Gerard ’t HooftDublin

November 13, 2007

Utrecht University

on

CERN

LHC

LargeHadronCollider

* *

7 TeV + 7 TeV

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 :Quantum Gravity

LHC

The Universal Force Law:

nst 1 22

CQ Q

ForceR

Gravitation:

1 22

M MForce G

R

Distance

ForceMaxwell & YM:

General Relativity

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

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

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

The Black Hole

Electromagnetism: like charges repel, opposite charges attract → chargestend to neutralize

Gravity: like masses attract → masses tend to accumulate

horizon

Where is the gravitational field strongest? The formation of a Black Hole

even light cannot

escape from within this

region ...

Black Hole

The Schwarzschild Solution to Einstein’s equations

( )2

2 2 222

2 2 2d sid

d 1 d ( )d1

nMr M

r

rs t r q q j= - - + + +

-

Karl Schwarzschild1916

“Über das Gravitationsfeldeines Massenpunktes nachder Einsteinschen Theorie”

2

dd ;

2

2 2

2

r

r M

r M

r M

The Schwarzschild Solution to Einstein’s equations

( )2

2 2 222

2 2 2d sid

d 1 d ( )d1

nMr M

r

rs t r q q j= - - + + +

-

Karl Schwarzschild1916

“Über das Gravitationsfeldeines Massenpunktes nachder Einsteinschen Theorie”

Universe I

Universe II“Time” stands still at the horizon

So, one cannot travel from

one universe to the other

Black Hole

As seen by distantobserver

As

experienced by astro-

naut himself

They experience time differently. Mathematics tells usthat, consequently, they experience particles differently

as well

Time stands stillat the horizon

Continueshis waythrough

Stephen Hawking’s great discovery:the radiating black hole

negativeenergy

positiveenergy

horizon

Region I

Region II

3

HBH8

ckT

G Mp=

h

While emitting particles, the black hole loosesenergy, hence mass ... they become smaller.

Lighter (smaller) black holes emit more intense radiation than heavier (larger) ones

The emission becomes more and more intense,and ends with ...

12

639

12

639

¬Black hole plus matter ® Heavier black hole

compare Hawking’s particle emission process with the absorption process:

→ Heavier black hole

In a black hole:

If the heavier black hole could exist in much more quantum states than the lighter one, the absorption process would be favored ...

If the heavier black hole could exist in much fewer quantum states than the lighter one, the emission process would be favored ...

Comparing the probabilities of these twoprocesses, gives us the number of quantumstates !

2

Probability

| Amplitude| (Volume of Phase Space)

=

´

time reversal

symmetry (PCT):

forwards and

backwards in time:

the same

65 2

One bit of

information

on every

cm0 724 10 -.

The black hole as an information processing machine

The constant of integration: a few“bits” on the side ...

Are black holes just“elementary particles”?

Black hole“particle”

Implodingmatter

Hawking particles

Are elementary particles just “black holes”?

Entropy = ln ( # states ) = ¼ (area of horizon)

Dogma: We should be able to derive all propertiesof these states simply by applying General Relativityto the black hole horizon ... [ isn’t it ? ]

That does NOT seem to be the case !!

For starters: every initial state that forms a black hole generates the same thermal final state

But should a pure quantum initial state not evolveinto a pure final state?

The calculation of the Hawking effect suggests thatpure states evolve into mixed states !

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 ...

Alternative 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

How do we reconcile these with LOCALITY?

paradox

Black Holes require new axioms for thequantization of gravity

Unitarity,Causality, ...

paradox

Black Hole Quantum Coherence is realized in String/Membrane Theories !

-- at the expense of locality? -- How does Nature process information ?

The physical description of the difficulty ...

horizon

Here, gravitational interactions become

strong !!

brick wall

interaction

horizon

b

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

Black Hole Formation & Evaporation by Closed Strings

BLACK HOLE WHITE HOLE

A black hole is a quantum superposition ofwhite holes and vice versa !!

The Difference between

Particles and horizons, the hybrid picture