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