Torsion Balance tests of
Gravity
Blayne Heckel
University of Washington
TOPICS COVERED
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Equivalence Principle tests
short-range inverse-square law tests
Planck-scale preferred-frame tests
WILL SUMMARIZE
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motivations
techniques
results
the Eöt-Wash group in
experimental gravitation
Faculty
Eric Adelberger
Jens Gundlach
Blayne Heckel
Postdocs
Frank Fleischer
Seth Hoedl
Stephan Schlamminger
Current Graduate Students
Ted Cook
Charlie Hegedorn
William Terrano
Matt Turner
Todd Wagner
Part of this talk is based on PhD thesis work of recent graduates
Dan Kapner (currently Kavli Fellow KCCP in Chicago)
Claire Cramer (currently at Harvard University)
Primary support from NSF Grant PHY0653863 with supplements from the DOE
Office of Science and to a lesser extent NASA
Unifying gravity with the other forces in physics
is the central problem in fundamental science
must find a way to account for the extreme weakness
of gravity and the observed dark energy
string or M theory provides a framework for the
unification
BUT: it inherently contains features that have to be
hidden from experiment:
10 or 11 dimensions
numerous massless scalar particles with “gravitational”
couplings
some of these new features could show up in
Equivalence Principle and/or inverse-square law tests
A brief history of Equivalence Principle tests:
classic view: do all materials have the same mi /mg ?
Galileo test
Newton-Bessel test
Eötvös test
ω
l
d
θ
are fall times equal?
are periods equal?
are angles equal?
T=(2d/g (mi/mg))
T=2π (l/g (mi/mg))
ε=ω2R sin2θ/(2g) (mi/mg)
a/a0.1
a/a10-4
a/a 10-9
implementation as a null experiment
if the EP is violated, down is not a unique direction
balance twists only if force vectors are not parallel
i.e. if EP is violated or if gravity field is not uniform
modern era in EP tests was ushered in by
Fischbach’s reanalysis of Eötvös’s results
Fischbach at el., PRL 56, 3 (1986)
This result along with
geophysical measurements
was taken as evidence for
a “5th force”
with
 ≈ .01
30m    1000m
k= a/a
torsion pendulum of the recent Eöt-Wash EP test
S. Schlamminger et al., PRL 100, 041101 (2008)
20 m diameter 108 cm long
tungsten fiber
eight 4.84 g test masses
(4 Be & 4 Ti) or (4 Be & 4 Al)
4 mirrors
tuning screws adjust the mass
multipole moments & minimize
sensitivity to gravity gradients
5 cm
free osc freq:
quality factor:
decay time:
machining tolerance:
total mass :
1.261 mHz
4000
11d 6.5 hrs
5 m
70 g
turntable of the new EP balance
servoed rotary contactor
for electric signals
thermal insulation
air-bearing turntable
angle encoder electronics
thermal expansion feet
fedback to keep turntable
rotation axis level
torsion balance hangs
from the bearing which
rotates at 0.833 mHz
gravity-gradiometer pendulums
q41 configuration on a table
q21 configuration installed
gravity-gradient compensation
Pb
Q21 compensators
Total mass: 880 kg
Q21= 1.8 g/cm3
Compensators
can be rotated
by 360°
Al
Pb
Q31 compensators
Total mass: 2.4 kg
Q31 =6.710-4 g/cm4
hillside &
local masses
limitations on gradient cancellation
these data were taken in early November, 2008
1σ statistical + systematic uncertainties
from our Equivalence Principle experiment
with beryllium and titanium test bodies
Source
Earth
Δa (cm/s2)
Δa/asource
(+0.6 ± 3.1) x 10-13 (+0.3 ± 1.8) x 10-13
Sun
(-2.4 ± 2.8)×10-13
(-4.0 ± 4.7)×10-13
Milky Way
(-2.1 ± 3.1)×10-13
(-1.1 ± 1.6)×10-5
CMB
(-2.9 ± 2.7)×10-13
(-2.1 ± 1.9)×10-3
95% confidence level exclusion plot
for interactions coupled to B - L
Is gravity the only
long-range force
between dark and
luminous matter?
Could there be
a long-range
scalar interaction
that couples to
dark-matter &
standard-model
particles?
95% confidence limits on non-gravitational acceleration of
hydrogen by galactic dark matter
at most 5% of the acceleration can be non-gravitational
motivations for sub-millimeter tests
of the inverse-square law
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untested regime
probes the dark energy length scale
large extra dimensions?
chameleons?
“fat gravitons”?
95% confidence limits as of 2000
Does dark energy define a new
fundamental length scale in
physics?
a second “Planck length”?
the 42-hole inverse-square law pendulum
PhD project of Dan Kapner
Mary Levin photo
rotating attractor and its electrostatic shield
• tightly stretched,
10- μm thick, Aucoated BeCu foil
shields electrostatic
effects.
• placed 12 μm
above rotating
attractor
power spectral density of the twist signal
d = detector/foil separation
measuring the detector-membrane separation
signal processing
raw signal
these data
were taken
with the
calibration
turn-table
stationary
2-pt digital filter
used in our
earlier work
5-pt digital filter
data from 42-hole experiment III
42ω
this is 1 of
3 very similar
data sets
taken with
slightly
different
attractor
geometries
21ω
95% confidence upper limits on ISL
violation
some 2σ implications of our data
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inverse-square law holds down to 56 microns
largest possible size of an extra dimension is
R =(=8/3) = 44 microns
for ADD’s 2 equal extra dimensions scenario
M* 3.4 TeV/c2
radion exchange with n extra dimensions gives a
Yukawa force with =n/(n+2) and
≈2.4 mm [ 1 TeV/M*c2]; this implies M*(n=6) ≈ 6.4
TeV/c2
dilaton must have mass mc2  3.5 meV
the chameleon mechanism
can circumvent experimental evidence against
string theory’s gravitationally coupled low-mass
scalars by adding a self-interaction term
to the effective potential density
natural values of  &  are
in presence of matter, massless
chameleons acquire an effective mass
so that an object’s external field comes only from
a thin skin of material of thickness ~ 1/meff ( 60μm)
2σ chameleon constraints
natural
value
EXCLUDED
the Fourier-Bessel pendulum
will be the PhD project of Ted Cook
cosmic preferred frames?
We all were taught that there are no preferred frames.
But the Universe defines a frame in which the CMB is
essentially isotropic. Could there be other preferred frame
effects defined by the Universe?
Kostelecky et al. developed a scenario where vector and
axial-vector fields were spontaneously generated in the
early universe and then inflated to enormous extents;
particles couple to these preferred-frame fields in
Lorentz-invariant manners.
This “Standard Model Extension” predicts lots of new
observables many of which violate CPT. One observable is
E = σe· b̃e where b̃e is fixed in inertial space - its
benchmark value is me2/ MPlanck ≈ 2 × 10-17 eV
non-commutative space-time
geometry
string theorists have suggested that the space-time
coordinates may not commute, i.e. that
where Θij has units of area and represents the
mimimum observable patch of area, just as the
commutator of x and px represents the minimum
observable product of Δx Δpx
“Review of the Phenomenology of Noncommutative
Geometry”
I. Hinchliffe, N Kersting and Y.L. Ma
hep-ph/0205040
effect of non-commutative
geometry on a spin
non-commutative geometry is
equivalent to a “pseudo-magnetic”
field and thus couples to spins
B
Anisimov, Dine, Banks and Graesser
Phys Rev D 65, 085032 (2002)
 is a cutoff assumed to be 1TeV
A
the Eöt-Wash spin pendulum
•
•
•
•
•
•
•
•
9.8 x 1022 polarized electrons
negligible mass asymmetry
negligible composition asymmetry
flux of B confined within octagons
negligible external B field
Alnico: all B comes from electron
spin: spins point opposite to B
SmCo5: Sm 3+ ion has spin
pointing along total B and its spin
B field is nearly canceled by its
orbital B field--so B of SmCo5
comes almost entirely from the
Co’s electron spins
therefore the spins of Alnico and
Co cancel and pendulum’s net spin
comes from the Sm and J =  S
the Eöt-Wash rotating torsion
balance
vacuum can
prehanger
fiber
HH coils
autocollimator
compensation
masses
thermal
shield
magnetic
shielding
pendulum
feet
turntable
measuring the stray magnetic field of the spin pendulum
B inside = 9.6±0.2 kG
B outside ≈ few mG
spin-pendulum data span a period of 36 months
a 113 hour stretch is shown below
definition of β:
Epend= Np β·σ
2ß=energy needed
to flip a spin
-simulated
- - -signal
-from assumed
bx=2.5×10-20 eV
best fit out-of-phase sine
waves--corresponds to
preferred-frame signal:
bx=(-0.20±0.76)10-21 eV
by=(-0.23±0.76)10-21 eV
lab-fixed spin pendulum signal
gyrocompass
effect
The gyrocompass
Our gyrocompass.
Earth’s rotation Ω acting on J
of pendulum produces a
steady torque along
suspension fiber
Anschütz’s gyrocompass.
Anschuetz-Kaempfe and Sperry
separately patented gyrocompasses in
UK and US. In 1915 Einstein ruled that
Anschütz’s patent was valid.
| Ω × J · n | where n is unit
vector along local vertical.
Because S= ̶ J this is
equivalent to βN = ̶ 1.616
× 10-20 eV
Lorentz-symmetry violating rotation
parameters
our work
Cane et al, PRL 93(2004) 230801 Phillips et al, PRD 63(2001) 111101
95% confidence upper limits on monopolemonopole-dipole interactions
effect of non-commutative
geometry on spin
B
A
 is a cutoff assumed to be 1TeV
Anisimov, Dine, Banks and Graesser
hep-ph/2010039
minimum observable patch of area
implied by our results
|
 6  10–58 m2
6  10–58 m2 seems very small
and indeed it is
but in another sense it is also quite large
6  10–58 m2 ~ (106 LP)2
where LP is the Planck Length
√(ħ G/c3)=1.6 × 10-35 m
or ~ (103 LU)2
where LU is the Grand Unification length
LU = ħc /1016 GeV
but 1013 GeV is pretty good for a table-top
result
references
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Equivalence Principle tests
S. Baessler et al., PRL 83, 3585 (1999)
G.L. Smith et al., PRD 61, 022001 (2000)
S. Schlamminger et al. PRL 100, 041101 (2008)
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Inverse-square law tests
D.J. Kapner et al., PRL 98, 021101 (2007)
E.G. Adelberger et al., PRL 98, 13104 (2007)
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Preferred-frame tests
B.R. Heckel et al., PRL 97, 021603 (2006)
B.R. Heckel et al., arXiv:00808.2673
Eötvös’s instrument
Eötvös first
used torsion
balances to
test the EP
in 1889. His
most famous
work was
done
between
1904 and
1909
Eötvös et al
studied a range
of materials and
claimed
a/a<510-9
Roll, Krotkov and Dicke’s instrument
they watched bodies fall toward the sun
Roll, Krotkov and Dicke,
Ann. Phys. 26, 442 (1964)
1 sigma result a/a=(1.0±1.5)10–11
only 280 times more precise than Eotvos
“If one of the suspended weights
in Eötvös’ apparatus contained
a strongly magnetized iron fragment
weighing only a few millionths of
a gram it would produce a deflection
1000 times greater than the error
claimed by Eötvös”
ELECTRICALLY CHARGED PLATES
Dicke made similar comments about
temperature variations and the gravity
field of Eötvös himself
This claim turned out to be wrong,
but as sometimes happens in physics
a wrong result* can be very useful
scientifically:
• µ –> e γ
• Weber’s “discovery” of gravity waves
• “fifth force”
* that gets corrected
Leveling
feet
turntable
z
correction for tilt of the
turntable rotation axis
Feedback
nulls signal
of upper tilt
sensor
1.70m
Gravity
gradient
compensator
• Feedback removes tilt at upper tilt
sensor
• However, local vertical varies with
height
– gives a spurious deflection of
the pendulum due to residual
tilt
Lower tilt sensor measures:
local earth field (~60 nrad)
+ off-center compensator field (~15 nrad)
= measured tilt (~45 nrad)
0.23m
Tilt at pendulum is only due to local earth field:
~50 nrad of tilt  ~2.5 nrad correction to
Lower tilt
sensor
pendulum signal
the Irvine experiment
Hoskins et al. PRD 32, 3084 (1985)
some amusing numbers
our differential acceleration resolution of
Δa310-13 cm/s2
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is comparable to the difference in g
between 2 spots in this room separated vertically
by  1 nm
if an object had been given this steady acceleration
starting in the time of Pericles (450 BC) it would
now be moving as fast as the end of the hour hand
on a typical wall clock
Gauss’s Law and extra dimensions
illustration from Savas Dimopoulos
Top view of the plate pendulum
torsion
pendulum
Ti, = 4.6 g/cm ³
Thin Pt attractor sheet,
backing made from Ti:
a rim makes the finite
attractor look “infinite”:
homogenous gravity field
Ta, = 16.6 g/cm ³
stretched Ti foil 4
m
This will be the PhD project of Charlie Hagedorn
Earth’s spin axis
Eöt-Wash lab
Z
Earth’s velocity around Sun
Y
X
to vernal equinox
In more general terms
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our upper limit on the energy
required to invert an electron spin
about an arbitrary axis fixed in inertial
space is ~10-22 eV
this is comparable to the electrostatic
energy of two electrons separated by
~ 90 astronomical units