Gerard t Hooft

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Gerard t Hooft
Utrecht University
CONTROVERSIES in PHYSICS at the PLANCK SCALE
Galileo Galilei Colloquium, Pisa, March 3,
2006
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BANG !!
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Gravity free fall in curved space-time
curved space and time
heavy planet
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A Black Hole
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Black Hole
Universe I
Universe II
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The part of the universe that we know
contains about particles
Only a small fraction of them are of the
kind that build up the world that is
familiar to us
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The Universe of the sub-atomic particles
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Quantum Mechanics
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Unification
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Super Symmetry
?
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SU (5)
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Unification ?
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0 2 4 6 8 10 12
14 16 18
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The highway across the desert
GUTs
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The Photon
The Graviton
Spin 2
Spin 1
Equal masses attract one another ...
Equal charges repel one another ...
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Gravity becomes more importantat extremely
tiny distance scales !
However, mass is energy ...
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Planck Units
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Force and spin
strength of force
Earth
This is the wave function of a spin 2
particle
Graviton
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super string theory?
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
? bad understanding of UV region
Wheeler DeWitt equn?
? bad understanding of probability and
causality
Statistics of universes ?
? the real universe isnt closed ...
Non-local theories ?
? 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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horizon
Region I
Region II
negative energy
positive energy
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The black hole as an information processing
machine
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Are black holes just elementary particles?
Are elementary particles just black holes?
Imploding matter
Hawking particles
Black hole particle
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Horizon
The quantum states in regions I and II
are coherent.
Region I
Region II
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
• 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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One must take interactions into account
interaction
horizon
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By taking back reaction into account, one
can obtain a unitary scattering matrix
b
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Particles and horizons, the hybrid picture
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SuperSymmetry and SuperGravity
Spin along z-axis
-2 -1½ 1½ 2
-1 -½ 0 ½ 1
1 1
N 1
1 1
1 1
1 1
SUSY
1 2 1
N 2
1 2 1
1 2 1
N 4
1 4 6 4 1
N 1
1 1
1 1
N 2
1 2 1
1 2 1
SUGRA
1 4 6 4 1
N 4
1 4 6 4 1
N 8
1 8 28 56 70 56 28 8
1
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Loop quantum gravity
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The SuperString Theory
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Could the Planck length be muchlarger? Do
extra dimensions exist ?
4-d world on D -brane
x
Horizon of Big Hole
Little Hole
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Super Gravity in 11 dimensions
Type I Open Superstring
Heterotic String SO(32)
M - theory
Type IIA Closed Superstring
Heterotic String E8 x E8
Type IIB Closed Superstring
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The Landscape
Our Universe ?
x
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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 ?
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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 ?
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The Cosmological Constant Problem
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 actually created by
ordinary physical processes at the Planck
scale? Determinism at the Planck length (
cm) Why not ?
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 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 non- synchronous (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)
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• What is the true nature of space
• and time ?

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