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Sub-Millimeter Tests of the Gravitational Inverse-Square Law

Sub-Millimeter Tests of the Gravitational Inverse-Square Law. C.D. Hoyle University of Washington In collaboration with: E.G. Adelberger J.H. Gundlach B.R. Heckel D.J. Kapner U. Schmidt H.E. Swanson. Outline. Motivation Experimental techniques Published results Limitations

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Sub-Millimeter Tests of the Gravitational Inverse-Square Law

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  1. Sub-Millimeter Tests of the Gravitational Inverse-Square Law C.D. Hoyle University of Washington In collaboration with: E.G. Adelberger J.H. Gundlach B.R. Heckel D.J. Kapner U. Schmidt H.E. Swanson

  2. Outline • Motivation • Experimental techniques • Published results • Limitations • Present work • Conclusions

  3. Motivation • Theoretical Predictions* • Extra dimensions • Modify 1/r2 at short distances • Massive partners of the graviton • May cause additional interactions • In general, these modify the gravitational potential to V = VN (1+ e-r/) • Experimental • Gravity not even shown to exist at length scales below  1 mm *N. Arkani-Hamed, et al., Phys. Lett. B 429, 263 (1998) S. Dimopoulos and G. Guidice, Phys. Lett. B 379, 105 (1996) E.G. Floratos and G.K. Leontaris , Phys. Lett. B 465, 95 (1999) A. Kehagias and K. Sfetsos, Phys. Lett. B 472, 39 (2000) R. Sundrum, J. High Energy Phys. 9907, 001 (1999) D.B. Kaplan and M.B. Wise, ibid. 0008, 037 (2000), Etc.

  4. Apparatus Pendulum • Attractor rotates at frequency  • Holes produce a torque on the pendulum which varies at 10, 20, 30, etc. • Lower disk has “out of phase” holes • Measure torque as a function of vertical and horizontal separation • Compare to calculated Newtonian values • Stationary electrostatic screen between pendulum and attractor 2 disks 1.85 mm 7.83 mm Attractor

  5. 10 • Attractor rotates once every 2 hours • 17 free torsion oscillations per revolution • (Free oscillations have been filtered out above)

  6. Tilt Adjustment • Use leveling legs to make adjustments • Find minimum capacitance:

  7. Calibration 14.1 cm • Spheres are simple. • Large sphere separation eliminates effects from short-range interactions • 2 torque = 4.007±0.001 10-7 dyne-cm

  8. Measured Torques =3, =250m

  9. Results V = VN (1+ e-r/) 95% C.L. Phys. Rev. Lett. 86, 1418 (2001) • We found no deviations from Newtonian physics •  < 190 m for  = 3 • Corresponding unification scale > 3.5 TeV

  10. Limitations • To probe gravitational strength interaction of range , need known pendulum/attractor separation   • Want separations  100 m • Limiting factors of previous data (minimum separation was 218 m) • Membrane (20 m) • Alignment (5 m) • Flatness of disks (5 m) • Seismic excitations (50-100 m) • Dirt (?) • Residual coupling • Electrostatic • Magnetic • Gravitational • Characterization of holes • Torque noise

  11. For plane geometry, N holes on a radius R=N d/, << plate thickness, separation s, • And ratio to Newtonian torque: • Want • thin plates • many small holes • high density

  12. Seismic Damping Magnetic Damper B Copper Bellows Torsion Fiber Bounce Swing

  13. Recent Experiment • Sensitivity optimized for smaller  • Newtonian torques minimized 26-fold symmetry

  14. Separation = 97 m 26

  15. Future Improvements • Active damping of bounce and swing modes • Higher precision (non-magnetic) machining techniques • High  conducting membrane? • Cleaner and more seismically quiet apparatus enclosure • Optimization of pendulum/attractor geometry • Etc.

  16. Summary • There is a need to test gravity below the millimeter scale • We were able to measure gravity for the first time in this region • Our experiment saw no deviation from Newtonian physics down to separations of  200 m • Primary limitations are • Minimum separation • Magnetic coupling • Characterization of mass distribution • Torque noise • We are currently addressing these issues

  17. Goals for next experiment • Separation below 100 m • Already achieved • Non magnetic pendulum/attractor • Optimized geometry • Sensitivity of =1 for  100 m

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