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Recent Progressand Future Developmentsin Gravitational Physics
Gerhard Schäfer
Institute for Theoretical PhysicsFriedrich-Schiller-University Jena
www.tpi.uni-jena.de
Budapest, 29. August 2002
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Contents
The most Fundamental Principles in Physics
Testing the Principle of Lorentz Invariance
Testing the Equivalence Principle
Universality of Free Fall
Universality of Gravitational Red Shift
Predictions of General Relativity
Evidence for Black Holes
Detection of Gravitational Waves
Cosmology
Beyond General Relativity
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The Principle of Lorentz Invariance
Universal constant: speed of light
Resulting framework: Special Theory of Relativity
Unification of space and time:
spacetime
Fundamental Principles in Physics
2 2 2 2 2 2ds c dt dx dy dz
c
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The Principle of Equivalence of Gravitation and Inertia
Universal constant:
Resulting framework: General Theory of Relativity
Unification of inertia and gravity:
curved spacetime
Fundamental Principles in Physics
4
1 8
2
GR Rg T
c
4G c
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The Principle of Superposition of Microscopic States
Universal constant:
Resulting framework: Quantum Theory
Unification of particles and fields: quantum fields
Fundamental Principles in Physics
i H
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Principle of Lorentz Invariance
Robertson-Mansouri-Sexl line element (for )
Propagation of light:
anisotropy: Michelson-Morley
velocity dependence: Kennedy-Thorndike
anomal time dilation: Doppler shift
2 2 2 22
20
21( ) ( ) ( )g v g v gds c dt dx dv y dz
xv e
1 2g g
1 0g g
0 1g
2 0ds
2
20( 1)i ig v gv
c
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Principle of Lorentz Invariance
Method Accuracy Experiment
Isotropy cavity Müller et al 2002
Velocity independence
cavity Braxmaier et al 2002
Time dilation2 beam spectroscopy
Grieser et al 1994
0 0 91 2 2 10g g
0 0 51 0 2 10g g
0 70 1 8 10g
Future: OPTIS / DLR and SUMO / NASA:MM and KT 3 orders improvement
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OPTIS
OPTIS
• Michelson-Morley
• Kennedy-Thorndike
1
2
• Univ. grav. red-shift
1( )U x
2( )U x
to Sun
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Universality of Free Fall
Action of point mass
Violation of EP: fundamental field
Acceleration of mass 1:
cosmological value
c d
mc g dx dx
,m m
gg i3 311 132 2
i 131 13
G mm ma G
m r r
i 0 0 0, ,m m
2g A g
g
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Universality of Free Fall
Composition-dependent gravitational constant:
Eötvös coefficient:
gg 013 311 3
i i 01 3
ln1 with
mm mG
G m m
1 2 13 231 2 3
1 2 13 23
2 2a a G G
a a G G
13 23r r
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Loránd Eötvös (1848 - 1919)
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Universality of Free Fall
Method Accuracy Experiment
Pendula 10-3 Newton (1686)
Pendula 2 x 10-5 Bessel (1832)
Torsion balance 5 x 10-9 Eötvös, Pekar, Fekete (1922)
Torsion balance 10-11 Roll, Krotkov, Dicke (1964)
Torsion balance 10-12 Braginski, Panov (1972)
Torsion balance 10-12 Adelberger et al. (1994)
Earth-Moon motion 5 x 10-13 Williams et al. (1996)
future
Free fall in orbit 10-15 MICROSCOPE (2005)
Free fall in orbit 10-17 GG
Free fall in orbit 10-18 STEP
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Universality of Gravitational Red Shift
Gravitational Red shift: Clocks at larger distances from gravitating objects go faster than nearby clocks.
Universality of Gravitational Red Shift:All kinds of clocks show the same behaviour.
Interpretation: Universality of coupling of gravity to all kinds of particles and fields; constancy of the basic coupling parameters.
002
( ) ( )( ) 1 ( )
U x U xx x
c
GM
Ur
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Universality of Gravitational Red Shift
No universality (absolute measurement):
Comparison of two clocks (differential mmt.):
Zero in GR: Null test
cl0
02ock
( ) ( )( ) 1 ( )
U x U xx x
c
clock 2clock 1 clock 1
2clo
cck 2 clock
lo2
ck 1x
U
c
0x
x
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Universality of Gravitational Red Shift
Atomic (hf) clock H-maser Cs atomic clock Ion clock Atomic fountain clock
Cavity clock
Molecule clock (rotation, vibration)
2 ( )E f
L
rot,vib rot,vib ,e
p
mE f
m
c
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Universality of Gravitational Red Shift
ComparisonAccuracy
Experiment
Red Shift (H-maser) am (7 x 10-5)GP-A, Vessot et al 1980
(ACES: 2 ord. impr. pos.)
Mg – Cs (fine structure) dm 7 x 10-4 Godone et al 1995
Resonator – I2 (electronic) dm 4 x 10-2 Braxmaier et al 2002
Cs – H-Maser (hf) dm 2.1 x 10-5 Bauch et al 2002
2 1
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The Consequence: General Relativity
Lorentz Invariance
Universality of Free Fall
Universality of Grav. Red Shift
Equations for the metric: Einstein field equations
Gravity is Geometry(Riemann Geometry)
g
4
1 8
2
GR Rg T
c
geometry matter
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Predictions of General Relativity
1843: Perihelion shift (Mercury orbit)
1915: General Theory of Relativity
1919: Deflection of light (solar eclipse)
1960: Gravitational redshift (Mössbauer effect)
1967: Shapiro time delay (radar ranging to Mercury)
1974: Periastron shift (binary pulsar)
1978: Gravitational radiation damping (binary pulsar)
1987: Geodetic precession (Earth-Moon gyroscope)
1997: Lense-Thirring effect (LAGEOS satellites)
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Predictions of General Relativity
Perihelion shift
Sun
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Predictions of General Relativity
Deflection of light
Shapiro time delay
ApparentApparentpositionposition
TrueTruepositionposition
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Predictions of General Relativity
Gravitomagnetism (Lense-Thirring effect)
J
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Predictions of General Relativity
Binary pulsar
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Predictions of General Relativity
Effect Method ReferencePerihelion shift Mercury orbital motion Shapiro (1990)
Periastron shift binary pulsar Taylor (1993)
Deflection of light VLBI Lebach et al (1995)
Shapiro time delay Viking radar ranging Reasenberg et al (1979)
Geodetic precession lunar laser ranging Williams et al (1996)
Lense-Thirring effect satellite ranging Ciufolini et al (1997)
Gravitational radiation damping
binary pulsar Taylor (1993)
0.9996 0.0017 0.9997 0.0005
accuracy for strong field effects: 0.03% evidence for gravitational waves
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The Metric
2222
00 2 2 2
0 3 3
222
2 2
21 1 3cos 1 2
2
1
21 1 3cos 1
2
ii
ij ij
GM JR GMg
rc r rc
GJ rg
rc
GM JRg
rc r
NewtonNewton
quadrupole momentnon-linearity
NewtonNewton
quadrupole moment
rotation
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Future Test: GP-B (NASA)
Scientific objectives
Test of frame dragging to 0.1% accuracy
Test of geodetic precession to 0.001% accuracy
Launch: 2003
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Evidence for Black Holes
Black Hole horizon
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Evidence for Black Holes
X-Ray Source Name Mass of Companion Mass of Black Hole
Cygnus X-1 24 – 42 11 – 21
V404 Cygni ~ 0.6 10 –15
GS 2000+25 ~ 0.7 6 – 14
H 1705-250 0.3 – 0.6 6.4 – 6.9
GRO J1655-40 2.34 7.02
A 0620-00 0.2- 0.7 5 – 10
GS 1124-T68 0.5 – 0.8 4.2 – 6.5
GRO J042+32 ~ 0.3 6 – 14
4U 1543-47 ~ 2.5 2.7 – 7.5
R. Blandford & N. Gehrels (1999)
Stellar Black Hole Candidates in the Milky Way
MMass in units of
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Evidence for Black Holes
Name Mass Method
M87 2 x 109 stars + optical disc
NGC 3115 109 stars
NGC 4486 B 5 x 108 stars
NGC 4594 (Sombrero) 5 x 108 stars
NGC 3377 8 x 107 stars
NGC 3379 5 x 107 stars
NGC 4258 4 x 107 masing H2O disc
M 31 (Andromeda) 3 x 107 stars
M 32 3 x 106 stars
Galactic Centre 2.5 x 106 stars + (3-D motions)
Supermassive Black Hole Candidates
M.J. Rees (1997)MMass in units of
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Detection of Gravitational Waves
Resonant bar detectors
• ALLEGRO (Louisiana/USA)
• AURIGA (Legnaro/Italy)
• NAUTILUS (Frascati/Italy)
• EXPLORER (CERN)
• NIOBE (Perth/Australia)
Laserinterferometric detectors
Earth-based
• LIGO (USA)
• VIRGO (France - Italy)
• GEO600 (Germany - UK)
• TAMA300 (Japan)
Space-borne
• LISA (ESA - NASA)
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Detection of Gravitational Waves
h
l 2
hl l
proton
1000
rl
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Detection of Gravitational Waves
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Detection of Gravitational Waves
h
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ESA-NASA mission: LISA
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Cosmology
Friedmann-Lemaître Universes:
4
1 8
2
GR Rg g T
c
Cosmological Constant
2 2 2 2 2( )ds c dt R t d
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Cosmology
Curvature
Hubble parameter
Deceleration parameter
2 0, 1K k R k
H R R 2q R RH
t
A A A ABBBB ( )R t( )R t( )R t( )R t
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Cosmology
11
2M K Mq
M crit
2
2
3
K
H
K H
2crit
29 3
65 km/s Mpc
3 /8
10 g cm
H
H G
0p
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Cosmology
.Present values
CMB and GRS
0.11 0.40
0.65 0.85
( 0.05) ( 0.04)
( 0.79) ( 0.45)
M
K
q
AcceleratingUniverse !
X. Wang et al (2001)
Efstathiou et al (2001)
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Cosmology
. SN -Ia: 1.3 0.45M
Leibundgut (2001)
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Beyond General Relativity
Unification of Gravity with Electro-Weak and Strong Interactions
Observation: General Relativity
is effective theory (low-energy limit):
: vacuum-expectation value of fundamental field at the present epoch
- term is of vacuum-energy type with pressure
4
1 8
2
GR Rg g T
c
0 0, G
0 0 0
2vacc
2vac vacp c
vac2
8 G
c
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Beyond General Relativity
Unification-Ansatze: String and brane theories in
higher-dimensional spacetimes with non-trivial topologies
However, the effective cosmological constant is infinitesimal
by particle-physics standards
Quintessence scenarios (ad hoc)
4 32 2 46crit 10 GeVc c c
2 8c G
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The Future: Summary and Outlook
M I S S I O N S and E X P E R I M E N T S
Special Relativity and Foundations of General Relativity:
SUMO, OPTIS, PHARAO/ACES, HYPER; MICROSCOPE, GG, STEP
General Relativity:
GP-B; Gravitational Wave Detectors; GAIA
Cosmology:
Planck (CMB), SNAP (SN-Ia), DEEP (Redshift)
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