Casimir effect information

In quantum field theory, the Casimir effect (or Casimir force)^[1] is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of a field. It is named after the Dutch physicist Hendrik Casimir, who predicted the effect for electromagnetic systems in 1948.

Video of silver micromirrors in solution under optical darkfield microscope demonstrating Brownian motion, Casimir effect and colorful scattering of surface plasmons

In the same year, Casimir together with Dirk Polder described a similar effect experienced by a neutral atom in the vicinity of a macroscopic interface, which is called the Casimir–Polder force.^[2] Their result is a generalization of the London–van der Waals force and includes retardation due to the finite speed of light. The fundamental principles leading to the London–van der Waals force, the Casimir force, and the Casimir–Polder force can be formulated on the same footing.^[3]^[4]

In 1997 a direct experiment by Steven K. Lamoreaux quantitatively measured the Casimir force to within 5% of the value predicted by the theory.^[5]

The Casimir effect can be understood by the idea that the presence of macroscopic material interfaces, such as electrical conductors and dielectrics, alter the vacuum expectation value of the energy of the second-quantized electromagnetic field.^[6]^[7] Since the value of this energy depends on the shapes and positions of the materials, the Casimir effect manifests itself as a force between such objects.

Any medium supporting oscillations has an analogue of the Casimir effect. For example, beads on a string^[8]^[9] as well as plates submerged in turbulent water^[10] or gas^[11] illustrate the Casimir force.

In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; in applied physics it is significant in some aspects of emerging microtechnologies and nanotechnologies.^[12]

^ Lamoreaux, Steven K. (2005). "The Casimir force: Background, experiments, and applications". Reports on Progress in Physics. 68 (1): 201–236. Bibcode:2005RPPh...68..201L. doi:10.1088/0034-4885/68/1/r04. S2CID 21131414.
^ Cite error: The named reference :3 was invoked but never defined (see the help page).
^ Cite error: The named reference :2 was invoked but never defined (see the help page).
^ Intravaia, Francesco; Behunin, Ryan (28 December 2012). "Casimir effect as a sum over modes in dissipative systems". Physical Review A. 86 (6): 062517. arXiv:1209.6072. Bibcode:2012PhRvA..86f2517I. doi:10.1103/PhysRevA.86.062517. ISSN 1050-2947. S2CID 119211980.
^ Cite error: The named reference Lamoureaux1997 was invoked but never defined (see the help page).
^ E. L. Losada" Functional Approach to the Fermionic Casimir Effect Archived 31 May 2011 at the Wayback Machine"
^ Michael Bordag; Galina Leonidovna Klimchitskaya; Umar Mohideen (2009). "Chapter I; § 3: Field quantization and vacuum energy in the presence of boundaries". Advances in the Casimir effect. Oxford University Press. pp. 33 ff. ISBN 978-0-19-923874-3. Reviewed in Lamoreaux, Steve K. (2010). "Advances in the Casimir Effect Advances in the Casimir Effect, M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko Oxford U. Press, New York, 2009. $150.00 (749 pp.). ISBN 978-0-19-923874-3". Physics Today. 63 (8): 50–51. Bibcode:2010PhT....63h..50B. doi:10.1063/1.3480079.
^ Griffiths, D. J.; Ho, E. (2001). "Classical Casimir effect for beads on a string". American Journal of Physics. 69 (11): 1173. Bibcode:2001AmJPh..69.1173G. doi:10.1119/1.1396620.
^ Cooke, J. H. (1998). "Casimir force on a loaded string". American Journal of Physics. 66 (7): 569–572. Bibcode:1998AmJPh..66..569C. doi:10.1119/1.18907.
^ Denardo, B. C.; Puda, J. J.; Larraza, A. S. (2009). "A water wave analog of the Casimir effect". American Journal of Physics. 77 (12): 1095. Bibcode:2009AmJPh..77.1095D. doi:10.1119/1.3211416.
^ Larraza, A. S.; Denardo, B. (1998). "An acoustic Casimir effect". Physics Letters A. 248 (2–4): 151. Bibcode:1998PhLA..248..151L. doi:10.1016/S0375-9601(98)00652-5.
^ Astrid Lambrecht, Serge Reynaud and Cyriaque Genet (2007) "Casimir In The Nanoworld" Archived 22 November 2009 at the Wayback Machine

[1] Lamoreaux, Steven K. (2005). "The Casimir force: Background, experiments, and applications". Reports on Progress in Physics. 68 (1): 201–236. Bibcode:2005RPPh...68..201L. doi:10.1088/0034-4885/68/1/r04. S2CID 21131414.

[:3-2] Cite error: The named reference :3 was invoked but never defined (see the help page).

[:2-3] Cite error: The named reference :2 was invoked but never defined (see the help page).

[4] Intravaia, Francesco; Behunin, Ryan (28 December 2012). "Casimir effect as a sum over modes in dissipative systems". Physical Review A. 86 (6): 062517. arXiv:1209.6072. Bibcode:2012PhRvA..86f2517I. doi:10.1103/PhysRevA.86.062517. ISSN 1050-2947. S2CID 119211980.

[Lamoureaux1997-5] Cite error: The named reference Lamoureaux1997 was invoked but never defined (see the help page).

[6] E. L. Losada" Functional Approach to the Fermionic Casimir Effect Archived 31 May 2011 at the Wayback Machine"

[Mohideen-7] Michael Bordag; Galina Leonidovna Klimchitskaya; Umar Mohideen (2009). "Chapter I; § 3: Field quantization and vacuum energy in the presence of boundaries". Advances in the Casimir effect. Oxford University Press. pp. 33 ff. ISBN 978-0-19-923874-3. Reviewed in Lamoreaux, Steve K. (2010). "Advances in the Casimir Effect Advances in the Casimir Effect, M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko Oxford U. Press, New York, 2009. $150.00 (749 pp.). ISBN 978-0-19-923874-3". Physics Today. 63 (8): 50–51. Bibcode:2010PhT....63h..50B. doi:10.1063/1.3480079.

[8] Griffiths, D. J.; Ho, E. (2001). "Classical Casimir effect for beads on a string". American Journal of Physics. 69 (11): 1173. Bibcode:2001AmJPh..69.1173G. doi:10.1119/1.1396620.

[9] Cooke, J. H. (1998). "Casimir force on a loaded string". American Journal of Physics. 66 (7): 569–572. Bibcode:1998AmJPh..66..569C. doi:10.1119/1.18907.

[10] Denardo, B. C.; Puda, J. J.; Larraza, A. S. (2009). "A water wave analog of the Casimir effect". American Journal of Physics. 77 (12): 1095. Bibcode:2009AmJPh..77.1095D. doi:10.1119/1.3211416.

[11] Larraza, A. S.; Denardo, B. (1998). "An acoustic Casimir effect". Physics Letters A. 248 (2–4): 151. Bibcode:1998PhLA..248..151L. doi:10.1016/S0375-9601(98)00652-5.

[12] Astrid Lambrecht, Serge Reynaud and Cyriaque Genet (2007) "Casimir In The Nanoworld" Archived 22 November 2009 at the Wayback Machine

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