A number of experimental measurements of the Casimir force have observed a logarithmic distance variation of the voltage that minimizes electrostatic force between the plates in a sphere-plane geometry. We show that this variation can be simply under
stood from a geometric averaging of surface potential patches together with the Proximity Force Approximation.
The imperfect termination of static electric fields at semiconducting surfaces has been long known in solid state and transistor physics. We show that the imperfect shielding leads to an offset in the distance between two surfaces as determined by el
ectrostatic force measurements. The effect exists even in the case of good conductors (metals) albeit much reduced.
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 myria
d of problems associated with both patch potentials and electrostatic calibrations are discussed and the remaining open questions are brought forward.
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.
We present calculations of contact potential surface patch effects that simplify previous treatments. It is shown that, because of the linearity of Laplaces equation, the presence of patch potentials does not affect an electrostatic calibration (of f
orce and/or distance) of a two-plate Casimir measurement apparatus. Using models that include long-range variations in the contact potential across the plate surfaces, a number of experimental observations can be reproduced and explained. For these models, numerical calculations show that if a voltage is applied between the plates which minimizes the force, a residual electrostatic force persists, and that the minimizing potential varies with distance. The residual force can be described by a fit to a simple two-parameter function involving the minimizing potential and its variation with distance. We show the origin of this residual force by use of a simple parallel capacitor model. Finally, the implications of a residual force that varies in a manner different from 1/d on the accuracy of previous Casimir measurements is discussed.
The existence of a monotonic distance dependent contact potential between two plates in a Casimir experiment leads to an additional electrostatic force that is significantly different from the case of a constant potential. Such a varying potential ca
n arise if there is a uniform gradient in the work function or contact potential across a plate, as opposed to random microscopic fluctuations associated with patch potentials. A procedure to compensate for this force is described for the case of an experiment where the electrostatic force is minimized at each measurement distance by applying a voltage between the plates. It is noted that the minimizing voltage is not the contact potential.
The recent discovery that silicon nitride membranes can be used as extremely high Q mechanical resonators makes possible a number of novel experiments, which include improved long range vacuum Casimir force measurements, and measurments of the proper
ties of liquid helium below the lambda point. It is noted that in the thermal correction to the Casimir force, the phase velocity of the excitations does not enter, with the force per unit area between parallel plates depending only on the temperature and distance between the plates. Thus it appears as possible to measure the phonon analog of the finite temperature Casimir force in liquid helium.
