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Fundamental physics in our time

Gerhard SchäferInstitute of Theoretical Physics

from quantum to cosmos(2), bremen, june 10 - 13, 2007

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from quantum to cosmos

In 1968 J. Schwinger formulated

empirical scaling laws that interconnect

the cosmos, the laboratory, and the atoms

,

Does the quantum stabilize the cosmos?

Gm hg

2

1~

1 p

M kg

kg m

2 2

2~p

p

Gm

R m R

2

1~

1 / p

R cm

cm m c

56 22

110 cm

R

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from quantum to cosmos

empirical law (Zel`dovich 1967/68):

Gm hg

21

~p

p

Gm

c m c

23810pGm

c

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goals of fundamental physics (FP)

FP is exploring the basic aspects of Nature Space and time Particles and fields

FP aims at Finding more comprehensive concepts and laws Testing the existing ones Resolving basic inconsistencies

FP includes Unification of the fundamental forces Discovery of new particles and fields Test of GR and of the equivalence principle Verification and exploration of black holes Detection and observation of gravitational waves

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current problems in FP

Conceptual problems

Dark Energy & Dark Matter Big Bang & Inflation Black Holes Irreversibility of phys. proc.

Mathematical problems

Grav. waves astrophysics Global aspects of spacetime Unification of all forces Phase transitions

Experimental problems

Gravitational Waves Black Holes Big Bang & Inflation Dark Energy & Dark Matter

Need for Space MissionsNeed for Space Missions

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Why missions in space?

Space conditions

Infinitely long gravity-free environment

Large gravitational potential differences

Large velocity differences

Quiet environment

Straight view to the Universe

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frame theories

Special Relativity Einstein 1905

General Relativity Einstein 1915

Quantum Theory Heisenberg 1925Schrödinger 1926Dirac 1927

non-relativistic non-relativistic

relativisticrelativistic

c

c G

c

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special relativity (SR)

Fundamental principle: constancy of speed of lightc = universal constant

Unification of space and time: spacetime

Poincare´ group; causality cone

Proper time and action

299,792.458km secc

2

21 t

c

2i S m c

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general relativity (GR)

Fundamental principle: Equivalence Principle

Unification of inertia and gravity: curved spacetime

Group of coordinate transformations; horizons

Proper time and spacetime metric

282

0.74 10 cm g 1.48 kmG

Mc

i g m m universally constant

00 02 ji ii ijg g g tc c c

00 2

21 ...

GMg

r c

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quantum theory (QT)

Fundamental principle: Superposition Principle

Unification of particles and waves: probability amplitudes

Unitary group; coherence

Antimatter

27 21.05 10 gcm s2

h

113.86 10 cm emc

2 2 1 1paths

, , iSr t r t e 2 2,r t

1 1,r t

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Spin in SR & GR & QT

SR: min. transvers. extension of body with mass m and spin S

GR: radius of ring singularity of Kerr BH

QT: Compton wavelength

QT: transversal extension of massless particle

Sa

mc

23

02z

x y

PR R

P

/ 22C mc

2

21

ac Sc

Gm m G

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dynamical theories

electrodynamics [U(1)]: photon quarks, leptons (charged) infinite range

weak int. th. [SU(2)]: Z-, W-bosons quarks, leptons

chromodynamics [SU(3)]: gluon

quarks

U(1) x SU(2) - unified theory [Higgs boson]

GR [GL(4)]: gravitation infinite range

1

137

610W

1S

310 fm

1 fm

3910G

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from microphysics to macrophysics

Transition from coherence to incoherence

Transition from time to temperature:

Arrow of time:

No quantization of time: negative prob.

iS S ke e 1t

ikT

[ , ]x ii x

[ , ]t i it

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GR and the quantum Unification of gravity with electro-weak and strong interaction

Observation: General Relativity

is effective theory (low-energy limit):

: vacuum-expectation value of fundamental field at present epoch

- term is of vacuum-energy type with pressure

0 0, G

0 0 0

2vacc

2vac vacp c

vac2

8 G

c

4

1 8

2

GR Rg g T

c

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GR and the quantum

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

4 32 2 46crit 10 GeVc c c

2 8c G

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cosmology

Curvature

Hubble parameter

Deceleration parameter

2 0, 1k R k

0H R R 2q R RH

t

A A A ABBBB ( )R t( )R t( )R t( )R t

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cosmology

11

2q

M crit

20

20

/ 3

,( 0)

H

H

0

2crit 0

29 3

65 km/s Mpc

3 /8

10 g cm

H

H G

0p

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Energy and Matter in the Universe

accelerated expansion at present epoch

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inflation area

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inflation - inflaton action of massive scalar field

action of 3-dimensional spaces (space-slices)

3 34 4

16 8

c cS R gd x gd x

G G

2 2

2 42

1

2

m cS g gd x

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`´square root`´ of GR square root of metric: tetrad field

invariance group: local Lorentz group [S0(3,1),SL(2,C)]

connection to SUSY (unification of fermions and bosons)

a b a bab abg g e e e e

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string theory action of point particle (m = m[i] = m[pg] = m[ag])

action of global part of 3-dimensional spaces

action of string

224 s

S Gd G X Xl

3 44 3

8 8

c cS gd x d x Ndt

G G

2S mc ds mc d

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the structure of gravity

Foundations of GR

Einstein‘s Equivalence Principle

• Univ. free fall• Lorentz invariance• Univ. grav. red shift• Constancy of fund. const.

metricgravity

g

MatterMatter Grav. fieldGrav. field

Geodetic eqnGeodetic eqn

Einstein field eqnEinstein field eqn

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equivalence principle (EP)

Why testing the EP in Space?

The EP is deduced from experimental facts by `infinite‘ extrapolation.

Present fundamental physics framework is incomplete. The most sensitive low-energy tests of new, gravity-

related theories are those involving the EP. There exist theoretical models which predict a violation of

the EP at a level that is smaller than the presently tested level of about 10-13 but could be within reach of a Space experiment.

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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

S c g dx dx m

,m m

g g 12 i1 2 21 2 2

i 121 12

m G m G ma

m r r

i 0 0 0, ,m m

2g A g

g

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test of EP – the concept

Why testing the EP in Space?

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the structure of gravity

Framework: PPN-formalism (variable G included)

2

00 2 4 7

0 3 6

2 5

2 21 ... ...

1(3 4 ) ... ...

22

1 ... ...

ii

ij ij

U U rrg

c c cV rr

gc c

U rrg

c c

gMetric gravity

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the structure of gravity

Non-cosmological effects of the gravitational field

2

00 2 4 7

0 3 6

2 5

2 21 ... ...

1(3 4 ) ... ...

22

1 ... ...

ii

ij ij

U U rrg

c c cV rr

gc c

U rrg

c c

g

• Perihelion shiftPerihelion shift

• Deflection of lightDeflection of light

• Grav. redshiftGrav. redshift

• Time delayTime delay

• GravitomagnetismGravitomagnetism

• Black holesBlack holes

• Gravitational wavesGravitational waves

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the binary pulsar

Hulse-Taylor pulsar (PSR B1913 + 16)

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polarization of gravit. wave in GR

h

l 2h

l l

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gravitational wave detectors in space

Fundamental Physics with gravitational-wave detectorsin space

Gravitational waves Black holes/strong-field GR

• direct confirmation of existence of Black Holes• Measurement of Lense-Thirring effect better than 1%

Cosmological background:• Direct signature of cosmic strings and/or inflation• Observation of conditions close to Big Bang

Measurement of total density of the Universe,determination of all dark matter

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black holes

Schwarzschild radiusSchwarzschild radiusHorizonHorizon

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Einstein-Rosen bridge

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Schwarzschild geometry

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GR and the quantum W. Israel in 2003:

You can pick anyone off the street and say `Einstein´.

They will at once write .

But if you ask what this formula means,

the response will be quite different.

At best, you may get some mumbling about `atomic bomb´.

It is sobbering that after a quarter-century we are in a hardly

better position regarding the formula

2E mc

BH 24 pl

k AS

l

3

2pl

66 22.6 10G

l cmc

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missions & main FP objectives

ASTROD, Bepi-Col., Gaia, LATOR, Cassini, GP-B, LAGEOS:

PPN-metric

ACES/PHARAO: PPN-metric, foundations of GR

GG, MICROSCOPE, POEM, STEP: equivalence principle

LISA: gravitational waves, black holes, big bang

Constellation-X: black holes, dark matter

Planck: dark matter, dark energy

GAUGE: unification of forces