Download Gerard `t Hooft

Utrecht University
Gerard ’t Hooft
Galileo Galilei Colloquium,
Pisa,
March 3, 2006
Gravity =
free fall in curved space-time
curved
space and
time
heavy planet
A Black Hole
Black Hole
Universe I
“Time”
stands still
at the
horizon
Universe II
So, one cannot travel from
one universe to the other
The part of the universe that we know
contains about
80
10
particles
Only a small fraction of them are of the kind
that build up the world that is familiar to us
The Universe of the
sub-atomic particles
Quantum Mechanics
4p / g2
60
Unification
x
Super Symmetry
U (1)
?
50
40
30
SU (5)
SU (2)
x
20
10
Unification ?
SU (3)
x
0
2
4
6
8
10
12
14
16
18
log( m)
The
highway
across
the
desert
Planck length :10 35 m
10 33 m
10 30 m
GUTs
10 27 m
10 24 m
Today’s
Limit …
10 21 m
10 18 m
10 15 m
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
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
G N  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
Force and spin
Moon
Moon
strength of force
0o
180o
360o
Earth
Sun
This is the wave function
of a spin 2 particle
Graviton
When gravity becomes strong:
super string
theory?
- space-time fluctuations run out of control:
infinities
 bad understanding of UV region
- the definition of time becomes ambiguous:
one cannot talk of “the state of the Wheeler –
universe at a given time”.
DeWitt equ’n?
 bad understanding of probability and causality
- the universe might close into itself, in
which case the use of quantum mechanics
Statistics of
becomes ambiguous.
 the real universe isn’t closed ...
universes ?
- notions such as “distance” and “locality”
become ambiguous
Non-local
 and what about reduction ?
theories ?
Where does the gravitational field become
as strong as it ever can get ?
microscopic
black holes
kT H
hc 3
=
8pG M BH
horizon
Region I
Region II
negative
energy
positive
energy
The black hole as an information processing machine
One bit of
information
on every
0. 724  10 - 65 cm2
Are black holes just
“elementary particles”?
Imploding
matter
Are elementary particles
just “black holes”?
Hawking particles
Black hole
“particle”
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 ...
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
One must take interactions into account:
interaction
horizon
By taking back reaction into account, one can
obtain a unitary scattering matrix
b
Particles and horizons, the hybrid picture
SuperSymmetry and SuperGravity
-2 -1½ -1 -½ 0 ½ 1 1½ 2
N=1
1
1
1
2
1
2
1
1
4
6
N=2
N=4
N=1
1
1
N=2
1
2
1
1
4
6
N=4
N=8
1
1
1
1
1
8 28
4
56
1
1
1
2
1
1
4
1
SUSY
1
1
1
2
1
6
4
1
70 56 28
8
1
1
1
4
Spin along
z-axis
SUGRA
“Loop quantum gravity”
The SuperString Theory
Could the Planck length be much
larger? Do “extra dimensions” exist ?
4-d world on
“D -brane”
y
y
x
Horizon of
“Big Hole”
“Little Hole”
Super Gravity
in 11 dimensions
Type I
Heterotic String
SO(32)
Open Superstring
M - theory
Type IIA
Closed Superstring
Heterotic String
E8 x E8
Type IIB
Closed Superstring
The Landscape
Our Universe ?
x
All degrees of freedom of some section of
the universe reside on its BOUNDARY
How do we reconcile this with LOCALITY?
paradox
Unitarity,
Causality,
...
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 the
UV divergence in thermal radiation (Planck, 1900)
But Quantum Mechanics generates new infinity
problems of its own at the Planck scale ...
Could Quantum Mechanics not be replaced by
something better there ?
The Cosmological Constant Problem
L=
stretchability
very small
g( 
1
8 G
R)
stiffness
very large
Super Nova Luminosity against Red Shift
The cellular automaton
How does God produce random numbers ?
Could these random numbers be actually
created by “ordinary” physical processes
at the Planck scale?
33
Determinism at the Planck length (10
cm)
Why not ?
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 energies
must be positive (but both being negative could
also be allowed)
Modest discovery : such a constraint might come
about if the two clocks are allowed to be nonsynchronous (due to grav. fields), while we have
the following restriction:
if time goes forward in one system, it must
also go forward in the other (and vice versa):
dt1
0
dt2
What is the true nature of space
and time ?