The End of Space and Time

7/29/2019 The End of Space and Time

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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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The End of Space and Time