Geen diatitel

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Utrecht University
BLACK HOLES
and
Quantum Physics
Gerard t Hooft Spinoza Institute, Utrecht
University
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The 4 Force Laws
Force
Distance
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Gravity becomes more importantat extremely
tiny distance scales !
However, mass is energy ...
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The highway across the desert
Quantum Gravity
GUTs
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Planck Units
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The Black Hole
Electromagnetism like charges repel,
opposite charges attract ? charges tend to
neutralize
Gravity like masses attract ? masses tend
to accumulate
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The Schwarzschild Solution to Einsteins
equations
Karl Schwarzschild 1916 Über das
Gravitationsfeld eines Massenpunktes nach der
Einsteinschen Theorie
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The Schwarzschild Solution to Einsteins
equations
Karl Schwarzschild 1916 Über das
Gravitationsfeld eines Massenpunktes nach der
Einsteinschen Theorie
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Black Hole
or wormhole?
Universe I
Universe II
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As seen by distant observer
As experienced by
astro- naut himself
Time stands still at the horizon
Continues his way through
They experience time differently. Mathematics
tells us that, consequently, they experience
particles differently as well
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Stephen Hawkings great discovery
the radiating black hole
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While emitting particles, the black hole
looses energy, hence mass ... it becomes
smaller.
Lighter (smaller) black holes emit more
intense radiation than heavier (larger) ones
The emission becomes more and more
intense, and ends with ...
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In a black hole
compare Hawkings particle emission process
with the absorption process
Black hole plus matter
Heavier black hole
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Probability
Amplitude 2 (Volume of Phase Space)
of the final states
time reversal symmetry (PCT) forwards and
backwards in time the same
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The black hole as an information processing
machine
The constant of integration a few bits
on the side ...
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Entropy ln ( states ) ¼ (area of
horizon)
Are black holes just elementary particles?
Are elementary particles just black holes?
Imploding matter
Hawking particles
Black hole particle
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Dogma We should be able to derive all
properties of these states simply by
applying General Relativity to the black
hole horizon ... isnt 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 !
?
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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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• Alternative 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)

• Information is in the Hawking radiation

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paradox
Unitarity, Causality, ...
?
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The physical description of the horizon
problem ...
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Here, gravitational interactions become
strong !!
brick wall
horizon
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interaction
horizon
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Particles and horizons, the hybrid picture
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Black hole complementarity principle
An observer going into a black hole can
detect all other material that went in,
but not the Hawking radiation
An observer outside the black hole can
detect the Hawking particles, but not all
objects that have passed the horizon.
Yet both observers describe the same
reality
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Elaborating on this complementarity principle
An observer going into a black hole treats
ingoing matter as a source of gravity,
but Hawking radiation has no gravitational
field.
An observer outside the black detects the
gravitational field due to the Hawking
particles, but not the gravitational fields
of the particles behind the horizon.
Yet both observers describe the same
space-time
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Space-time as seen by ingoing observer
Space-time as seen by late observer
outside
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This may be a conformal transformation of
the interior region Light-cones remain where
they are, but distances and time intervals
change!
An exact local symmetry transformation,
which does not leave the vacuum invariant,
unless
(the conformal transformation)
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This local scale invariance is a local U
(1) symmetry electromagnetism as originally
viewed by H. Weyl.
Fields may behave as a representation of
this U (1) symmetry.
????????
Is this a way to unify EM with gravity?
The cosmological constant (Dark energy)
couples directly to scales
Is this a way to handle the cosmological
constant problem?
???????????????
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By taking back reaction into account, one
can obtain a unitary scattering matrix
b
?
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Gravitational effect from ingoing objects
in
particles out
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Also for electro-magnetism
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The string world-sheet
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Black Hole Formation Evaporation by
Closed Strings
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The Difference between
A black hole is a quantum superposition
of white holes and vice versa !!
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Black holes and extra dimensions
4-d world on D -brane
Horizon of Big Hole
Little Hole
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These would have a thermal distribution
with equal probabilities for all particle
species, corresponding to Hawkings
temperature
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THE END