Unveiling Gravity Mysteries: From Earth to Cosmos

1. C.D. Hoyle for the Eöt-Wash Group at the University of Washington ? Testing Gravity from the Dark Energy Scale to the Moon and BeyondC.D. Hoyle

2. 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

3. Newton 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: +  r is distance between two bodies of mass M1 and M2

4. More That We Know • 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/r2form 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 • ….

5. What we Don’t Know S. Carroll • 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?

6. A “Golden Age” for Gravitational Physics • 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

7. Short-Range 1/r2 Tests • 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.

8. R* 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: From G. Landsberg Moriond ’01 Talk

9. From Adelberger, et al., Ann. Rev. Nuc. Part. Phys. (2003) Parameterization and Background • General deviation from Newtonian gravity: • Until recently (last few years), gravitation not even shown to exist between test masses separated by less than about 1 mm!

10. 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

11. 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.

12. Torsion Pendulums thin fiber M1 M2 up r • 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

13. Fiber, 18m diameter, 80cm length, tungsten Leveling mechanism 3 aluminum calibration spheres 4 mirrors for measuring angular deflection 21-fold axial symmetry, molybdenum disc, 1mm thick s Not pictured: 10m thick Au-coated BeCu membrane - electrostatic shield Attractor :rotating pair of discs, shifted out of phase with each other to reduce Newtonian torque 2.75” Eöt-Wash Torsion Pendulum (best to date)

14. s 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

15. Noise Predicted thermal noise for Q = 3500 (internal dissipation) Data Readout Noise

16. Recent Results (Thesis of D. Kapner) ISL

17. 95% C.L. Bounds on ||

18. 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

19. New Promising Techniques • Vertical plate “Step Pendulum”: • Analytical expression for (very small) Newtonian background torque • Yukawa torque now falls as 2instead of 3 for small : • Drawbacks: • Minimum separation may not be so small • Possible Systematics at 1 R Modulate attractor plate/pendulum separation

20. Future High-sensitivity 1/r2 Test Top view: Attractor:“Infinite” plane 2mm thick MoHomogenous gravity field No change in torque on pendulum if 1/r² holds. Moves back and forth by 1mm Torsion pendulum Be, = 1.84 g/cm ³ • Advantages over hole pendulum: • True null test • Slower fall-off with (³ for holes vs. ² for plates) • Much larger signal • Simpler machining Pt, = 21.4 g/cm ³ Stretched metal membrane

21. Current and Future Limits Current Step pendulum

22. Shooting the Moon Testing General Relativity with Lunar Laser Ranging

23. 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) < 2.510-5 (Cassini) • (–1) < 1.110-4 (LLR)

24. 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 4.610-10 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 )

25. Sluggish orbit Nominal orbit: Moon follows this, on average Sun 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

26. The Strong Equivalence Principle • Earth’s energy of assembly amounts to 4.610-10 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 ≤4.510-4 LLR is the best way to test the strong EP

27. 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

28. LLR through the Decades Previously 100 meters APOLLO

29. 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

30. The APOLLO Collaboration UCSD: Tom Murphy (PI) Eric Michelsen Evan Million U Washington: Eric Adelberger Erik Swanson *Russell Owen *Larry Carey Humboldt State: C.D. Hoyle Liam Furniss Harvard: Christopher Stubbs James Battat JPL: Jim Williams Slava Turyshev Dale Boggs Jean Dickey Northwest Analysis: Ken Nordtvedt Lincoln Labs: Brian Aull Bob Reich

31. 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

33. Lunar Retroreflector Arrays Corner cubes Apollo 11 retroreflector array Apollo 14 retroreflector array Apollo 15 retroreflector array

34. 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)

35. 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

36. The Link Equation • = one-way optical throughput (encountered twice) f = receiver narrow-band filter throughput Q = detector quantum efficiency nrefl = 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

37. 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

38. 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 5105 • But can discriminate laser return from background at the 1 ns level5107 background suppression • In all, get about 1016 background suppression • Yields signal-to-noise of 103

39. 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

40. 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

41. Laser Mounted on Telescope

42. First Light: 7/24/05

43. 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

44. 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

45. 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? ?