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Quantum entanglement
at all distances
2021 H.L. Welsh Lectures in Physics University of Toronto
May 6, 2021Subir Sachdev
HARVARDTalk online: sachdev.physics.harvard.edu
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Newton showed (1687) that the same laws of motion applied onplanetary length scales (⇠ 1 trillion meters)
and the length scale of an apple tree (1 meter).
What happens on smaller and larger distances ?
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Newton showed (1687) that the same laws of motion applied onplanetary length scales (⇠ 1 trillion meters)
and the length scale of an apple tree (1 meter).
Going small…..
Hydrogen atom
<latexit sha1_base64="trWnrZ96RKDAXHYth1kMYXo8LJ4=">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</latexit>
) 10�10 meters (<latexit sha1_base64="4vbYp/uxnYaIe3iHtQFjUzxZ00Y=">AAACjHicdVFda9swFJW9r9bb2qx73ItYGOzJc5x0TSiDssHYYwdNW4hCkOXrRFSWjHQ9MCa/Zv9ob/s3k90U2rFdEJx7zr1XV0dZpaTDJPkdhI8eP3n6bG8/ev7i5cHh4NXRpTO1FTAXRhl7nXEHSmqYo0QF15UFXmYKrrKbL51+9QOsk0ZfYFPBsuRrLQspOHpqNfjJMlhL3QrQCHYbXWyAlqbTqCko+gwUCLQ+59bUOu+5yhr0jHS0ZRKpNrilOThhZQY5zRrG+jLHS+iAsQ3lrqcezq4U14Du/mhX65ixiIHO75ZaDYZJnIwnxycT6sFscjxOPJjNpuk4paM46WNIdnG+GvxiuRF16duF4s4tRkmFy5ZblELBNmK1g4qLG76GhYfar+mWbW/mlr7zTE4LY/3RSHv2fkfLS+eaMvOVJceN+1vryH9pixqL6bKVuqoRtLi9qKgVRUO7n6G5tN5p1XjAvZN+Vyo23HLhPXCRN+HupfT/4DKNRx/j9Hs6PPu8s2OPvCFvyXsyIifkjHwj52RORLAffAimwSw8CCfhafjptjQMdj2vyYMIv/4BZC3GyQ==</latexit>
The motion of the electron around the proton is not described bythe same theory as the motion of the planets around the sun.
Hydrogen atom
<latexit sha1_base64="trWnrZ96RKDAXHYth1kMYXo8LJ4=">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</latexit>
) 10�10 meters (<latexit sha1_base64="4vbYp/uxnYaIe3iHtQFjUzxZ00Y=">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</latexit>
The motion of the electron around the proton is not described bythe same theory as the motion of the planets around the sun.
<latexit sha1_base64="0wWwkSNUbMgwszY7POUUxbiiBBw=">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</latexit>
It is described by the quantum theory
of Schrodinger and Heisenberg (1925).
<latexit sha1_base64="agTi6wt8io+FMEmF/M2VhSEf9oc=">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</latexit>
The most remarkable new idea in the quantum theory is theprinciple of superposition:
a physical system can be in asuperposition of two (or more) distinct states.
Quantum superposition in a hydrogen molecule
Hydrogen atom:
=1⌃2
(|⇥⇤⌅ � |⇤⇥⌅)
Hydrogen molecule:
= _
Quantum Entanglement
_
Einstein, Podolsky, Rosen (1935)
Quantum Entanglement
_
Einstein, Podolsky, Rosen (1935)
Quantum Entanglement
_
Einstein, Podolsky, Rosen (1935)
_
Quantum EntanglementEinstein, Podolsky, Rosen (1935)
Measurement of one electron instantaneously
determines the state of the other electron very far away
Quantum Entanglement
_
Einstein, Podolsky, Rosen (1935)
Measurement of one electron instantaneously
determines the state of the other electron very far away
http://nyti.ms/1OIO2WJ
SCIENCE
Sorry, Einstein. Quantum Study Suggests‘Spooky Action’ Is Real.By JOHN MARKOFF OCT. 21, 2015
In a landmark study, scientists at Delft University of Technology in theNetherlands reported that they had conducted an experiment that they say provedone of the most fundamental claims of quantum theory — that objects separated bygreat distance can instantaneously affect each other’s behavior.
The finding is another blow to one of the bedrock principles of standardphysics known as “locality,” which states that an object is directly influenced onlyby its immediate surroundings. The Delft study, published Wednesday in thejournal Nature, lends further credence to an idea that Einstein famously rejected.He said quantum theory necessitated “spooky action at a distance,” and he refusedto accept the notion that the universe could behave in such a strange andapparently random fashion.
In particular, Einstein derided the idea that separate particles could be“entangled” so completely that measuring one particle would instantaneouslyinfluence the other, regardless of the distance separating them.
Einstein was deeply unhappy with the uncertainty introduced by quantumtheory and described its implications as akin to God’s playing dice.
But since the 1970s, a series of precise experiments by physicists are1 of 2
© 2015 The New York Times Company
Part of the laboratory setup for an experiment
at Delft University of Technology, in which
two diamonds were set 1.3 kilometers apart, entangled and then shared information.
Going big (and heavy)…..
Objects so dense that light is gravitationally bound to them.
Black Holes
<latexit sha1_base64="26Q+sxivxP1+reVYvsLV8mZtAxc=">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</latexit>
We need corrections toNewton’s equationswhich are given byEinstein’s theory of
general relativity (1915),to describe black holes
Objects so dense that light is gravitationally bound to them.
Black Holes
Objects so dense that light is gravitationally bound to them.
Black Holes
Horizon radius R =2GM
c2<latexit sha1_base64="DmHY5rKnFNBAMp1nOXUIIHLQ/tU=">AAACd3icdZFNb9NAEIbXLh/FfDSUGxwYiIEeqshO1IYekCqQgAuoINJWiqNovRnHq+6HtbsuRFb+Aj+OG/+DCzfWaUCAYE6j533HM/s6rwS3Lkm+BuHGpctXrm5ei67fuHlrq3N7+9jq2jAcMS20Oc2pRcEVjhx3Ak8rg1TmAk/ysxetfnKOxnKtPrhFhRNJ54oXnFHn0bTzOctxzlXDUDk0yyh+FcNb/Oi0emKBaWUdVW4XYh bDOQrNuFuALkDwedniNzFIam2LckHZGZRaYJZFL7Xx4rMYkBpX+k+1Lu9/DxmtKqM/wUG2C1LGD6IM1ezX+mmnm/QGw729YR+SXrIqaMn+YHAA6Zp0ybqOpp0v2UyzWvp5JvyOcZpUbtL4rZwJXEZZbbHyh9E5jn2rqEQ7aVa5LeGRJzMo/K2FVg5W9PeJhkprFzL3Tkldaf/WWvgvbVy74umk4aqqHSp2saioBTgN7U+AGTfInFj4hjLD/a3ASmoo8yHYNoSfL4X/N8f9XrrfS971u4fP13FsknvkIdkhKRmSQ/KaHJERYeRbcDfoBnHwPbwfPg53LqxhsJ65Q/6oMP0BSZW6hg==</latexit>
G Newton’s constant, c velocity of light, M mass of black holeFor M = earth’s mass, R ⇡ 9mm!
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We need corrections toNewton’s equationswhich are given byEinstein’s theory of
general relativity (1915),to describe black holes
LOFAR LBA Sky Survey showing 25000 supermassive black holes on 4% of the northern sky.
Obtained by 52 radio telescopes across Europe
de Gasperin et al. (2021)
<latexit sha1_base64="MTeH33sJPcw6/6rcRrBYn7lVy5k=">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</latexit>
Each black hole has a size ⇠ 1010 meters,and is at the center of its own galaxy (like the Milky way)
Applying the theory of the very small
to the very big (black holes)….
_
Quantum Entanglement across a black hole horizon
_
Quantum Entanglement across a black hole horizon
Black hole horizon
_
Black hole horizon
Quantum Entanglement across a black hole horizon
Black hole horizon
Quantum Entanglement across a black hole horizon
There is quantum entanglement between the inside and outside of
a black hole
Black hole horizon
Quantum Entanglement across a black hole horizon
Hawking (1975) used other arguments to show that black hole horizons have a temperature(The entanglement reasoning: to an outside observer, the state of the electron inside the
black hole cannot be known, and so the outside electron is in a random state. )
Going small and big…..
We don’t have a completely general quantum theory of black holes today.
Such a theory requires
that we understand multi-particle entanglement for
many-many particles.
We don’t have a completely general quantum theory of black holes today.
Such a theory requires
that we understand multi-particle entanglement for
many-many particles.
The problem of multi-particle entanglement also appears in other problems
in modern physics:
Quantum computing: control entanglement of many qubits
(really hard to isolate from the environment).
Quantum materials: crystals with multiple elements naturally display phases with multi-electron entanglement.
The problem of multi-particle entanglement also appears in other problems
in modern physics:
Quantum computing: control entanglement of many qubits
(really hard to isolate from the environment).
Quantum materials: crystals with multiple elements naturally display phases with multi-electron entanglement.
The problem of multi-particle entanglement also appears in other problems
in modern physics:
Quantum computing: control entanglement of many qubits
(really hard to isolate from the environment).
Quantum materials: crystals with multiple elements naturally display phases with multi-electron entanglement.
The problem of multi-particle entanglement also appears in other problems
in modern physics:
Quantum computing: control entanglement of many qubits
(really hard to isolate from the environment).
Quantum materials: crystals with multiple elements naturally display phases with multi-electron entanglement.
The problem of multi-particle entanglement also appears in other problems
in modern physics:
Quantum computing: control entanglement of many qubits
(really hard to isolate from the environment).
Quantum materials: crystals with multiple elements naturally display phases with multi-electron entanglement.
YBa2Cu3O6+x
High temperature superconductors
Julian Hetel and Nandini Trivedi, Ohio State University
Nd-Fe-B magnets, YBaCuO superconductor
pc
Strange Metal
The SYK model:a theory of entanglement,
from the very small to the very big…..
The SYK model has a scale-invariant entanglement structure:
i.e. electrons are entangled at all distance and time scales
In one set of variables, it describes
certain strange metals
In a dual set of variables it describes certain black holes
The Sachdev-Ye-Kitaev (SYK) model
Sachdev (2010), Kitaev (2015), Maldacena Stanford (2015)
Sachdev, Ye (1993)
The SYK model has a scale-invariant entanglement structure:
i.e. electrons are entangled at all distance and time scales
In one set of variables, it describes
certain strange metals
In a dual set of variables it describes certain black holes
The Sachdev-Ye-Kitaev (SYK) model
Sachdev (2010), Kitaev (2015), Maldacena Stanford (2015)
Sachdev, Ye (1993)
The SYK model has a scale-invariant entanglement structure:
i.e. electrons are entangled at all distance and time scales
In one set of variables, it describes
certain strange metals
In a dual set of variables it describes certain black holes
The Sachdev-Ye-Kitaev (SYK) model
Sachdev (2010), Kitaev (2015), Maldacena Stanford (2015)
Sachdev, Ye (1993)
The Sachdev-Ye-Kitaev (SYK) model
Pick a set of random positions
Sachdev, Ye (1993); Kitaev (2015)
Place electrons randomly on some sites
The SYK modelSachdev, Ye (1993); Kitaev (2015)
The SYK model
Place electrons randomly on some sites
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Place electrons randomly on some sites
Sachdev, Ye (1993); Kitaev (2015)
Entangle electrons pairwise randomly
The SYK modelSachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model
Entangle electrons pairwise randomly
Sachdev, Ye (1993); Kitaev (2015)
The SYK model has a scale-invariant entanglement structure:
i.e. electrons are entangled at all distance and time scales
In one set of variables, it describes
certain strange metals
In a dual set of variables it describes certain black holes
The Sachdev-Ye-Kitaev (SYK) model
Sachdev (2010), Kitaev (2015), Maldacena Stanford (2015)
Sachdev, Ye (1993)
More on metals,
ordinary and strange)
Ordinary metals
Ordinary metals are shiny, and they conduct heat and electricity efficiently. Each atom donates electrons which
are delocalized throughout the entire crystal
Almost all many-electron systems are described by the quasiparticle concept: a quasiparticle is an “excited lump” in the many-electron state which responds just like an ordinary particle. The existence of quasiparticles implies limited many-particle entanglement
R.D. Mattuck
Current flow with quasiparticles
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Flowing quasiparticles scatter o↵ eachother in a typical scattering time ⌧
This time is much longer than a limiting
‘Planckian time’~
kBT.
The long scattering time implies thatquasiparticles are well-defined.
18
Table 1 | Slope of T-linear resistivity and Planckian limit in seven materials.
Material n (1027 m-3)
m*(m0)
A1 / d (! / K)
h / (2e2 TF)(! / K)
⍺
Bi2212 p = 0.23 6.8 8.4 ± 1.6 8.0 ± 0.9 7.4 ± 1.4 1.1 ± 0.3
Bi2201 p ~ 0.4 3.5 7 ± 1.5 8 ± 2 8 ± 2 1.0 ± 0.4
LSCO p = 0.26 7.8 9.8 ± 1.7 8.2 ± 1.0 8.9 ± 1.8 0.9 ± 0.3
Nd-LSCO p = 0.24 7.9 12 ± 4 7.4 ± 0.8 10.6 ± 3.7 0.7 ± 0.4
PCCO x = 0.17 8.8 2.4 ± 0.1 1.7 ± 0.3 2.1 ± 0.1 0.8 ± 0.2
LCCO x = 0.15 9.0 3.0 ± 0.3 3.0 ± 0.45 2.6 ± 0.3 1.2 ± 0.3
TMTSF P = 11 kbar 1.4 1.15 ± 0.2 2.8 ± 0.3 2.8 ± 0.4 1.0 ± 0.3
Table 1 | Slope of T-linear resistivity vs Planckian limit in seven materials.
Comparison of the measured slope of the T-linear resistivity in the T = 0 limit,
A1 , with the value predicted by the Planckian limit (Eq. 1; penultimate column),
for four hole-doped cuprates (Bi2212, Bi2201, LSCO and Nd-LSCO), two
electron-doped cuprates (PCCO and LCCO) and the organic conductor
(TMTSF)2PF6 , as discussed in the text (and Supplementary Information).
The ratio α of the experimental value, A1☐ = A1 / d, over the predicted value,
is given in the last column. Although A1☐ varies by a factor 5, the ratio m* / n
(~1/TF) is seen to vary by the same amount, so that α = 1.0 in all cases,
within error bars.
A. Legros, S. Benhabib, W. Tabis, F. Laliberté, M. Dion, M. Lizaire, B. Vignolle, D. Vignolles, H. Raffy, Z. Z. Li, P. Auban-Senzier, N. Doiron-Leyraud, P. Fournier, D. Colson, L. Taillefer, and C. Proust, Nature Physics 15, 142 (2019)
1
⌧= ↵
kBT
~<latexit sha1_base64="Q0pGo+lkjPvE7fTn3atRPbcYr7A=">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</latexit>
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Electron scattering time ⌧ in 7 di↵erent strange metals
18
Table 1 | Slope of T-linear resistivity and Planckian limit in seven materials.
Material n (1027 m-3)
m*(m0)
A1 / d (! / K)
h / (2e2 TF)(! / K)
⍺
Bi2212 p = 0.23 6.8 8.4 ± 1.6 8.0 ± 0.9 7.4 ± 1.4 1.1 ± 0.3
Bi2201 p ~ 0.4 3.5 7 ± 1.5 8 ± 2 8 ± 2 1.0 ± 0.4
LSCO p = 0.26 7.8 9.8 ± 1.7 8.2 ± 1.0 8.9 ± 1.8 0.9 ± 0.3
Nd-LSCO p = 0.24 7.9 12 ± 4 7.4 ± 0.8 10.6 ± 3.7 0.7 ± 0.4
PCCO x = 0.17 8.8 2.4 ± 0.1 1.7 ± 0.3 2.1 ± 0.1 0.8 ± 0.2
LCCO x = 0.15 9.0 3.0 ± 0.3 3.0 ± 0.45 2.6 ± 0.3 1.2 ± 0.3
TMTSF P = 11 kbar 1.4 1.15 ± 0.2 2.8 ± 0.3 2.8 ± 0.4 1.0 ± 0.3
Table 1 | Slope of T-linear resistivity vs Planckian limit in seven materials.
Comparison of the measured slope of the T-linear resistivity in the T = 0 limit,
A1 , with the value predicted by the Planckian limit (Eq. 1; penultimate column),
for four hole-doped cuprates (Bi2212, Bi2201, LSCO and Nd-LSCO), two
electron-doped cuprates (PCCO and LCCO) and the organic conductor
(TMTSF)2PF6 , as discussed in the text (and Supplementary Information).
The ratio α of the experimental value, A1☐ = A1 / d, over the predicted value,
is given in the last column. Although A1☐ varies by a factor 5, the ratio m* / n
(~1/TF) is seen to vary by the same amount, so that α = 1.0 in all cases,
within error bars.
A. Legros, S. Benhabib, W. Tabis, F. Laliberté, M. Dion, M. Lizaire, B. Vignolle, D. Vignolles, H. Raffy, Z. Z. Li, P. Auban-Senzier, N. Doiron-Leyraud, P. Fournier, D. Colson, L. Taillefer, and C. Proust, Nature Physics 15, 142 (2019)
1
⌧= ↵
kBT
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Remarkable recent observation of‘Planckian’ strange metal transport in cuprates,pnictides, magic-angle graphene, andultracold atoms: the resistivity, ⇢, is
⇢ =m⇤
ne21
⌧
with a universal scattering rate
1
⌧⇡ kBT
~ ,
independent of the strength of interactions!
Current flow without quasiparticles
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Electron scattering time ⌧ in 7 di↵erent strange metals
More on quantum black holes
J. D. Bekenstein, PRD 7, 2333 (1973)S. W. Hawking, Nature 248, 30 (1974)
Quantum Black holes
• Black holes have an entropy anda temperature, TH = ~c3/(8⇡GMkB).
• The entropy is proportional totheir surface area.
• They relax to thermal equilib-rium in a Planckian time⇠ ~/(kBTH).
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J. D. Bekenstein, PRD 7, 2333 (1973)S. W. Hawking, Nature 248, 30 (1974)
Quantum Black holes
• Black holes have an entropy anda temperature, TH = ~c3/(8⇡GMkB).
• The entropy is proportional totheir surface area.
• They relax to thermal equilib-rium in a Planckian time⇠ ~/(kBTH).
<latexit sha1_base64="CtCuY4XtgqWdISPYGjZpgV6IJPk=">AAADCnicdVLLbtNAFLVdHiU8msKSzRUJUpBQaidN2g1SFRZ0gxSkpK0Uh2g8uYmHjMdmZlwarPwBC7bwGewQW36Cr+AXuHkABcGVRjq6z3PPnSiTwljf/+Z6W1euXru+faN089btOzvl3bsnJs01xz5PZarPImZQCoV9K6zEs0wjSyKJp9Hs6TJ+eo7aiFT17DzDYcKmSkwEZ5Zco113K4xwKlQhLCbiLS5K4RKVOpLxGcSpRAMxO0dgClBZnWZzgmNgQFkZamZzjY+h2hsdwxMI44hp4C+be7VDCDMBz+A5zEadR9X6pm8vxl99hIGMQKqXVJgEm4KNUWgwuZ4wTjNpk0uFc9Ao2cUmTydUgq9zIUWkRZ6AUMSqK5niM0FsrUgQqqERyZrWXo2IAPFckUE1/r3yqFzx6+2G32oH4Nf9/cBvtggE+62DZhuCur+yirOx7qj8PRynPE9oEy6ZMYPAz+ywYLQJl0sNc4MZCcimOCCoWIJmWKyutYCH5BnDJNX0lIWV93JFwRJj5klEmQmzsfk7tnT+KzbI7eRwWAiV5RYVXw+a5Gtd6fQwFhq5lXMCjGtBXIHHTDNu6YOUQoP0e9TUxkVo8cK+EWOaUzTqDaEWpNBPGeD/4KRRD0i2F43KUWej1bZz33ng1JzAOXCOnGOn6/Qd7r5y37sf3I/eO++T99n7sk713E3NPecP877+ANI08yQ=</latexit><latexit sha1_base64="CtCuY4XtgqWdISPYGjZpgV6IJPk=">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</latexit><latexit sha1_base64="CtCuY4XtgqWdISPYGjZpgV6IJPk=">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</latexit><latexit sha1_base64="CtCuY4XtgqWdISPYGjZpgV6IJPk=">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</latexit>
All many-body quantum systems (without quantum gravity)
have an entropy proportional to their volume !?!?
Bekenstein-Hod Universal Bound onInformation Emission Rate Is Obeyed byLIGO-Virgo Binary Black Hole RemnantsGregorio Carullo, Danny Laghi, John Veitch, andWalter Del Pozzo
Phys. Rev. Lett. 126, 161102 (2021)
Published April 22, 2021
Recent ArticlesThe Weird Wiggle of PolymersAccording to the results of new neutronscattering experiments, polymer molecules inplastics move in ways that aren’t captured bycommonly used models.
Linking Glaciers on Earth to the Climate onMarsGeophysicist Jack Holt explains how Earth’sdebris-covered glaciers can teach us about theclimate history of Mars.
Sizing Up the Most Massive Neutron StarA satellite experiment has revealed that theheaviest known neutron star is unexpectedlylarge, which suggests that the matter in the star’sinner core is less “squeezable” than some modelspredict.
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ASTROPHYSICS
Compiling Messages from NeutronStarsMay 3, 2021
The combination of gravitational-wave and x-ray observations ofneutron stars provides new insight into the structure of thesestars, as well as new confirmation of Einstein’s theory of gravity.Read More »
GRAVITATION
Rising Tides on Black HolesMarch 30, 2021
New calculations show that spinning black holes—unlikenonspinning ones—can be tidally deformed by a nonsymmetricgravitational field. Read More »
PARTICLES AND FIELDS
Wormholes Open for TransportMarch 9, 2021
New theories of wormholes—postulated tunnels throughspacetime—explore whether they could be traversable byhumans. Read More »
SYNOPSIS
Black Holes Obey Information-EmissionLimitsApril 22, 2021 • Physics 14, s47
An analysis of the gravitational waves emitted from black hole mergers confirms that black holes are the fastestknown information dissipaters.
The extreme nature of black holes means that they o!er unique opportunities for testing the limits of physics laws.One law that researchers have wanted to test in this way is the one describing the maximum rate at whichinformation can flow out from a system. But until recently, this test was impossible with black holes because of alack of suitable candidates. That changed with the first measurements of gravitational waves. Now, an analysis ofthe gravitational waves detected from eight black hole mergers confirms that the law applies to these extremeobjects [1].
Any perturbed object will emit information about its state until it returns to equilibrium. Theory predicts a limit tothe rate of this information emission, with that limit depending on the object’s temperature and its relaxation time(how fast it regains equilibrium). For freshly merged black holes, these parameters are encoded in the emittedgravitational waves.
Of the roughly 50 black hole mergers so-far detected, researchers from the University of Pisa, Italy, and theUniversity of Glasgow, UK, selected eight from which they could make confident measurements of relaxation times.For each of these mergers, the team calculated the maximum average rate of information emission per unit ofenergy. They found that these rates are the fastest for any known object: about bits per second perjoule, or 75% of the theoretical maximum. At this extreme rate, perturbed black holes broadcast information at arate roughly 11 orders of magnitude higher than those involving “everyday” room-temperature objects that areroughly a meter wide.
The result confirms that black holes obey fundamental principles of general relativity, information theory, andthermodynamics—a finding that the team says wasn’t guaranteed to be true. Any future extensions to generalrelativity, they say, must obey this information bound as well.
–Christopher Crockett
Christopher Crockett is a freelance writer based in Arlington, Virginia.
References1. G. Carullo et al., “Bekenstein-Hod universal bound on information emission rate is obeyed by LIGO-Virgo
binary black hole remnants,” Phys. Rev. Lett. 126, 161102 (2021).
Subject Areas
Gravitation
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evidence case (amax ¼ bmax ¼ 100), we employ aconservative choice. In Fig. 2 we display, in blue, themedian and 90% credible intervals of the posterior prob-ability distributions pðHjDN; a; bÞ. Single-event likeli-hoods are shown in gray for comparison. We finallycompute the probability that the Bekenstein-Hod bound(gold vertical line) is obeyed on a population level, bycomputing the p-value (p ≔ pðH < 1jDN; a; bÞ) for eachof a; b sample obtained from Eq. (3). The result yields a p-value distribution strongly peaked towards unity withmedian and 90% credible levels given by p ¼ 0.94þ0.05
−0.14,where p ¼ 1 would indicate perfect agreement with theprediction, while p ¼ 0 perfect disagreement. TheBekenstein-Hod bound is respected with very high con-fidence by the observed BBH population. As an additionalcheck, we compared our result with the correspondingvalue coming from a naive point-estimate of the averageHlikelihood, the latter being insensitive to specific hierar-chical modeling choices. A weighted average over singleevents likelihoods, with weights given by the respectiveevidences, yields the red curve displayed in Fig. 2, corre-sponding to p ¼ 0.93. The excellent agreement betweenthis un-modelled estimate and the median of the hierar-chical population posterior confirms the robustness of theadopted population model.Conclusions.—BHs are expected to be the fastest dis-
sipating objects in the Universe, in the sense that they
possess the shortest possible relaxation time for a giventemperature [18]. In this Letter, we obtained an observa-tional verification of the Bekenstein-Hod informationemission bound using a Bayesian time-domain analysisapplied to the binary black holes of the LIGO-VirgoGWTC-2 catalog. The result is consistent with the pre-dictions of GR, BH thermodynamics, and informationtheory. Our analysis provides the first experimental veri-fication of a long-standing prediction on the dynamicalinformation-emission process of a BH.Software.—Open-software PYTHON packages, accessible
through PyPi, used in this work comprise CORNER,GWSURROGATE, H5PY, MATPLOTLIB, NUMBA, NumPy,SciPy, SEABORN, and surfinBH [74,75,86–92].
The authors would like to thank Aditya Vijaykumar,Giancarlo Cella, and Tjonnie Li for stimulating discussionsand Huan Yang, Alessandro Pesci for comments on themanuscript. J. V. was partially supported by STFC GrantNo. ST/K005014/2. This research has made use of data,software, and/or web tools obtained from the GravitationalWave Open Science Center [93], a service of LIGOLaboratory, the LIGO Scientific Collaboration, and theVirgo Collaboration. LIGO is funded by the U.S. NationalScience Foundation. Virgo is funded by the French CentreNational de Recherche Scientifique (CNRS), the ItalianIstituto Nazionale di Fisica Nucleare (INFN), and the DutchNikhef, with contributions by Polish and Hungarianinstitutes.
[1] R. Penrose, Phys. Rev. Lett. 14, 57 (1965).[2] S. W. Hawking and G. F. R. Ellis, The Large Scale Structure
of Space-Time (Cambridge University Press, Cambridge,England, 1973).
[3] V. Ginzburg and L. Ozernoy, Zh. Eksp. Teor. Fiz. 147, 1030(1964).
[4] A. Doroshkevic, Y. B. Zeldovich, and I. Novikov, Sov. Phys.JETP 36, 1 (1965).
[5] W. Israel, Phys. Rev. 164, 1776 (1967).[6] B. Carter, Phys. Rev. Lett. 26, 331 (1971).[7] S. W. Hawking, Commun. Math. Phys. 25, 152 (1972).[8] D. C. Robinson, Phys. Rev. Lett. 34, 905 (1975).[9] P. O. Mazur, J. Phys. A 15, 3173 (1982).
[10] G. Bunting, Ph. D. thesis University of New England,Armidale, N. S. W. (1983, to be published).
[11] F. Pretorius, Gravitational Wave Observation of Dynamical,Strong-Field Gravity, Stephen Hawking 75th BirthdayConference on Gravity and Black Holes (DAMTP, Cambridge,2017).
[12] M. Dafermos and I. Rodnianski, Clay Math. Proc. 17, 97(2013).
[13] C. W. Misner, K. S. Thorne, and J. A. Wheeler, GravitationCosmol. (1973).
[14] S. W. Hawking, Commun. Math. Phys. 43, 199 (1975).[15] R. Brito, V. Cardoso, and P. Pani, Classical Quantum
Gravity 32, 134001 (2015).
FIG. 2. Median and 90% credible levels on the Bekenstein-Hodparameter H parent distribution, obtained through a hierarchicalmodel (blue area). Single-events likelihood (grey curves) are alsodisplayed, together with their evidence-weighted average (redcurve). The probability that the bound (gold dashed line) isobeyed by the whole population are p ¼ 0.94þ0.05
−0.14 when assum-ing the posterior distribution and p ¼ 0.93 when assuming theaverage likelihood.
PHYSICAL REVIEW LETTERS 126, 161102 (2021)
161102-5
Bekenstein-Hod Universal Bound onInformation Emission Rate Is Obeyed byLIGO-Virgo Binary Black Hole RemnantsGregorio Carullo, Danny Laghi, John Veitch, andWalter Del Pozzo
Phys. Rev. Lett. 126, 161102 (2021)
Published April 22, 2021
Recent ArticlesThe Weird Wiggle of PolymersAccording to the results of new neutronscattering experiments, polymer molecules inplastics move in ways that aren’t captured bycommonly used models.
Linking Glaciers on Earth to the Climate onMarsGeophysicist Jack Holt explains how Earth’sdebris-covered glaciers can teach us about theclimate history of Mars.
Sizing Up the Most Massive Neutron StarA satellite experiment has revealed that theheaviest known neutron star is unexpectedlylarge, which suggests that the matter in the star’sinner core is less “squeezable” than some modelspredict.
More Recent Articles »
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Compiling Messages from NeutronStarsMay 3, 2021
The combination of gravitational-wave and x-ray observations ofneutron stars provides new insight into the structure of thesestars, as well as new confirmation of Einstein’s theory of gravity.Read More »
GRAVITATION
Rising Tides on Black HolesMarch 30, 2021
New calculations show that spinning black holes—unlikenonspinning ones—can be tidally deformed by a nonsymmetricgravitational field. Read More »
PARTICLES AND FIELDS
Wormholes Open for TransportMarch 9, 2021
New theories of wormholes—postulated tunnels throughspacetime—explore whether they could be traversable byhumans. Read More »
SYNOPSIS
Black Holes Obey Information-EmissionLimitsApril 22, 2021 • Physics 14, s47
An analysis of the gravitational waves emitted from black hole mergers confirms that black holes are the fastestknown information dissipaters.
The extreme nature of black holes means that they o!er unique opportunities for testing the limits of physics laws.One law that researchers have wanted to test in this way is the one describing the maximum rate at whichinformation can flow out from a system. But until recently, this test was impossible with black holes because of alack of suitable candidates. That changed with the first measurements of gravitational waves. Now, an analysis ofthe gravitational waves detected from eight black hole mergers confirms that the law applies to these extremeobjects [1].
Any perturbed object will emit information about its state until it returns to equilibrium. Theory predicts a limit tothe rate of this information emission, with that limit depending on the object’s temperature and its relaxation time(how fast it regains equilibrium). For freshly merged black holes, these parameters are encoded in the emittedgravitational waves.
Of the roughly 50 black hole mergers so-far detected, researchers from the University of Pisa, Italy, and theUniversity of Glasgow, UK, selected eight from which they could make confident measurements of relaxation times.For each of these mergers, the team calculated the maximum average rate of information emission per unit ofenergy. They found that these rates are the fastest for any known object: about bits per second perjoule, or 75% of the theoretical maximum. At this extreme rate, perturbed black holes broadcast information at arate roughly 11 orders of magnitude higher than those involving “everyday” room-temperature objects that areroughly a meter wide.
The result confirms that black holes obey fundamental principles of general relativity, information theory, andthermodynamics—a finding that the team says wasn’t guaranteed to be true. Any future extensions to generalrelativity, they say, must obey this information bound as well.
–Christopher Crockett
Christopher Crockett is a freelance writer based in Arlington, Virginia.
References1. G. Carullo et al., “Bekenstein-Hod universal bound on information emission rate is obeyed by LIGO-Virgo
binary black hole remnants,” Phys. Rev. Lett. 126, 161102 (2021).
Subject Areas
Gravitation
Related Articles
ABOUT BROWSE PRESS COLLECTIONS Search articles
Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement.
Physics Magazine PhysicsCentral APS News Log inJournals
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2. 2 × 1034
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Bekenstein-Hod Universal Bound onInformation Emission Rate Is Obeyed byLIGO-Virgo Binary Black Hole RemnantsGregorio Carullo, Danny Laghi, John Veitch, andWalter Del Pozzo
Phys. Rev. Lett. 126, 161102 (2021)
Published April 22, 2021
Recent ArticlesThe Weird Wiggle of PolymersAccording to the results of new neutronscattering experiments, polymer molecules inplastics move in ways that aren’t captured bycommonly used models.
Linking Glaciers on Earth to the Climate onMarsGeophysicist Jack Holt explains how Earth’sdebris-covered glaciers can teach us about theclimate history of Mars.
Sizing Up the Most Massive Neutron StarA satellite experiment has revealed that theheaviest known neutron star is unexpectedlylarge, which suggests that the matter in the star’sinner core is less “squeezable” than some modelspredict.
More Recent Articles »
APS News and Announcements Join APS Contact Us
APS JOURNALS
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Authors
Referees
Subscriptions
STUDENTS
Physics
PhysicsCentral
Student Membership
APS MEMBERS
Subscriptions
Article Packs
Membership
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APS News
Meetings & Events
Privacy Policies Contact Information Feedback
ASTROPHYSICS
Compiling Messages from NeutronStarsMay 3, 2021
The combination of gravitational-wave and x-ray observations ofneutron stars provides new insight into the structure of thesestars, as well as new confirmation of Einstein’s theory of gravity.Read More »
GRAVITATION
Rising Tides on Black HolesMarch 30, 2021
New calculations show that spinning black holes—unlikenonspinning ones—can be tidally deformed by a nonsymmetricgravitational field. Read More »
PARTICLES AND FIELDS
Wormholes Open for TransportMarch 9, 2021
New theories of wormholes—postulated tunnels throughspacetime—explore whether they could be traversable byhumans. Read More »
SYNOPSIS
Black Holes Obey Information-EmissionLimitsApril 22, 2021 • Physics 14, s47
An analysis of the gravitational waves emitted from black hole mergers confirms that black holes are the fastestknown information dissipaters.
The extreme nature of black holes means that they o!er unique opportunities for testing the limits of physics laws.One law that researchers have wanted to test in this way is the one describing the maximum rate at whichinformation can flow out from a system. But until recently, this test was impossible with black holes because of alack of suitable candidates. That changed with the first measurements of gravitational waves. Now, an analysis ofthe gravitational waves detected from eight black hole mergers confirms that the law applies to these extremeobjects [1].
Any perturbed object will emit information about its state until it returns to equilibrium. Theory predicts a limit tothe rate of this information emission, with that limit depending on the object’s temperature and its relaxation time(how fast it regains equilibrium). For freshly merged black holes, these parameters are encoded in the emittedgravitational waves.
Of the roughly 50 black hole mergers so-far detected, researchers from the University of Pisa, Italy, and theUniversity of Glasgow, UK, selected eight from which they could make confident measurements of relaxation times.For each of these mergers, the team calculated the maximum average rate of information emission per unit ofenergy. They found that these rates are the fastest for any known object: about bits per second perjoule, or 75% of the theoretical maximum. At this extreme rate, perturbed black holes broadcast information at arate roughly 11 orders of magnitude higher than those involving “everyday” room-temperature objects that areroughly a meter wide.
The result confirms that black holes obey fundamental principles of general relativity, information theory, andthermodynamics—a finding that the team says wasn’t guaranteed to be true. Any future extensions to generalrelativity, they say, must obey this information bound as well.
–Christopher Crockett
Christopher Crockett is a freelance writer based in Arlington, Virginia.
References1. G. Carullo et al., “Bekenstein-Hod universal bound on information emission rate is obeyed by LIGO-Virgo
binary black hole remnants,” Phys. Rev. Lett. 126, 161102 (2021).
Subject Areas
Gravitation
Related Articles
ABOUT BROWSE PRESS COLLECTIONS Search articles
Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement.
Physics Magazine PhysicsCentral APS News Log inJournals
the_lightwriter/stock.adobe.com
2. 2 × 1034
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Bekenstein-Hod Universal Bound onInformation Emission Rate Is Obeyed byLIGO-Virgo Binary Black Hole RemnantsGregorio Carullo, Danny Laghi, John Veitch, andWalter Del Pozzo
Phys. Rev. Lett. 126, 161102 (2021)
Published April 22, 2021
Recent ArticlesThe Weird Wiggle of PolymersAccording to the results of new neutronscattering experiments, polymer molecules inplastics move in ways that aren’t captured bycommonly used models.
Linking Glaciers on Earth to the Climate onMarsGeophysicist Jack Holt explains how Earth’sdebris-covered glaciers can teach us about theclimate history of Mars.
Sizing Up the Most Massive Neutron StarA satellite experiment has revealed that theheaviest known neutron star is unexpectedlylarge, which suggests that the matter in the star’sinner core is less “squeezable” than some modelspredict.
More Recent Articles »
APS News and Announcements Join APS Contact Us
APS JOURNALS
About
Authors
Referees
Subscriptions
STUDENTS
Physics
PhysicsCentral
Student Membership
APS MEMBERS
Subscriptions
Article Packs
Membership
FAQ
APS News
Meetings & Events
Privacy Policies Contact Information Feedback
ASTROPHYSICS
Compiling Messages from NeutronStarsMay 3, 2021
The combination of gravitational-wave and x-ray observations ofneutron stars provides new insight into the structure of thesestars, as well as new confirmation of Einstein’s theory of gravity.Read More »
GRAVITATION
Rising Tides on Black HolesMarch 30, 2021
New calculations show that spinning black holes—unlikenonspinning ones—can be tidally deformed by a nonsymmetricgravitational field. Read More »
PARTICLES AND FIELDS
Wormholes Open for TransportMarch 9, 2021
New theories of wormholes—postulated tunnels throughspacetime—explore whether they could be traversable byhumans. Read More »
SYNOPSIS
Black Holes Obey Information-EmissionLimitsApril 22, 2021 • Physics 14, s47
An analysis of the gravitational waves emitted from black hole mergers confirms that black holes are the fastestknown information dissipaters.
The extreme nature of black holes means that they o!er unique opportunities for testing the limits of physics laws.One law that researchers have wanted to test in this way is the one describing the maximum rate at whichinformation can flow out from a system. But until recently, this test was impossible with black holes because of alack of suitable candidates. That changed with the first measurements of gravitational waves. Now, an analysis ofthe gravitational waves detected from eight black hole mergers confirms that the law applies to these extremeobjects [1].
Any perturbed object will emit information about its state until it returns to equilibrium. Theory predicts a limit tothe rate of this information emission, with that limit depending on the object’s temperature and its relaxation time(how fast it regains equilibrium). For freshly merged black holes, these parameters are encoded in the emittedgravitational waves.
Of the roughly 50 black hole mergers so-far detected, researchers from the University of Pisa, Italy, and theUniversity of Glasgow, UK, selected eight from which they could make confident measurements of relaxation times.For each of these mergers, the team calculated the maximum average rate of information emission per unit ofenergy. They found that these rates are the fastest for any known object: about bits per second perjoule, or 75% of the theoretical maximum. At this extreme rate, perturbed black holes broadcast information at arate roughly 11 orders of magnitude higher than those involving “everyday” room-temperature objects that areroughly a meter wide.
The result confirms that black holes obey fundamental principles of general relativity, information theory, andthermodynamics—a finding that the team says wasn’t guaranteed to be true. Any future extensions to generalrelativity, they say, must obey this information bound as well.
–Christopher Crockett
Christopher Crockett is a freelance writer based in Arlington, Virginia.
References1. G. Carullo et al., “Bekenstein-Hod universal bound on information emission rate is obeyed by LIGO-Virgo
binary black hole remnants,” Phys. Rev. Lett. 126, 161102 (2021).
Subject Areas
Gravitation
Related Articles
ABOUT BROWSE PRESS COLLECTIONS Search articles
Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement.
Physics Magazine PhysicsCentral APS News Log inJournals
the_lightwriter/stock.adobe.com
2. 2 × 1034
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<latexit sha1_base64="NYV50rAFYBh9+xBO5uYZuT4tlWg=">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</latexit>
H =1
⇡
~/⌧kBT
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Gravity waveobservations of
8 di↵erent black holesshow a relaxation time
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⌧ ⇠ ~kBT
G. Carullo, D. Laghi, J. Veitch, W. Del Pozzo, Phys. Rev. Lett. 126, 161102 (2021)
Quantum Black holes
• Black holes have an entropy anda temperature, TH = ~c3/(8⇡GMkB).
• The entropy is proportional totheir surface area.
• They relax to thermal equilib-rium in a Planckian time⇠ ~/(kBTH).
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All many-body quantum systems (without quantum gravity)
have an entropy proportional to their volume !?!?
Quantum Black holes
• Black holes have an entropy anda temperature, TH = ~c3/(8⇡GMkB).
• The entropy is proportional totheir surface area.
• They relax to thermal equilib-rium in a Planckian time⇠ ~/(kBTH).
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Black holes are represented as a `hologram’ by a quantum many-body system in one lower dimension.
Duality: a `change of variables’ between the
many-particle configurations and the metric of spacetime
Susskind, Maldacena…..
Quantum Black holes
• Black holes have an entropy anda temperature, TH = ~c3/(8⇡GMkB).
• The entropy is proportional totheir surface area.
• They relax to thermal equilib-rium in a Planckian time⇠ ~/(kBTH).
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The hologram of a black holein d dimensions
is a quantum many-particle systemin (d� 1) dimensions
which relaxes to thermal equilibriumin a Planckian time ⇠ ~/(kBT )
~x⇣
Maxwell’s electromagnetism and Einstein’s general relativity
allow black hole solutions with a net charge
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The near-horizongeometry of a
charged black hole isone-dimensional (⇣)
~x⇣
Maxwell’s electromagnetism and Einstein’s general relativity
allow black hole solutions with a net charge
The hologram of the 1+1 dimensional gravity near the
horizon of a charged black hole is the 0+1 dimensional
SYK model
Sachdev (2010); Kitaev (2015); Sachdev (2015); Maldacena, Stanford, Yang (2016) ; Moitra, Trivedi, Vishal (2018) ; Gaikwad, Joshi, Mandal, Wadia (2018); Iliesiu, Turaci (2020)
The SYK model has a scale-invariant entanglement structure:
i.e. electrons are entangled at all distance and time scales
In one set of variables, it describes
certain strange metals
In a dual set of variables it describes certain black holes
The Sachdev-Ye-Kitaev (SYK) model
Sachdev (2010), Kitaev (2015), Maldacena Stanford (2015)
Sachdev, Ye (1993)
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