Casimir Effect Invalidates the Drude Model for Transverse Electric Evanescent Waves

Abstract

We consider the Casimir pressure between two metallic plates and calculate the four contributions to it determined by the propagating and evanescent waves and by the transverse magnetic and transverse electric polarizations of the electromagnetic field. The range of interplate separations is considered where nearly the whole pressure has its origin in the electromagnetic response of conduction electrons. In the Casimir physics, this response is described either by the dissipative Drude model resulting in contradictions with the measurement data or by the experimentally consistent but dissipationless plasma model. It is shown that the total transverse magnetic contribution to the Casimir pressure due to both the propagating and evanescent waves and the transverse electric contribution due to only the propagating waves, computed by means of the Drude model, correlate well with the corresponding results obtained using the plasma model. We conclude that the disagreement between the theoretical predictions obtained using the Drude model and precision measurements of the Casimir force is not caused by the account of dissipation in itself, but arises from an incorrect description of the response of metals to the low-frequency transverse electric evanescent waves by this model. It is demonstrated that the Drude model has no supporting experimental evidence in the range of transverse electric evanescent waves, so that the above conclusion is consistent with all available information. The alternative test of the Drude model for the transverse electric evanescent waves suggested in the framework of classical electrodynamics is discussed.

Force Metrology with Plane Parallel Plates: Final Design Review and Outlook

“…More generally, within the Lifshitz framework, the disagreement between the experimental measurements and theoretical predictions obtained using the Drude model is related to the description of the optical response of metals at low frequency. This can substantially affect the contribution of the transverse electric (σ =TE) polarization [160][161][162][163]. More specifically, in the limit of large separations a, the difference between the two models discussed here arises because for the Drude model with γ ̸ = 0, in agreement with the Bohr-van Leeuwen theorem [164,165], the contribution of the TE-polarization in Equation ( 11) vanishes at large distance [163].…”

“…This can substantially affect the contribution of the transverse electric (σ =TE) polarization [160][161][162][163]. More specifically, in the limit of large separations a, the difference between the two models discussed here arises because for the Drude model with γ ̸ = 0, in agreement with the Bohr-van Leeuwen theorem [164,165], the contribution of the TE-polarization in Equation ( 11) vanishes at large distance [163]. The model resulting by setting γ = 0 in Equation ( 12), often called the plasma model, is equivalent to a relatively simple description of a superconductor [166], which does not fulfill the Bohr-van Leeuwen theorem.…”

The Casimir Force between Two Graphene Sheets: 2D Fresnel Reflection Coefficients, Contributions of Different Polarizations, and the Role of Evanescent Waves

“…At so large separations, however, there are no reliable measurement data available. As to the experimental separations between metallic plates, both the TM and TE polarizations contribute to the Casimir pressure irrespective of whether the experimentally consistent plasma model or the Drude model excluded by the measurement data is used [18].…”

“…If, however, the low-frequency response is described by the dissipationless plasma model, which should not be applicable at low frequencies, the theory gives results in agreement with the experiment (see [12,[14][15][16][17] for a review). Quite recently, it was shown [18] that the roots of the problem are not in the Drude model as a whole, but only in its possible incorrectness in the restricted area of transverse electric evanescent waves where it has no sufficient experimental confirmation.…”

Axion Electrodynamics and the Casimir Effect

“…As one important example, a semiclassical derivation of Casimir effects in magnetic media was presented by Peter Richmond and Barry Ninham [23] already in 1971. Many theoretical [24][25][26][27][28][29][30][31][32][33][34][35][36] and experimental studies [37][38][39][40][41][42][43][44] have followed in the last 50 years. More information related to Casimir effects in traditional systems can be found in the extensive literature [45][46][47][48][49][50][51].…”