Experiment, theory and the Casimir effect

TL;DR

This paper reviews theoretical and experimental issues in measuring the Casimir effect, discusses the validity of various models and approximations, and examines recent approaches to thermal Casimir forces, highlighting inconsistencies with thermodynamics and experiments.

Contribution

It clarifies the physical and theoretical foundations of Casimir force calculations, evaluates the validity of the proximity force approximation, and critiques recent models including screening effects.

Findings

Rectangular box results agree with piston configurations.

Proximity force approximation has limitations beyond first principles.

Screening-based thermal Casimir models are inconsistent with thermodynamics.

Abstract

Several problems at the interface between the field-theoretical description of the Casimir effect and experiments on measuring the Casimir force are discussed. One of these problems is connected with the definition of the Casimir free energy in ideal metal rectangular boxes satisfying the general physical requirements. It is shown that the consideration of rectangular boxes with a partition (piston) does not negate the previously known results obtained for boxes without a piston. Both sets of results are found to be in mutual agreement. Another problem is related to the use of the proximity force approximation for the interpretation of the experimental data and to the search of analytical results beyond the PFA based on the first principles of quantum field theory. Next, we discuss concepts of experimental precision and of the measure of agreement between experiment and theory. The fundamental difference between these two concepts is clarified. Finally, recent approach to the thermal Casimir force taking screening effects into account is applied to real metals. It is shown that this approach is thermodynamically and experimentally inconsistent. The physical reasons of this inconsistency are connected with the violation of thermal equilibrium which is the basic applicability condition of the Lifshitz theory.