of 92
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The End of Space and Time
Robbert Dijkgraaf
University of Amsterdam
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Galileos `Book of Nature
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Galileo GalileiIl Saggiatore
The Book of Nature
The universe cannot be read
until we have learned thelanguage and become familiarwith the characters in which it
is written. It is written inmathematical language, and theletters are triangles, circles and
other geometrical figures,without which means it is
humanly impossible tocomprehend a single word.
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To those who do not know mathematics itis difficult to get across a real feeling as tothe beauty, the deepest beauty, of nature ...
If you want to learn about nature,to appreciate nature, it is necessary tounderstand the language that she speaks
in.
Anonymous
Mathematician
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If all mathematics disappeared today,
physics would be set backexactly one week.
.
Anonymous
Mathematician
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That was the week
that God created the world.
Richard Feynman
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Universe
Relativity
Particles
Quantum
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Space
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Absolute, true and
mathematical time, of itself,
and by its own nature, flows
uniformly on, without regard
to anything external.
- Newton
Time
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Time is the fourth dimension
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time
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Mass curves space and time
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Gravity = Curvature of Space-Time
Mass = Energy
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Physics is Geometry
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My biggestblunder!
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Hubble, 1929
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1965: Penzias & Wilson
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Cosmic Microwave Background
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WMAP Sattelite (2003)
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Very Early Universe
First Light,400,000 yr after Big Bang
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Why is the Universe
so flat, large, and full of structure?
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Cosmic Inflationt = 10-35 ~ 10-32 s
Scale 1026
Big Bang
quantum
classical
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The Quantum World
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Black Box
?in uit
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in uit
Black Box
?
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Standard Model
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u
u
u
d
d
d u
u
u
d
d
d
e
e
Grand Unified Theory?
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Dark Matter
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Dark Matter
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Large Scale Structure of the Universe
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Supernovae (type Ia)
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Supernovae Survey
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> 0: Dark Energy
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73% dark energy
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73% dark energy
Weight of the Universe
23% dark matter
4% known matter
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Why is every electron
exactlythe same?
NATURES
ELECTRON
FACTORY
e
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There is only
one electron in
the universe!
John Wheeler
Richard Feynman
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time
Space-Time
++
+
+
+
-
- - --
-
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time
Virtual Particles
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time
Vacuum Fluctuations
l
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time
Vacuum Fluctuations
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Dark Energy
Quantum Space Time
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Universe
Relativity
Particles
Quantum
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QuantumGravity
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Strong
Force
Weak
Force
Electro
Magnetism Gravity
Energ
y(GeV)
Unification 1015
1010
105
1
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Space Time Foam
Planck length 10-35 m
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Max Planck
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}
Planck length
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Hierarchy of Scales
3510 m
510 m
2510 m
Hubble ScaleLifePlanck Scale
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Black Holes
G l ti Bl k H l
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Galactic Black Hole
Million of Suns
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Center of the Galaxy
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Imploding
Star
Time
Horizon
Singularity
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Time
Time
2nd Law Black Hole Thermodynamics
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2nd Law Black Hole Thermodynamics
1 2
A A A
black hole merger
Geometric Entropy = Area Horizon
Hawking Radiation
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Hawking Radiation
Horizon
Time
Thermal Radiation
Temperature = Surface Gravity
Evaporating Black Holes
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Imploding
Evaporating Black Holes
Quantum Black Hole Instable Particle
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Quantum Black Hole Instable Particle
[space,time] 0
It from bit
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It from bit
BH
horizon
Horizon
1 bit/Planck
2
Geometric Entropy
S = Area Horizon
= log(# quantum states)
Th H l hi i i l
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The Holographic principle
The information associatedwith a certain part of spacemay be (heuristically )represented as bits on thesurface surrounding it.
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String Theory
Black Holes in String Theory
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Closed strings
Black Holes in String Theory
Horizon
Black Hole
Open strings
O St i Y Mill G Th
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Open Strings: Yang-Mills Gauge Theory
O St i Y Mill G Th
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j
i
NN matrix of strings Aij
Open Strings: Yang-Mills Gauge Theory
Geometry is Emergent
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Geometry is Emergent
Low energy
Gravity
High energy
Large N
Gauge Theory
ADS/CFT Correspondence
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ADS/CFT Correspondence
Equivalence between
field theory on the
boundary and
gravity in the bulk
Holography
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g p y
Emergent Space Dimension
IR UVradial distance = energy scaleRenormalization Group Flow
Strings in Anti-de Sitter Space
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Strings in Anti de Sitter Space
G /G i D li
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gauge = gravity
Gauge/Gravity Duality
4 dim
Yang-Mills
5 dim
strings
St i
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= gravitygauge
Strings
QCD string fundamental
string
Th l h t iti
L T t
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= gravitygauge
Thermal phase transition
thermal
vacuum
confining
Low Temperature
Hi h T t
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High Temperature
=Black Hole
deconfining
Black Holes at Accelerators?
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Black Holes at Accelerators?
Quark Gluon
Plasma
Erik Verlinde (2009)
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Erik Verlinde (2009)Gravity as an Entropic Force
m
F
T
FD x =TD S
i f f h d i
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Entropic force of thermodynamics
Entropic force due to the tendency for
entropy to increase
Polymer molecule
i i f L
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Derivation of Newtons Laws
m
F
T
FD x =TD SD S= 2p kcmD xT=
2p cka
F=ma
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Beauty
Reduction
Garbage
Standard Model
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Emergence
Navier-Stokes
HydrodynamicsH2O
BeautyGarbage
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Space-Time
Geometry
Quantum
Information
Emergence
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