Force from Equilibrium Fluctuations
Particles: Pressure is a function of state.
Force per unit area of the wall is a bulk property;
independent of the shape of the container and potentials at the wall
independent of the dynamics of the particles (momentum integrations)
For a dilute gas: 
(non-universal corrections)
Radiation: Photon density depends on temperature:
Stefan-Boltzmann law of black-body pressure:
Casimir Force: Virtual photons (QED fluctuations) at low temperatures: 
"On
the attraction between two perfectly conducting plates," H.B.G.
Casimir, Proc. K. Ned. Akad. Wet. 51,
793 (1948)
Quantum fluctuations
of electromagnetic field in the vacuum between leads to an attractive force between perfect mirrors
"Pressure" =>"Interaction"; Force per unit area of the wall is
Attractive
Strongly dependent on the shape of the container
Since 1995 confirmed in myriad experiments.
"The
Theory of Molecular Attractive Forces Between Solids," E.M.
Lifshitz, Soviet Physics 2,
73 (1956),
Generalizes above by considering fluctuating current sources in the bodies, and at finite temperatures.
At distances shorter than a material dependent (e.g.. plasma) frequency 
, (the near field regime)
force is reduced by order of 
(cf retarded/non-retarded van der Waals forces)
Experimental Verification
Early experiments
provided at best qualitative support for an attractive force:
Abrikosova & Deriagin,
Sov. Phys. JETP 4, 1957 (1957). [Silica
lenses]
M.J.
Sparnaay, Physica 24, 751 (1958). [Aluminum
plates at distances H~1-100
nm]
J.
N. Israelachvili & D. Tabor, Proc. R. Soc. Lon A 331,
19 (1972) [mica H>1µm]
van
Blokland & Overbeek, J. Chem. Soc. F-T. I 74, 2637
(1978). [H~1-100 nm]
The era of
high precision tests, started with S. K. Lamoreaux
"Demonstration
of the Casimir Force in the 0.6 to 6µm Range," (using
a torsion pendulum)
S.K. Lamoreaux, Phys. Rev.
Lett. 78, 5 (1997)
U.
Mohideen (and collaborators at UC Riverside), using atomic force
microscopy
"Precision Measurements of
the Casimir Force from 0.1 to 0.9µm,"
U. Mohideen and A. Roy,
Phys. Rev. Lett. 81, (1998)
T. Ederth (geometry
of crossed cylinders)
"Template-stripped gold surfaces
... Casimir force in the 20–100-nm range,"
T. Ederth, Phys. A 62,
062104 (2000)
G.
Bressi, G. Carugno, R. Onofrio, and G. Ruoso,
"Measurement of the Casimir Force
between Parallel Metallic Surfaces,"
Phys. Rev. Lett. 88,
041804 (2002)
R.S. Decca,
D. Lopez, E. Fischbach, and D.E. Krause, Phys.
Rev. Lett. 91, 050402 (2003)
"Measurement of the Casimir Force
between dissimilar metals,"
Applications
Important in microelectromechanical systems (MEMS): micron-scale metallic machines
"Quantum Mechanical Actuation
of Microelectromechanical Systems by the Casimir Force,"
H.
B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, Federico Capasso, Science 291,
1941 (2001)
Stiction due to the attractive Casimir force is a challenge to design and operation of MEMs
"The role of the Casimir effect
in the static deflection and stiction of membrane strips in MEMS,"
F.
Michael Serry, Dirk Walliser, and G. Jordan Maclay, J. Appl. Phys. 84,
2501 (1998)
"Stiction, adhesion energy, and
the Casimir effect in micromechanical systems,"
E.
Buks and M. L. Roukes, Phys. Rev. B 63,
033402 (2001)
G.
Palasantzas and J. Th. M. De Hosson,
"Pull-in characteristics of electromechanical
switches in the presence of Casimir forces: Influence of self-affine
surface roughness,"
Phys. Rev. B 72,
115426 (2005)
Fabrizio
Pinto, InterstellarTechCorp
Reducing/removing Casimir attraction is of technological value:
Can Casimir forces be weakened or made repulsive? [Scientific American]
Challenges
to high precision tests come from:
Geometry:
non-planar shapes, roughness, ...
Material:
non-ideal metals, impurities, ...
Environment:
finite temperatures, ...
Particles: Thermal fluctuation-induced forces emerge when inter-particle forces lead to large correlation lengths.
( 
is needed for long-range, as opposed to short-range "depletion" forces.)
Finite-size corrections for free energy confined between plates take a universal form at criticality
M.E. Fisher and P.-G. de
Gennes, C. R. Acad. Sci. Ser. B 287, 207 (1978)
Experimental confirmation of force in critical oil/water mixture. [measurement, lateral force]
Hertlein,
Helden, Gambassi, Dietrich & Bechinger, Nature 451, 172
(2008)
Long-range correlations lead to long-range (universal) fluctuation-induced interactions.
Colloidal particles in
a critical binary mixture
"Direct
measurement of critical Casimir forces,"
Hertlein,
Helden, Gambassi, Dietrich & Bechinger, Nature 451, 172
(2008)
Depending on boundary conditions, these forces can be attractive or repulsive:
"Critical
Casimir forces in colloidal suspensions on chemically patterned surfaces,"
F. Soyka, O. Zvyagolskaya, C. Hertlein, L. Helden, & C.
Bechinger, Phys.
Rev. Lett. 101, 208301 (2008) (movie)
Like boundaries attract, unlike boundaries repel.
Goldstone mode fluctuations following continuous symmetry breaking are long-range correlated
H. Li . Kardar, Phys.
Rev. Lett. 67, 3275 (1991)
Experimental confirmation in wetting of super fluid films
R. Garcia and M.H.W. Chan, Phys. Rev. Lett. 83, 1187 (1999)
