Proof that Casimir force does not originate from vacuum energy
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_{em}, the pure matter term H_{matt} and the interaction term H_{int}. The H_{em}term commutes with all matter fields because it does not have any explicit dependence on matter fields. As a consequence, H_{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_{em} attains an implicit dependence on matter fields by the use of the equations of motion and to 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_{int}.
 Publication:

Physics Letters B
 Pub Date:
 October 2016
 DOI:
 10.1016/j.physletb.2016.08.036
 arXiv:
 arXiv:1605.04143
 Bibcode:
 2016PhLB..761..197N
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics;
 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 14 pages, revised, accepted for publication in Phys. Lett. B