sub-millimeter tests of the gravitational inverse-square law c.d. hoyle university of washington in...
TRANSCRIPT
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