The Casimir Effect

1
The Casimir Effect

• Kevin Bell

2
History

• Investigated Van der Waals force in colloids in
  1948
• Considered the force between a grounded plate and
  a neutral atom
• Moved on to the case of two neutral conducting
  plates

3
History

• Published an additional paper in the same year
  with his findings

4
A Force From Nothing

• Consider a cube enclosed by neutral, conducting
  walls
• Additional wall distance a away from the wall in
  the xy plane

5
Casimirs Calculation

• Wave solutions to Maxwells equations are normal
  modes defined by
• With wave numbers
• Just like a rectangular waveguide

6
Casimirs Calculation

• Classically, energy in the fields is
• Equivalent to classical Hamiltonian
• Plug in EM normal modes and integrate
• Result has the form

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Casimirs Calculation

• Terms analogous to momentum, position
• Looks like quantum harmonic oscillator
• Quantum field theory treats each resonant mode
  like a harmonic oscillator
• For each mode,

8
Casimirs Calculation

• n is number of EM wave quanta (photons) occupying
  each mode
• Even without any (real) photons, ground state
  energy remains
• Energy in vacuum is the sum of GS energy over all
  resonant modes
• WAIT! Thats infinite!

9
Casimirs Calculation

• Casimir found the (finite) difference in vacuum
  energy with plate in two positions
• Interpreted this to be a real force
• Force from nothing! Fundamental constants!

10
Confirmation

• 1958--Sparnay et al
• Measured the force between conducting plates
• Results did not contradict Casimirs theoretical
  predictions
• 1961--Lifshitz et al
• General Theory of Van der Waals Forces
• Considered temperature, conductivity, etc.

11
Confirmation

• 1997--Lamoreaux (at UW!)
• Torsion balance, plane and sphere geometry
• 5 Agreement with theory at d1µm
• 1998--Mohideen et al
• AFM, Plane and sphere geometry
• lt2 agreement at d50nm
• And more

12
MEMS Significance

• Thin, flexible strips are very useful
• Casimir force dominates
• Stiction

13
MEMS Applications

• Oscillators and other components
• Optimization by calculating Casimir force

14
Cosmological Implications

• Cosmological constant
• Thought to be zero
• Accelerating expansion measured
• Dark Energy?

15
Cosmological Implications

• Is vacuum energy this dark energy?
• Constant measured to be very small
• Vacuum energy is infinite
• But the Casimir effect demonstrates that the
  energy is real (?)

16
Debate Over Realness

• 2005--MIT physicist Brian Jaffe publishes a paper
  attacking the reality of the force
• Points to alternative derivation of the force
• Claims it is no different from the
  perturbations/fluctuations of the Van der Waals
  force in atoms

17
Debate Over Realness

• Force depends on more than fundamental constants
  when conductivity, temperature considered
• Assuming perfect conductor, perfectly smooth
  surface demonstrated a certain limit of the
  general case
• Back to square one with the cosmological constant?