Paik-1Lecture 8Tests of the 1/r2Law at Sub-millimeter DistancesHo Jung PaikUniversity of MarylandFebruary 20, 2007 Physics 798G Spring 2007Paik-2Extra dimensions• Kaluza and Klein (1920’s) attempted to unify gravity and electromagnetism in 5-D spacetime.⇒ If the extra dimension is curled up, precisely 4-D Lorentzsymmetry of general relativity and the gauge symmetry of Maxwell’s theory were recovered. ⇒ Theory failed because of the extreme mismatch of strengths between electromagnetism and gravity (by 1040) and infinities that plagued quantum gravity.• Superstring theories (1970’s and 80’s) attempt to unify gravity with the other three forces in 10-D spacetime.⇒ Successfully incorporates gravity in a quantum theory without the troubling infinities.⇒ Gravity-only large extra dimensions could explain why gravity is so weak (“hierarchy problem”).Paik-3Gravity-only extra dimensions?• Gravity may escape into n gravity-only extra dimensions (Arkani-Hamed, Dimopoulos and Dvali, 1998).•For n = 2, the law of gravity changes from 1/r2to 1/r4, as r is reduced to below R2, the “radius of compactification.”•For r > Ri, ⇒ If extra dimensions are compactifiedon an n-torus, α= 2n.⇒ For two large dimensions of similar size, α= 4, R1 ≈ R2≈ 1 mm (Arkani-Hamed et al., 1999).• The present experimental limit on the 1/r2law ⇒ R1≤ 50 µm.()iRrrGMr/e 1)(−+−=αφh1Paik-4Gauss’s Law• Gauss’s law:ρGmGdaS4ππ4total−=⋅∇⇒−=⋅≡Φ∫gngTotal flux of field lines ∝ Total mass enclosedxgˆm±∝rgˆrGm−∝rgˆ2rGm−=rgˆ3rGm−∝1-D2-D 3-D4-D?Paik-5Hierarchy problem in cosmology• “Empty” space is not empty.Galactic rotation curve ⇒ Dark matterAccelerating expansion ⇒ Dark energy• The observed accelerating expansion of the universe is consistent with a non-vanishing cosmological constant Λ, which corresponds to a vacuum-energy density of ρv≈ 4 keV/cm3. ⇒ Length scale of 100 µm.• Cosmological constant problem: Such a small energy density is extremely puzzling because the quantum corrections to ρvimply Λ120 orders of magnitude larger!• Possible solution: Gravity may be cut off at R ≤ 100 µm. ⇒ “Fat gravitons” (Sundrum, 2004)Paik-6Strong CP puzzle• Strong CP puzzle in Standard Model: CP symmetry is not violated in strong interaction as it should. • Possible solution: There may exist a pseudoscalar particle, “axion”(Weinberg, 1978; Wilczek, 1978).• Axions are expected to mediate short-range spin-spin, spin-mass, and mass-mass interactions.⇒ Apparent violation of the 1/r2law:with 200 µm ≤ R ≤ 20 mm.• Axion is a strong candidate for cold dark matter.• Short-range 1/r2tests complement the ongoing cavity search for the dark matter axion.()RrrGMr/e 1)(−+−=αφPaik-7Sub-millimeter tests 1• Long et al. (2003): λ≈ 300 µmSource mass: vibrating plane at ~ 1 kHzDetector: resonant torsionaloscillator• Chiaverini et al. (2003):λ≈ 100 µmSource mass: linearly driven meanderDetector: micro-machined resonant cantileverPaik-8Sub-millimeter tests 2•Hoyle et al. (2004): λ≈ 1 mmSource mass: Cu plate w/ 10 holesDetector: Al disk w/ 10 holes on torsion balance • Kapner et al. (2007): λ≈ 100 µmSource mass: Mo disk w/ 42 holes atop Ta disk w/ 21 holesDetector: Mo ring w/ 42 holes ona torsion balancePaik-9UM translating-source experiment•Principle: ∇φNis constant on either side of an infinite plane slab, independent of position.• Source: Ta (ρ= 16.6 g cm−3) disk of large diameter (null source)• Detector: 1-axis SGG formed by two thin Ta disks, located at 150 µm from the source • Frequency discrimination:As the source is driven at f, the differential signal appears at 2f. ⇒ This greatly reduces mechanical and magnetic cross talk.Paik-10Exploded view of the experimentSource MassTemperature SensingCoilCover PlateTest MassSource Driving CoilShieldTensioningScrewAlignment CoilS/C ShieldSensingCoilPaik-11Experimental hardware (1)HousingInterior w/ Nb shieldInteriorExteriorSource massTest massPaik-12Experimental hardware (2)LASERTURNTABLEPhotodiodeLiquidHeliumVoice CoilActuatorMumetal(2-Wall)Rubber TubeMicrometerInstrumentMirrorApparatus integrated with the cryostatPaik-13Superconducting circuits(b) Temperature sensing circuit(a) DM sensing circuit(c) Source driving circuit11223DM112iScosωt211122T2Paik-14Expected signal• The violation signal appears at almost purely 2f.-80 -40 0 40 80Source Mass Position (µm)012345678Acceleration ( × 10-14 m s-2)Yukawa(α = 10-3)Newtonianx 10Paik-15Error budget• Metrology errors• Total error budgetError SourceError × 10–15m s–2Metrology 0.5Random (τ= 106s)intrinsic 4.2temperature 0.9seismic 0.5Source dynamic 0.2Gravity noise < 0.1Magnetic coupling < 0.1Electrostatic forces < 0.1Total 4.4SourceAllowedError× 10–16m s–2Baseline25 µm0.02Source masssuspension spring 0.06absolute thickness10 µm0.016density fluctuations 10–40.01thickness variation1 µm1.3radial taper10 µm0.41bowing (static)10 µm0.004bowing (dynamic)0.06 µm4.6Test massessuspension spring 0.80radial misalignment50 µm< 0.01Total error 4.8Paik-16Potential resolution• The ground experiment could improve the resolution by 4 orders of magnitude over the existing limit (2004) at 100 µm.• The experiment could probe extra dimensions down to R2≈ 10 µm.Paik-17UM rotating-source experiment• Source: Two thin layers of materials mounted on a rotating circular disk (null source)• Detector: A differential angularaccelerometer formed by two thin test masses• Advantage of the rotating experiment: A levitated, rotating source does not exert a time-varying force on the housing and does not itself get distorted. ⇒ Could allow a smaller spacing to be maintained to the shield, and thus a higher sensitivity at short distancesSource centering coilSensing coilSource levitation coilTest mass levitation coilCapacitor platesTaAlSource leveling coilSource massTest massesSupercon-ducting shieldPaik-18Expected resolutions of the UM