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International Conference on General Relativity:
Centennial Overviews and Future Perspectives
Dec. 21 2015 ~ Dec. 23 2015, 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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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
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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:
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Newton
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M 1M 2
 F G
2
r
r is distance between two
bodies of mass M1 and M2
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
• ….
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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
Gravity
General
Relativity
Equivalence
Principle
Most of quantum gravity theories predicted the violation of the EP!
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Tests of the Equivalence Principle
• classical view: establish bounds on the Eötvös parameter
a1  a2

(a1  a2 ) / 2
• modern view: establish bounds on ,  for any plausible
“charges” q, where
m1m2
V (r )  G
r

 q   q  (r / ) 
1       e

  1    2


• Requirements for a good Equivalence Principle test
– uniform gravitational field
– test bodies that differ in important ways
– very sensitive differential accelerometer
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A Brief History of Equivalence Principle Tests
Galileo test
h
Are fall times equal?
T
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2h mi
g mg
A Brief History of Equivalence Principle Tests
Newton-Bessel test
l
Are periods equal?
T  2
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l mi
g mg
A Brief History of Equivalence Principle Tests
Eötvös test
ω
ε
Fi  mi 2 r cos 
θ
Fg  mg g
R
Are angles equal?

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 2 R Sin 2 mi
2g
mg
A Brief History of Equivalence Principle Tests
Dicke’s idea : Using the Sun as a Source mass
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Eötvös Parameter ()
Eöt-Wash
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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
5 cm
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resonant frequency:
quality factor:
decay time:
machining tolerance:
total mass :
1.261 mHz
~ 4000
~ 12 days
5 m
~ 70 g
Principle of Experiment
Composition dipole pendulum
(Be-Ti)
aBe
Source Mass
Rotation
13.3min
1 rev./ 20min
aTi
EP-violating signal
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source mass
(m)
local masses (hill)
1 - 104
entire earth
106 - 107
Sun
1011 - ∞
Milky Way (incl. DM)
1020 - ∞
Autocollimator
(optical readout)
The Apparatus of the Equivalence Principle Test
magnetic
damper
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Results
PRL 100, 041101 (2008)
Signal
aNorth,Be-Ti
(10-15 m/s2)
(10-15 m/s2)
as measured
2.0 ± 2.3
-1.2 ± 2.3
Due to gravity gradients
1.6 ± 0.2
0.3 ± 1.7
Tilt induced
1.2 ± 0.6
-0.2 ± 0.7
Temperature gradients
0 ± 1.7
0 ± 1.7
Magnetic coupling
0 ± 0.3
0 ± 0.3
Corrected
-0.8 ± 3.0 -1.3 ± 3.4
 Be Ti  (0.3  1.8) 10
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aWest,Be-Ti
13
Eötvös parameter ()
Eöt-Wash
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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)
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Lunar Retroreflector Arrays
Corner cubes
Apollo 14 retroreflector array
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Apollo 11 retroreflector array
Apollo 15 retroreflector array
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Historical LLR Accuracy
1-mm precision with a 7-picosecond
round-trip travel-time error
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  ~ 1014
Eötvös parameter ()
Eöt-Wash
LLR
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Acknowledgement
Eric Adelberger
Jens Gundlach
Stephan Schlamminger
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Todd Wagner
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!
Thanks for your attention
Gradiometer Pendulum
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q41 configuration
q21 configuration installed