Reply to “Comment on ‘Anomalies in electrostatic calibrations for the measurement of the Casimir force in a sphere-plane geometry’”

Abstract

In a recent Comment, Decca et al. have discussed the origin of the anomalies recently reported by us in [Phys. Rev. A 78, 036102(R) (2008)]. Here we restate our view, corroborated by their considerations, that quantitative geometrical and electrostatic characterizations of the conducting surfaces (a topic not discussed explicitly in the literature until very recently) are critical for the assessment of precision and accuracy of the demonstration of the Casimir force, and for deriving meaningful limits on the existence of Yukawian components possibly superimposed to the Newtonian gravitational interaction.In the last decade, various efforts have been focused on demonstrating the Casimir force and exploring hypothetical short-range forces of gravitational origin [1]. Limits to the existence of these forces -or their tentative discovery -in the micrometer range rely on the control at the highest level of accuracy of the Casimir force and the related systematic effects [2,3].In this context we have investigated the celebrated sphere-plane geometry in a range of parameters for which the hypothetical Yukawian contribution of gravitational origin should be optimally detected [4]. This implies exploiting a combination of spheres with large radius of curvature, such as the one already used in [5], and small separation gaps between the sphere and the planar surface, similar to the ones explored in [6,7,8] with spheres having order of 100 µm radius of curvature. Notice that large radius of curvature and relatively large distances as in [5] are not adequately sensitive to Yukawian forces with small interaction range. Conversely, microspheres at small distances as used in [6,7,8] have small sensitivity to the amplitude of Yukawa forces, due to the smaller expected signal arising from the reduced effective surfaces of interaction. In this regard, limits to the Yukawa force based on a formal mapping between an ideal parallel plate geometry and the sphere-plane configuration actually used in the experimental setup as in [9] are invalid, as the Proximity Force Approximation (PFA), typically used for forces acting between surfaces [10], does not hold for forces of volumetric character such as the gravitational force or its hypothetical short-range relatives.In [4], we reported two anomalies in the electrostatic calibration of our apparatus, after discussing and ruling out some systematic effects. This has triggered the interest of the authors of [11] who have added two interesting points, first attempting to explain our first anomaly in terms of a systematic deviation from the ideal, singlecurvature pattern for the spherical surface, and second presenting a distance independent contact potential in one of their experimental setups. We welcome these different insights and would like to discuss here their implications in the general context of both accurate demonstrations of the Casimir force and precision experiments on Yukawian gravitational forces, as in the following.Deviation from ideal spherical geometry: Among the possible re...

Gradient of the Casimir force between Au surfaces of a sphere and a plate measured using an atomic force microscope in a frequency-shift technique

“…III, the dependence of V 0 on separation was observed in different experiments on the Casimir force (see, e.g., Refs. [46][47][48]54,56,62 ). It might be caused for different reasons including the mechanical drift considered above.…”

Effect of surface contact potential in atomic-size contacts

“…First, the actual capacitance near the contact regime (d ≈ 10 Å) is not precisely known. Because a typical capacitance measurement at the closest distance is performed at a few-μm separation [38,46], the capacitance value 100 pF is a conservative estimate. Note that the measured value also reflects the parasitic capacitance near and around the tip-sample contact, which is only specific to a particular experimental setup.…”

What Is Credible and What Is Incredible in the Measurements of the Casimir Force

“…In particular, depending on the quality of lens used, bubbles and pits with a diameter varying from 30 µm to 1.2 mm are allowed on the surface. 19 There may be also scratches 19 with a width varying from 3 to 120 µm. The problem of bubbles on the centimeter-size lens surface should not be reduced to the fact that lens curvature radius R is determined with some error.…”

“…To illustrate this fact, we perform calculations for three typical model imperfections on the spherical surface near the point of closest approach to the plate allowed by the optical surface specification data. 19 As the first example, we consider a bubble of the curvature radius R 1 = 25 cm which is larger than the curvature radius R = 15 cm of the lens used [see Fig. 1(a)].…”

“…The radius of the bubble is determined from r 2 = 2R 1 D 1 − D 2 1 ≈ 0.25 mm 2 , leading to 2r = 1 mm < 1.2 mm, i.e., less than a maximum value allowed by the optical surface specification data. 19 Respective quantity d defined in Fig. 1(a) The general formulation of the PFA (4) should be applied taking into account that the surfaces of the bubble and of the lens are described by the equations…”