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1C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Special and General Relativity:Einstein‘s New Views of Space and Time
Max-Planck-Institute for Physicsand
Ludwig-Maximilians-University, Munich
Christian Kiesling
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2C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
(December 1916)
Einstein‘s book for the public audience:
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3C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
„The mathematical Principles of Natural Philosophy"
Knowledge
The first modern experimentalist
HypothesisExperiment
TheoryGalileo Galilei
1564-1642
Newton‘sMechanics :The first moderntheory
Isaac Newton1642-1727
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4C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Newton‘s Law of Gravitation
Third Law of Kepler
Johannes Kepler (1571-1630)
M
311
26.673 10m
Gkg s
− ⎡ ⎤⎢ ⎥= × ⎢ ⎥⋅⎣ ⎦
2m MF GR⋅=
Gravitational constant
R
22 34T RGMπ=
revolution time
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5C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Newtonian Mechanics, Galilei-Transformation
train (system S‘)x x ′= +Δ
embankment (system S)
train 0v v= =S
x
S‘x ′
S
x
S‘x ′
Δ(analogously for und ) y z
Transformation of space coordinates:
train (still) at rest:
Transformation of velocity:
dxvdt
=
U
U ′Ball 0w w′ ′= =
w w ′=t t′ =
dxw
dt
′′ =
′
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6C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
( )x x t′= +Δ
w v=S
x
S‘
v
x ′
S
x
S‘
v
x ′
0w ′ =
x x vt′= +
( )t vtΔ =
t t′ =w w v′= +
Δ(t)
(constant velocity)
velocity of the ball, measuredfrom the embankment:
Newtonian Mechanics, Galilei-Transformation
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7C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Test of the Galilei-Transformation
0w ′ >
S
x
S‘
v
x ′
S‘
v
x ′
S‘
v
x ′
w w v′= +x x vt′= +
Now the ball is rolling in the trainagainst the train‘s direction ofmovement:let w v′ = −
Then the ball has to be at restin system S:
S
x
0w w v v v′= + = − + =
0w =
q.e.d.
The ball is rolling in the train along the train‘s direction of movement:
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8C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
The Principle of Relativity (A. Einstein, 1905)
( )F q E v B= ⋅ + ×
„The laws of Physics are independent of the frame of reference“(the frames of reference have constant relative velocities)
Fadenstrahlrohr
S
x
S‘
v
x ′
Example: the Lorentz force
A current-carrying wire generatesa magnetic field
An electron moving in a wire‘s B-Feldis pushed towards the wire No force on the electron
in system S‘ ???
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9C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
S
x
S‘
v
x ′
torch light
Example: the speed of light in different systems of reference
cc−c = speed of light
(~300.000 km/sec)
S
S
c c v
c c v+
−
= += −
???
Experiment by Michelson & Morley (1887)
„Light propagates with the same speedin all systems of reference“
(compare, e.g., air planes flying fromEast to West against West to East)
S
S
c c
c c+
−
==
The Principle of Relativity (A. Einstein, 1905)„The laws of Physics are independent of the frame of reference“
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10C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
The Special Theory of Relativity (A. Einstein, 1905)
w w v′ = −x x vt′ = −
2 21 /
x vtx
v c
−′ =−
2
2 2
/
1 /
t vx ct
v c
−′ =−
21
w vw
w vc
′ += ′
+
2
2 21 /
mcE
v c=
−
2 21 /
mvp
v c=
−Speed of light c now thesame in each frame of
referencec is also the largest
possible velocity
v c
y y′ =
z z′ =
0 :v = 2E mc=
Galilei-Transformationno longer valid for largevelocities
Instead: Lorentz-Transformation
w ′S
x
S‘
v
x ′
145 10mm
−Δ = ×
350 km/h:
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11C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Effects of the Special Theory of Relativity (I)
Matter (and anti-matter) from energy
Electron und anti-electron („Positron“) are producedfrom light (very energetic light particles, or „Photons“)
2E mc=
Direction of flightof the photon
Particle trackscurve in a magnetic field(Lorentz force)
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12C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Time-Dilation
2 21 /
tt
v c
′ΔΔ =
−
S
x
S‘
vx ′
U
U ′ Moving watches are running slower !
Surface of the earth
Boundary of atmosphere (~10 km height)
μ Lifetime of the muons: 2.2 sτ μ=
Range ~ 8 63 10 2.2 10cτ −= × × ×660m=
Examples: The twin paradox Muons from cosmic rays
Effects of the Special Theory of Relativity (II)
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13C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Contraction of length
2 21 /x x v c′Δ = Δ −S
x
S‘
vx ′
x ′Δ
xΔ
Effects of the Special Theory of Relativity (III)
Cavity seen by themoving electrons
Cavity seen by an electron at rest
Relativistic contraction of length (Lorentz-contraction)
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14C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
… and how a relativistic bicycle rider wouldperceive his environment ….
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15C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
STR: The World has 4 Dimensions: Space (3) and Time (1)
x
z
tEx
Et
Ez
„Event E“
… the best is still to come !
theGeneral Theory of
Relativity
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16C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
The extended („general“) Principle of Relativity
0dwdt
′≠
Sx
0dv
adt
= ≠
S‘x ′
Train is being accelerated:ball rolls backwards „by itself“
in a gravitationalfield
in an acceleratingrocket
… can one not always tell, which frame of referenceis the accelerated one ?
Einstein says: NO !!
(also in accelerated systems !!)„The laws of Physics are independent of the frame of reference“
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17C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Gravitation, Acceleration: The Principle of Equivalence
inertF m a= ⋅heavF m g= ⋅
inert heavm m=
heav
inert
ma gm
= ⋅
„Principle of Equivalence“
masses move oncurved trajectoriesin a GF
Straight linetrajectories:„free fall“
„No difference between accelerationand graviational field (GF)“:
General Relativity (GR)1915
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18C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Gravitation: Curved Trajectories in Space
Gravitational pull at the earth‘s surface: Mass M of Earth, distance R from the earth‘s center
2 29.81M m
g GR s
⎡ ⎤= = ⎢ ⎥
⎣ ⎦
Very different curvatures !
Free fall in the gravitational field:a curved trajectory !
Can they bededucedfrom a commonprinciple(„curvature of space-time“) ?
F m g= ⋅
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19C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
ct
Space-Time has aunique (local) curvature
„Worldline“ of the ball
Space and Time are united (4-dimensional World)
world line of the bullet
GTR: also light „falls“ in thegravitaional field, here:
[ ]151.4 10 m−×
lightray
10m
Matter curvesspace-time !
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20C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Light rays also move on curved trajectories …Marvellous experiment to verify GTR:
Arthur Eddington (& A. Crommins)Isle of Principe (Gulfe of Guinea, close to the coast of West Africa)
Einstein‘s prediction: 1.75 arc seconds
Total eclipse onMai 29, 1919
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21C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
An English Castle and the General Theory of Relativity …
… how it would look like, if the mass of planet Saturn, compressed to 10 m, stoodin front of it …
viewed through a „gravitational lens“
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22C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
… and here a „real“ gravitational lens …
The little blue „cigars“ arethe gravitationally distortedpictures of a single galaxybehind a massive clusterof galaxies in theforeground.
(picture taken by theHubble Space Telescope)
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23C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
GTR: the speed of clocks in a gravitational field(and in accelerated frames of reference)
L
Clock A sends one light pulse per second,received by clock B
1 1 /t L c=1. pulse needs time
2 2 /t L c=2. Pulse needs time
1L L< , because rocket has moved
2 1L L< , since rocket accelerates
Result: Clock A runs FASTER than clock B,(viewed from clock B).
GTR: same things happen for clocksin a gravitationsal field
Clocks on ground run slower thanclocks at high altitude
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24C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
GTR: Without it GPS would not work …Satellite-based„Global Positioning System“
Principle of GPS:Determination of location via time measurement of signals from satelliteto location (A).
satellite sends:own position, own clock reading
runtime: comparison of satellite clockwith own clock in A
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25C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Erde
~ 26000km
[ ]3900 /v m s≈ 2 effects: STR und GTR
satellite flies „fast“according to STR, its clock is running slowerthan the clock in A (viewed from A)
A
2 2 101 1 / 0.835 10 st t
v ct
−′Δ −Δ = − − = ×Δ
satellite flies „high“According to GTR, its clock is running fasterthan the clock in A (viewed from A)
105.28 10 st tt
−′Δ −Δ =− ×Δ
6 times as big!
[ ] [ ]13.3 cm sl tΔ = ×ΔError without GTR: (correponds to 500 m in one hour of measuring time!!!)
GTR: Without it GPS would not work …
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26C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
What Einstein did not foresee: The Expanding Universe
Edwin Hubble, 1929:All light from distant galaxiesis red-shifted („Doppler-effect“)
Einstein‘s equations of GRlead to a (non-static) expandingor contracting universe.
Einstein later:„The greatest blunder of my life“
The Universe expands !
1 172 8[ ]H kms Mpc− −= ±
He dismissed such a modeland introduced an additional„Cosmological Term“ intohis equations
Λ
v H d= ⋅ Hubble constant H
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27C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
0( ) ( )
( )
r t r R t
RH t
RdR
Rdt
=
=
⎛ ⎞⎟⎜ = ⎟⎜ ⎟⎝ ⎠
From Einstein‘s equations of GR: 2 2
2
2
83 3
4 33 3
R G KcR R
R G pR c
πρ
πρ
⎛ ⎞ Λ⎟⎜ = − +⎟⎜ ⎟⎜ ⎟⎝ ⎠
Λ⎛ ⎞⎟⎜= − + +⎟⎟⎜⎝ ⎠
( )r t
ρG
p
Newton‘s constant
energy (matter) density
pressure
0r
curvature parameter
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28C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Dark Matter in the Galaxies
Andromeda nebula, distance about 2 Mio light years
Rotational velocity of stars about 200 km/sec, Independent of radius
Galactic disc apparentlyembedded in a “halo” ofnon-luminous matter
New formof matter ?
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29C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Distant Supernovae
Supernovae arefarther away thanexpected frompresent rate of expansion of theUniverse
Expansionaccelerates !
White dwarfRed giant
Crab nebula,discovered in 1054by Chinese astronomers
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30C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
The Cosmic Microwave Background Radiation
…originating about 380.000 years afterthe Big Bang , 3000 °K
red-shifted over 13 Gy:2.72 °K
very isotropic (< 10-5)
discovered in 1964by A. Penzias andR. Wilson
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31C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Expansion History of the Universe
13.7GyBig Bang
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32C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
A New Form of Energy:
Dark Energy
CMB measurements:curvature of space-timeis close to zero(„flat Universe“):
„critical“ energy density3
crit. 4 protons/mρ ∼
crit.M
ρρ Λ
Ω = = Ω +Ω
1.02 0.02Ω = ±
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33C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
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34C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
:KR R=[ ]151.4 10 m−×
photon
gravitationalfield of Earth
10m
ctz
KR2
Mg G
R=
light cannot escape from such a stronggravitational field „black hole“
Examples
[ ]1SR cm=Earth:
[ ]1.5SR km=Sun:
View into the center of theMilky Way
83.6 10M ×∼ solar masses
„Schwarzschild-Radius“
Speculation: a massive Black Hole is loomingin the center of the Milky Way
2
2MR G
c=
SR
Gravity in the Extreme: Black Holes
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35C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Black Holes
The Center of our Milky Way
… within a few light yearsseveral 10.000 stars,circulating the galacticcenter (on Kepler-orbits).
The revolution times allowmeasuring the mass in thecenter
Result: a super-massiveBlack Hole in the center
the speculation : mostgalaxies have Black Holesin their centers
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36C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
electriccharge
0
0
0
±1
electriccharge
+2/3
-1/3
0
-1
„particles“: Spin ½(Fermions)
TheThe MicroMicro--CosmosCosmos: : ElementaryElementary ParticlesParticles
Masses of particles (in GeV):
0.1 1.5 175 0
0.1 0.5 5 0
>0 >0 >0 91
0.0005 0.1 1.8 80
„fields“:Spin 1(Bosons)
„Standard Model“of Particle Physics
remarkable symmetry !
Leptons
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37C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
The Fundamental Forces of Nature
Electroweak Interaction,Prediction of the Z0
“Grand Unified Theories”, prediction of Leptoquarks
Theory Of Everything ?
Fieldquantum
Range
Effects Gravity Radioactivity Electricity Nuclear Force
10-38 10-5 10-2 1
∞ ∞10-15 cm 10-13 cm
“Graviton” W + , W - Photon γ Gluon g
Gravitation Weak Electromag. Strong
Strength
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38C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
General Relativity and Quantum Mechanics
"Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us closer to the secret of the „Old One“. I, at any rate, am convinced thatHe is not playing at dice."
Einstein and Quantum Mechanics:
Macro-Cosmos (Universe):
Micro- Cosmos (particle physics):(or Gravitiy in extreme cases !) probabilistic theory
Quantum Mechanics
deterministic theory
General Relativity
xx p hΔ ⋅Δ ≥Heisenberg‘sUncertainty Relation
Both theories mutually incompatible
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39C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
Combine QM and GR: Superstring Theory
Relativistic Quantum Mechanics („Quantum Field Theory“):
particles (quarks, leptons) are „points“,have no spacial extension
Superstring Theory: particles are „extended strings“(open or closed)
time
Size of strings: 34~ 10 [ ]m−SST only consistent in10 space-time dimensions!
(6 space dimensions must be„curled up“ to describe thereal world)
Can we measure such shortdistances?
with present accelerators: 1810 [ ]m−>
time
e+
e−
μ+
μ−
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40C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
… The next Generation of Particle Colliders
LHC @CERN: 14 TeVpp 2007
ILC
>2015
: 500 GeVe e+ −
Do supersymmetric particles exist?
Are there extra dimensions of space?
What is Dark Matter ?
Einstein‘s dream of Unified ForcesDo all forces become one?
Can we solve the Mystery of Dark Energy?
How did the Universe come to be?
Where did all the antimatter go? … many open questions,waiting to be answered……..
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41C. Kiesling, MPI f. Physics, Munich, Einstein Forum, Lanzhou, China, 11.10.2005
proton-protoncollisionsat the LHC
(starting in2007)
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