1. Gravitation: Theories & Experiments Clifford Will James S. McDonnell Professor of Physics McDonnell Center for the Space Sciences Department of Physics Washington University, St. Louis USA http://wugrav.wustl.edu/people/CMW cmw@wuphys.wustl.edu Clifford M. Will and Gilles Esposito-Farèse Part 1

2. Outline of the Lectures Lecture 1: The Einstein Equivalence Principle Lecture 2: Post-Newtonian Limit of GR Lecture 3: The Parametrized Post-Newtonian Framework Lecture 4: Tests of the PPN Parameters

3. Outline of the Lectures Lecture 1: The Einstein Equivalence Principle  Review of dynamics in special relativity  The weak equivalence principle  The Einstein equivalence principle  Tests of EEP o Tests of WEP o Tests of local Lorentz invariance o Tests of local position invariance  Metric theories of gravity  Non metric theories of gravity  Physics in curved spacetime Lecture 2: Post-Newtonian Limit of GR Lecture 3: The Parametrized Post-Newtonian Framework Lecture 4: Tests of the PPN Parameters

4. Special Relativistic Electrodynamics

5. 400 CE Ioannes Philiponus: “ …let fall from the same height two weights of which one is many times as heavy as the other …. the difference in time is a very small one” 1553 Giambattista Benedetti proposed equality 1586 Simon Stevin experiments 1589-92 Galileo Galilei Leaning Tower of Pisa? 1670-87 Newton pendulum experiments 1889, 1908 Baron R. von Eötvös torsion balance experiments (10 -9 ) 1990sUW (Eöt-Wash) 10 -13 The Weak Equivalence Principle (WEP) Bodies fall in a gravitational field with an acceleration that is independent of mass, composition or internal structure

7. The Einstein Equivalence Principle (EEP)  Test bodies fall with the same acceleration Weak Equivalence Principle (WEP)  In a local freely falling frame, physics (non- gravitational) is independent of frame’s velocity Local Lorentz Invariance (LLI)  In a local freely falling frame, physics (non- gravitational) is independent of frame’s location Local Position Invariance (LPI)

8. Tests of the Weak Equivalence Principle APOLLO (LLR) 10 -13 Microscope 10 -15 (2008) STEP 10 -18 (?)

9. Lorentz non-invariant EM action Under a Lorentz transformation, eg

10. Tests of Local Lorentz Invariance

11. Light falling down a tower

12. Tests of Local Position Invariance ACES(2010) 10 -6

13. ConstantLimit (yr -1 )ZMethod <30 X 10 -16 0Clock comparisons <0.5 X 10 -16 0.15Oklo reactor  <3.4 X 10 -16 0.45 187 Re decay (6.4±1.4) X 10 -16 3.7Quasar spectra <1.2 X 10 -16 2.3Quasar spectra WW <1 X 10 -11 0.15Oklo reactor <5 X 10 -12 10 9 BBN m e /m p <3 X 10 -15 2-3Quasar spectra Tests of Local Position Invariance

14. Metric Theories of Gravity  Spacetime is endowed with a metric g   The world lines of test bodies are geodesics of that metric  In a local freely falling frame (local Lorentz, or inertial frame), the non-gravitational laws of physics are those from special relativity “universal coupling principle”

15. Metric theories, nonmetric theories and electrodynamics

18. The Th  Framework T, H, ,  are functions of an external static spherical potential U(r) Metric theory action iff with

19. Metric theories, nonmetric theories and electrodynamics

20. TH  Framework: Violation of WEP

21. TH  Framework: Violation of LLI

22. Standard Model Extension (SME) If the universe is fundamentally isotropic Clock comparisons Clocks vs cavities Time of flight of high energy photons Birefringence in vacuum Neutrino oscillations Threshold effects in particle physics Kostelecky et al D. Mattingly, Living Reviews in Relativity 8, 2005-5

23. Electrodynamics in curved spacetime

24. Outline of the Lectures Lecture 1: The Einstein Equivalence Principle Lecture 2: Post-Newtonian Limit of GR Lecture 3: The Parametrized Post-Newtonian Framework Lecture 4: Tests of the PPN Parameters