Transcript Geen diatitel - science.uu.nl project csg

Utrecht University
on
Gerard ’t Hooft
Dublin
November 13, 2007
CERN
LHC
Large
Hadron
Collider
**
7 TeV + 7 TeV
Quantum
Gravity
The
highway
across
the
desert
Today’s
Limit …
LHC
Planck length : 10 35 m
10 33 m
10 30 m
10 27 m
GUTs
10 24 m
10 21 m
10
18
10
m
15
m
The Universal Force Law:
Maxwell & YM:
Force
Q1  Q2
Force  C 
2
R
nst
Gravitation:
M1  M 2
Force  G 
2
R
Distance
General Relativity
M1  M 2
Force  G 
2
R
However, mass is energy ...
E
h/c
M 2 
c
Wavelength
2
Gh
1
Force  2  4
c
R
Gravity becomes more important
at extremely tiny distance scales !
h / 2    1.05461034 kg m2 sec-1
GN  6.672 1011 m3 kg-1 sec-2
c  2.99792458  108 m / sec
Planck Units
LPlanck 
GN

3
c
M Planck 
c
GN
TPlanck 
1.616  10 33 cm

21.8  g
GN

5
c
5.39  10 44 sec
The Photon
The Graviton
Spin = 2
Spin = 1
Equal masses attract
one another ...
Equal charges repel
one another ...
P
P
photon
P

P
graviton
P
P
P
g
P
Force and spin
Moon
Moon
strength of force
0o
180o
360o
Earth
Sun
This is the wave function
of a spin 2 particle
Graviton
Electromagnetism: like charges repel,
opposite charges attract → charges
tend to neutralize
Gravity: like masses attract
→ masses tend to accumulate
The Black Hole
Where is the gravitational field strongest?
The formation of a Black Hole
even light
cannot escape
from within this
region ...
horizon
The Schwarzschild Solution to Einstein’s equations
2
d
r
2
2
2
2
ds 2 = - (1 - 2rM )dt 2 +
+
r
(
d
q
+
si
n
q
d
j
)
2
M
1- r
Karl Schwarzschild
1916
“Über das Gravitationsfeld
eines Massenpunktes nach
der Einsteinschen Theorie”
dr
d ;
r  2M
   2 r  2M
 2  r  2M
The Schwarzschild Solution to Einstein’s equations
2
d
r
2
2
2
2
ds 2 = - (1 - 2rM )dt 2 +
+
r
(
d
q
+
si
n
q
d
j
)
2
M
1- r
Karl Schwarzschild
1916
“Über das Gravitationsfeld
eines Massenpunktes nach
der Einsteinschen Theorie”
Black Hole
Universe I
“Time”
stands still
at the
horizon
Universe II
So, one cannot travel from
one universe to the other
As seen by distant
observer
Time stands still
at the horizon
As
experienced
by astronaut
himself
Continues
his way
through
They experience time differently. Mathematics tells us
that, consequently, they experience particles differently
as well
Stephen Hawking’s great discovery:
the radiating black hole
kT H
hc 3
=
8pG M BH
horizon
Region I
Region II
negative
energy
positive
energy
While emitting particles, the black hole looses
energy, 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 ...
In a black hole:
compare Hawking’s particle emission process
with the absorption process:
9
12
6
3
Black hole plus matter
9
12
6
3
→
¨
Heavier
Heavierblack
blackhole
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 two
processes, gives us the number of quantum
states !
P robability
2
| Amplitude | ´
=
(Volume of P hase Space)
The black hole as an information processing machine
One bit of
information
on every
0. 724  10 - 65 cm2
The constant of
integration: a few
“bits” on the side ...
Entropy = ln ( # states ) = ¼ (area of horizon)
Are black holes just
“elementary particles”?
Imploding
matter
Are elementary particles
just “black holes”?
Hawking particles
Black hole
“particle”
Dogma: We should be able to derive all properties
of these states simply by applying General Relativity
to 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 evolve
into a pure final state?
The calculation of the Hawking effect suggests that
pure states evolve into mixed states !
Horizon
Region II
Region I
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
Black Holes require new axioms for the
quantization of gravity
How do we reconcile these with LOCALITY?
paradox
Unitarity,
Causality,
...
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 ...
Here, gravitational interactions
become strong !!
horizon
brick
wall
interaction
horizon
By taking back reaction into account, one can
obtain a unitary scattering matrix
b
Black Hole Formation & Evaporation by Closed Strings
The Difference between
BLACK HOLE
WHITE HOLE
A black hole is a quantum superposition of
white holes and vice versa !!
Particles and horizons, the hybrid picture