Sub-Millimeter Tests of the Gravitational

Inverse-Square LawC.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/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.

Apparatus

1.85 mm7.83 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:

- 2 - 1 0 1 2Tilt@mradD

136

138

140

142

144

146

148

150

ecnaticapaC@FpD

Calibration

•Spheres are simple.

•Large sphere separation eliminates effects from short-range interactions

•2 torque = 4.007±0.001 10-7 dyne-cm

14.1 cm

Measured Torques

=3, =250m

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 = VN (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 (50-100 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

s

RG s

Y

)/-(2421 e

Att

s

N

Y

21

)/(4e

Seismic Damping

Bounce

Swing

Copper Bellows

B

Magnetic Damper

Torsion Fiber

• Sensitivity optimized for smaller • Newtonian torques minimized

Recent Experiment

26-fold symmetry

Sep

arat

ion

= 9

7 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