The Casimir Effect
What is the Casimir Effect?
Attractive force between two uncharged parallel
plates
F=(πhcA)/(480d4)
Discovered by H.B.G. Casimir in 1948
Caused by the restriction of electromagnetic
modes
E=0 at surface of each conductor (think waves on a string)
As the plates are moved together, fewer modes are viable
With fewer modes available, the energy density of the space
between the plates becomes less than the surrounding
vacuum
Lower energy density means there must be a force pulling
the plates together.
Comparison of Forces
Consider a parallel plate capacitor with area A=0.01m2 and the
distance between them, d, to be 0.01m. The voltage, V, between
them is 30V
Comparison of Forces
Consider a parallel plate capacitor with area A=0.01m2 and the
distance between them, d, to be 0.01m. The voltage, V, between
them is 30V
Electric Force:
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Q=CV
C=ε0A/d,
V=Ed
F=EQ=V2C/d=(V2 ε0A)/d2
F=7.97*10-7 N
Comparison of Forces
Consider a parallel plate capacitor with area A=0.01m2 and the
distance between them, d, to be 0.01m. The voltage, V, between
them is 30V.
Now, Consider the same plates, but with no potential difference
between them.
Casimir Force
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F=(πhcA)/(480d4)
F=1.30*10-21 N
Comparison of Forces
Consider a parallel plate capacitor with area A=0.01m2 and the
distance between them, d, to be 0.01m. The voltage, V, between
them is 30V.
Now, Consider the same plates, but with no potential difference
between them. Lets make a rough comparison of the gravitational
force by approximating them as point masses and saying that each
plate has a mass of 0.1kg.
Gravitational Force
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F=Gm2/d2
F=6.67*10-9 N
But, because of the 1/r4 dependence, if d is very very small then the
Casimir force will start to dominate.
Why is the Casimir force is
attractive?
E field
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Forces
Why is the Casimir force is
attractive?
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Forces
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Image Particles
Measurement of the Casimir Force
Problems
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Casimir force is very weak
Has a very short range (1/r4 dependence)
Plates must be parallel
First tentative experiments done by in 1958 (Spaarnay)
In 1997, the technique of using a spherical “plate” with large radius
overcame the problem of keeping the plates parallel. (Lamoreaux)
Real World Applications
Microelectromechanical systems (MEMS)
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Used in the manufacture of car airbag systems
Casimir Force can make parts of MEMS stick together
Casimir Force can also be used to control the movement of
MEMS devices
References
“The Casimir effect: a force from nothing” from the September 2002
issue of Physics World
“Resource Letter CF-1: Casimir Force” by S.K. Lamorceaux from the
American Journal of Physics 67 (10) (October 1999)
“Essentials of the Casimir effect and its computation” by E. Elizalde
and A. Romeo from the American Journal of Physics 59 (8) (August
1991)