Present status of controversies regarding the thermal Casimir force

Dark Matter Axions, Non-Newtonian Gravity and Constraints on Them from Recent Measurements of the Casimir Force in the Micrometer Separation Range

We consider axionlike particles as the most probable constituents of dark matter, the Yukawa-type corrections to Newton’s gravitational law and constraints on their parameters following from astrophysics and different laboratory experiments. After a brief discussion of the results by Prof. Yu. N. Gnedin in this field, we turn our attention to the recent experiment on measuring the differential Casimir force between Au-coated surfaces of a sphere and the top and bottom of rectangular trenches. In this experiment, the Casimir force was measured over an unusually wide separation region from 0.2 to 8μm and compared with the exact theory based on first principles of quantum electrodynamics at nonzero temperature. We use the measure of agreement between experiment and theory to obtain the constraints on the coupling constant of axionlike particles to nucleons and on the interaction strength of a Yukawa-type interaction. The constraints obtained on the axion-to-nucleon coupling constant and on the strength of a Yukawa interaction are stronger by factors of 4 and 24, respectively, than those found previously from gravitational experiments and measurements of the Casimir force but weaker than the constraints following from a differential measurement where the Casimir force was nullified. Some other already performed and planned experiments aimed at searching for axions and non-Newtonian gravity are discussed, and their prospects are evaluated.

Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution

This paper provides a review of the complicated problems in Lifshitz theory describing the Casimir force between real material plates composed of metals and dielectrics, including different approaches to their resolution. For both metallic plates with perfect crystal lattices and any dielectric plates, we show that the Casimir entropy calculated in the framework of Lifshitz theory violates the Nernst heat theorem when the well-approved dielectric functions are used in computations. The respective theoretical Casimir forces are excluded by the measurement data of numerous precision experiments. In the literature, this situation has been called the Casimir puzzle and the Casimir conundrum for the cases of metallic and dielectric plates, respectively. This review presents a summary of both the main theoretical and experimental findings on this subject. Next, a discussion is provided of the main approaches proposed in the literature to bring the Lifshitz theory into agreement with the measurement data and with the laws of thermodynamics. Special attention is paid to the recently suggested spatially nonlocal Drude-like response functions, which consider the relaxation properties of conduction electrons, as does the standard Drude model, but lead to the theoretical results being in agreement with both thermodynamics and the measurement data through the alternative response to quantum fluctuations of the mass shell. Further advances and trends in this field of research are discussed.

The State of the Art in Constraining Axion-to-Nucleon Coupling and Non-Newtonian Gravity from Laboratory Experiments

Constraints on the Yukawa-type corrections to Newton’s gravitational law and on the coupling constant of axionlike particles to nucleons obtained from different laboratory experiments are reviewed and compared. The constraints on non-Newtonian gravity under discussion cover the wide interaction range from nanometers to millimeters and follow from the experiments on neutron scattering, measuring the Casimir force and Cavendish-type experiments. The constraints on the axion-to-nucleon coupling constant following from the magnetometer measurements, Cavendish-type experiments, Casimir physics, and experiments with beams of molecular hydrogen are considered, which refer to the region of axion masses from 10−10 to 200 eV. Particular attention is given to the recent constraints obtained from measuring the Casimir force at nanometer separation distance between the test bodies. Several proposed experiments focussed on constraining the non-Newtonian gravity, axionlike particles and other hypothetical weakly interacting particles, such as chameleons and symmetrons, are discussed.

Casimir interaction from magnetically coupled eddy currents

We study the quantum and thermal fluctuations of eddy (Foucault) currents in thick metallic plates. A Casimir interaction between two plates arises from the coupling via quasistatic magnetic fields. As a function of distance, the relevant eddy current modes cross over from a quantum to a thermal regime. These modes alone reproduce previously discussed thermal anomalies of the electromagnetic Casimir interaction between good conductors. In particular, they provide a physical picture for the Casimir entropy whose nonzero value at zero temperature arises from a correlated, glassy state.

Thermal Casimir versus Casimir-Polder forces: equilibrium and nonequilibrium forces

We critically discuss whether and under what conditions Lifshitz theory may be used to describe thermal Casimir-Polder forces on atoms or molecules. An exact treatment of the atom-field coupling reveals that for a ground-state atom (molecule), terms associated with virtual-photon absorption lead to a deviation from the traditional Lifshitz result; they are identified as a signature of nonequilibrium dynamics. Even the equilibrium force on a thermalized atom (molecule) may be overestimated when using the ground-state polarizability instead of its thermal counterpart.

Comment on "Analytical and numerical verification of the Nernst theorem for metals"

Recently, Høye, Brevik, Ellingsen, and Aarseth [Phys. Rev. E 75, 051127 (2007)] 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 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 that the approximation of temperature independent relaxation frequency used in the paper leads to incorrect values of numerical coefficients in the obtained asymptotic expressions for metals with impurities.

Analytical and numerical verification of the Nernst theorem for metals

In view of the current discussion on the subject, an effort is made to show very accurately both analytically and numerically how the Drude dispersion model gives consistent results for the Casimir free energy at low temperatures. Specifically, for the free energy near T=0 we find the leading term proportional to T2 and the next-to-leading term proportional to T(5/2). These terms give rise to zero Casimir entropy as T-->0 and are thus in accordance with Nernst's theorem.

Casimir edge effects

We compute Casimir forces in open geometries with edges, involving parallel as well as perpendicular semi-infinite plates. We focus on Casimir configurations which are governed by a unique dimensional scaling law with a universal coefficient. With the aid of worldline numerics, we determine this coefficient for various geometries for the case of scalar-field fluctuations with Dirichlet boundary conditions. Our results facilitate an estimate of the systematic error induced by the edges of finite plates, for instance, in a standard parallel-plate experiment. The Casimir edge effects for this case can be reformulated as an increase of the effective area of the configuration.