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The Casimir Effect

The Casimir Effect. Kevin Bell. 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. History. Published an additional paper in the same year with his findings:.

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The Casimir Effect

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  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. Casimir’s Calculation • Wave solutions to Maxwell’s equations are normal modes defined by • With wave numbers • Just like a rectangular waveguide

  6. Casimir’s Calculation • Classically, energy in the fields is • Equivalent to classical Hamiltonian • Plug in EM normal modes and integrate • Result has the form

  7. Casimir’s 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. Casimir’s 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! That’s infinite!

  9. Casimir’s 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 Casimir’s 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 d~1µm • 1998--Mohideen et al • AFM, Plane and sphere geometry • <2% agreement at d~50nm • 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?

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