# 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. - Highlights: • A toy model for Casimir-like effect with only 3 degrees of freedom is constructed. • Casimir vacuum can be related to the photon vacuum by a non-trivial Bogoliubov transformation. • Casimir vacuum 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 vanmore »

- Authors:

- Publication Date:

- OSTI Identifier:
- 22701513

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics

- Additional Journal Information:
- Journal Volume: 383; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOGOLYUBOV TRANSFORMATION; CASIMIR EFFECT; DEGREES OF FREEDOM; GROUND STATES; HAMILTONIANS; PHOTONS; VAN DER WAALS FORCES

### Citation Formats

```
Nikolić, Hrvoje.
```*Is zero-point energy physical? A toy model for Casimir-like effect*. United States: N. p., 2017.
Web. doi:10.1016/J.AOP.2017.05.013.

```
Nikolić, Hrvoje.
```*Is zero-point energy physical? A toy model for Casimir-like effect*. United States. doi:10.1016/J.AOP.2017.05.013.

```
Nikolić, Hrvoje. Tue .
"Is zero-point energy physical? A toy model for Casimir-like effect". United States. doi:10.1016/J.AOP.2017.05.013.
```

```
@article{osti_22701513,
```

title = {Is zero-point energy physical? A toy model for Casimir-like effect},

author = {Nikolić, Hrvoje},

abstractNote = {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. - Highlights: • A toy model for Casimir-like effect with only 3 degrees of freedom is constructed. • Casimir vacuum can be related to the photon vacuum by a non-trivial Bogoliubov transformation. • Casimir vacuum 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.},

doi = {10.1016/J.AOP.2017.05.013},

journal = {Annals of Physics},

issn = {0003-4916},

number = ,

volume = 383,

place = {United States},

year = {2017},

month = {8}

}