Testing general relativity experimentally: Equivalence Principle Tests International Conference on General Relativity: Centennial Overviews and Future Perspectives Dec. 21 2015 ~ Dec. 23 2015, Ewha Womans University Testing general relativity experimentally: Equivalence Principle Tests Ki-Young Choi Seoul National University (Eotwash gravity group at the University of Washington)

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Outline Newton & Einstein’s Gravity Equivalence Principle Eötvös Parameter A Brief History of Equivalence Principle Tests The Equivalence Principle Test by Using a Torsion Balance Lunar Laser Ranging 4

Newton’s Gravity 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 M1 and M2 5

Einstein’s Gravity 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 …. 6

The Equivalence Principle 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 Equivalence Principle General Relativity Gravity Most of quantum gravity theories predicted the violation of the EP! 7

Tests of the Equivalence Principle classical view: establish bounds on the Eötvös parameter modern view: establish bounds on ,  for any plausible “charges” q, where Requirements for a good Equivalence Principle test uniform gravitational field test bodies that differ in important ways very sensitive differential accelerometer 8

A Brief History of Equivalence Principle Tests Galileo test h Are fall times equal? 9

A Brief History of Equivalence Principle Tests Newton-Bessel test l Are periods equal? 10

A Brief History of Equivalence Principle Tests Eötvös test ω θ R ε Are angles equal? 11

A Brief History of Equivalence Principle Tests Dicke’s idea : Using the Sun as a Source mass 12

Eötvös Parameter () Eöt-Wash 13

Equivalence Principle Torsion Pendulum 20 m diameter, 108 cm long tungsten fiber 4 Be & 4 Ti test masses (each 4.84 g) 4 mirrors for monitoring pendulum twist tuning screws for nulling mass moments to minimize effects of gravity gradients resonant frequency: 1.261 mHz quality factor: ~ 4000 decay time: ~ 12 days machining tolerance: 5 m total mass : ~ 70 g 5 cm 14

Principle of Experiment Composition dipole pendulum (Be-Ti) Source Mass Rotation 1 rev./ 20min 13.3min aBe aTi EP-violating signal Autocollimator (optical readout) source mass (m) local masses (hill) 1 - 104 entire earth 106 - 107 Sun 1011 - ∞ Milky Way (incl. DM) 1020 - ∞ 15

The Apparatus of the Equivalence Principle Test magnetic damper 16

Results Signal aNorth,Be-Ti aWest,Be-Ti as measured 2.0 ± 2.3 -1.2 PRL 100, 041101 (2008) Signal aNorth,Be-Ti (10-15 m/s2) aWest,Be-Ti as measured 2.0 ± 2.3 -1.2 Due to gravity gradients 1.6 0.2 0.3 1.7 Tilt induced 1.2 0.6 -0.2 0.7 Temperature gradients Magnetic coupling Corrected -0.8 3.0 -1.3 3.4 17

Eötvös parameter () Eöt-Wash 18

Apache Point Observatory Lunar Laser Ranging Operation (APOLLO) uses a 3.5-meter telescope and 532 nm Nd:YAG laser (100 ps pulse duration, 115 mJ/pulse, 20 Hz) 19

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Lunar Retroreflector Arrays Corner cubes Apollo 11 retroreflector array Apollo 14 retroreflector array Apollo 15 retroreflector array 21

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Historical LLR Accuracy 1-mm precision with a 7-picosecond round-trip travel-time error 23

Eötvös parameter () Eöt-Wash LLR 24

Acknowledgement Eric Adelberger Jens Gundlach Todd Wagner Stephan Schlamminger 25

Einstein Rules! despite amazing improvements in experimental sensitivity, no confirmed result disagrees with General Relativity yet many of us expect that some deviations must show up GR is not consistent with quantum mechanics unifying gravity with the rest of physics is the greatest challenge of fundamental physics!

Thanks for your attention

Gradiometer Pendulum q41 configuration q21 configuration installed 28