What is credible and what is incredible in the measurements of the Casimir force

TL;DR

The paper critically examines the reliability of Casimir force measurements, highlighting flaws in experiments using large spherical lenses and proposing new models that account for surface imperfections, which significantly affect the force estimates.

Contribution

It introduces a rigorous approach to evaluating measurement accuracy and derives new expressions for the Casimir force considering surface imperfections on large lenses.

Findings

Measurements with centimeter-sized lenses are flawed due to surface bubbles and pits.

The proximity force approximation is invalid for large lenses.

Surface imperfections cause deviations of tens of percent in force measurements.

Abstract

We comment on progress in measurements of the Casimir force and discuss what is the actual reliability of different experiments. In this connection a more rigorous approach to the usage of such concepts as accuracy, precision, and measure of agreement between experiment and theory, is presented. We demonstrate that all measurements of the Casimir force employing spherical lenses with centimeter-size curvature radii are fundamentally flawed due to the presence of bubbles and pits on their surfaces. The commonly used formulation of the proximity force approximation is shown to be inapplicable for centimeter-size lenses. New expressions for the Casimir force are derived taking into account surface imperfections. Uncontrollable deviations of the Casimir force from the values predicted using the assumption of perfect sphericity vary by a few tens of percent within the separation region from 1 to $3\,\mu$m. This makes impractical further use of centimeter-size lenses in experiments on measuring the Casimir force.