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 Present work Conclusions

Motivation Theoretical Predictions * –Extra dimensions Modify 1/r 2 at short distances –Massive partners of the graviton May cause additional interactions –In general, these modify the gravitational potential to V = V N (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.

Apparatus 1.85 mm 7.83 mm 2 disks Pendulum Attractor 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

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

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

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

Measured Torques  =3, =250  m

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

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 (   m) Dirt (?) Residual coupling –Electrostatic –Magnetic –Gravitational Characterization of holes Torque noise Limitations

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

Seismic Damping Bounce Swing Copper Bellows B Magnetic Damper Torsion Fiber

Sensitivity optimized for smaller Newtonian torques minimized Recent Experiment 26-fold symmetry

Separation = 97  m 26 

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. Future Improvements

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 Summary

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