Outline of the Lectures Lecture 1: The Einstein Equivalence Principle Lecture 2: Post-Newtonian Limit of GR Lecture 3: The Parametrized Post-Newtonian.

Outline of the LecturesOutline of the Lectures

Lecture 1: The Einstein Equivalence PrincipleLecture 2: Post-Newtonian Limit of GRLecture 3: The Parametrized Post-Newtonian FrameworkLecture 4: Tests of the PPN Parameters

Outline of the LecturesOutline of the Lectures

Lecture 1: The Einstein Equivalence PrincipleLecture 2: Post-Newtonian Limit of GRLecture 3: The Parametrized Post-Newtonian FrameworkLecture 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 TheoriesLight Bending and Alternative Gravitation Theories

Deflection =

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12 (1+ γ )1".7505 /d

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a + ′ b + ′ c = 180o

a + b + c = 180o − γ (0".875 /d)

SpaceCurvature

GR=1

Cavendish 1784von Soldner 1803Einstein 1911

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v → c

a

b’ c’

b c

The parameter (1+The parameter (1+)/2)/2

Measuring light deflection using VLBIMeasuring light deflection using VLBI

541 quasars1977-199987 VLBI sites1.7 million measurement

S. S. Shapiro et al (2004)

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ai = −mx i

r31− (2γ + 2β )

m

r+ γv 2 − (2 + α 1 − 2ς 2)

μ

r

⎡ ⎣ ⎢

+ 12 (6 + α 1 + α 2 + α 3)

μ

mv 2 − 3

2 (1+ α 2)μ

m(v ⋅ ˆ n )2 ⎤

⎦ ⎥

+m(x ⋅v)v i

r3(2γ + 2) −

μ

m(2 −α 1 + α 2)

⎡ ⎣ ⎢

⎤ ⎦ ⎥

m = m1 + m2 μ = m1m2 /m

PPN Equation of motion for a binary systemPPN Equation of motion for a binary system

Mercury’s Perihelion: from Trouble to TriumphMercury’s Perihelion: from Trouble to Triumph

• 1687 Newtonian triumph

• 1859 Leverrier’s conundrum

• 1900 A turn-of-the century crisis

575 “percentury

Cause Rate (per century)

Venus 278 ‘’

Earth 90 ‘’Jupiter 154 ‘’

Others 10 ‘’

Total 532 ‘’

Discrepancy 43 ‘’

Modern value 42.98 + 0.04 ‘’GR Prediction 42.98 ‘’

Tests of the Weak Equivalence PrincipleTests of the Weak Equivalence Principle

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

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