# Is zero-point energy physical? A toy model for Casimir-like effect

## TL;DR

This paper clarifies the nature of zero-point energy and the Casimir effect, showing that the Casimir vacuum involves photon states and is best understood as a manifestation of van der Waals forces rather than a simple zero-point energy phenomenon.

## Contribution

It introduces a simple toy model to analyze the Casimir effect, revealing its relation to photon vacuum states and van der Waals forces, clarifying conceptual confusions.

## Key findings

- Casimir vacuum involves photon states and is related to the photon vacuum via Bogoliubov transformation.
- Casimir force can be viewed as a manifestation of van der Waals forces.
- The Casimir vacuum is a ground state only for an effective Hamiltonian at fixed plate distance.

## Abstract

Zero-point energy is generally known to be unphysical. Casimir effect, however, is often presented as a counterexample, giving rise to a conceptual confusion. To resolve the confusion we study foundational aspects of Casimir effect at a qualitative level, but also at a quantitative level within a simple toy model with only 3 degrees of freedom. In particular, we point out that Casimir vacuum is not a state without photons, and not a ground state for a Hamiltonian that can describe Casimir force. Instead, Casimir vacuum can be related to the photon vacuum by a non-trivial Bogoliubov transformation, and it is a ground state only for an effective Hamiltonian describing Casimir plates at a fixed distance. At the fundamental microscopic level, Casimir force is best viewed as a manifestation of van der Waals forces.