C.D. Hoyle

for the Eöt-Wash Group at the University of Washington?

Testing Gravity from the Dark Energy Scale to the Moon and Beyond

C.D. Hoyle

Testing Gravity from the Dark Energy Scale to the Moon and Beyond

C.D. Hoyle

Overview• Brief review of gravity and the Inverse-Square Law (ISL)• Motivation for precision gravitational tests

• What we don’t know about gravity• What gravity may tell us about the nature of the universe

• Testing the ISL at the “Dark Energy Scale”• Using the Earth-Moon system to precisely test Einstein’s

General Relativity• Future prospects for precision gravitational tests

What We Know: Gravity in the 21st Century• Gravity is one of the 4 known fundamental interactions

• Others: Electromagnetism, Strong and Weak Nuclear Forces

• Gravity holds us to the earth (and makes things fall!)• It also holds things like the moon and satellites in orbits• Newton expressed this “unification” mathematically in the 1660’s:

Newton

+ 1 22

M MF G

r

r is distance between two bodies of mass M1 and M2

• Newton’s “Inverse-Square Law” worked well for about 250 years, but troubled Einstein

• “Action at a distance” not consistent with Special Relativity

• Einstein incorporated gravity and relativity with another great unification in 1915:

• 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

• 1/r2 form of Newton’s Law has a deeper significance: it reflects Gauss’ Law in 3-dimensional space

• Very successful so far: • Planetary precession• Deflection of light around massive objects• ….

More That We Know

• General Relativity works well, but is fundamentally inconsistent with the Standard Model based on quantum mechanics

• Will String Theory provide us a further unification?

• Why is gravity so weak compared to the other forces?• “Hierarchy” or “Naturalness” Problem• Why is ?• E & M force ~1040 times greater than gravitational force in an H atom!• Is gravity’s strength diluted throughout the “extra dimensions” required by

string theory?

• Does an unknown property of gravity explain the mysterious “Dark Energy” which seems to cause our universe’s expansion to accelerate?

S. Carroll

Planck EWM M

What we Don’t Know

Can gravitational effects explain the Dark Energy? What can gravity tell us about the nature of spacetime? Are there observable effects of String Theory? Are there new particles and forces associated with gravity’s

(unknown) quantum-mechanical nature? Experimental prospects

Laboratory-scale tests of the 1/r2 law and Equivalence Principle Astronomical tests of General Relativity Gravitational wave searches (LIGO, LISA, etc.) Signatures of quantum gravity in high-energy collider experiments

A “Golden Age” for Gravitational Physics

• Are there observable consequences of String Theory?• Extra dimensions – maybe , but gravity is diluted throughout

more dimensions than the rest of the Standard Model forces. Extra dimensions could be large (mm scale!)

e.g. N. Arkani-Hamed, S. Dimopoulos, G.R. Dvali, Phys. Lett. B 436, 257 (1998)

• What is the mechanism behind the cosmic acceleration?• “Fat” graviton - gravity may observe a cut-off length scale in the sub-mm

regime and thus does not “see” small-scale physics. R. Sundrum, hep-th/0306106 (2003)

• Does the observed dark energy density suggest a new, fundamental “Dark Energy Scale” in physics?

S. Beane, hep-ph/9702419 (1997)

• Are there new forces mediated by exotic particles?

e.g. S. Dimopoulos and A. Geraci, hep-phys/0306168 (2003), I. Antoniadis et al.,

hep-ph/0211409 (2003), D. Kaplan and M. Wise, hep-ph/0008116 (2000), etc.

Planck EWM M

4 0.1 mmVac

c

Short-Range 1/r2 Tests

Example: Extra Dimensions• Test masses and ED:

• Near test mass (r R*), we must satisfy Gauss’ Law in 3+1+n dimensions:

• Far away (r >> R*) we must recover the usual 3-D form:

R*

3 1 21

nn

G m mV r

r

3 1 2 3

* *

n nn n

G m m GV r G

R r R

From G. Landsberg

Moriond ’01 Talk

Parameterization and Background• General deviation from Newtonian gravity:

1 2 / 1Gm m rV r e

r

• Until recently (last few years), gravitation not even shown to exist between test masses separated by less than about 1 mm!

From Adelberger, et al., Ann. Rev. Nuc. Part. Phys. (2003)

Previous Short Range Limits

• 95% C.L., as of 1999 (when we started our work)• All previous limits from torsion pendulum experiments

For references see CDH et al., Phys Rev. D. 70 (2001) 042004

Experimental Challenges• Extreme weakness of gravity

– Electrostatic interactions• Need extremely high charge balance (10-40) to attain gravitational

sensitivity!• Casimir force, patch charges become strong at close distances• Fortunately, effective shielding is possible, but at a cost of distance!

– Magnetic impurities• Strong distance dependence• Requires high purity materials and clean fabrication techniques

• Need to get large mass at small separations– Alignment and characterization of masses– Seismic noise

• Temperature fluctuations and thermal noise• Etc., etc.

• Torsion Pendulum still the best instrument for measuring the ISL:

• Vary separation, r, between masses M1 and M2

• Force on M1 causes the pendulum to twist

• Measure twist angle • Compare with inverse-square prediction

M1 M2

thin fiber

r

up

Torsion Pendulums

Eöt-Wash Torsion Pendulum (best to date)

s

Fiber, 18m diameter, 80cm length, tungsten

21-fold axial symmetry, molybdenum disc, 1mm thick

Attractor : rotating pair of discs, shifted out of phase with each other to reduce Newtonian torque

Not pictured: 10m thick Au-coated BeCu membrane - electrostatic shield

3 aluminum calibration spheres

4 mirrors for measuring angular deflection

Leveling mechanism

2.75”

Technique• Attractor disks rotate below pendulum

• “Missing mass” of the holes causes pendulum to twist

• Measure the torque on pendulum at harmonics (21, 42, 63) of the attractor rotation frequency, , as a function of S

• Compare observed torque to ISL prediction

• Twist angle measured to a nanoradian (imagine a pea in Seattle)

• Force measured equals 1/100 trillionth the weight of a single postage stamp

s

Noise

Readout Noise

Data

Predicted thermal noise for Q = 3500

(internal dissipation)

22

2 22

4( )

[( ) ]

Bk T

Q IQ

Recent Results (Thesis of D. Kapner)

ISL

95% C.L. Bounds on ||

1 2 / 1Gm m rV r e

r

More Distant Future: Even Shorter Distances• Why Look to Shorter Distances?

– Short range 1/r2 tests place model-independent constraints on:• Single largest possible extra dimension

• New interactions (properties of exchange particles)

– Other, more specific scenarios (dilaton, moduli, etc.)

– Unexplored parameter space

New Promising Techniques• Vertical plate “Step Pendulum”:

Modulate attractor plate/pendulum separation

• Analytical expression for (very small) Newtonian background torque

• Yukawa torque now falls as 2 instead of 3 for small :

• Drawbacks:

• Minimum separation may not be so small

• Possible Systematics at 1

2 /sY p aN G RA e R

Future High-sensitivity 1/r2 Test

Be, = 1.84 g/cm ³

Pt, = 21.4 g/cm ³

Stretched metal membrane

Torsion pendulum

Attractor:“Infinite” plane 2mm thick Mo Homogenous gravity field

Moves back and forth by 1mm

Advantages over hole pendulum:• True null test• Slower fall-off with (³ for holes vs. ² for plates)• Much larger signal• Simpler machining

Top view:

No change in torque on pendulum if 1/r² holds.

Current and Future Limits

1 2 / 1Gm m rV r e

r

Current

Step pendulum

Shooting the MoonShooting the Moon

Testing General Relativity with Lunar Laser Ranging

Testing General Relativity with Lunar Laser Ranging

A Modern, Post-Newtonian View

The Post-Newtonian Parameterization (PPN) looks at deviations from General Relativity

The main parameters are and tells us how much spacetime

curvature is produced per unit mass tells us how nonlinear gravity is

(self-interaction) and are identically 1.00 in GR

Current limits have: (–1) < 2.510-5 (Cassini) (–1) < 1.110-4 (LLR)

Relativistic Observables in the Lunar Range Equivalence Principle (EP) Violation

Earth and Moon fall at different rates toward the sun Appears as a polarization of the lunar orbit Range signal has form of cos(D) (D is lunar phase angle)

Weak EP Composition difference: e.g., iron in earth vs. silicates in moon Probes all interactions but gravity itself

Strong EP Applies to gravitational “energy” itself

Earth self-energy has equivalent mass (E = mc2) Amounts to 4.610-10 of earth’s total mass-energy

Does this mass have MG/MI = 1.00000? Another way to look at it: gravity pulls on gravity

This gets at the nonlinear aspect of gravity (PPN )

Equivalence Principle Signal

If, for example, Earth has greater inertial mass than gravitational mass (while the moon does not): Earth is sluggish to move Alternatively, pulled weakly

by gravity Takes orbit of larger radius

(than does Moon) Appears that Moon’s orbit is

shifted toward sun: cos(D) signal

Sun

Nominal orbit:Moon follows this, on average

Sluggish orbit

The Strong Equivalence Principle

Earth’s energy of assembly amounts to 4.610-10 of its total mass-energy

The ratio of gravitational to inertial mass for this self energy is

The resulting range signal is then

Currently is limited by LLR to be ≤4.510-4

LLR is the best way to test the strong EP

Other Relativistic Observables Most sensitive test of 1/r2 force law at any length scale Time-rate-of-change of Newton’s gravitational constant

Could be signature of Dark Energy (quintessence) Currently limited to less than 1% change over age of Universe

Geodetic precession tested to 0.35% Precession of inertial frame in curved spacetime of sun

Gravitomagnetism (frame-dragging) is also seen to be true to 0.1% precision via LLR

LLR through the DecadesPreviously100 meters

APOLLO

APOLLO: the New Big Thing in LLR

APOLLO offers order-of-magnitude improvements to LLR by: Using a 3.5 meter telescope Gathering multiple photons/shot Operating at 20 pulses/sec Using advanced detector technology Achieving millimeter range precision Having the best acronym

The APOLLO Collaboration

UCSD:Tom Murphy (PI)Eric MichelsenEvan Million

U Washington:Eric AdelbergerErik Swanson*Russell Owen*Larry Carey

Harvard:Christopher StubbsJames Battat

JPL:Jim WilliamsSlava TuryshevDale BoggsJean Dickey

Lincoln Labs:Brian AullBob Reich

Northwest Analysis:Ken Nordtvedt

Humboldt State:C.D. HoyleLiam Furniss

Measuring the Lunar Distance• It takes light 1.25 seconds to get to the moon – thanks to foresight we

can reflect light off the surface!

• Retroreflector arrays always send light straight back at you (like hitting a racquetball into a corner):

retroreflector

Lunar Retroreflector Arrays

Corner cubes

Apollo 14 retroreflector array

Apollo 11 retroreflector array

Apollo 15 retroreflector array

APOLLO’s Secret Weapon: Aperture

The Apache Point Observatory’s 3.5 meter telescope Southern NM (Sunspot) 9,200 ft (2800 m) elevation Great “seeing”: 1 arcsec Flexibly scheduled, high-class

research telescope 6-university consortium (UW, U

Chicago, Princeton, Johns Hopkins, Colorado, NMSU)

APOLLO Basics

• 2.5 second round-trip time, 20 Hz laser pulse rate (50 pulses in the air at any one time)

• Outbound pulses have 3 x 1017 green photons (532 nm), 3.5 meter diameter• We get about 1 (!) back per pulse (beam spreads to 15 km diameter)• Arrival time must be measured to less than a nanosecond

The Link Equation

= one-way optical throughput (encountered twice)f = receiver narrow-band filter throughputQ = detector quantum efficiencynrefl = number of corner cubes in array (100 or 300)d = diameter of corner cubes (3.8 cm) = outgoing beam divergence (atmospheric “seeing”)r = distance to moon = return beam divergence (diffraction from cubes)D = telescope aperture (diameter)

• APOLLO should land safely in the multi-photon regime• Current LLR gets < 1 photon per 100 pulses• Even at 1% of expected rate, 1 photon/sec good enough for feedback

Differential Measurement Scheme

Corner Cube at telescope exit returns time-zero pulse

Same optical path, attenuated by 1010

Same detector, electronics Diffused to present identical

illumination on detector elements Result is differential over 2.5 seconds Must correct for distance between

telescope axis intersection and corner cube

Needle in a Haystack

Signal is dim (19th magnitude), while full moon is bright (–13th magnitude) 1013 contrast ratio

We must filter in every available domain Spectral: 1 nm bandpass gets factor of 200 Spatial: 2 square arcsec gets factor of 106

Temporal: detector is on for 100 ns every 50 ms This itself is factor of 5105

But can discriminate laser return from background at the 1 ns level5107 background suppression

In all, get about 1016 background suppression Yields signal-to-noise of 103

Systematic Error Sources We can cut the 50 mm random uncertainty (due mostly to moon

orientation) down to 1 mm with 2500 photons 2 minutes at 20 Hz and 1 photon per pulse

Systematic uncertainties are more worrisome Atmospheric delay (2 meter effective path delay) Deflection of earth’s crust by:

Ocean: even in NM, tidal buildup on CA coast few mm deflection Atmosphere: 0.35 mm per millibar pressure differential ground water: ???? Accurate modeling still needs to be done

Thermal expansion of telescope and retroreflector arrays Radiation pressure (3.85 mm differential signal) Implementation systematics

Detector illumination Strong signal bias Temperature-dependent electronic timing Observation schedule/sampling: danger of aliasing

Periodicity: Our Saving Grace If we don’t get all this supplemental metrology right, we’re still okay:

Our science signals are at discrete, well-defined frequencies Equivalence Principle signal at 29.53 days Other science via 27.55 day signal (eccentricity)

Meteorological influences are broadband Atmospheric, ground-water loading are random Even tides, ocean loading don’t have power at EP period Thermal effects are seasonal

Laser Mounted on Telescope

First Light: 7/24/05

First Results: 10/19/05!

Two night total: 4000 photons As many as the best previous station got in the last 3 years! Calculated distance agrees well with JPL model However, rate is slightly lower than expected and intermittent

100 ns

Future Work Optimization of signal, stabilize laser Software refinement/development Gravimeter/Precision GPS installation Precision geophysical modeling of site motion Sufficient data for order-of-magnitude improvement in

EP test in ~1 year Continued data collection/analysis for years to come

Summary• Many reasons to test gravity, much we still do not understand

• Is there a “Grand Unified Theory” that describes all fundamental interactions?• Is gravity causing the mysterious acceleration of our universe’s expansion?• Are there possibly more than 3 dimensions of space?

• We are entering a “Golden Age” of experimental gravity research• Laboratory torsion pendulum tests:

• Inverse-square law• Equivalence principle• more…

• Astronomical tests of General Relativity• APOLLO lunar laser ranging experiment

• Gravity wave experiments• LISA• LIGO

• Research is exciting for students of all levels

• So far Einstein is still correct… but for how long?

?