the equivalence principle test by using a torsion balance
TRANSCRIPT
The Equivalence Principle Testby Using a Torsion Balance
Ki-Young ChoiSeoul National University
(Eotwash gravity group at the University of Washington)
The 7th Korea-Japan Workshop on KAGRA
The Equivalence Principle
2
• 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!
The 7th Korea-Japan Workshop on KAGRA
3
Tests of the Equivalence Principle
• Classical view: establish bounds on the Eötvös parameter
• Test of the universality of free fall
• Requirements for a good Equivalence Principle test– uniform gravitational field
– test bodies that differ in important ways
– very sensitive differential accelerometer
1 2
1 2
( ) / 2a aa a
The 7th Korea-Japan Workshop on KAGRA
Historical Overview ()
4
Eöt-Wash
Galileo < 10-1
Type of experiments
Drop
Pendula
Torsion balance
Modulated torsion balance
The 7th Korea-Japan Workshop on KAGRA
• Torsion Pendulum is still the most sensitive instrument for measuring the gravitational signal:
• Vary separation, r, between masses M1 and M2
• Force on M1 causes the pendulum to twist• Measure twist angle
5
thin torsion fiber
Torsion Pendulum
mirror M2M1
r
readout oftwist angle
The 7th Korea-Japan Workshop on KAGRA
6
readout oftwist angle
thin torsion fiber
attractor mass
Torsion Pendulum
mirror
• For uniform gravitational field: Sensitive to the difference of forces perpendicular to the torsion fiber.
The 7th Korea-Japan Workshop on KAGRA
7
readout oftwist angle
thin torsion fiber
attractor mass
Torsion Pendulum
mirror
appliedN : gravitational force
restoreN W : linear response
4
2
fNm2.4
sW
s
W
M rL
MrL
μrad
: shear modulus
: fiber radius: fiber length
The 7th Korea-Japan Workshop on KAGRA
Principle of Experiment
Source Mass
EP-violating signal
composition dipole pendulum(Be-Ti)
source mass (m) modulated period
local masses 1 - 104 20 min.
entire earth 106 - 107 20 min.
Sun 1011 - ∞ 20 min. & solar day
Milky Way (incl. DM) 1020 - ∞ 20 min. & sidereal day
aBe
aTi
rotation1 rev./ 20 min.
autocollimator(optical readout)
13.3min
8 The 7th Korea-Japan Workshop on KAGRA
The Apparatus of the Equivalence Principle Test
9
magneticdamper
The 7th Korea-Japan Workshop on KAGRA
Equivalence Principle Torsion Pendulum
10
resonant frequency: 1.261 mHzquality factor: ~ 4000decay time: ~ 12 daysmachining tolerance: 5 mtotal mass : ~ 70 g
20 m diameter, 108 cm long tungsten fiber
tuning screws for nullingmass moments to minimizeeffects of gravity gradients
4 Be & 4 Ti test masses (each 4.84 g)
5 cm
4 mirrors for monitoringpendulum twist
The 7th Korea-Japan Workshop on KAGRA
Gradiometer Pendulum
q21 = 35.5 gcm2 q31 = 105.0 gcm3
With Φ 7mm 16 Ti balls (mave = 0.795 g)total mass 69 g
q31 configurationq21 configuration
3 10-3 gcm2 0.2 gcm3EP pendulum values
The 7th Korea-Japan Workshop on KAGRA
Gravity Gradient Compensators
Pb
Pb
Q31 compensatorstotal mass: 5.5 kgQ31 = 1.0610-3 g/cm4
Al
attractor masses(hillside & local masses)
360° rotatableQ21 compensatorstotal mass: 880 kgQ21 = 1.78 g/cm3
The 7th Korea-Japan Workshop on KAGRA
Raw Data
13
Signal + free Oscillation
ωSIG = 2/3 ωPEND = 2π/(1200 s)
The 7th Korea-Japan Workshop on KAGRA
Filtered Data:
14
These data were taken before the pendulum was trimmed. The signal is a result of the gravitational coupling.
θF(t) = θ(t -T/4) + θ(t +T/4)
The 7th Korea-Japan Workshop on KAGRA
Data in the Frequency Space
16
Noise level at the signal-frequency:
≈ 1000 nrad/√Hz ≈ 3 nrad √day
Free oscillation
Signal
Filtered data
Raw data
Thermal noise
The 7th Korea-Japan Workshop on KAGRA
Results
17
PRL 100, 041101 (2008)
Signal aNorth,Be-Ti(10-15 m/s2)
aWest,Be-Ti(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
13 (0.3 1.8) 10 Be Ti
The 7th Korea-Japan Workshop on KAGRA