Tests of the gravitational 1/r2 law: motivations, techniques and results

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Tests of the gravitational 1/r2 law motivations,
techniques and results

• Eric G. Adelberger
• University of Washington

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outline

• motivations for testing short-distance gravity
• extra dimensions
• dark-energy length scale
• fat gravitons
• chameleons
• summary of previous results
• techniques and results from recent work
• implications of the new results
• prospects for further advances

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unifying gravity with the other forces in physics
is the central problem in fundamental
sciencestring or M theory provides the only
known frameworkfor doing thisBUT it has
inherent problemscontains features that have to
be hidden from experiment 10 or 11
dimensions dilaton hundreds of massless scalar
modulimust find a way to account for the
extreme weaknessof gravity and the observed dark
energy each of these issues is addressed by
experimental tests of the gravitational
inverse-square law
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Motivation 1
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String theory is not just a theory of strings but
it also contains branes
Brane-world solution to the hierarchy
problem Gravity isnt actually terribly weak we
just cannot see its full strength because most of
it has leaked off into the extra dimensions
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Gausss Law and extra dimensions
illustration from Savas Dimopoulis
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Motivation 2Does dark energy define a new
fundamental length scale in physics?
a second Planck length?
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Motivation 3
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Sundrums fat graviton force
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Motivation 4 the chameleon mechanism
circumvents experimental evidence against
the gravitationally coupled low-mass scalars
predicted by string theory by adding a
self-interaction term to the effective potential
density
natural values of ? and ? are 1
in presence of matter this gives massless
chameleons an effective mass
so that a test bodys external field comes only
from a thin skin of material of thickness
1/meff
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This drastically weakens experimental constraints
obtained from conventional test bodies. For
example, the natural value of the skin thickness
for molybdenum is 60 microns To see massless
chameleons need to look for tiny forces from
very small test bodies
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95 confidence limits as of 2000
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the Irvine experiment
Hoskins et al. PRD 32, 3084 (1985)
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95 confidence limits as of 2000
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the Eöt-Wash group in experimental gravitation

• Faculty Current Grad students
• EGA Ted Cook
• Jens Gundlach Charlie
  Hagedorn
• Blayne Heckel Matt Turner
• Staff Todd Wagner
• Postdocs
• Frank Fleischer 1/r2
• Seth Hoedl EP
• Stephan Schlamminger spin
• 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

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the 42-hole ISL pendulum
PhD project of Dan Kapner
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some advantages of our design

• plane geometry optimizes short-range signal
• frequencies of the gravitational signal at high
  multiples of of the disturbance frequency
• torques from Newtonian gravity are highly
  suppressed, but essentially no attenuation of
  torques from new short-range physics
• complete Faraday shield to eliminate
  electrostatic and Casimir forces

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Rotating attractor and its electrostatic shield

• tightly stretched, 10- µm thick, Au-coated BeCu
  foil shields electrostatic effects.
• placed 12 µm above rotating attractor

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signal processing
raw signal
2-pt digital filter used in our 10-hole work
these data Were taken with calibration
turn-table stationary
5-pt digital filer
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Problems not addressed by our design

• Alignment
• Temperature effects
• Dust
• Electrostatic noise

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making the attractor parallel to the detector
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gravitational centering of the detector on the
attractor
y0 0.0040.002 mm
x0 -0.0150.007 mm
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measuring the detector-membrane separation
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Dan Kapner assembling the 42-hole instrument
One piece of dust can prevent you from getting to
small separations
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power spectral density of twist signal
d detector/foil separation
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data from 42-hole Experiment I
42?
21?
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data from 42-hole Experiment II
42?
after we reduced the lower attractor
disk thickness by 140 microns and straightened
the 3.5 micron curvature of the detector ring
21??
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data from 42-hole experiment III
42?
21?
after replacing the gold coatings on the
detector and membrane. In the process we
inadvertantly increased the detector bend
to 3.9 microns
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data fitting procedure
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Scanning tunneling microscope study of our
molybdenum surfaces
Surface roughness correction increased hole radii
and decreased hole thicknesses by 2.2 µm and 2.3
µm, respectively
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some gee-whiz numbers

• typical error corresponds to light spot on
  detector moving by 0.6 nm
• typical torque in our 42-hole experiments is
  1fN-m with statistical uncertainty of 0.006 fN-m
• corresponds to a force (400.24) fN
• suppose you could cut a postage stamp into 1012
  equal pieces
• typical force is 60 times the weight of 1 of
  those pieces
• typical statistical error is 1/3 the weight of 1
  piece

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combined analysis of all 3 UW experiments
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Experiment of L-G. Tu et al. PRL 98, 201101
(2007)
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the Stanford ISL Experiment using
low-temperature micro-cantilevers
J. Chiaverini et al, PRL 90, 15101 (2003) S.J.
Smullin et al., PRD 72, 122001 (2005)
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some 2s implications of our data
D.J. Kapner et al., PRL 98, 021101 (2007)

• largest possible size of an extra dimension is
• R ?(?8/3) 44 microns
• for ADDs 2 equal extra dimensions scenario
• M? 3.4 TeV/c2
• radion exchange with n extra dimensions gives a
  Yukawa force with ?n/(n2) and
• ?2.4 mm 1 TeV/Mc2 this implies M(n6)
  6.4 TeV/c2

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more 2s implications of these data

• The dilaton is string theorys spin-0 partner of
  the spin-2 graviton. Its exchange force violates
  the equivalence principle so experiments tell us
  that the dilaton cannot be massless. Kaplan and
  Wise worked out its couplings to hadronic matter
  and predict a Yukawa force with 1 ? ? ? 1000
  which implies a dilaton mass mc2 ? 3.5 meV

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2s chameleon constraints
natural value
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fat graviton constraints
constraints are poorer than on Yukawas because
the tail of the fat graviton modification falls
must faster than a Yukawa
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Ted Cooks Fourier-Bessel ISL pendulum
Active elements of pendulum and attractor are
made from 50 micron thick W plates. Signal is
the ratio of 18 and 120 omega torques
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Pendulum
20mm tungsten fiber
top-hat leveling mechanism
aluminum calibration spheres
mirror cube
titanium body
3mm thick Pyrex backing for W spokes
drumhead electrostatic shield
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Foil Flatness

• 1656 points with CMM
• Height variance 1.4mm

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attractor drive mechanism
peltier temp. control
bearing assembly
piezo nano-motor
ceramic ring
encoder electronics
ferrofluidic rotary feed through
6 vacuum flange
bellows clutch
This is shown upside down
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Charlie Hagedorns parallel plate experiment
Charlie Hagedorns parallel-plate experiment
attractorinfinite plane, homogenous gravity
field
schematic top view
No change in torque on pendulum when infinite
plane moves back and forth and if 1/r² holds.
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top view of actual implementation
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120 spokes
42 holes
26 holes
10 holes
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summary

• our tests have shown that the ISL holds down to
  56 ?m (??1) with 95 confidence
• largest extra dimension must have a size
• R ? 44 ?m
• ADD 2-equal large extra dimension scenario needs
  M? 3.4 TeV/c2
• strong constraints on couplings of proposed light
  scalar or vector bosons including chameleons
• possible anomalies at much shorter scales

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conclusions

• to probe the true geometry of the universe must
  study gravity
• this is done most directly by testing the ISL
• ISL experiments not yet limited by fundamental
  considerations
• ISL experiments already probe interesting regimes
  that test many current speculations
• theorists keep dreaming up possible new phenomena
• testing these ideas provides a demanding
  challenge for experimentalists

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some references

• very accessible reading
• "The Universe's Unseen Dimensions", N.
  Arkani-Hamed, S. Dimopoulos and G. Dvali,
  Scientific American August 2000, Vol. 283 Issue 2
  
• details of our inverse-square law
  tests
• CD Hoyle et al., PRD 70, 042004 (2004)
• D.J. Kapner et al., PRL 98, 021101(2007)
• E.G. Adelberger et al., PRL 98, 131104(2007)
• comprehensive review
• E.G. Adelberger, B.R. Heckel and A.E. Nelson
• Ann. Rev. Nucl. and Part. Sci. 53, 77 (2003)

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but the scale of the experiments is quite
different!
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CD Hoyle working on an earlier version of this
experiment
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Yukawa interactions from generic scalar or
vector boson exchange
q B-L
mf 1 meV
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• pseudoscalar exchange force vanishes between
  unpolarized bodies, but 2nd-order exchange of ?5
  coupled pseudoscalars gives a spin-independent
  force

1s constraint on ?5 coupling to neutrons
SN1987A constraint
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Ted Cooks Fourier-Bessel ISL pendulum
Signal is ratio of 120 to 18 omega torques Active
elements of pendulum and attractor are machined
from 50 micron thick tungsten sheets
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the Colorado ISL Experiment

• 200 µm-thick tungsten model airplane
  oscillates at 1173 Hz with Q of 25000
• diving board vibrates at resonant frequency of
  the airplane oscillator
• effectively null for Newtonian gravity
• gold-coated, 60 µm sapphire shield reduces
  electrostatic and acoustic coupling

J.C. Long et al., Nature 421, 922 (2003)
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schematic top view
attractorinfinite plane, homogenous gravity
field
No change in torque on pendulum infinite plane
moves back and forth and if 1/r² holds.

• Advantages
• true null test
• slower fall-off with ? (?³ for holes vs. ?²
  for plates)
• large signal
• simple to make

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data from 42-hole Experiment I
42?
21??
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temperature effects
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assembling the pendulum and attractor
Pendulum is Au-coated conducting membrane and
Au-coated magnetic shield (not shown) surround it
to minimize electrostatic interactions.