Galileo Galilei Colloquium,Pisa,

March 3, 2006

Gerard ’t Hooft

Utrecht University

BANG !!

curvedspace andtime

heavy planet

Gravity = free fall in curved space-time

A Black Hole

Universe I

Universe II“Time” stands still at the horizon

So, one cannot travel from

one universe to the other

Black Hole

The part of the universe that we know contains about

particles

8010

Only a small fraction of them are of the kindthat build up the world that is familiar to us

The Universe of thesub-atomic particles

Quantum Mechanics

?

log( )m

24 / gp

10

Unification

0 2 4 6 8 10 12 14 16 18

20

30

40

50

60

x

SU (3)

xSU (2)

xU (1) Super Symmetry

SU (5)

Unification ?

1510 m

1810 m

2110 m

2410 m

2710 m

3010 m

3310 m

The highwa

y across the

desert

Today’sLimit …

GUTs

3510 mPlanck length :

photon graviton g

The PhotonSpin = 1 Spin = 2

PP PP

PPPP

PPPP

PP PP

Equal charges repel one another ...

Equal masses attractone another ...

The Graviton

Gravity becomes more importantat extremely tiny distance scales !

2

2

2 4

1

/

Wavelength

G

E h cM

hForce

c R

c

However, mass is energy ...

1 22

M MForce G

R

Planck Units

-12 34 sec m kg 100546.12/ h

11 3 1 2NG 6.672 10 m kg sec- -

33Planck 3

Planck

44Planck 5

1.616 10 cm

21.8 g

5.39 10 sec

N

N

N

GL

c

cM

G

GT

c

82.99792458 10 m / secc

MoonMoon

Moon

Earth

Sun 0 180 360o o o

strength of force This is the wave function of a spin 2 particle

Graviton

Force and spin

When gravity becomes strong:

- space-time fluctuations run out of control: infinities

- the definition of time becomes ambiguous: one cannot talk of “the state of the universe at a given time”.

- the universe might close into itself, in which case the use of quantum mechanics becomes ambiguous.

- notions such as “distance” and “locality” become ambiguous

super string theory?

Wheeler – DeWitt equ’n?

Statistics ofuniverses ?

Non-localtheories ?

bad understanding of UV region

bad understanding of probability and causality

the real universe isn’t closed ...

and what about reduction ?

microscopic black holes

Where does the gravitational field become as strong as it ever can get ?

negativeenergy

positiveenergy

horizon

Region I

Region II

3

HBH8

ckT

G Mp=

h

65 2

One bit of

information

on every

cm0 724 10 -.

The black hole as an information processing machine

Are black holes just“elementary particles”?

Black hole“particle”

Implodingmatter Hawking particles

Are elementary particles just “black holes”?

Region IRegion II

Horizon

The quantum states in regions I and II are coherent.

This means that quantum interference experiments in region I cannot be carried out without considering the states in region II

But this implies that the state in region I is not a “pure quantum state”; it is a probabilistic mixture of different possible states ...

Three competing theories:

1. No scattering, but indeed loss of quantum coherence

(problem: energy conservation)

2. After explosion by radiation: black hole remnant

(problem: infinite degeneracy of the

remnants)

3. Information is in the Hawking radiation

interaction

horizon

One must take interactions into account:

b

By taking back reaction into account, one can obtain a unitary scattering matrix

Particles and horizons, the hybrid picture

SuperSymmetry and SuperGravity

-1 -½ 0 ½ 11 1

1 11 1

1 11 2 1

1 2 1

1 2 1

1 4 6 4 1

1 11 1

1 2 1 1 2 1

1 4 6 4 11 4 6 4 1

1 8 28 56 70 56 28 8 1

N = 1

N = 2

N = 4

N = 1

N = 2

N = 4

N = 8

SUSY

SUGRA

-2 -1½ 1½ 2Spin along

z-axis

“Loop quantum gravity”

The SuperString Theory

y

Could the Planck length be muchlarger? Do “extra dimensions” exist ?

xy

4-d world on “D -brane”

Horizon of “Big Hole” “Little

Hole”

Type IIAClosed Superstring

Super Gravityin 11 dimensions

Type IOpen Superstring

Type IIBClosed Superstring

Heterotic StringSO(32)

Heterotic StringE8 x E8

M - theory

The Landscape

x

Our Universe ?

How do we reconcile this with LOCALITY?

paradox

All degrees of freedom of some section of the universe reside on its BOUNDARY

Unitarity,Causality, ...

paradox

Thie paradoxical behaviour is indeed reproduced in string / membrane

theories !-- at the expense of locality? --

How does Nature process information ?

Quantum Mechanics is usually seen as a blessing

Quantum Mechanics solves the problem of theUV divergence in thermal radiation (Planck, 1900)

But Quantum Mechanics generates new infinityproblems of its own at the Planck scale ...

Could Quantum Mechanics not be replaced bysomething better there ?

The Cosmological Constant Problem

18( )Gg R L =

stretchability

very small stiffness

very large

Super Nova Luminosity against Red Shift

The cellular automaton

How does God produce random numbers ?

Could these random numbers be actuallycreated by “ordinary” physical processesat the Planck scale?Determinism at the Planck length ( cm)Why not ?

3310

Simple-minded, “direct” approaches are doomed to fail.

Problem that keeps coming up:why is energy always positive ?

Energy is related to time.

If two systems are compared, both energiesmust be positive (but both being negative couldalso be allowed)

Modest discovery : such a constraint might comeabout if the two clocks are allowed to be non-synchronous (due to grav. fields), while we have

the following restriction:

1

2

0dt

dt

if time goes forward in one system, it mustalso go forward in the other (and vice versa):

What is the true nature of space and time ?