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Register a new userSystematic Correction for Demonstration of the Casimir Force in the 0.6 to 6 micrometer Range
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S.K. Lamoreaux
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A new systematic correction for Casimir force measurements is proposed and applied to the results of an experiment that was performed more than a decade ago. This correction brings the experimental results into good agreement with the Drude model of the metallic plates permittivity. The systematic is due to time-dependent fluctuations in the distance between the plates caused by mechanical vibrations or tilt, or position measurement uncertainty, and is similar to the correction for plate roughness.
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The low-temperature asymptotic expressions for the Casimir interaction between two real metals described by Leontovich surface impedance are obtained in the framework of thermal quantum field theory. It is shown that the Casimir entropy computed using the impedance of infrared optics vanishes in the limit of zero temperature. By contrast, the Casimir entropy computed using the impedance of the Drude model attains at zero temperature a positive value which depends on the parameters of a system, i.e., the Nernst heat theorem is violated. Thus, the impedance of infrared optics withstands the thermodynamic test, whereas the impedance of the Drude model does not. We also perform a phenomenological analysis of the thermal Casimir force and of the radiative heat transfer through a vacuum gap between real metal plates. The characterization of a metal by means of the Leontovich impedance of the Drude model is shown to be inconsistent with experiment at separations of a few hundred nanometers. A modification of the impedance of infrared optics is suggested taking into account relaxation processes. The power of radiative heat transfer predicted from this impedance is several times less than previous predictions due to different contributions from the transverse electric evanescent waves. The physical meaning of low frequencies in the Lifshitz formula is discussed. It is concluded that new measurements of radiative heat transfer are required to find out the adequate description of a metal in the theory of electromagnetic fluctuations.
Several new experiments have extended studies of the Casimir force into new and interesting regimes. This recent work will be briefly reviewed. With this recent progress, new issues with background electrostatic effects have been uncovered. The myriad of problems associated with both patch potentials and electrostatic calibrations are discussed and the remaining open questions are brought forward.
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 preprints suggestion concerning the resolution of the apparent violation of the Third Law of Thermodynamics is shown to be incorrect.
Up to now there has been no reliable method to calculate the Casimir force when surface roughness becomes comparable with the separation between bodies. Statistical analysis of rough Au films demonstrates rare peaks with heights considerably larger than the root-mean-square (rms) roughness. These peaks define the minimal distance between rough surfaces and can be described with extreme value statistics. We show that the contributions of high peaks to the force can be calculated independently of each other while the contribution of normal roughness can be evaluated perturbatively beyond the proximity force approximation. The developed method allows a reliable force estimation for short separations. Our model explains the strong hitherto unexplained deviation from the normal Casimir scaling observed experimentally at short separations.
Hard momentum cutoff is used for estimating IR/UV corrections to the Casimir force. In contrast to the power-law corrections arising from the IR cutoff, one will find the UV cutoff-dependent corrections to be exponentially suppressed. As a consequence of this fact, there is no chance to detect the corrections due to UV cutoff arising for instance from the minimum-length scenarios even if fundamental quantum-gravity scale is taken around $sim$ TeV (as is the case, for example, in various models with extra dimensions).
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