Proof that Casimir force does not originate from vacuum energy

TL;DR

This paper provides a straightforward proof that the Casimir force does not originate from electromagnetic vacuum energy but instead arises from van der Waals interactions mediated by the interaction Hamiltonian.

Contribution

It clarifies the true origin of the Casimir force, challenging the common misconception that it stems from vacuum energy, and emphasizes the role of the interaction Hamiltonian.

Findings

Vacuum energy does not generate Casimir force.

Casimir force originates from van der Waals interactions.

Misinterpretations in literature are due to implicit dependence assumptions.

Abstract

We present a simple general proof that Casimir force cannot originate from the vacuum energy of electromagnetic (EM) field. The full QED Hamiltonian consists of 3 terms: the pure electromagnetic term $H_{\rm em}$, the pure matter term $H_{\rm matt}$ and the interaction term $H_{\rm int}$. The $H_{\rm em}$-term commutes with all matter fields because it does not have any explicit dependence on matter fields. As a consequence, $H_{\rm em}$ cannot generate any forces on matter. Since it is precisely this term that generates the vacuum energy of EM field, it follows that the vacuum energy does not generate the forces. The misleading statements in the literature that vacuum energy generates Casimir force can be boiled down to the fact that $H_{\rm em}$ attains an implicit dependence on matter fields by the use of the equations of motion and the illegitimate treatment of the implicit dependence as if it was explicit. The true origin of the Casimir force is van der Waals force generated by $H_{\rm int}$.