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

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.

21 pages, version accepted for publication in Annals of Physics

References in corpus (3)

• Proof that Casimir force does not originate from vacuum energy
• Harmonic oscillator model for the atom-surface Casimir-Polder interaction energy
• Phonon-polaritons in Bose-Einstein condensates induced by Casimir-Polder interaction with graphene

Cited by in corpus (5)

• Quantum signatures in quadratic optomechanics
• Why zero-point quantum noise cannot be detected at thermal equilibrium: Casimir force and zero-point contribution in the fluctuation-dissipation theorem
• Casimir-like effect from thermal field fluctuations
• The zero-point energy of elementary quantum fields
• Emergent diffeomorphism invariance in toy models