100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

216 C. M. Willcurvature; J is the angular momentum of the Earth, and v, n and r arethe velocity, direction, and distance of the gyroscope. The second line ineach case is the corresponding value for a gyroscope in polar Earth orbit atabout 650 km altitude (Gravity Probe B, Sec. 3.3).In general relativity, γ = 1, β = 1, and the remaining parameters allvanish.3.2. Bounds on the PPN parametersFour decades of experiments, ranging from the standard light-deflectionand perihelion-shift tests, to Lunar laser ranging, planetary and satellitetracking tests of the Shapiro time delay, and geophysical and astronomicalobservations, have placed bounds on the PPN parameters that areconsistent with general relativity. The current bounds are summarized inTable 1.To illustrate the dramatic progress of experimental gravity since thedawn of Einstein’s theory, Figure 3 shows a history of results for (1 + γ)/2,from the 1919 solar eclipse measurements of Eddington and his colleagues(which made Einstein a public celebrity), to modern-day measurements usingvery-long-baseline radio interferometry (VLBI), advanced radar trackingof spacecraft, and orbiting astrometric satellites such as Hipparcos. Themost recent results include a measurement of the Shapiro delay using theCassini spacecraft 48 , and a measurement of the bending of light via analysisTable 1.Current limits on the PPN parameters.Parameter Effect Limit Remarksγ − 1 (i) time delay 2.3 × 10 −5 Cassini tracking(ii) light deflection 3 × 10 −4 VLBIβ − 1 (i) perihelion shift 3 × 10 −3 J 2 = 10 −7 fromhelioseismology(ii) Nordtvedt effect 5 × 10 −4 η = 4β − γ − 3 assumedξ Earth tides 10 −3 gravimeter dataα 1 orbital polarization 10 −4 Lunar laser rangingPSR J2317+1439α 2 solar spin 4 × 10 −7 alignment of Sunprecessionand eclipticα 3 pulsar acceleration 2 × 10 −20 pulsar P ˙ statisticsη 1 Nordtvedt effect 10 −3 Lunar laser rangingζ 1 – 2 × 10 −2 combined PPN boundsζ 2 binary motion 4 × 10 −5 ¨P p for PSR 1913+16ζ 3 Newton’s 3rd law 10 −8 Lunar accelerationζ 4 – – not independent1 Here η = 4β − γ − 3 − 10ξ/3 − α 1 − 2α 2 /3 − 2ζ 1 /3 − ζ 2 /3