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
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 Deflection of light Shapiro time delay Perihelion advance Nordtvedt effect and lunar laser ranging Gyroscope precession & Gravity Probe B LAGEOS tracking Tests of the Strong Equivalence Principle Summary of bounds on the PPN Parameters
Light Bending and Alternative Gravitation Theories Deflection = Space Curvature GR =1 Cavendish 1784 von Soldner 1803 Einstein 1911 a b’c’ b c
The parameter (1+ )/2
Measuring light deflection using VLBI 541 quasars VLBI sites 1.7 million measurement S. S. Shapiro et al (2004)
PPN Equation of motion for a binary system
Mercury’s Perihelion: from Trouble to Triumph 1687 Newtonian triumph 1859 Leverrier’s conundrum 1900 A turn-of-the century crisis 575 “ per century CauseRate (per century) Venus278 ‘’ Earth 90 ‘’ Jupiter154 ‘’ Others 10 ‘’ Total532 ‘’ Discrepancy 43 ‘’ Modern value ‘’ GR Prediction ‘’
Tests of the Weak Equivalence Principle
GRAVITY PROBE B Goal 0.4 mas/yr Launch April 20, 2004 Mission ended Sept 2005
Gravity Probe B: The Experiment -- Payload
Gravity Probe B: The Experiment -- Gyroscopes
ParameterEffect or ExperimentBoundRemarks - 1 Time delay2.3 X Cassini tracking Light deflection4 X VLBI - 1 Perihelion shift3 X J 2 = 2 X Nordtvedt effect2.3 X LLR, < 3 X Earth tides10 -3 gravimeters Orbit polarization LLR 2 X J Spin precession4 X Sun axis Self-acceleration4 X Pulsar spindown --2 X Combined bounds Binary acceleration4 X PSR Newton’s 3rd law10 -8 Lunar acceleration --Not independent Bounds on the PPN Parameters =4 -y-3-10 /3- 1 +2 2 /3-2 1 /3- 2 /3 Bound on scalar-tensor gravity: > 40,000