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

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

Origin Interaction of a pair of neutral, parallel conducting planes due to the disturbance of the vacuum of the EM-field 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:

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

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

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

Overview measurements

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

Plate-sphere Plate-sphere Use the PFA to calculate the Casimir force Use the PFA to calculate the Casimir force

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

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

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

Constraints: mathematics

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

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

Improvements Comparison between theory and experiment gives constraints Comparison between theory and experiment gives constraints Increase accuracy of theory: take into account surface roughness, finite conductivity and 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 Increase accuracy of measurement: Smoother coatings and wider range of distances

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, (2003) The Casimir effect: a force from nothing, A. Lambrecht,