desitter public
TRANSCRIPT
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 1/117
UnexpectedUnexpectedConnections in Physics:Connections in Physics:
From SuperconductorsFrom Superconductorsto Black Holesto Black Holes
Talk online:
sachdev.physics.harvard.edu
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 2/117
The main unsolved problem intheoretical physics today:
Unification of
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 3/117
The main unsolved problem intheoretical physics today:
Unification of
Quantum theory of electrons,protons, neutron, atoms,
molecules..
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 4/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 5/117
$or" over the past %&' years has finallyled to a candidate theory hich unifies
ravitation and the )uantum theory, andhich is internally consistent.
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 6/117
$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+
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 7/117
$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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 8/117
The deepest ne principle of physicsto emere from strin theory is the
e)uivalence beteen
Th d i i l f h i
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 9/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 10/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 11/117
-dimensional )uantum ravity
can be represented as a*holoram+ in% dimensions
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 12/117
This e)uivalence has led to:
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 13/117
This e)uivalence has led to:
omplete formulations of consistenttheories of )uantum ravity
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 14/117
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!
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 15/117
Quantumsuperposition and
entanlement
Quantum phase transitionsand
Quantum critical points
/uperconductivity
0lac"1oles
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 16/117
Quantumsuperposition and
entanlement
Quantum phase transitionsand
Quantum critical points
/uperconductivity
0lac"1oles
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 17/117
Quantumsuperposition and
entanlement
Quantum phase transitionsand
Quantum critical points
/uperconductivity
0lac"1oles
Q
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 18/117
QuantumSuperposition The double slit experiment
Interference of water waves
Q t
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 19/117
The double slit experiment
Interference of electrons
QuantumSuperposition
Q t
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 20/117
The double slit experiment
Interference of electrons
Whichslit does
anelectronpass
through
QuantumSuperposition
Q t
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 21/117
The double slit experiment
Interference of electrons
Whichslit does
anelectronpass
through
!ointerferen
ce whenyou watch
the
electrons
QuantumSuperposition
Q t
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 22/117
The double slit experiment
Interference of electrons
Whichslit does
anelectronpass
through
QuantumSuperposition
"achelectron
passesthrough
both
slits #
Q t
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 23/117
The double slit experiment
QuantumSuperposition
Q t
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 24/117
The double slit experiment
QuantumSuperposition
Q t
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 25/117
The double slit experiment
QuantumSuperposition
Quantum "ntanglement: $uantum
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 26/117
Quantum "ntanglement: $uantumsuperposition with more than one
particle
Quantum "ntanglement: $uantum
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 27/117
Hydrogen atom:
Quantum "ntanglement: $uantumsuperposition with more than one
particle
Quantum "ntanglement: $uantum
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 28/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 29/117
_
Quantum "ntanglement: $uantumsuperposition with more than one
particle
Quantum "ntanglement: $uantum
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 30/117
_
Quantum "ntanglement: $uantumsuperposition with more than one
particle
Quantum "ntanglement: $uantum
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 31/117
_
Quantum "ntanglement: $uantumsuperposition with more than one
particle
Quantum "ntanglement: $uantum
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 32/117
_
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 33/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 34/117
Resonance in benzene leads to a symmetric
configuration of chemical bonds
( F. Kekulé, L. Pauling )
ntanglement of chemical bonds
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 35/117
Quantumsuperposition and
entanlement
Quantum phase transitionsand
Quantum critical points
/uperconductivity
0lac"1oles
Q
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 36/117
Quantumsuperposition and
entanlement
Quantum phase transitionsand
Quantum critical points
/uperconductivity
0lac"1oles
bidi i i
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 37/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 38/117
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% , (.//.)#
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 39/117
* +ose%"instein condensate:*n $uantum superpositionof all the atoms in allpositions
* li$uid which ,ows withoutresistance -a super,uid
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 40/117
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 41/117
* single atom issuperposed between
all positions
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 42/117
* single atom issuperposed between
all positions
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 43/117
* single atom issuperposed between
all positions
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 44/117
* single atom issuperposed betweenall positions
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 45/117
* single atom issuperposed betweenall positions
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 46/117
* single atom issuperposed betweenall positions
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 47/117
* single atom issuperposed betweenall positions
+ose%"instein condensate:
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 48/117
superposition between all atoms
+ose%"instein condensate:
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 49/117
2arge fluctuations in number of atoms in each site 3
superfluidity (atoms can 4flow5 without dissipation)
superposition between all atoms
+ose%"instein condensate:
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 50/117
2arge fluctuations in number of atoms in each site 3
superfluidity (atoms can 4flow5 without dissipation)
superposition between all atoms
+ose%"instein condensate:
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 51/117
2arge fluctuations in number of atoms in each site 3
superfluidity (atoms can 4flow5 without dissipation)
superposition between all atoms
+ose%"instein condensate:
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 52/117
2arge fluctuations in number of atoms in each site 3
superfluidity (atoms can 4flow5 without dissipation)
superposition between all atoms
+ose%"instein condensate:
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 53/117
2arge fluctuations in number of atoms in each site 3
superfluidity (atoms can 4flow5 without dissipation)
superposition between all atoms
+ose%"instein condensate:
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 54/117
2arge fluctuations in number of atoms in each site 3
superfluidity (atoms can 4flow5 without dissipation)
superposition between all atoms
+ose%"instein condensate:
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 55/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 56/117
y p
light% the Rubidium atoms form a
+ose-instein condensate
"# $reiner% &# "andel% '#
sslinger% '# # Hnsch% and
+loch% Nature 415% , (.//.)#
+ose%"instein condensate:
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 57/117
superposition between all atoms
-Strictly speaking: this is notentanglement between the atoms
because the +"/ is a product of simple(wave) states of the atoms
* d t +
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 58/117
* superconductor: a +osecondensate of pairs of electrons in a
(chemical bond) in a metal
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 59/117
Ca1.90
a0.10
Cu!"Cl
" Bi"."Sr1.#Ca0.#$y0."Cu"! y
High temperature superconductors
High temperature
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 60/117
High temperature
superconductors
S6uare lattice of 7u sites
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 61/117
S6uare lattice of 7u sites
S6uare lattice of 7u sites
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 62/117
S6uare lattice of 7u sites
0. 'emovesomeelectrons
S6uare lattice of 7u sites
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 63/117
S6uare lattice of 7u sites
0. 'emovesomeelectrons
1. "lectronsentangle intochemicalbonds
S6uare lattice of 7u sites
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 64/117
S6uare lattice of 7u sites
0. 'emovesomeelectrons
1. "lectronsentangle intochemicalbonds
2. /hemicalbondsundergo+ose%"insteincondensation
S6uare lattice of 7u sites
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 65/117
S6uare lattice of 7u sites
0. 'emovesomeelectrons
1. "lectronsentangle intochemicalbonds
2. /hemicalbondsundergo+ose%"insteincondensation
S6uare lattice of 7u sites
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 66/117
S6uare lattice of 7u sites
0. 'emovesomeelectrons
1. "lectronsentangle intochemicalbonds
2. /hemicalbondsundergo+ose%"insteincondensation
S6uare lattice of 7u sites
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 67/117
S6uare lattice of 7u sites
0. 'emovesomeelectrons
1. "lectronsentangle intochemicalbonds
2. /hemicalbondsundergo+ose%"insteincondensation
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 68/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 69/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 70/117
Quantumentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"1oles
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 71/117
Quantumentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"1oles
hat is a 4phase transition5 ;
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 72/117
hat is a phase transition ;
0 change in the collecti!e properties of a
macroscopic number of atoms
hat is a 4quantum phase transition5 ;
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 73/117
hat is a quantum phase transition ;
7hange in the nature of
6uantum superposition in amacroscopic 6uantum system#
>uantum 7riticality
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 74/117
'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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 75/117
g p
and standing wa!es of laser light
"# $reiner% &# "andel% '#
sslinger% '# # Hnsch% and
+loch% Nature 415% , (.//.)#
*ncrease the intensity of laser light
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 76/117
y g
"# $reiner% &# "andel% '#
sslinger% '# # Hnsch% and
+loch% Nature 415% , (.//.)#
*ncrease the intensity of laser light
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 77/117
"# $reiner% &# "andel% '#
sslinger% '# # Hnsch% and
+loch% Nature 415% , (.//.)#
y g
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 78/117
"# $reiner% &# "andel% '#
sslinger% '# # Hnsch% and *#
+loch% Nature 415% , (.//.)#
Strong laser light
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 79/117
4ggs in an egg carton5
Strong laser light
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 80/117
4ggs in an egg carton5
Strong laser light
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 81/117
4ggs in an egg carton5
Super,uid Insulator
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 82/117
Intensity of laserlightQuantum critical
point
Super,uid Insulator
Super,uid Insulator
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 83/117
Intensity of laserlight"ntanglement
between atoms at
Super,uid Insulator
Superfluid-insulator 6uantum phase transition
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 84/117
"# $reiner% &# "andel% '# sslinger% '# # Hnsch% and *# +loch% Nature 415% , (.//.)#
>uantum 7riticality
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 85/117
'he comple< and non-localentanglement at the critical point
between two 6uantum phases#'here is entanglement between
electronsatoms at all distance scales#
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 86/117
Quantumentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"1oles
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 87/117
Quantumentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"1oles
+lac1 Holes
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 88/117
&b?ects so massi!e that light isgra!itationally bound to them#
+lac1 Holes
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 89/117
&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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 90/117
*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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 91/117
_
hole hori>on
Quantum "ntanglement across a blackhole hori>on
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 92/117
_
hole hori>on
Quantum "ntanglement across a blackhole hori>on
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 93/117
_
hole hori>on
Black hole
horizon
Quantum "ntanglement across a blackhole hori>on
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 94/117
_
Black hole
horizon
hole hori>on
Quantum "ntanglement across a blackhole hori>on
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 95/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 96/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 97/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 98/117
Quantumentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"1oles
Q t
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 99/117
9
9
Quantumentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"1oles
Quantum "ntanglement across a blackhole hori>on
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 100/117
hole hori>on
There is a non%local
$uantum entanglementbetween the inside andoutside of a black hole
Quantum "ntanglement across a blackhole hori>on
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 101/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 102/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 103/117
"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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 104/117
"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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 105/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 106/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 107/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 108/117
Intensity of laserlightQuantum critical
point
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 109/117
Quantum critical
point
Intensity of laserlight
riction of atom ,owdescribed by waves near a
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 110/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 111/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 112/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 113/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 114/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 115/117
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
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 116/117
superposition andentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"1oles
Quantumsuperposition and
7/21/2019 Desitter Public
http://slidepdf.com/reader/full/desitter-public 117/117
superposition andentanlement
Quantum phase transitions
andQuantum critical points
/uperconductivity
0lac"