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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 :Quantum Gravity
LHC
The Universal Force Law:
nst 1 22
CQ Q
ForceR
Gravitation:
1 22
M MForce G
R
Distance
ForceMaxwell & YM:
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
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
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
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
The Black Hole
Electromagnetism: like charges repel, opposite charges attract → chargestend to neutralize
Gravity: like masses attract → masses tend to accumulate
horizon
Where is the gravitational field strongest? The formation of a Black Hole
even light cannot
escape from within this
region ...
Black Hole
The Schwarzschild Solution to Einstein’s equations
( )2
2 2 222
2 2 2d sid
d 1 d ( )d1
nMr M
r
rs t r q q j= - - + + +
-
Karl Schwarzschild1916
“Über das Gravitationsfeldeines Massenpunktes nachder Einsteinschen Theorie”
2
dd ;
2
2 2
2
r
r M
r M
r M
The Schwarzschild Solution to Einstein’s equations
( )2
2 2 222
2 2 2d sid
d 1 d ( )d1
nMr M
r
rs t r q q j= - - + + +
-
Karl Schwarzschild1916
“Über das Gravitationsfeldeines Massenpunktes nachder Einsteinschen Theorie”
Universe I
Universe II“Time” stands still at the horizon
So, one cannot travel from
one universe to the other
Black Hole
As seen by distantobserver
As
experienced by astro-
naut himself
They experience time differently. Mathematics tells usthat, consequently, they experience particles differently
as well
Time stands stillat the horizon
Continueshis waythrough
While emitting particles, the black hole loosesenergy, 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 ...
12
639
12
639
¬Black hole plus matter ® Heavier black hole
compare Hawking’s particle emission process with the absorption process:
→ Heavier black hole
In a black 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 twoprocesses, gives us the number of quantumstates !
2
Probability
| Amplitude| (Volume of Phase Space)
=
´
time reversal
symmetry (PCT):
forwards and
backwards in time:
the same
65 2
One bit of
information
on every
cm0 724 10 -.
The black hole as an information processing machine
The constant of integration: a few“bits” on the side ...
Are black holes just“elementary particles”?
Black hole“particle”
Implodingmatter
Hawking particles
Are elementary particles just “black holes”?
Entropy = ln ( # states ) = ¼ (area of horizon)
Dogma: We should be able to derive all propertiesof these states simply by applying General Relativityto 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 evolveinto a pure final state?
The calculation of the Hawking effect suggests thatpure states evolve into mixed states !
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 ...
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
How do we reconcile these with LOCALITY?
paradox
Black Holes require new axioms for thequantization of gravity
Unitarity,Causality, ...
paradox
Black Hole Quantum Coherence is realized in String/Membrane Theories !
-- at the expense of locality? -- How does Nature process information ?
BLACK HOLE WHITE HOLE
A black hole is a quantum superposition ofwhite holes and vice versa !!
The Difference between