a high precision test of the equivalence principle · a high precision test of the equivalence...

A High Precision Test of the Equivalence Principle

Stephan Schlamminger

Eotwash GroupCenter for Experimental Physics and Astrophysics (CENPA)

University of Washington

[email protected]

March 4th 2010 Physics 294

What and where is CENPA?

A close look at the N part of campus

Now: CENPA

Center for Experimental Nuclear Physics and Astrophysics

Machine shop

Gravity lab

Inside CENPA

Check it out: www.npl.washington.edu

http://www.npl.washington.edu/research.html

Eötwash groupEric Adelberger

Jens Gundlach

Blayne Heckel

Stephan Schlamminger

Erik Swanson

Frank Fleischer

Seth Hoedl

Ted Cook

Charles Hagedorn

William Terrano

Matt Turner

Todd Wagner

Graduate students

-Do all bodies drop with the same acceleration?

-Is there a preferred frame or direction in the universe?

-Is there a large (>µm) extra dimension? (02/18/10 Talk by Charles Hagedorn)

- Search for Axions.

- Crucial measurements for LISA (Laser Interferometer Space Antenna).

- Research for LIGO

Torsion balance

Mass does not add up

Proton Electron 1H


Proton Electron 1H

938 272 013 eV/c2 510 999 eV/c2 938 782 999 eV/c2


Proton Electron 1H

938 272 013 eV/c2 510 999 eV/c2 938 782 999 eV/c2

938 272 013 eV /c2 510 999 eV/c2 938 783 012 eV/c2

13.6 eV/c2Mass defect = binding Energy

Binding Energy = ΔEpot-ΔEkin

The non-linearity is rather small

Mass defect for 1 kg of

Earth: Δm=0.46 μg

Mass defect for 1 kg of

Moon: Δm=0.02 μg

but occurs also in gravitationally bound systems

The mass of an object

m = ∑ mc + ∑ Ekin/c2 - ∑ Epot/c2

Newton’s Principia (1689)

Newton’s 2nd Law

Fi = mi a

Gravitational Law

FG= G mg1 mg2 /r2


Newton’s 2nd Law

Fi = mi a

Gravitational Law

FG= G mg1 mg2 /r2

Equivalence Principle (EP): mi = mg


Newton’s 2nd Law

Fi = mi a

Gravitational Law

FG= G mg1 mg2 /r2

Equivalence Principle (EP): mi = mg

Weak Equivalence Principle: Gravitational binding energy is excluded.

Strong Equivalence Principle: Includes all 4 fundamental interactions.

The Equivalence Principle

Our Current theory of gravity, General Relativity,

is based on the Equivalence Principle:

All bodies fall in a gravitational field with the same acceleration regardless of their mass or internal structure.

Einstein realized, that:

It is impossible to distinguish between an uniform gravitational field and an acceleration.

-a

F=-ma

The Equivalence Principle

g

F=mg

Gravitational field g Acceleration a

Inertial mass = gravitational mass, mI=mG for all bodies

General Relativity and the EP

Three classical tests:

Perihelion shift of Mercury

Deflection of light by the Sun

Gravitational red shift of light

The last two can be explained and calculated with the EP alone!

The known unknowns

• GR is not a quantum theory.

• Cosmological constant problem.

• Dark matter.

EP-Testsprovide a big bang for the buck!

The unknown unknowns

• Is there another force (5th force)?

• …

Searching for New Interactions

Assumed charge

Beryllium

q/μ

Titanium q/μ

Difference

Baryon number B 0.99868 1.001077 -2.429x10-3

r / 21

2

2

1

1 e r

mm

qqG V(r)

r

1 mm (r)V 21grav G

Source Test mass

Strength relative to gravity

Interaction range

Good model for a new interaction:

r /

21 e r

1 QQ V(r) k

q/µ

Mass (u) q=B q/µ

11p 1.007 3 1 0.992 8

10n 1.008 7 1 0.991 4

94Be 9.101 2 9 0.998 7

4822Ti 47.947 9 48 1.001 1

B/μ varies, because

1st Tests of the Equivalence Principle

gmF G

gm

ma

I

G

gm

ma

I

G

a2a1

gm

m

ht

I

G

2

gm

ma

I

GamF I

h

Time t to fall from h:

1600 Galileo:

1.0)( 212

1

21

aa

aa

2nd Generation Tests

G

I

m

m

g

LT 2l

Measurement of the swing periods of pendula:

Newton (1686), Bessel (1830), Potter (1923)

5102 x

Eötvös Experiments

cos2rmF II

ω

θ

ε

r

)2sin(2

2

g

r

m

m

G

IgmF GG

The torsion balance

• A violation of the EP would yield to different plumb-line for different materials.

•A torsion balance can be used to measure the difference in plumb-lines:

Torsion fiber hangs like the average plumb line.

Difference in plumb lines produces a torque on the beam.

-> twist in the fiber

Eötvös (1922)

9105 x

Dicke’s idea

Sun

Using the Sun as a source

11101 x

Historical overview

Galileo

Newton

Bessel

Potter

EötvösDicke

Braginsky

UW

)( 2121

21

aa

aa

drop

pendula

Type of experiment

torsionbalance

modulatedtorsionbalance

Principle of our experiment

Source Mass

EP-Violating signal

Composition dipole pendulum

(Be-Ti)Rotation

1 rev./ 20min

Autocollimator (=optical readout)

source mass λ (m)

local masses (hill) 1 - 104

entire earth 106 - 107

Sun 1011 - ∞

Milky Way (incl. DM) 1020 - ∞

aBe

aTi

13.3min

modulated

20 m diameter tungsten fiber

(length: 108 cm)

Κ=2.36 nNm

tuning screws for adjusting

tiny asymmetries

8 test masses (4 Be & 4 Ti )

4.84 g each (within 0.1 mg)

(can be removed)

5 cm

4 mirrors

EP torsion pendulum

torsional frequency: 1.261 mHz

quality factor: 4000

decay time: 11d 6.5 hrs

machining tolerance: 5 m

total mass : 70 g

The upper part of the apparatus

thermal expansion feet

to level turntable

air bearing turntable

electronics of angle encoder

feedthrough for

electric signals

thermal insulation

The lower part of the apparatusvacuum chamber (10-5 Pa)

ion pump

autocollimator

support structure for

gravity gradient

compensators

gravity gradient

compensators

Raw-data

Signal + free Oscillation

ωSIG=2/3 ωPEND=2π/(1200 s)

Filter: F(t)=θ(t-T/4)+θ(t+T/4)

These data were taken

before the pendulum was

trimmed. The signal is a

result of the gravitational

coupling

Data reductionN

ort

hW

es

t

A complete day of data

σ≈ 3 nrad √day

Differential acceleration

dFdF 21

amdaamddmadma )( 2121

Deflection from equilibrium: φ

is caused by a torque:

mda

m

m

d

F1

F2

Some numbers

mda

4

κ 2.36 x 10-9 Nm

m 4.84 x 10-3 kg

d 1.9 x 10-2 m

6.41 x 10-15 m/s2 / nrad

Can be measured withAn uncertainty of3 nrad per day

Δa can be measured to20 fm/s2

A feel for numbers

φ=3 nrad

Seattle

San Francisco

Δa=20 fm/s2

g=9.81 m/s2 g=9.81 m/s2-Δa

Δh=?

Δx=?

A feel for numbers

φ=3 nrad

Seattle

San Francisco

Δa=20 fm/s2

g=9.81 m/s2 g=9.81 m/s2-Δa

Δh=7 nm

Δx=3 mm

Data taking sequence (1/3)We rotate the pendulum (and thus the dipole) in respect to the readout every day by 1800.

Data taking sequence (2/3)

50 days

The 12 days of data from the previous slide are condensed into a single point.

Dipole is orthogonal to readout.

Dipole is (anti-) parallel to readout.

Rotate every day

Rotate every day

Resolved signal in WE-direction!

Data taking sequence (3/3)After a 2 months of data taking and systematic checks we physically invert the dipole on the pendulum and put it back into the apparatus.

Ti-Be Be-Ti

Ti-Be differential acc.

These data points have been corrected for systematic effects.

Only statistical uncertainties shown.

Corrected result

ΔaN,Be-TI ΔaW,Be-TI

(10-15 m/s2) (10-15 m/s2)

as measured 3.3 ± 2.5 -2.4 ± 2.4

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 0.6 ± 3.1 -2.5 ± 3.5

l

lm

im

l

el

lmlm

0

qQ 12

1G π4 w

Gravitational potential energy between the pendulum and

the source masses is given by

11 q 12

1G 8 ll

lQ

Torque for 1 (m=1) signal:

gravity gradient field

)ˆ( )(ρ d q

)ˆ( )(ρdQ

*

pend

3

lm

)1(

source

3

lm

rYrrr

rYrrr

lm

l

lm

l

gravity multipole moment

.

q11

not possible for

a torsion pendulum

q21 q31

Gravity gradients (1/4)

Pb

Pb

Al

hillside &

local masses

360° rotatableQ21 compensators

Total mass: 880 kg

Q21= 1.8 g/cm3

Q31 compensators

Total mass: 2.4 kg

Q31 =6.710-4 g/cm4


q41 configuration q21 configuration installed



Without

compensation:

Q21=1.78 gcm-3

0.2 fm/s2 N

1.7 fm/s2 W

Uncertainty due

to fluctuating

fields:

Tilt coupling

Tilt coupling

Tilt of the suspension point+ anisotropies of the fiber

will rotate

rotation axis

Tilt coupling


will rotate

1. Thicker fiber atthe top providesmore torsionalstiffness

rotation axis

Tilt coupling


will rotate

1. Thicker fiber atthe top providesmore torsionalstiffness

2. Feedback minimizes tilt of TT

rotation axis

More tiltActive foot

zturntable

PID

14 nrad

60 nrad

No signal!

1.70m

0.23m 53 nrad Remaining tilt uncertainty:

0.6 fm/s2 N

0.7 fm/s2 W

Thermal

50 nrad Signal

ΔT =7K

During data taking

ΔT≈0.053 K

0.38 nrad

1.7 fm/s2 N

1.7 fm/s2 W

Effect on the applied gradient on the signal

(measurement was done on one mirror):

Effect of a 7 K

gradient on

two different

mirrors.

Recent improvementszturntable

Lamp on a ruler

used to find the

sensitive spot

Highest sensitivity to the lamp

Additional insulation (@ 41 in) reduced the temperature feedthrough.

Interpreting our result

North: aBe-aTi= (0.6 ± 3.1) x 10-15 m/s2

West: aBe-aTi= (-2.5 ± 3.5) x 10-15 m/s2


North: aBe-aTi= (0.6 ± 3.1) x 10-15 m/s2

West: aBe-aTi= (-2.5 ± 3.5) x 10-15 m/s2

cos2rmF II

ω

θ

ε

r

gmF GG ½|a1+a2|η=

|a1-a2|


North: aBe-aTi= (0.6 ± 3.1) x 10-15 m/s2

West: aBe-aTi= (-2.5 ± 3.5) x 10-15 m/s2

cos2rmF II

ω

θ

ε

r

gmF GG

η(Be-Ti)= (0.3 ±1.8) x 10-13

½|a1+a2|η=

|a1-a2|

Results

17 x

Str

ength

rela

tive t

o g

ravity

Charge: B

Range of a hypothetical “fifth” force (m)

Acceleration to the center of our galaxy

Hypothetical signal:

(7 times larger)

20 x 10-15 m/s2

Differential acceleration to the center of the galaxy:

(-2.1 ± 3.1) x 10-15 m/s2

In quadrature:

(2.7 ± 3.1) x 10-15 m/s2

1825 h of data taken over 220 days

Galactic dark matter

Milky Way

Earth


Halo of dark matter

Milky Way

Earth


Dark matter inside the Earth’s galactic orbit causes 25-30% of the total acceleration.

Halo of dark matter

Milky Way

Earth


Our acceleration towards the galactic center is:

agal= adark+ aordinary= 1.9 10-10 m/s2 => adark= 5 10-11 m/s2


Halo of dark matter

Milky Way

Earth





Halo of dark matter

Milky Way

Earth

Measured differential acceleration towards the galactic center is:

agal =(-2.1 ±3.1) 10-15 m/s2 => ηdark= |agal|/adark = (-4±7) 10-5





Halo of dark matter

Milky Way

Earth

Measured differential acceleration towards the galactic center is:

agal =(-2.1 ±3.1) 10-15 m/s2 => ηdark= |agal|/adark = (-4±7) 10-5

The acceleration of Be and Ti towards dark matter does not differ by more than 150 ppm (with 95 % confidence).

Summary

• Test of the equivalence principle with a rotating torsion balance.

• Principle of the measurement

• Main systematic effects

• Results

– Earth fixed (North): aBe-aTi=(0.6 ± 3.1) x 10-15 m/s2.

– η=(0.3 ± 1.8) x 10-13.

– Towards Galaxy: aBe-aTi=(-2.1 ± 3.1) x 10-15 m/s2.

– ηDM=(-4 ± 7) x 10-5.

– 10x improved limits on a long range interaction.

Outlook

• Ideas for improvement:

– Decouple damper systematic from pendulum.

– Integrated q21 measurement.

– Higher Q fiber to reduce thermal noise

• Earth-like and moon-like TB to keep pace with improvements in LLR.

Acknowledgement

Jens GundlachTodd Wagner

Ki-Young Choi

Eric Adelberger

END

This talk stops here.


x

x

xx q

u

mNq

xQ

/ r

12

21

2

2

1

1 12e r

mm

qqG V(r)

/ r

122

2

1

1

2

2

12e r

1

qq

4 V(r)

u

g

Yukawa potential

/ r

12

21

2

12e r

1 QQ

4 V(r)

g

G

1 u = 1.66 x 10-27 kg

/ r

12

21

2

2

1

1 12e r

mm

qqG V(r)

SourceTest mass

Strength relative to gravity

Interaction range

Assumed charge

Beryllium

q/μ

Titanium q/μ

Difference

Baryon number B 0.99868 1.001077 -2.429x10-3

Lepton number L 0.44385 0.459742 -1.565x10-2

Other possible charges: B-L, 3B+L, ..


Signal

Free oscillation

Filtered data

Thermal noise

In frequency space

Noise level at the signal-frequency:

≈1000 nrad/√Hz ≈ 3 nrad √day

Source integration

Local

topography

Preliminary

Earth

Reference

Model

Source integration

Local

topography

Preliminary

Earth

Reference

Model

Difficult a

nd t

edio

us

a high precision test of the equivalence principle · a high precision test of the equivalence...

Documents