the confrontation between general relativity and experiment
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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 - PowerPoint PPT PresentationTRANSCRIPT
The Confrontation betweenThe Confrontation betweenGeneral Relativity and ExperimentGeneral Relativity and Experiment
Clifford WillWashington University, St. Louis
John Archibald WheelerInternational School on Astrophysical Relativity
The Confrontation betweenThe Confrontation betweenGeneral Relativity and ExperimentGeneral 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 TestingGround
J. A. Wheeler School
The Einstein Equivalence PrincipleThe Einstein Equivalence Principle
Test bodies fall with the same accelerationWeak 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
• locally ˜ symmetric g
• “comma” ˜ “semicolon
Gravity = Geometry
Tests of the Weak Equivalence PrincipleTests of the Weak Equivalence Principle
APOLLO (LLR) 10-13
Microscope 10-15(2008)
STEP 10-18 (?)
5th Force, Strings, Extra Dimensions and EEP5th Force, Strings, Extra Dimensions and EEP
•exchange of scalaror vector bosons ofmass m•ultra-small massfor long range effects•gravitational strengthcoupling
•Gravity “leaks” into extradimensions of macroscopic scale (1/r2 --> 1/rn)
Violation of EEP or Inverse Square Lawcould signal new physics
No evidenceto 1/100 of
gravity at 1 mm& to 1 X gravity
At 10 m
€
VAB (r)∝(1+ α ABe
−r
λ )
r
Tests of Local Lorentz InvarianceTests of Local Lorentz Invariance
•Clock comparisons•Clocks vs cavities•Time of flight of
high energy photons•Birefringence in
vacuum•Neutrino
oscillations•Threshold effects in
particle physics
Extended frameworks
by Kostelecky,Jacobson et al.
The Confrontation betweenThe Confrontation betweenGeneral Relativity and ExperimentGeneral 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 TestingGround
J. A. Wheeler School
ParameterWhat it measures, relative
to general relativityValue in
GR
Value in scalar
tensor theory
Value in semi-conservative
theories
How much space curvature produced by unit mass?
1(1+)/(2+)
How “nonlinear’’ is gravity? 1 1 +
Preferred-location effects? 0 0
Preferred-frame effects?
0 0
0 0
0 0 0
Is momentum conserved?
0 0 0
0 0 0
0 0 0
0 0 0
PPN Parameters and their SignificancePPN Parameters and their Significance
Light Bending and Alternative Gravitation TheoriesLight Bending and Alternative Gravitation Theories
Deflection =
€
12 (1+ γ )1".7505 /d
€
a + ′ b + ′ c = 180o
a + b + c = 180o − γ (0".875 /d)
SpaceCurvature
GR=1
Cavendish 1784von Soldner 1803Einstein 1911
€
v → c
a
b’ c’
b c
The parameter (1+The parameter (1+)/2)/2
Parameter Effect or Experiment Bound Remarks
- 1Time delay 2.3 X 10-5 Cassini tracking
Light deflection 4 X 10-4 VLBI
- 1Perihelion shift 3 X 10-3 J2 = 2 X 10-7
Nordtvedt effect 2.3 X 10-4 LLR, < 3 X 10-4
Earth tides 10-3 gravimeters
Orbit polarization10-4 LLR
2 X 10-4 J2317+1439
Spin precession 4 X 10-7 Sun axis
Self-acceleration 4 X 10-20 Pulsar spindown
-- 2 X 10-2 Combined bounds
Binary acceleration 4 X 10-5 PSR 1913+16
Newton’s 3rd law 10-8 Lunar acceleration
-- Not independent
Bounds on the PPN ParametersBounds on the PPN Parameters
=4-y-3-10/3-1+22/3-21/3-2/3
Bound on scalar-tensor gravity: > 40,000
Parameter Effect or Experiment Bound Remarks
- 1Time delay 2.3 X 10-5 Cassini tracking
Light deflection 4 X 10-4 VLBI
- 1Perihelion shift 3 X 10-3 J2 = 2 X 10-7
Nordtvedt effect 5 X 10-4 LLR, < 3 X 10-4
Earth tides 10-3 gravimeters
Orbit polarization10-4 LLR
2 X 10-4 J2317+1439
Spin precession 4 X 10-7 Sun axis
Self-acceleration 2 X 10-20 Pulsar spindown
-- 2 X 10-2 Combined bounds
Binary acceleration 4 X 10-5 PSR 1913+16
Newton’s 3rd law 10-8 Lunar acceleration
-- Not independent
Bounds on the PPN Parameters
=4-y-3-10/3-1+22/3-21/3-2/3
Bound on scalar-tensor gravity: > 40,000
GAIA (2011) 10-6
LATOR 10-8 BepiColombo (2012) J2 ~ 10-8
APOLLO 3 X 10-5
GRAVITY PROBE BGRAVITY PROBE B
Goal 0.4 mas/yrLaunch April 20, 2004
Mission ended Sept 2005
Gravity Probe B: The Experiment -- Payload
Gravity Probe B: The Experiment -- GyroscopesGravity Probe B: The Experiment -- Gyroscopes
The Confrontation betweenThe Confrontation betweenGeneral Relativity and ExperimentGeneral 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 TestingGround
J. A. Wheeler School
The Binary Pulsar: Gravitational Waves Exist!The Binary Pulsar: Gravitational Waves Exist!
Discovery: 1974Pulse period: 59 ms (16cps)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 (d/dt o/yr) 4.226595(5)
Pulsar Clock Shifts (ms) 4.2919(8)
Orbit Decay (dPb/dt 10-12) -2.4184(9)
Decay of the orbit of PSR 1913+16Decay of the orbit of PSR 1913+16
From Weisberg& Taylor(astro-ph/0407149)
The Binary Pulsar ZooThe Binary Pulsar Zoo
PSR 2127+11C•a clone of 1913+16PSR 1534+12•distance poorly known
J 1141-6545•0.19 day orbit•1 M0 WD companion•dPb/dt to 25%
J 0737-3039•0.10 day orbit•two pulsars seen!•d/dt = 17o/yr•sin i = 0.9995•dPb/dt to 6%
J 1756-2251•0.32 day orbit• d/dt = 2.6 o/yr•m2 < 1.25 Msun
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
A 3.6 million Msun black hole in the Milky Way
Genzel et al, Max Planck InstituteGhez et al, UCLA
Probing BH spacetime using starsProbing BH spacetime using stars
Next generation adaptive optics
telescopes (eg GRAVITY - VLTI)
10 as precision
faint stars
periods ~ 1 year
periholion 100 Rs
measure periholion shift, frame
dragging orbit precession
Imaging and Spectroscopy of Accretion DisksImaging and Spectroscopy of Accretion Disks
Evolution of Fe fluorescence lines during X-ray flare sensitive to M and J of BH Constellation-X mission
C. Reynolds, U. Md
High resolution imaging of hot spot in accretion onto BH at Galactic Center45º inclination a=0 and 0.998
Broderick & Loeb, CFA
QuickTime™ and aFLIC Animation decompressorare needed to see this picture.
QuickTime™ and aFLIC Animation decompressorare needed to see this picture.
The Confrontation betweenThe Confrontation betweenGeneral Relativity and ExperimentGeneral 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 TestingGround
J. A. Wheeler School
Interferometers Around The WorldInterferometers Around The WorldLIGO Hanford 4&2 km
LIGO Livingston 4 km
GEO Hannover 600 m
TAMA Tokyo300 m
Virgo Cascina 3 km
LISA: a space interferometer
for 2013
Inspiralling Compact Binaries - Strong-gravity GR tests?Inspiralling Compact Binaries - Strong-gravity GR tests?
Fate of the binary pulsar in 100 MyGW energy loss drives pair toward merger
LIGO-VIRGO Last few minutes (10K cycles)
for NS-NS40 - 700 per year by 2010BH inspirals could be more numerous
LISAMBH pairs(105 - 107 Ms) in galaxiesWaves from the early universe
Last 7 orbits
A chirp waveform
Compare measured shape with detailed predictions from GR
(parts per 106)[Scharre,Yunes,Berti,Buonanno &
CW]
Inspiralling Compact Binaries - Strong-gravity GR tests?Inspiralling Compact Binaries - Strong-gravity GR tests?
Fate of the binary pulsar in 100 MyGW energy loss drives pair toward merger
LIGO-VIRGO Last few minutes (10K cycles)
for NS-NS40 - 700 per year by 2010BH inspirals could be more numerous
LISAMBH pairs(105 - 107 Ms) in galaxiesWaves from the early universe
Last 7 orbits
A chirp waveform
Merging horizons, twisting
spacetime -computer
solutions of GR critical
Inspiralling Compact Binaries - Strong-gravity GR tests?Inspiralling Compact Binaries - Strong-gravity GR tests?
Fate of the binary pulsar in 100 MyGW energy loss drives pair toward merger
LIGO-VIRGO Last few minutes (10K cycles)
for NS-NS40 - 700 per year by 2010BH inspirals could be more numerous
LISAMBH pairs(105 - 107 Ms) in galaxiesWaves from the early universe
Last 7 orbits
A chirp waveform
Uniquely determined by M and S of hole - test of GR’s black
holes?[Berti,Cardoso & CW]
The Confrontation betweenThe Confrontation betweenGeneral Relativity and ExperimentGeneral 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 TestingGround
J. A. Wheeler School