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Galileo Galilei Colloquium,Pisa,
March 3, 2006
Gerard ’t Hooft
Utrecht University
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BANG !!
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curvedspace andtime
heavy planet
Gravity = free fall in curved space-time
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A Black Hole
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Universe I
Universe II“Time” stands still at the horizon
So, one cannot travel from
one universe to the other
Black Hole
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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
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The Universe of thesub-atomic particles
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Quantum Mechanics
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?
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 ?
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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 :
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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
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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
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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
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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
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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 ?
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microscopic black holes
Where does the gravitational field become as strong as it ever can get ?
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negativeenergy
positiveenergy
horizon
Region I
Region II
3
HBH8
ckT
G Mp=
h
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65 2
One bit of
information
on every
cm0 724 10 -.
The black hole as an information processing machine
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Are black holes just“elementary particles”?
Black hole“particle”
Implodingmatter Hawking particles
Are elementary particles just “black holes”?
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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 ...
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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
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interaction
horizon
One must take interactions into account:
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b
By taking back reaction into account, one can obtain a unitary scattering matrix
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Particles and horizons, the hybrid picture
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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
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“Loop quantum gravity”
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The SuperString Theory
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y
Could the Planck length be muchlarger? Do “extra dimensions” exist ?
xy
4-d world on “D -brane”
Horizon of “Big Hole” “Little
Hole”
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Type IIAClosed Superstring
Super Gravityin 11 dimensions
Type IOpen Superstring
Type IIBClosed Superstring
Heterotic StringSO(32)
Heterotic StringE8 x E8
M - theory
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The Landscape
x
Our Universe ?
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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 ?
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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 ?
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The Cosmological Constant Problem
18( )Gg R L =
stretchability
very small stiffness
very large
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Super Nova Luminosity against Red Shift
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The cellular automaton
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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 ?
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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):
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What is the true nature of space and time ?
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