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The Casimir force

The Casimir force. Is there a fifth force in nature?. Marian Otter, 15 June 2006. History. Discovered by Casimir in 1948 Quantum mechanical origin, macroscopic effect Caused by vacuum fluctuations. Origin.

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The Casimir force

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  1. The Casimir force Is there a fifth force in nature? Marian Otter, 15 June 2006

  2. History • Discovered by Casimir in 1948 • Quantum mechanical origin, macroscopic effect • Caused by vacuum fluctuations

  3. Origin • Interaction of a pair of neutral, parallel conducting planes due to the disturbance of the vacuum of the EM-field Casimir derived force for parallel plates:

  4. Beyond the standard model • Standard model has 4 forces: • Gravitational force • Electromagnetic force • Strong interaction • Weak interaction • Extensions of the standard model predict more forces

  5. Fundamental force theories • Space-time has 4 + n dimensions • n dimensions are compactified • Yukawa potential corrections to Newton’s law • Casimir force measurements used to test Newtonian gravity

  6. Some numbers • Early believe: R ≈ 10^-33 cm • Energy ≈ 10^19 GeV, to high to measure • For n = 1, R ≈ 10^15 cm, excluded • For n = 2, R ≈ 1 mm • For n = 3, R ≈ 5 nm

  7. Overview measurements

  8. Measurements • Decca et al., 2003 • Static and dynamic • Range 0.2-1.2 μm • Torque τ = bF(z) = κθ • θ~ ΔC

  9. Plate-sphere • Use the PFA to calculate the Casimir force

  10. Corrections • Three corrections should be taken into account: • Surface roughness • Finite conductivity • Non-zero temperature Accuracy ≈ 1%

  11. Static measurement • Error = 3 pN • confidence level 95% • 19 runs • 300 point/run

  12. Dynamic measurements • Error = 0.54 – 0.62 mPa • Confidence level 95% • 5 runs • 300 points/run

  13. Constraints: mathematics

  14. Constraints: result • Curve 1 from Decca • Other curves from older measurments • Region above the curve excluded

  15. Constraints: result • Strongest constraints for 56 nm ≤ λ ≤ 330 nm • Largest improvement, factor 11 at λ = 150 nm • Gap between AFM measurements (4) and torsion pendulum (3) almost completely filled • Earlier the constraints in this gap were based on less reliable measurements between dielectrics (2)

  16. Improvements • Comparison between theory and experiment gives constraints • Increase accuracy of theory: take into account surface roughness, finite conductivity and non-zero temperature to higher precision • Increase accuracy of measurement: Smoother coatings and wider range of distances

  17. Questions? References: Improved tests of extra-dimensional physics and thermal quantum field theory from new Casimir force measurments, Decca et al., Physical Review D 68, 116003 (2003) The Casimir effect: a force from nothing, A. Lambrecht, http://physicsweb.org/articles

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