the equivalence principle test by using a torsion balance

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!


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


Historical Overview ()

4

Eöt-Wash

Galileo < 10-1

Type of experiments

Drop

Pendula

Torsion balance

Modulated torsion balance


• 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


6


thin torsion fiber

attractor mass

Torsion Pendulum

mirror

• For uniform gravitational field: Sensitive to the difference of forces perpendicular to the torsion fiber.


7


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


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


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


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


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


Raw Data

13

Signal + free Oscillation

ωSIG = 2/3 ωPEND = 2π/(1200 s)


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)


Data Reduction

15

Nor

th

Wes

t


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


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


Eötvös parameter ()

Eöt-Wash

18 The 7th Korea-Japan Workshop on KAGRA

Thanks for your attention


the equivalence principle test by using a torsion balance

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