formula is made use o…
Recently, Høye, Brevik, Ellingsen and Aarseth (quant-ph/0703174) claimed that the use of the Drude dielectric function leads to zero Casimir entropy at zero temperature in accordance with Nernst's theorem. We demonstrate that their proof is not applicable to metals with perfect crystal lattices having no impurities. Thus there is no any contradiction with previous results in the literature proving that the Drude dielectric function violates the Nernst theorem for the Casimir entropy in the case of perfect crystal lattices. We also indicate mistakes in the coefficients of their asymptotic expre…
We comment on the recent work [1], and on its relations with our papers [2,3] cited therein. In particular we show that, contrarily to what stated in [1], the Casimir energy density determined therein in the case of a single delta-like singularity coincides with the energy density obtained previously in our paper [2] using a different approach.
We comment on progress in measurements of the Casimir force and discuss what is the actual reliability of different experiments. In this connection a more rigorous approach to the usage of such concepts as accuracy, precision, and measure of agreement between experiment and theory, is presented. We demonstrate that all measurements of the Casimir force employing spherical lenses with centimeter-size curvature radii are fundamentally flawed due to the presence of bubbles and pits on their surfaces. The commonly used formulation of the proximity force approximation is shown to be inapplicable fo…
We study novel type of contributions to the partition function of the Maxwell system defined on a small compact manifold ${\mathbb{M}}$ such as torus. These new terms can not be described in terms of the physical propagating photons with two transverse polarizations. Rather, these novel contributions emerge as a result of tunnelling events when transitions occur between topologically different but physically identical vacuum winding states. These new terms give an extra contribution to the Casimir pressure, yet to be measured. We argue that if the same system is considered in the background of…
We consider the Casimir effect between two parallel plates localized on a brane. In order to properly compute the contribution to the Casimir energy due to any higher dimensional field, it is necessary to take into account the localization properties of the KK modes. When no massless mode appears in the spectrum, the correction to the Casimir energy is exponentially suppressed. When a massless mode is present in the spectrum, the correction to the Casimir energy can be, in principle, sizeable. Here we illustrate a new method to compute the correction to the Casimir energy between two parallel …
The main part of this paper is to present an updated review of the Casimir energy at zero and finite temperature for the transverse oscillations of a piecewise uniform closed string. We make use of three different regularizations: the cutoff method, the complex contour integration method, and the zeta-function method. The string model is relativistic, in the sense that the velocity of sound is for each string piece set equal to the velocity of light. In this sense the theory is analogous to the electromagnetic theory in a dielectric medium in which the product of permittivity and permeability …
We study novel contributions to the partition function of the Maxwell system defined on a small compact manifold ${\mathbb{M}}$ with nontrivial mappings $π_1[U(1)]\cong\mathbb{Z}$. These contributions cannot be described in terms of conventional physical propagating photons with two transverse polarizations, and instead emerge as a result of tunneling transitions between topologically different but physically identical vacuum winding states.\exclude{These new terms give an extra contribution to the Casimir pressure, yet to be measured.} We argue that if the same system is considered in the bac…
