a high precision test of the equivalence principle · a high precision test of the equivalence...
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![Page 1: A High Precision Test of the Equivalence Principle · A High Precision Test of the Equivalence Principle Stephan Schlamminger Eotwash Group Center for Experimental Physics and Astrophysics](https://reader034.vdocuments.net/reader034/viewer/2022042214/5eba98bdb121db4cbe1ed55f/html5/thumbnails/1.jpg)
A High Precision Test of the Equivalence Principle
Stephan Schlamminger
Eotwash GroupCenter for Experimental Physics and Astrophysics (CENPA)
University of Washington
March 4th 2010 Physics 294
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What and where is CENPA?
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A close look at the N part of campus
Now: CENPA
Center for Experimental Nuclear Physics and Astrophysics
Machine shop
Gravity lab
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Inside CENPA
Check it out: www.npl.washington.edu
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http://www.npl.washington.edu/research.html
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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
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Mass does not add up
Proton Electron 1H
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Mass does not add up
Proton Electron 1H
938 272 013 eV/c2 510 999 eV/c2 938 782 999 eV/c2
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Mass does not add up
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
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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
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The mass of an object
m = ∑ mc + ∑ Ekin/c2 - ∑ Epot/c2
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Newton’s Principia (1689)
Newton’s 2nd Law
Fi = mi a
Gravitational Law
FG= G mg1 mg2 /r2
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Newton’s Principia (1689)
Newton’s 2nd Law
Fi = mi a
Gravitational Law
FG= G mg1 mg2 /r2
Equivalence Principle (EP): mi = mg
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Newton’s Principia (1689)
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.
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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.
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-a
F=-ma
The Equivalence Principle
g
F=mg
Gravitational field g Acceleration a
Inertial mass = gravitational mass, mI=mG for all bodies
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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!
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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)?
• …
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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
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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
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B/μ varies, because
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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
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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
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Eötvös Experiments
cos2rmF II
ω
θ
ε
r
)2sin(2
2
g
r
m
m
G
IgmF GG
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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
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Dicke’s idea
Sun
Using the Sun as a source
11101 x
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Historical overview
Galileo
Newton
Bessel
Potter
EötvösDicke
Braginsky
UW
)( 2121
21
aa
aa
drop
pendula
Type of experiment
torsionbalance
modulatedtorsionbalance
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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
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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
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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
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The lower part of the apparatusvacuum chamber (10-5 Pa)
ion pump
autocollimator
support structure for
gravity gradient
compensators
gravity gradient
compensators
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Raw-data
Signal + free Oscillation
ωSIG=2/3 ωPEND=2π/(1200 s)
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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
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Data reductionN
ort
hW
es
t
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A complete day of data
σ≈ 3 nrad √day
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Differential acceleration
dFdF 21
amdaamddmadma )( 2121
Deflection from equilibrium: φ
is caused by a torque:
mda
m
m
d
F1
F2
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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
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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=?
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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
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Data taking sequence (1/3)We rotate the pendulum (and thus the dipole) in respect to the readout every day by 1800.
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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!
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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.
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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
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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)
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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
Gravity gradients (2/4)
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q41 configuration q21 configuration installed
Gravity gradients (3/4)
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Gravity gradients (4/4)
Without
compensation:
Q21=1.78 gcm-3
0.2 fm/s2 N
1.7 fm/s2 W
Uncertainty due
to fluctuating
fields:
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Tilt coupling
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Tilt coupling
Tilt of the suspension point+ anisotropies of the fiber
will rotate
rotation axis
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Tilt coupling
Tilt of the suspension point+ anisotropies of the fiber
will rotate
1. Thicker fiber atthe top providesmore torsionalstiffness
rotation axis
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Tilt coupling
Tilt of the suspension point+ anisotropies of the fiber
will rotate
1. Thicker fiber atthe top providesmore torsionalstiffness
2. Feedback minimizes tilt of TT
rotation axis
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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
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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.
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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.
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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
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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
cos2rmF II
ω
θ
ε
r
gmF GG ½|a1+a2|η=
|a1-a2|
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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
cos2rmF II
ω
θ
ε
r
gmF GG
η(Be-Ti)= (0.3 ±1.8) x 10-13
½|a1+a2|η=
|a1-a2|
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Results
17 x
Str
ength
rela
tive t
o g
ravity
Charge: B
Range of a hypothetical “fifth” force (m)
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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
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Galactic dark matter
Milky Way
Earth
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Galactic dark matter
Halo of dark matter
Milky Way
Earth
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Galactic dark matter
Dark matter inside the Earth’s galactic orbit causes 25-30% of the total acceleration.
Halo of dark matter
Milky Way
Earth
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Galactic dark matter
Our acceleration towards the galactic center is:
agal= adark+ aordinary= 1.9 10-10 m/s2 => adark= 5 10-11 m/s2
Dark matter inside the Earth’s galactic orbit causes 25-30% of the total acceleration.
Halo of dark matter
Milky Way
Earth
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Galactic dark matter
Our acceleration towards the galactic center is:
agal= adark+ aordinary= 1.9 10-10 m/s2 => adark= 5 10-11 m/s2
Dark matter inside the Earth’s galactic orbit causes 25-30% of the total acceleration.
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
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Galactic dark matter
Our acceleration towards the galactic center is:
agal= adark+ aordinary= 1.9 10-10 m/s2 => adark= 5 10-11 m/s2
Dark matter inside the Earth’s galactic orbit causes 25-30% of the total acceleration.
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).
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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.
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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.
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Acknowledgement
Jens GundlachTodd Wagner
Ki-Young Choi
Eric Adelberger
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END
This talk stops here.
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Searching for New Interactions
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
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
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/ 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, ..
Searching for New Interactions
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Signal
Free oscillation
Filtered data
Thermal noise
In frequency space
Noise level at the signal-frequency:
≈1000 nrad/√Hz ≈ 3 nrad √day
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Source integration
Local
topography
Preliminary
Earth
Reference
Model
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Source integration
Local
topography
Preliminary
Earth
Reference
Model
Difficult a
nd t
edio
us