Theory confronts experiment in the Casimir force measurements: Quantification of errors and precision

Abstract

We compare theory and experiment in the Casimir force measurement between gold surfaces performed with the atomic force microscope. Both random and systematic experimental errors are found leading to a total absolute error equal to 8.5 pN at 95% confidence. In terms of the relative errors, experimental precision of 1.75% is obtained at the shortest separation of 62 nm at 95% confidence level (at 60% confidence the experimental precision of 1% is confirmed at the shortest separation). An independent determination of the accuracy of the theoretical calculations of the Casimir force and its application to the experimental configuration is carefully made. Special attention is paid to the sample-dependent variations of the optical tabulated data due to the presence of grains, contribution of surface plasmons, and errors introduced by the use of the proximity force theorem. Nonmultiplicative and diffraction-type contributions to the surface roughness corrections are examined. The electric forces due to patch potentials resulting from the polycrystalline nature of the gold films are estimated. The finite size and thermal effects are found to be negligible. The theoretical accuracy of about 1.69% and 1.1% are found at a separation 62 nm and 200 nm, respectively. Within the limits of experimental and theoretical errors very good agreement between experiment and theory is confirmed characterized by the root mean square deviation of about 3.5 pN within all measurement range. The conclusion is made that the Casimir force is stable relative to variations of the sample-dependent optical and electric properties, which opens new opportunities to use the Casimir effect for diagnostic purposes.

Experimental Investigation of the Casimir Force beyond the Proximity-Force Approximation

“…The values of from the force measurements provide weaker constraints on than those obtained for 0 from the force gradient measurements, and the latter provide new and very useful constraints on the errors associated with the use of the PFA in these types of experiments. As noted earlier, in the analysis of previous experiments it has been assumed that the relative errors arising from the PFA are ' z=R (i.e., 0 ' 1) [3,5,8], but our results show that this overestimates the effect for z & 400 nm. For z & 300, we find j 0 z j < 0:4 at the 95% confidence level.…”

“…Unfortunately, the unusual nature of the PFA prevents one from easily calculating its leading order corrections which could be used to assess its range of applicability [15]. In the analysis of experimental results, one presently estimates that the fractional error arising from the use of the PFA is ' z=R [3,5,8], but this estimate cannot yet be supported by a calculation from first principles. If one is to use the results of Casimir force measurements to test theories of the Casimir force, or to set improved limits on new submicron-ranged forces, it is important to have a reliable understanding of the PFA.…”

“…Since the modern experimental investigation of the Casimir force began ten years ago, most measurements [1][2][3][4][5][6][7][8] have used a configuration that studies the interaction of a spherical probe with a flat substrate. Because of the difficulty of maintaining parallelism between two flat plates, only one experiment [9] has been performed using the parallel-plate configuration originally envisioned by Casimir, for which the theory has been developed to a high degree.…”

Review of Experimental Concepts for Studying the Quantum Vacuum Field

“…This force is an attraction between parallel uncharged metallic plates that has now been well measured (Lamoreaux, 1997;Mohideen, 1998;Chen et al, 2004) and can be attributed to a minute imbalance in the zero-point energy density inside the cavity between the plates versus the region outside the plates as shown in Figure 1. However, this is not useful for propulsion since it symmetrically pulls on the plates.…”

Torque on birefringent plates induced by quantum fluctuations

“…The theory has been verified in several high precision experiments, and although the investigation has been mainly focused on the interaction between metallic surfaces in vacuum, there are no doubts about its general validity [11,12,13,14,15,16,17,18,19] (for a review of previous measurements, see [8,20]; for a critical discussion on the precision of the most recent experiments, see [21,22,23,24]). Less precise measurements in liquids have been reported [8,25,26], and experimental evidence for repulsive van der Waals forces between dielectric surfaces in different fluids has also been reported [27,28,29].…”