# Casimir Force and its Relation to Surface Tension

## TL;DR

This paper demonstrates that the work done by Casimir forces during slow plate displacements corresponds to the surface tension free energy in ionic fluids, linking quantum field theory parameters to physical surface properties.

## Contribution

It explicitly relates Casimir energy to surface tension free energy in ionic fluids and discusses how experimental surface tension data can inform quantum cutoff parameters.

## Key findings

- Casimir work equals surface tension free energy in ionic fluids.
- Surface-associated free energy is half of the Casimir energy.
- Cutoff time-splitting parameter is of atomic scale, consistent with physical intuition.

## Abstract

From energy considerations there is reason to expect that the work done by Casimir forces during a slow displacement of the parallel plates reflects the free energy of the surface tension of the adjacent surfaces. We show this explicitly, for a one-component ionic fluid or plasma with $q_c$ as ionic charge, where the particles are neutralized by a uniform continuous oppositely charged background. For two equal half-planes, the surface-associated free energy for one half-plane turns out to be just one half of the total Casimir energy for the conventional Casimir setup. We also comment, from a wider perspective, on the intriguing possibility that knowledge about the magnitude of the surface tension coefficient obtained from statistical mechanics or experiments may give insight into the value of the conventional cutoff time-splitting parameter $\tau=t-t'$ occurring in quantum field theory. A simple analysis suggests that the minimal distance $\tau c$ is of the order of atomic dimensions, which is a physically natural result.