Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution

Abstract

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.

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

“…An inclusion of the relaxation of conduction electrons (i.e., using the dissipative Drude model at low frequencies) results in a strong contradiction between experiment and theory over the range of separations from 0.2 to 4.8 µm. These results are in line with previous precise experiments on measuring the Casimir interaction at shorter sphere-plate separations [61,[71][72][73][74][75][76][77][78][79][80][81] and discussions of the so-called Casimir puzzle [82][83][84] (see also recent approaches to the resolution of this problem [85][86][87]).…”

Puzzling Low-Temperature Behavior of the Van Der Waals Friction Force between Metallic Plates in Relative Motion

“…This fact greatly complicates experimental measurements of entropy and, accordingly, the resolution of another long-standing problem--the so-called Casimir puzzle and Casimir conundrum [23][24][25][26] in the case of metallic and dielectric plates: violating the Nernst heat theorem when calculating the force of attraction between the plates in the framework of the Lifshitz theory using conventional, well-tested dielectric functions of materials. A recent comprehensive review on this issue is given in [27]. In contrast, the van der Waals friction force with a linear dependence on velocity turns out to be most sensitive precisely to the low-temperature dielectric properties of materials, and its measurement can also give a new impetus in solving the Casimir puzzle.…”

Effective Hamiltonians in Nonrelativistic Quantum Electrodynamics

“…This does not contrast with the fluctuation-dissipation theorem and the Kramers-Krönig dispersion relations, which indeed consider the response of a system to an external applied field (linear response theory), while in our case only vacuum field fluctuations act, which cannot induce real transitions. This result could be important also for macroscopic polarizable bodies and their role as boundary conditions in the Casimir effect, as well as for the long-lasting dispute in the literature about the most appropriate dielectric model (plasma or Drude model, for example) to be used in the Casimir effect for dielectrics [33][34][35]. We will address this point in a forthcoming publication.…”