Experimental Foundations of General Relativity

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Experimental Foundations of General Relativity

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Title: Experimental Foundations of General Relativity

1
Experimental Foundationsof General Relativity
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Rafael Lang
Monash University
Southern Hemisphere Spring 2002

2
Competing Theories of Gravity

Newton 1686

Poincaré 1890
Einstein 1912
Nordstrøm 1912
Nordstrøm 1913
Einstein and Fokker 1914
Einstein 1916
Whitehead 1922
Cartan 1923
Birkhoff 1943
Milne 1948
Thiry 1948
Papapetrou 1954
Fierz and Pauli 1939
Papapetrou 1954
Jordan 1955
Littlewood and Bergmann 1956
Brans and Dicke 1961
Yilmaz 1962
Whitrow and Morduch 1965
Whitrow and Morduch 1965
Kustaanheimo and Nuotio 1967
Deser and Laurent 1968
Page and Tupper 1968
Bergmann 1968
Nordtvedt 1970
Bollini, Giambiagi and Tiomno 1970
Wagoner 1970
Rosen 1971
Ni 1972
Ni 1972
Hellings and Nordtvedt 1972
Will and Nordtvedt 1972
Ni 1973
Yilmaz 1973
Lightman and Lee 1973
Lee, Lightman and Ni 1974
Rosen 1975
Belinfante and Swihart 1975
Lee et al. 1976
Bekenstein 1977
Barker 1978
Rastall 1979
Coleman (20thcentury)
Kaluza-Klein (20thcentury)
Overlooked (20thcentury)
3
Need Criteria for Viability

Basic conditions Theory must be
Complete
Self-consistent
Relativistic
Newtonian

4
Theories that fail already

Newton 1686

Test the Uniqueness of Free Fall (the Weak
Equivalence Principle)
All bodies fall with the same acceleration
Define test parameter

6
First Experiments

Newton (1686) uses Pendulum with different
compositions but equal masses
Eötvös 1922 uses torsion balance

7
Eötvös Experiment Principle

Centrifugal forces and other effects cause a
torque in the pendulum. This torque is modulated
with the rotation frequency.

?
m
m
g
8
Eöt-Wash Experiments

Most accurate experiments with sophisticated
torsion balances

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9
Upper limits on ?
10
Local Lorentz Invariance

The outcome of any local non-gravitational
experiment is independent of the velocity of the
freely-falling reference frame in which it is
performed
Well known from Special Relativity.
Violations would mean
Test parameter

11
Michelson-Morley Experiments

In various forms
Roundtrip or One-way propagation
Laser or Optical Fibre Link
Most accurate experiment compare phase of two
hydrogen maser clocks as fuction of Earths
orientation

12
Hughes-Drever Experiments

Search for galaxy-induced anisotropies in quantum
states of atoms
Drever 1961 Look for resonance in the four J2/3
ground states of the 7Li nucleus

13
Drever Experiment Data

Typical Oscilloscope Display

induced current
0
5
10
Time / s
14
Upper limits on ?
15
Local Position Invariance

The outcome of any local non-gravitational
experiment is independent of where and when in
the universe it is performed
Splits into
spatial invariance
invariance in time

16
PoundRebka Experiments

Examine the Gravitational Redshift to test the
Spatial Local Position Invariance
Compare acceleration of local Lorentz frames with
acceleration of test particles.

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17
Gravitational Red-Shift
ltBgt
ltAgt
gAH -
- gBH
hn
H
hn
ltBgt
ltAgt
Gravitating Body
18
Upper limits on a
19
Spatial variation of Constants

Get a spatial variation for nongravitational
constants
Finestructure constant

20
Constancy of Constants

Timelike aspect of the principle of Local
Position Invariance
The Oklo Natural Reactor gives for the fine
structure constant

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21
Einstein Equivalence Principle

Uniqueness of Free Fall
Local Lorentz Invariance
Local Position Invariance
How are those principles related?

22
Schiffs Conjecture
Uniqueness of Free Fall alone
Einstein Equivalence Principle
23
Plausible? Proofen?

Although principles seem to be independent
Mathematical formalism restricted by
Newtonian limit
Special relativistic limit
Experimental results
Some deeper connections likely to appear
Proof so far only within the TH??Formalism.

24
Schiffs Conjecture Example
ltAgt
WEP
H
Quantum State
LPI
Gravitating Body
25
Metric Theory Definition

Space-time is endowed with a symmetric metric
Trajectories of freely falling bodies are
geodesics of that metric

Einstein Equivalence Principle
Only Metric Theories viable
26
Universral (Metric) Coupling

All non-gravitational fields couple in the same
way to a single gravitational field
Gravity is a property of spacetime itself, not
just a field in spacetime
Space-time is curved

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27
Theories that violate EEP

Newton 1686

Main testing ground for gravitational physics is
the Solar System.
Take equations of any metric theory
Zeroth order expansion empty, flat space
First order expansion Newtonian physics
Second order terms Post-Newtonian effects

29
Parametrized Post-NewtonianFormalism (PPN)

Expand the metrics
Identify various potentials
They have 10 PPN parameters in front
Calculate those parameters
Compare with experiments

30
Strong Equivalence Principle

Generalized Uniqueness of Free Fall
All bodies fall with the same acceleration
Generalized Local Lorentz Invariance
All experiments are independent of the velocity
of the local Lorentz frame
Generalized Local Position Invariance
All experiments are independent of where and
when they are performed

31
Nordtvedt Effect

Violation of Generalized Uniqueness of Free Fall
Self-Gravitating bodies have different
accelerations
Polarization of Moons orbit
Depends on Nordtvedt Parameter
Shapiro 1976
Problem Only a combination of many parameters

32
Geophysical Measurements

Violation of Generalized Local Lorentz Invariance
? PPN parameter
Galaxy induced perihelion shift
Anisotropies in tides on Earth
Measurements on tides

33
Theories that violate GLLI

Newton 1686

Violation of Generalized Timelike Local Position
Invariance
Planets orbits (Shapiro 1970s)
? PPN parameters

35
Theories that violate GLPI

Newton 1686

This effect is (lt -1.75 arcsec)

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37
Deflection of Light Results

In General Relativity
First Experiment by Eddington with the total
solar eclipse 1919
Enough to rule out Newton, but not to
distinguish between alternative theories.

38
Theories that predict ?0 fail

Newton 1686

Locally speed of light is constant
But space-time curvature changes light path
? Globally effect appears as decrease in speed

Bending of Light
Artists Impression
Direct path
40
Shapiro Time Delay Results

Also depends on (
)
Use Very Long Baseline Interferometry and take
also Light Deflection into account to get

41
Time Delay Principle

Use data from radar or radio ranging experiments
Calculate orbit
from elongation data
(time delay neglible)
Compare with data
near superior conjunction
(strong time delay)

42
Unlikely Scalar-Tensor Theories

Newton 1686

Discovered by Le Verrier 1859
General Precession 5599.7 arcsec/century
Known contributions 5557.0 arcsec/century
Relativistic effect 42.7 arcsec/century
Today Radar measurements

44
Theories that fail

Newton 1686

Compare Einsteins Field Equations in relaxed
form with Maxwells Equations
Einstein
Maxwell
Expect gravitational effect produced by moving or
rotating matter Lense-Thirring Effect

46
Test Lens-Thirring Effect

LAGEOS satellites (2002) Effect exists
Gravity Probe-B (2003) Precise measurement with
Gyroscopes in
Low Polar Orbit

47
Current PPN Limits

Parameter Effect Limit
?-1 time delay 2 10-3
light deflection 3 10-4
?-1 perihelion shift 3 10-3
Nordtvedt effect 6 10-4
? Earth tides 1 10-3
?1 orbital polarization 2 10-4
?2 spin precession 4 10-7
?3 pulsar acceleration 2 10-20
?1 2 10-2
?2 binary acceleration 4 10-5
?3 Newton's third law 1 10-8
?4 (not independent)

48
Leaving Post-Newtonian Limit

Very difficult to obtain analytic solutions
? Compare experimental results with General
Relativistic calculations and look out for
inconsistencies

49
Binary Pulsar

Assume neutron stars orbiting
Neglect tidal interaction
Post-Keplerian Parameters
? Redshift and time delay
? Derivative of orbital period
? Rate of periastron advance
Feed ?,? in General Relativity Models
Then predict ?

BPSR191316
50
Binary Pulsar Test of GR
51
Theories that fail

Newton 1686

Newton 1686

General Relativity
2 modes
Scalar-Tensor Theories
3 modes
General Metric
up to 6 modes

54
Do we really need Aesthetics?

Malcolm MacCallum, 1976

... Unfortunately, any finite number of
effects can be fitted by a sufficiently
complicated theory. ... Aesthetic or
philosophical motives will therefore continue to
play a part in the widespread faith in Einstein's
theory, even if all tests verify its predictions.

55
Philosophical Aspect