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 Beyond C.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 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. 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: 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 +  r is distance between two bodies of mass M 1 and M 2

4. 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/r 2 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 …. 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/r 2 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

5. 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 ~10 40 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? 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 ~10 40 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 What we Don’t Know

6.  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/r 2 law and Equivalence Principle  Astronomical tests of General Relativity  Gravitational wave searches (LIGO, LISA, etc.)  Signatures of quantum gravity in high-energy collider experiments  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/r 2 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

7. 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. 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. Short-Range 1/r 2 Tests

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

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

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 Pendulum still the best instrument for measuring the ISL: Vary separation, r, between masses M 1 and M 2 Force on M 1 causes the pendulum to twist Measure twist angle Compare with inverse-square prediction Torsion Pendulum still the best instrument for measuring the ISL: Vary separation, r, between masses M 1 and M 2 Force on M 1 causes the pendulum to twist Measure twist angle Compare with inverse-square prediction M1M1 M2M2 thin fiber r up Torsion Pendulums

13. Eöt-Wash Torsion Pendulum (best to date) s Fiber, 18  m 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: 10  m thick Au-coated BeCu membrane - electrostatic shield 3 aluminum calibration spheres 4 mirrors for measuring angular deflection Leveling mechanism 2.75”

14. 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

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

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/r 2 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”: 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  R

20. Future High-sensitivity 1/r 2 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.

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) 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 = mc 2 ) Amounts to 4.6  10 -10 of earth’s total mass-energy Does this mass have M G /M I = 1.00000? Another way to look at it: gravity pulls on gravity This gets at the nonlinear aspect of gravity (PPN  ) 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 = mc 2 ) Amounts to 4.6  10 -10 of earth’s total mass-energy Does this mass have M G /M I = 1.00000? Another way to look at it: gravity pulls on gravity This gets at the nonlinear aspect of gravity (PPN  )

25. 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

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/r 2 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 Most sensitive test of 1/r 2 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 Harvard: Christopher Stubbs James Battat JPL: Jim Williams Slava Turyshev Dale Boggs Jean Dickey Lincoln Labs: Brian Aull Bob Reich Northwest Analysis: Ken Nordtvedt Humboldt State: C.D. Hoyle Liam Furniss

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): 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 14 retroreflector array Apollo 11 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 10 17 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 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 10 17 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 n refl = 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 10 10 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 (19 th magnitude), while full moon is bright (– 13 th magnitude) 10 13 contrast ratio We must filter in every available domain Spectral: 1 nm bandpass gets factor of 200 Spatial: 2 square arcsec gets factor of 10 6 Temporal: detector is on for 100 ns every 50 ms This itself is factor of 5  10 5 But can discriminate laser return from background at the 1 ns level  5  10 7 background suppression In all, get about 10 16 background suppression Yields signal-to-noise of 10 3 Signal is dim (19 th magnitude), while full moon is bright (– 13 th magnitude) 10 13 contrast ratio We must filter in every available domain Spectral: 1 nm bandpass gets factor of 200 Spatial: 2 square arcsec gets factor of 10 6 Temporal: detector is on for 100 ns every 50 ms This itself is factor of 5  10 5 But can discriminate laser return from background at the 1 ns level  5  10 7 background suppression In all, get about 10 16 background suppression Yields signal-to-noise of 10 3

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 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 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 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 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? 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? ?