The Casimir forceThe Casimir force

Is there a fifth force in nature?Is there a fifth force in nature?

Marian Otter, 15 June 2006

HistoryHistory

Discovered by Discovered by Casimir in 1948Casimir in 1948

Quantum mechanical Quantum mechanical origin, macroscopic origin, macroscopic effecteffect

Caused by vacuum Caused by vacuum fluctuationsfluctuations

OriginOrigin

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

Casimir derived force for parallel plates:

Beyond the standard modelBeyond the standard model

Standard model has 4 forces:Standard model has 4 forces:- Gravitational forceGravitational force- Electromagnetic forceElectromagnetic force- Strong interactionStrong interaction- Weak interactionWeak interaction Extensions of the standard Extensions of the standard

model predict more forcesmodel predict more forces

Fundamental force theoriesFundamental force theories

Space-time has 4 + n dimensionsSpace-time has 4 + n dimensions n dimensions are compactifiedn dimensions are compactified Yukawa potential corrections to Newton’s lawYukawa potential corrections to Newton’s law

Casimir force measurements used to test Casimir force measurements used to test

Newtonian gravityNewtonian gravity

Some numbersSome numbers

Early believe: R Early believe: R ≈ 10^-33 cm≈ 10^-33 cm Energy Energy ≈ 10^19 GeV, to high to ≈ 10^19 GeV, to high to

measuremeasure

For n = 1, R For n = 1, R ≈≈ 10^15 cm, excluded 10^15 cm, excluded For n = 2, R For n = 2, R ≈ 1 mm≈ 1 mm For n = 3, R ≈ 5 nmFor n = 3, R ≈ 5 nm

Overview measurementsOverview measurements

MeasurementsMeasurements

Decca Decca et al.et al., , 20032003

Static and Static and dynamicdynamic

Range 0.2-Range 0.2-1.2 1.2 μμmm

TorqueTorque

ττ = bF(z) = = bF(z) = κθκθ θθ ~ ~ ΔΔCC

Plate-spherePlate-sphere

Use the PFA to calculate the Casimir forceUse the PFA to calculate the Casimir force

CorrectionsCorrections

Three corrections should be taken into account:Three corrections should be taken into account: Surface roughnessSurface roughness Finite conductivityFinite conductivity Non-zero temperatureNon-zero temperature

Accuracy ≈ 1%

Static measurementStatic measurement

Error = 3 pNError = 3 pN confidence confidence

level 95%level 95% 19 runs19 runs 300 point/run300 point/run

Dynamic measurementsDynamic measurements

Error = Error = 0.54 – 0.62 mPa0.54 – 0.62 mPa Confidence level Confidence level

95%95% 5 runs5 runs 300 points/run300 points/run

Constraints: mathematicsConstraints: mathematics

Constraints: resultConstraints: result

Curve 1 from Curve 1 from DeccaDecca

Other curves Other curves from older from older measurmentsmeasurments

Region above Region above the curve the curve excludedexcluded

Constraints: resultConstraints: result

Strongest constraints for 56 nm Strongest constraints for 56 nm ≤ ≤ λ λ ≤ 330 nm≤ 330 nm Largest improvement, factor 11 at Largest improvement, factor 11 at λλ = 150 nm = 150 nm Gap between AFM measurements (4) and Gap between AFM measurements (4) and

torsion pendulum (3) almost completely filledtorsion pendulum (3) almost completely filled Earlier the constraints in Earlier the constraints in

this gap were based on this gap were based on less reliable measurements less reliable measurements between dielectrics (2)between dielectrics (2)

ImprovementsImprovements

Comparison between theory and experiment Comparison between theory and experiment gives constraintsgives constraints

Increase accuracy of theory: take into account Increase accuracy of theory: take into account surface roughness, finite conductivity and surface roughness, finite conductivity and

non-zero temperature to higher precisionnon-zero temperature to higher precision Increase accuracy of measurement: Smoother Increase accuracy of measurement: Smoother

coatings and wider range of distancescoatings and wider range of distances

Questions?Questions?

References:References:Improved tests of extra-dimensional physics and Improved tests of extra-dimensional physics and thermal quantum field theory from new Casimir thermal quantum field theory from new Casimir force measurments, force measurments, Decca et al., Physical Review Decca et al., Physical Review D 68, 116003 (2003)D 68, 116003 (2003)

The Casimir effect: a force from nothing, The Casimir effect: a force from nothing, A. Lambrecht, http://physicsweb.org/articlesA. Lambrecht, http://physicsweb.org/articles