How to confirm and exclude different models of material properties in the Casimir effect

TL;DR

This paper introduces a statistical method to confirm or exclude different material property models in Casimir force experiments, applying it to recent data and assessing model validity at various confidence levels.

Contribution

The paper develops a new method for model validation in Casimir force measurements, enabling clear exclusion or confirmation of models based on confidence intervals.

Findings

Drude model excluded at 95% confidence in some experiments.

Plasma model and other approaches agree with data at over 80% confidence.

Method successfully differentiates between competing material property models.

Abstract

We formulate a method allowing to confirm or exclude the alternative models of material properties at some definite confidence level in experiments on measuring the Casimir force. The method is based on the consideration of differences between the theoretical and mean measured quantities and the confidence intervals for these differences found at sufficiently high or low confidence probabilities. The developed method is applied to the data of four recent experiments on measuring the gradient of the Casimir force by means of a dynamic atomic force microscope. It is shown that in experiments with Au-Au and Ni-Ni test bodies, where the Drude model approach is excluded at a 95% confidence level, the plasma model approach agrees with the data at higher than 90% confidence. In experiments using an Au sphere interacting with either a Ni plate or a graphene-coated substrate the measurement data agree with the common prediction of the Drude and plasma model approaches and theory using the polarization tensor at 90% and 80% confidence levels, respectively.