The Confrontation between General Relativity and Experiment Clifford
The Confrontation between General Relativity and Experiment Clifford Will Washington University, St. Louis John Archibald Wheeler International School on Astrophysical Relativity
The Confrontation between General Relativity and Experiment • Introduction • The Einstein Equivalence Principle • Solar-System Tests of GR • Binary Pulsar and Strong-Field Tests of GR • Gravitational Waves -- A New Testing Ground J. A. Wheeler School
The Einstein Equivalence Principle § 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) EEP ˜ Metric theory of gravity • hmn locally ˜ symmetric gmn • “comma” ˜ “semicolon Gravity = Geometry
Tests of the Weak Equivalence Principle APOLLO (LLR) 10 -13 Microscope 10 -15(2008) STEP 10 -18 (? )
5 th Force, Strings, Extra Dimensions and EEP • exchange of scalar or vector bosons of mass m • ultra-small mass for long range effects • gravitational strength coupling • Gravity “leaks” into extra dimensions of macroscopic scale (1/r 2 --> 1/rn) No evidence to 1/100 of gravity at 1 mm & to 1 X gravity At 10 mm Violation of EEP or Inverse Square Law could signal new physics
Tests of Local Lorentz Invariance Extended frameworks by Kostelecky, Jacobson et al. • Clock comparisons • Clocks vs cavities • Time of flight of high energy photons • Birefringence in vacuum • Neutrino oscillations • Threshold effects in particle physics
The Confrontation between General Relativity and Experiment • Introduction • The Einstein Equivalence Principle • Solar-System Tests of GR • Binary Pulsar and Strong-Field Tests of GR • Gravitational Waves -- A New Testing Ground J. A. Wheeler School
PPN Parameters and their Significance Parameter What it measures, relative to general relativity Value in GR Value in scalar tensor theory Value in semiconservative theories g How much space curvature produced by unit mass? 1 (1+w)/(2+w) g b How “nonlinear’’ is gravity? 1 1+L b x Preferred-location effects? 0 0 x 0 0 a 1 0 0 a 2 a 3 0 0 0 z 1 0 0 0 a 1 a 2 z 3 z 4 Preferred-frame effects? Is momentum conserved?
Light Bending and Alternative Gravitation Theories Deflection = a b’ c’ b §Cavendish 1784 §von Soldner 1803 §Einstein 1911 GR g=1 c Space Curvature
The parameter (1+g)/2
Bounds on the PPN Parameters Parameter g-1 b-1 x Effect or Experiment Bound Remarks Time delay 2. 3 X 10 -5 Cassini tracking Light deflection 4 X 10 -4 VLBI Perihelion shift 3 X 10 -3 J 2 = 2 X 10 -7 Nordtvedt effect 2. 3 X 10 -4 LLR, h < 3 X 10 -4 Earth tides 10 -3 gravimeters 10 -4 LLR 2 X 10 -4 J 2317+1439 a 1 Orbit polarization a 2 Spin precession 4 X 10 -7 Sun axis a 3 Self-acceleration 4 X 10 -20 Pulsar spindown z 1 -- 2 X 10 -2 Combined bounds z 2 Binary acceleration 4 X 10 -5 PSR 1913+16 z 3 Newton’s 3 rd law 10 -8 Lunar acceleration z 4 -- Not independent h=4 b-y-3 -10 x/3 -a 1+2 a 2/3 -2 z 1/3 -z 2/3 Bound on scalar-tensor gravity: w > 40, 000
Bounds on the PPN Parameters Parameter Effect or Experiment Bound Remarks Time delay 2. 3 X 10 -5 Cassini tracking Light deflection 4 X 10 -4 VLBI Perihelion shift 3 X 10 -3 J 2 = 2 X 10 -7 Nordtvedt effect 5 X 10 -4 LLR, h < 3 X 10 -4 Earth tides 10 -3 gravimeters 10 -4 LLR 2 X 10 -4 J 2317+1439 Spin precession 4 X 10 -7 Sun axis a 3 Self-acceleration 2 X 10 -20 Bepi. Colombo (2012) J 2 ~ 10 -8 Pulsar spindown z 1 -- 2 X 10 -2 Combined bounds z 2 Binary acceleration z 3 Newton’s 3 rd law z 4 -- g-1 b-1 x -6 polarization 10 Orbit a 1 GAIA (2011) LATORa 10 -8 2 X 10 APOLLO 3 X 104 -5 -5 10 -8 PSR 1913+16 Lunar acceleration Not independent h=4 b-y-3 -10 x/3 -a 1+2 a 2/3 -2 z 1/3 -z 2/3 Bound on scalar-tensor gravity: w > 40, 000
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
The Confrontation between General Relativity and Experiment • Introduction • The Einstein Equivalence Principle • Solar-System Tests of GR • Binary Pulsar and Strong-Field Tests of GR • Gravitational Waves -- A New Testing Ground J. A. Wheeler School
The Binary Pulsar: Gravitational Waves Exist! Discovery: 1974 Pulse period: 59 ms (16 cps) Orbit period: 8 hours 1993 Nobel Prize to Joe Taylor & Russell Hulse Parameter Value Keplerian Pulse Period (ms) 59. 029997929613(7) Orbit Period (days) 0. 322997448930(4) Eccentricity 0. 6171338(4) Post-Keplerian Periastron Shift (dw/dt o/yr) 4. 226595(5) Pulsar Clock Shifts (ms) 4. 2919(8) Orbit Decay (d. Pb/dt 10 -12) -2. 4184(9)
Decay of the orbit of PSR 1913+16 From Weisberg & Taylor (astro-ph/0407149)
The Binary Pulsar Zoo PSR 2127+11 C • a clone of 1913+16 PSR 1534+12 • distance poorly known J 0737 -3039 • 0. 10 day orbit • two pulsars seen! • dw/dt = 17 o/yr • sin i = 0. 9995 • d. Pb/dt to 6% J 1141 -6545 • 0. 19 day orbit • 1 M 0 WD companion • d. Pb/dt to 25% J 1756 -2251 • 0. 32 day orbit • dw/dt = 2. 6 o/yr • m 2 < 1. 25 Msun
Probing BH spacetime using stars A 3. 6 million Msun black hole in the Milky Way Next generation adaptive optics telescopes (eg GRAVITY - VLTI) § 10 mas precision § faint stars § periods ~ 1 year § periholion 100 Rs § measure periholion shift, frame dragging orbit precession Genzel et al, Max Planck Institute Ghez et al, UCLA
Imaging and Spectroscopy of Accretion Disks §High resolution imaging of hot spot in accretion onto BH at Galactic Center § 45º inclination § a=0 and 0. 998 C. Reynolds, U. Md §Evolution of Fe fluorescence lines during X-ray flare § sensitive to M and J of BH § Constellation-X mission Broderick & Loeb, CFA
The Confrontation between General Relativity and Experiment • Introduction • The Einstein Equivalence Principle • Solar-System Tests of GR • Binary Pulsar and Strong-Field Tests of GR • Gravitational Waves -- A New Testing Ground J. A. Wheeler School
Interferometers Around The World LIGO Hanford 4&2 km LIGO Livingston 4 km GEO Hannover 600 m Virgo Cascina 3 km TAMA Tokyo 300 m
LISA: a space interferometer for 2013
Inspiralling Compact Binaries - Strong-gravity GR tests? §Fate of the binary pulsar in 100 My §GW energy loss drives pair toward merger LIGO-VIRGO §Last few minutes (10 K cycles) for NS-NS § 40 - 700 per year by 2010 §BH inspirals could be more numerous LISA §MBH pairs(105 - 107 Ms) in galaxies §Waves from the early universe A chirp waveform Last 7 orbits Compare measured shape with detailed predictions from GR (parts per 106) [Scharre, Yunes, Berti, Buonanno & CW]
Inspiralling Compact Binaries - Strong-gravity GR tests? §Fate of the binary pulsar in 100 My §GW energy loss drives pair toward merger LIGO-VIRGO §Last few minutes (10 K cycles) for NS-NS § 40 - 700 per year by 2010 §BH inspirals could be more numerous LISA §MBH pairs(105 - 107 Ms) in galaxies §Waves from the early universe A chirp waveform Last 7 orbits Merging horizons, twisting spacetime computer solutions of GR critical
Inspiralling Compact Binaries - Strong-gravity GR tests? §Fate of the binary pulsar in 100 My §GW energy loss drives pair toward merger LIGO-VIRGO §Last few minutes (10 K cycles) for NS-NS § 40 - 700 per year by 2010 §BH inspirals could be more numerous LISA §MBH pairs(105 - 107 Ms) in galaxies §Waves from the early universe A chirp waveform Last 7 orbits Uniquely determined by M and S of hole - test of GR’s black holes? [Berti, Cardoso & CW]
The Confrontation between General Relativity and Experiment • Introduction • The Einstein Equivalence Principle • Solar-System Tests of GR • Binary Pulsar and Strong-Field Tests of GR • Gravitational Waves -- A New Testing Ground J. A. Wheeler School
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