Desitter Public
Transcript of Desitter Public
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UnexpectedUnexpectedConnections in Physics:Connections in Physics:
From SuperconductorsFrom Superconductorsto Black Holesto Black Holes
Talk online:
sachdev.physics.harvard.edu
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The main unsolved problem intheoretical physics today:
Unification of
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The main unsolved problem intheoretical physics today:
Unification of
Quantum theory of electrons,protons, neutron, atoms,
molecules..
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The main unsolved problem intheoretical physics today:
Unification of
Quantum theory of electrons,protons, neutron, atoms,
molecules..
Einstein’s theory of General Relativity(ravitation! applied to stars, blac"holes, ala#ies, the universe....
and
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$or" over the past %&' years has finallyled to a candidate theory hich unifies
ravitation and the )uantum theory, andhich is internally consistent.
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$or" over the past %&' years has finallyled to a candidate theory hich unifies
ravitation and the )uantum theory, andhich is internally consistent.
This theory is popularly "non as*strin theory+
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$or" over the past %&' years has finallyled to a candidate theory hich unifies
ravitation and the )uantum theory, andhich is internally consistent.
$e do not "no yet if strintheory is the correct description
of our universe.
This theory is popularly "non as*strin theory+
Th d i i l f h i
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The deepest ne principle of physicsto emere from strin theory is the
e)uivalence beteen
Th d i i l f h i
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The deepest ne principle of physicsto emere from strin theory is the
e)uivalence beteen
the )uantum theory ofravity in space dimensions
Th d i i l f h i
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The deepest ne principle of physicsto emere from strin theory is the
e)uivalence beteen
the )uantum theory ofravity in space dimensions
a theory of special )uantum states ofmatter (electron, photons, )uar"s..!ithout ravity in % space dimensions
and
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-dimensional )uantum ravity
can be represented as a*holoram+ in% dimensions
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This e)uivalence has led to:
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This e)uivalence has led to:
omplete formulations of consistenttheories of )uantum ravity
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This e)uivalence has led to:
omplete formulations of consistenttheories of )uantum ravity
/olutions of previously unsolvedproblems in stronly interactin
theories of )uantum matter in %dimensions (ithout ravity!
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Quantumsuperposition and
entanlement
Quantum phase transitionsand
Quantum critical points
/uperconductivity
0lac"1oles
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Quantumsuperposition and
entanlement
Quantum phase transitionsand
Quantum critical points
/uperconductivity
0lac"1oles
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Quantumsuperposition and
entanlement
Quantum phase transitionsand
Quantum critical points
/uperconductivity
0lac"1oles
Q
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QuantumSuperposition The double slit experiment
Interference of water waves
Q t
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The double slit experiment
Interference of electrons
QuantumSuperposition
Q t
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The double slit experiment
Interference of electrons
Whichslit does
anelectronpass
through
QuantumSuperposition
Q t
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The double slit experiment
Interference of electrons
Whichslit does
anelectronpass
through
!ointerferen
ce whenyou watch
the
electrons
QuantumSuperposition
Q t
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The double slit experiment
Interference of electrons
Whichslit does
anelectronpass
through
QuantumSuperposition
"achelectron
passesthrough
both
slits #
Q t
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The double slit experiment
QuantumSuperposition
Q t
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The double slit experiment
QuantumSuperposition
Q t
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The double slit experiment
QuantumSuperposition
Quantum "ntanglement: $uantum
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Quantum "ntanglement: $uantumsuperposition with more than one
particle
Quantum "ntanglement: $uantum
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Hydrogen atom:
Quantum "ntanglement: $uantumsuperposition with more than one
particle
Quantum "ntanglement: $uantum
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Hydrogen atom:
Hydrogen molecule:
= _
Superposition of two electron states leads to non-local
correlations between spins
Quantum "ntanglement: $uantumsuperposition with more than one
particle
Quantum "ntanglement: $uantum
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_
Quantum "ntanglement: $uantumsuperposition with more than one
particle
Quantum "ntanglement: $uantum
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_
Quantum "ntanglement: $uantumsuperposition with more than one
particle
Quantum "ntanglement: $uantum
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_
Quantum "ntanglement: $uantumsuperposition with more than one
particle
Quantum "ntanglement: $uantum
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_
Quantum "ntanglement: $uantumsuperposition with more than one
particle
"instein%&odolsky%'osen (paradox): !on%
local correlations between observations
t l t f h i l b d
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Resonance in benzene leads to a symmetric
configuration of chemical bonds
( F. Kekulé, L. Pauling )
ntanglement of chemical bonds
t l t f h i l b d
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Resonance in benzene leads to a symmetric
configuration of chemical bonds
( F. Kekulé, L. Pauling )
ntanglement of chemical bonds
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Quantumsuperposition and
entanlement
Quantum phase transitionsand
Quantum critical points
/uperconductivity
0lac"1oles
Q
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Quantumsuperposition and
entanlement
Quantum phase transitionsand
Quantum critical points
/uperconductivity
0lac"1oles
bidi i i
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Rubidium atoms in a magnetic trap
and standing wa!es of laser light
"# $reiner% &# "andel% '#
sslinger% '# # Hnsch% and+loch% Nature 415% , (.//.)#
0t !ery low temperatures and for a wea1 laser
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0t !ery low temperatures and for a wea1 laser
light% the Rubidium atoms form a
+ose-instein condensate
"# $reiner% &# "andel% '#
sslinger% '# # Hnsch% and+loch% Nature 415% , (.//.)#
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* +ose%"instein condensate:*n $uantum superpositionof all the atoms in allpositions
* li$uid which ,ows withoutresistance -a super,uid
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* single atom issuperposed between
all positions
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* single atom issuperposed between
all positions
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* single atom issuperposed between
all positions
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* single atom issuperposed betweenall positions
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* single atom issuperposed betweenall positions
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* single atom issuperposed betweenall positions
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* single atom issuperposed betweenall positions
+ose%"instein condensate:
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superposition between all atoms
+ose%"instein condensate:
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2arge fluctuations in number of atoms in each site 3
superfluidity (atoms can 4flow5 without dissipation)
superposition between all atoms
+ose%"instein condensate:
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2arge fluctuations in number of atoms in each site 3
superfluidity (atoms can 4flow5 without dissipation)
superposition between all atoms
+ose%"instein condensate:
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2arge fluctuations in number of atoms in each site 3
superfluidity (atoms can 4flow5 without dissipation)
superposition between all atoms
+ose%"instein condensate:
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2arge fluctuations in number of atoms in each site 3
superfluidity (atoms can 4flow5 without dissipation)
superposition between all atoms
+ose%"instein condensate:
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2arge fluctuations in number of atoms in each site 3
superfluidity (atoms can 4flow5 without dissipation)
superposition between all atoms
+ose%"instein condensate:
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2arge fluctuations in number of atoms in each site 3
superfluidity (atoms can 4flow5 without dissipation)
superposition between all atoms
+ose%"instein condensate:
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2arge fluctuations in number of atoms in each site 3
superfluidity (atoms can 4flow5 without dissipation)
superposition between all atoms
0t !ery low temperatures and for a wea1 laser
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y p
light% the Rubidium atoms form a
+ose-instein condensate
"# $reiner% &# "andel% '#
sslinger% '# # Hnsch% and
+loch% Nature 415% , (.//.)#
+ose%"instein condensate:
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superposition between all atoms
-Strictly speaking: this is notentanglement between the atoms
because the +"/ is a product of simple(wave) states of the atoms
* d t +
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* superconductor: a +osecondensate of pairs of electrons in a
(chemical bond) in a metal
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Ca1.90
a0.10
Cu!"Cl
" Bi"."Sr1.#Ca0.#$y0."Cu"! y
High temperature superconductors
High temperature
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High temperature
superconductors
S6uare lattice of 7u sites
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S6uare lattice of 7u sites
S6uare lattice of 7u sites
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S6uare lattice of 7u sites
0. 'emovesomeelectrons
S6uare lattice of 7u sites
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S6uare lattice of 7u sites
0. 'emovesomeelectrons
1. "lectronsentangle intochemicalbonds
S6uare lattice of 7u sites
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S6uare lattice of 7u sites
0. 'emovesomeelectrons
1. "lectronsentangle intochemicalbonds
2. /hemicalbondsundergo+ose%"insteincondensation
S6uare lattice of 7u sites
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S6uare lattice of 7u sites
0. 'emovesomeelectrons
1. "lectronsentangle intochemicalbonds
2. /hemicalbondsundergo+ose%"insteincondensation
S6uare lattice of 7u sites
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S6uare lattice of 7u sites
0. 'emovesomeelectrons
1. "lectronsentangle intochemicalbonds
2. /hemicalbondsundergo+ose%"insteincondensation
S6uare lattice of 7u sites
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S6uare lattice of 7u sites
0. 'emovesomeelectrons
1. "lectronsentangle intochemicalbonds
2. /hemicalbondsundergo+ose%"insteincondensation
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QuickTime3 and a4otion 5&"6 7pen849 decompressor
are needed to see this picture.
8ulian Hetel and 9andini 'ri!edi% &hio State ni!ersity
!d%e%+ magnets; <+a/u7 superconductor
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QuickTime3 and a4otion 5&"6 7pen849 decompressor
are needed to see this picture.
8ulian Hetel and 9andini 'ri!edi% &hio State ni!ersity
!d%e%+ magnets; <+a/u7 superconductor
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Quantumentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"1oles
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Quantumentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"1oles
hat is a 4phase transition5 ;
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hat is a phase transition ;
0 change in the collecti!e properties of a
macroscopic number of atoms
hat is a 4quantum phase transition5 ;
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hat is a quantum phase transition ;
7hange in the nature of
6uantum superposition in amacroscopic 6uantum system#
>uantum 7riticality
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'he comple< and non-localentanglement at the critical point
between two 6uantum phases#'here is entanglement between
electronsatoms at all distance scales#
Rubidium atoms in a magnetic trap
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g p
and standing wa!es of laser light
"# $reiner% &# "andel% '#
sslinger% '# # Hnsch% and
+loch% Nature 415% , (.//.)#
*ncrease the intensity of laser light
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y g
"# $reiner% &# "andel% '#
sslinger% '# # Hnsch% and
+loch% Nature 415% , (.//.)#
*ncrease the intensity of laser light
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"# $reiner% &# "andel% '#
sslinger% '# # Hnsch% and
+loch% Nature 415% , (.//.)#
y g
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"# $reiner% &# "andel% '#
sslinger% '# # Hnsch% and *#
+loch% Nature 415% , (.//.)#
Strong laser light
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4ggs in an egg carton5
Strong laser light
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4ggs in an egg carton5
Strong laser light
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4ggs in an egg carton5
Super,uid Insulator
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Intensity of laserlightQuantum critical
point
Super,uid Insulator
Super,uid Insulator
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Intensity of laserlight"ntanglement
between atoms at
Super,uid Insulator
Superfluid-insulator 6uantum phase transition
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"# $reiner% &# "andel% '# sslinger% '# # Hnsch% and *# +loch% Nature 415% , (.//.)#
>uantum 7riticality
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'he comple< and non-localentanglement at the critical point
between two 6uantum phases#'here is entanglement between
electronsatoms at all distance scales#
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Quantumentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"1oles
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Quantumentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"1oles
+lac1 Holes
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&b?ects so massi!e that light isgra!itationally bound to them#
+lac1 Holes
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&b?ects so massi!e that light isgra!itationally bound to them#
In "instein=s theory; theregion inside the black
hole hori>on is
disconnected from therest of the universe.
+lac1 Holes @ >uantum theory
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*round 0?@A; +ekenstein andBawking showed that the
application of the $uantumtheory across a black holehori>on led to many
astonishing conclusions
Quantum "ntanglement across a blackhole hori>on
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_
hole hori>on
Quantum "ntanglement across a blackhole hori>on
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hole hori>on
Quantum "ntanglement across a blackhole hori>on
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hole hori>on
Black hole
horizon
Quantum "ntanglement across a blackhole hori>on
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_
Black hole
horizon
hole hori>on
Quantum "ntanglement across a blackhole hori>on
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Black hole
horizon
hole hori>on
There is a non%local
$uantum entanglementbetween the inside and
outside of a black hole
Quantum "ntanglement across a blackhole hori>on
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Black hole
horizon
hole hori>on
There is a non%local
$uantum entanglementbetween the inside and
outside of a black hole
Quantum "ntanglement across a blackhole hori>on
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hole hori>on
There is a non%local
$uantum entanglementbetween the inside and
outside of a black hole This entanglement leads toa
black hole temperature-the Bawking temperatureand a black hole entropy
Q t
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Quantumentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"1oles
Q t
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9
9
Quantumentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"1oles
Quantum "ntanglement across a blackhole hori>on
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hole hori>on
There is a non%local
$uantum entanglementbetween the inside andoutside of a black hole
Quantum "ntanglement across a blackhole hori>on
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hole hori>on
There is a non%local
$uantum entanglementbetween the inside andoutside of a black hole
In anti%de Sitter -*dS space;this entanglement is
e$uivalent to that of a$uantum critical point of
$uantum matter in 1
The $uantum theory of a black hole in a 2C0%dimensional negatively curved *dS universe is
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dimensional negatively curved *dS universe isholographically represented by the theory of a
$uantum critical point in 1C0 dimensions
"aldacena% $ubser% Alebano!% Bolya1o!% itten
3+1 dimensional
d! spa"e
The $uantum theory of a black hole in a 2C0%dimensional negatively curved *dS universe is
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"aldacena% $ubser% Alebano!% Bolya1o!% itten
3+1 dimensional
d! spa"e 0 .@C
dimensionalsystem at its
6uantum
critical point
dimensional negatively curved *dS universe isholographically represented by the theory of a
$uantum critical point in 1C0 dimensions
The $uantum theory of a black hole in a 2C0%dimensional negatively curved *dS universe is
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"aldacena% $ubser% Alebano!% Bolya1o!% itten
3+1 dimensional
d! spa"e >uantum
criticality in.@C
dimensions0lac" holetemperature
2temperatureof )uantumcriticality
dimensional negatively curved *dS universe isholographically represented by the theory of a
$uantum critical point in 1C0 dimensions
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5. 4c6reevy
9ength%scale of
entanglementrepresents (extra)
third dimension
The $uantum theory of a black hole in a 2C0%dimensional negatively curved *dS universe is
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3+1 dimensional
d! spa"e >uantum
criticality in.@C
dimensionsQuantumcritical
dynamics 2aves incurved space
"aldacena% $ubser% Alebano!% Bolya1o!% itten
dimensional negatively curved *dS universe isholographically represented by the theory of a
$uantum critical point in 1C0 dimensions
The $uantum theory of a black hole in a 2C0%dimensional negatively curved *dS universe is
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3+1 dimensional
d! spa"e >uantum
criticality in.@C
dimensions3riction of)uantum
criticality 2aves fallininto blac"
hole
Ao!tun% Bolicastro% Son
dimensional negatively curved *dS universe isholographically represented by the theory of a
$uantum critical point in 1C0 dimensions
Super,uid Insulator
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Intensity of laserlightQuantum critical
point
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Quantum critical
point
Intensity of laserlight
riction of atom ,owdescribed by waves near a
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Quantum critical
point
Intensity of laserlight
described by waves near ablack hole hori>on #
The $uantum theory of a black hole in a 2C0%dimensional negatively curved *dS universe is
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dimensional negatively curved *dS universe isholographically represented by the theory of a
$uantum critical point in 1C0 dimensions
The $uantum theory of a black hole in a 2C0%dimensional negatively curved *dS universe is
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dimensional negatively curved *dS universe isholographically represented by the theory of a
$uantum critical point in 1C0 dimensions
Question: if you lived in this world;would you think you lived in 1 or 2
spatial dimensions
The $uantum theory of a black hole in a 2C0%dimensional negatively curved *dS universe is
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dimensional negatively curved *dS universe isholographically represented by the theory of a
$uantum critical point in 1C0 dimensions
Question: if you lived in this world;would you think you lived in 1 or 2
spatial dimensions
*nswer: it
depends......
The $uantum theory of a black hole in a 2C0%dimensional negatively curved *dS universe is
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dimensional negatively curved *dS universe isholographically represented by the theory of a
$uantum critical point in 1C0 dimensions
Question: if you lived in this world;would you think you lived in 1 or 2
spatial dimensions *nswer: for some values of theparameters in the theory; the world
would appear 2 dimensional; whilefor other parameters; it wouldappear 1 dimensional; and there
many theories which would appear
The deepest ne principle of physicsto emere from strin theory is the
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ye)uivalence beteen
the )uantum theory ofravity in space dimensions
a theory of special )uantum states ofmatter (electron, photons, )uar"s..!ithout ravity in % space dimensions
and
Quantumsuperposition and
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superposition andentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"1oles
Quantumsuperposition and
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superposition andentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"