The Casimir Effect

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The Casimir Effect

• Consequences of a Zero Point Energy in Higher
  Dimensions
• Eric Clinton
• UMass/Jlab
• WM PHYS 690-02
• April 25,2005

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What is the Casimir Effect?

• A purely geometric consequence of zero point
  energy in the quantum EM spectrum.
• Best described as the collection of Harmonic
  Oscillator Ground States in the infinite space.
• Casimir was the first to realize the energy in
  the EM vacuum, and regularize the divergent
  integral
• Image from hep-ph/9912276

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How to calculate the Casimir Force

• Imagine the EM field as an infinite set of
  Harmonic oscillators.
• wjwk-,n c(k12 k22 (pn/a)2)½
• The EM ZPE due to the BC and topology is --
• Renormalizing the difference (topology- BC)
  between these two terms via an Abel-Plana contour
  integral gives us

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How is the Casimir Force a probe of higher
dimensions?

• Two ways
• You can look at it from the perspective of a
  Yukawa type force that only contributes at short
  distances, or
• A whole new ball-game, using Randall-Sundrum
  topology.
• Each provides unique interpretations of
  experimental results.

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Yukawa Interaction

• Mpl is order 1015 TeV in SUSY
• If large dimensions exist, Mpl 4n 1Tev
• This puts Mpl Mew.
• So, V(rgtgtR) r -1.
• But, if V(rltR) r (n1).
• Thus Mpl Mpl 4n R n/2 and
• R 1030/n-17.
• n 1, R 1013 m
• n 2, R 1 mm
• n 3, R 1 nm

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More Yukawa

• So, lets model this close range behaviour.
• V(r)
• Image from hep-ph/9912276

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Randall Sundrum Space Nuances

• There are two concepts to acknowledge when using
  RS topology.
• We are no longer talking about LXDs, where only
  the graviton may go.
• Universal Extra Dimensions (UXD) allow the
  propagation of all species of particles.
• This is now the dimension we are trying to
  constrain with experiment
• Tevatron constrains RUXD (300GeV-1) 10-9nm
• Do theory and Casimir experiments agree with
  Tevatron?

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Randall-Sundrum

• Lets take RS with a S1/Z2 orbifold.
• The frequency spectrum is modified.
• wjwk-,n c(k12 k22 (pn/a)2 (N/R)2 )½
• Note the extra term (N/R)2
• Following the previous renormalization scheme, we
  get
• Compare with

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RS comparison-theory vs. experimentImage from
hep-th/0309066
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AsideRadion stabilization in RS space

• All fields in the bulk contribute Casimir fields.
• For the radion
• l 1/Mpl(5)
• l (4p/3M3 l)½ is the radion
• A Veff(f) arises, and causes a re-normalization
  of the TeV brane tension.
• Veff(f) also has a minimum where the radion may
  live.

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Lamoreauxs Torsion Pendulum

• First modern Casimir experiment.
• Sub-millimeter test
• Timely, with respect to a burgeoning interest in
  the search for LXD
• Drove both theory and experimental advances.
• 0.6 mm lt d lt 0.16 mm. DF 5.
• Image from hep-ph/9912276
• Not quite Lamoreauxs pendulum-plate 2 was a
  feedback loop of capacitors.

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From hep-ph/9906062
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Atomic Force Microscopy Results

• Bordag, Geyer, Klimchitskaya, Mostepanenko.
  1999.
• 22 mm lt d lt 0.16 mm. DF 10-11 N.
• Bordag, Geyer, Klimchitskaya, Mostepanenko.
  2000.
• 5.9nm lt d lt 115 nm. DF 10-12 N.
• Mostepanenko Novello. 2001.
• 1.5nm lt d lt 11 nm. DF 10-9 N.
• Chen Mohideen. 2002.
• 80nm lt d lt 150 nm. DF 10-13 N.

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Latest Torsion Experiment

• Hoyle, Kapner, Heckel, Adelberger, Gundlach,
  Schmidt, Swanson. 2004.
• 80nm lt d lt 150 nm.
• DF 10-18.
• Image from hep-ph/9912276

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Some world data to date. From hep-ph/0405262
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References

• Bordag, Mohideen, Mostepanenko.
• quant-ph/0106045.
• Bordag, Geyer, Klimchitskaya, Mostepanenko.
• hep-ph/9804223.
• Chen Mohideen.
• quant-ph/0209167.
• Mostepanenko Novello.
• hep-ph/0101306.
• Bordag, Geyer, Klimchitskaya, Mostepanenko.
• hep-ph/0003011.
• Arkani-Hamed, Dimopoulos, Dvali.
• hep-ph/9803315.
• Roy, Lin, Mohideen.
• hep-ph/9906062
• Krause Fischbach.
• hep-ph/9912276.
• Appelquist, Cheng, Dobbresca.
• hep-ph/0012100.

• Hoyle, Kapner, Heckel, Adelberger, Gundlach,
  Schmidt, Swanson.
• hep-ph/0405262
• Bordag, Geyer, Klimchitskaya, Mostepanenko.
• hep-ph/9902456.
• Poppenhaeger, Hossenfelder, Hofmann, Bleicher.
• hep-th/0309066.
• Mostepanenko Novello.
• hep-ph/0008035.
• Arkani-Hamed, Dimopoulos, Dvali.
• hep-ph/9807344.
• Pujolàs.
• hep-th/0103193.
• Goldberger Rothstein.
• hep-th/0007065.
• Garriga Pomarol.
• hep-th/0212227.