1. Testing general relativity experimentally: Equivalence Principle Tests
International Conference on General Relativity:
Centennial Overviews and Future Perspectives
Dec ~ Dec , Ewha Womans University
Testing general relativity experimentally: Equivalence Principle Tests
Ki-Young Choi
Seoul National University
(Eotwash gravity group at the University of Washington)

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4. Outline Newton & Einstein’s Gravity Equivalence Principle
Eötvös Parameter
A Brief History of Equivalence Principle Tests
The Equivalence Principle Test by Using a Torsion Balance
Lunar Laser Ranging 4

5. Newton’s Gravity
Gravity is one of the 4 known fundamental interactions
Others: Electromagnetism, Strong and Weak Nuclear Forces
Gravity holds us to the earth (and makes things fall!)
It also holds things like the moon and satellites in orbits
Newton expressed this “unification” mathematically in the 1660’s:
Newton + 
r is distance between two bodies of mass M1 and M2 5

6. Einstein’s Gravity
Newton’s “Inverse-Square Law” worked well for about 250 years, but troubled Einstein
“Action at a distance” not consistent with Special Relativity
Einstein incorporated gravity and relativity with another great unification in 1915:
General Relativity
Gravitational attraction is just a consequence of curved spacetime
All objects follow this curvature (fall) in the same way, independent of composition: The Equivalence Principle
1/r2 form of Newton’s Law has a deeper significance: it reflects Gauss’ Law in 3-dimensional space
Very successful so far:
Planetary precession
Deflection of light around massive objects …. 6

7. The Equivalence Principle
General Relativity
Gravitational attraction is just a consequence of curved spacetime.
All objects follow this curvature (fall) in the same way, independent of composition: The Equivalence Principle
Equivalence Principle
General Relativity
Gravity
Most of quantum gravity theories predicted the violation of the EP! 7

8. Tests of the Equivalence Principle
classical view: establish bounds on the Eötvös parameter
modern view: establish bounds on ,  for any plausible “charges” q, where
Requirements for a good Equivalence Principle test
uniform gravitational field
test bodies that differ in important ways
very sensitive differential accelerometer 8

9. A Brief History of Equivalence Principle Tests
Galileo test h
Are fall times equal? 9

10. A Brief History of Equivalence Principle Tests
Newton-Bessel test l
Are periods equal? 10

11. A Brief History of Equivalence Principle Tests
Eötvös test ω θ R ε
Are angles equal? 11

12. A Brief History of Equivalence Principle Tests
Dicke’s idea : Using the Sun as a Source mass 12

13. Eötvös Parameter ()
Eöt-Wash 13

14. Equivalence Principle Torsion Pendulum
20 m diameter,
108 cm long tungsten fiber
4 Be & 4 Ti test masses
(each 4.84 g)
4 mirrors for monitoring pendulum twist
tuning screws for nulling
mass moments to minimize
effects of gravity gradients
resonant frequency: mHz
quality factor: ~ 4000
decay time: ~ 12 days
machining tolerance: 5 m
total mass : ~ 70 g
5 cm 14

15. Principle of Experiment
Composition dipole pendulum
(Be-Ti)
Source Mass
Rotation
1 rev./ 20min
13.3min
aBe
aTi
EP-violating signal
Autocollimator
(optical readout)
source mass
(m)
local masses (hill)
entire earth
Sun ∞
Milky Way (incl. DM) ∞ 15

16. The Apparatus of the Equivalence Principle Test
magnetic
damper 16

17. Results Signal aNorth,Be-Ti aWest,Be-Ti as measured 2.0 ± 2.3 -1.2
PRL 100, (2008)
Signal
aNorth,Be-Ti
(10-15 m/s2)
aWest,Be-Ti
as measured
2.0
2.3
-1.2
Due to gravity gradients
1.6
0.2
0.3
1.7
Tilt induced
1.2
0.6
-0.2
0.7
Temperature gradients
Magnetic coupling
Corrected
-0.8
3.0
-1.3
3.4 17

18. Eötvös parameter ()
Eöt-Wash 18

19. Apache Point Observatory Lunar Laser Ranging Operation (APOLLO)
uses a 3.5-meter telescope and 532 nm Nd:YAG laser (100 ps pulse duration, 115 mJ/pulse, 20 Hz) 19

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21. Lunar Retroreflector Arrays
Corner cubes
Apollo 11 retroreflector array
Apollo 14 retroreflector array
Apollo 15 retroreflector array 21

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23. Historical LLR Accuracy
1-mm precision with a 7-picosecond round-trip travel-time error 23

24. Eötvös parameter ()
Eöt-Wash
LLR 24

25. Acknowledgement Eric Adelberger Jens Gundlach Todd Wagner
Stephan Schlamminger 25

26. Einstein Rules!
despite amazing improvements in experimental sensitivity, no confirmed result disagrees with General Relativity
yet many of us expect that some deviations must show up
GR is not consistent with quantum mechanics
unifying gravity with the rest of physics is the greatest challenge of fundamental physics!

27. Thanks for your attention

28. Gradiometer Pendulum
q41 configuration
q21 configuration installed 28