AAWSAP DIRD, Warp Drive, Dark Energy, and the Manipulation of Extra Dimensions, April 2010

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Figure 2. The Interior Region of Parallel Conducting Plates. The region experiences a reduced quantum
vacuum energy density owing to the boundary condition the plates impose on the fields. This generates a
measurable attractive force that pushes the plates together.
For many years, the paper remained unknown (Reference 22), but from the 1970s
onward the Casimir effect received increasing attention, and over the last decade it has
become very popular (Reference 23). The Casimir effect is a purely quantum effect. In
classical electrodynamics the force between the plates is zero. The ideal scenario occurs
at zero temperature when there are no real photons (only virtual photons) between the
plates; thus, it is the ground state of the quantum electrodynamic vacuum which
causes the attraction. The most important feature of the Casimir effect is that even
though it is purely quantum in nature, it manifests itself macroscopically. For example,
for two parallel plates of area A = 1 cm 2 separated by a distance of d = 1 µm the force
of attraction is F ~ 1.3 x 10-7 N. This force is certainly within the range of laboratory
force-measuring techniques.
Typically, the calculations of the expectation value of the vacuum are divergent,6 so
some form of renormalization must be performed. A full review of the experimental
verifications of the Casimir effect are beyond the scope of this paper, but it is certainly
worth mentioning that experiments at Washington University using ultra-sensitive
Atomic Force Microscopes have experimentally verified the theoretical predictions of the
Casimir force to within 1 percent accuracy (Reference 24, 25). Needless to say, many
physicists consider this to be a real and well established phenomenon.
6 Divergent meaning the equation predicts an infinite result. Divergences are typical in many calculations using
quantum field theory, and an array of ingenious tools is used by physicists to extract finite and meaningful results.
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