Black hole complementarity and firewalls
Jonathan Shi
Physics 486
January 31, 2013
Jonathan Shi Physics 486 Black hole complementarity and firewalls 1 1 chance of |↑i and chance of |↓i 2 Z 2 Z 1 = chance of (|↑iX + |↓iX ) = |↑iX 2 1 and chance of (|↑i − |↓i ) 2 X X 1 1 =⇒ chance of |↑i and chance of |↓i 2 X 2 X
Pure and mixed states
Mixed states Pure states Example: Example: 1 √ (|↑i + |↓i ) 2 Z Z
Jonathan Shi Physics 486 Black hole complementarity and firewalls 1 1 chance of |↑i and chance of |↓i 2 Z 2 Z 1 = chance of (|↑i + |↓i ) 2 X X 1 and chance of (|↑i − |↓i ) 2 X X 1 1 =⇒ chance of |↑i and chance of |↓i 2 X 2 X
Pure and mixed states
Mixed states Pure states Example: Example: 1 √ (|↑i + |↓i ) 2 Z Z
= |↑iX
Jonathan Shi Physics 486 Black hole complementarity and firewalls 1 = chance of (|↑i + |↓i ) 2 X X 1 and chance of (|↑i − |↓i ) 2 X X 1 1 =⇒ chance of |↑i and chance of |↓i 2 X 2 X
Pure and mixed states
Mixed states Pure states Example: Example: 1 1 1 chance of |↑i and chance of |↓i √ (|↑i + |↓i ) 2 Z 2 Z 2 Z Z
= |↑iX
Jonathan Shi Physics 486 Black hole complementarity and firewalls Pure and mixed states
Mixed states Pure states Example: Example: 1 1 1 chance of |↑i and chance of |↓i 2 Z 2 Z √ (|↑iZ + |↓iZ ) 2 1 = chance of (|↑iX + |↓iX ) = |↑iX 2 1 and chance of (|↑i − |↓i ) 2 X X 1 1 =⇒ chance of |↑i and chance of |↓i 2 X 2 X
Jonathan Shi Physics 486 Black hole complementarity and firewalls State evolution: |ψ(t)i = U(t) |ψ(0)i Rotations: |ψi |φi → |φi |ψi or
|ψiZ |φiZ → |ψiX |φiX No-cloning theorem: |ψi |0i 6→ |ψi |ψi No information loss: |ψi 6→ |0i No evolution to mixed states: |ψi 6→ mixed state
Unitarity
Unitary transformation: U†U = I
Jonathan Shi Physics 486 Black hole complementarity and firewalls Rotations: |ψi |φi → |φi |ψi or
|ψiZ |φiZ → |ψiX |φiX No-cloning theorem: |ψi |0i 6→ |ψi |ψi No information loss: |ψi 6→ |0i No evolution to mixed states: |ψi 6→ mixed state
Unitarity
Unitary transformation: U†U = I State evolution: |ψ(t)i = U(t) |ψ(0)i
Jonathan Shi Physics 486 Black hole complementarity and firewalls No-cloning theorem: |ψi |0i 6→ |ψi |ψi No information loss: |ψi 6→ |0i No evolution to mixed states: |ψi 6→ mixed state
Unitarity
Unitary transformation: U†U = I State evolution: |ψ(t)i = U(t) |ψ(0)i Rotations: |ψi |φi → |φi |ψi or
|ψiZ |φiZ → |ψiX |φiX
Jonathan Shi Physics 486 Black hole complementarity and firewalls No information loss: |ψi 6→ |0i No evolution to mixed states: |ψi 6→ mixed state
Unitarity
Unitary transformation: U†U = I State evolution: |ψ(t)i = U(t) |ψ(0)i Rotations: |ψi |φi → |φi |ψi or
|ψiZ |φiZ → |ψiX |φiX No-cloning theorem: |ψi |0i 6→ |ψi |ψi
Jonathan Shi Physics 486 Black hole complementarity and firewalls No evolution to mixed states: |ψi 6→ mixed state
Unitarity
Unitary transformation: U†U = I State evolution: |ψ(t)i = U(t) |ψ(0)i Rotations: |ψi |φi → |φi |ψi or
|ψiZ |φiZ → |ψiX |φiX No-cloning theorem: |ψi |0i 6→ |ψi |ψi No information loss: |ψi 6→ |0i
Jonathan Shi Physics 486 Black hole complementarity and firewalls Unitarity
Unitary transformation: U†U = I State evolution: |ψ(t)i = U(t) |ψ(0)i Rotations: |ψi |φi → |φi |ψi or
|ψiZ |φiZ → |ψiX |φiX No-cloning theorem: |ψi |0i 6→ |ψi |ψi No information loss: |ψi 6→ |0i No evolution to mixed states: |ψi 6→ mixed state
Jonathan Shi Physics 486 Black hole complementarity and firewalls Outgoing radiation seemingly random... so in a mixed state Unitarity broken!
The black hole information paradox
Hawking radiation: strong gravitational field causes more pair production... sometimes one particle falls past the event horizon while the other particle escapes
Jonathan Shi Physics 486 Black hole complementarity and firewalls Unitarity broken!
The black hole information paradox
Hawking radiation: strong gravitational field causes more pair production... sometimes one particle falls past the event horizon while the other particle escapes Outgoing radiation seemingly random... so in a mixed state
Jonathan Shi Physics 486 Black hole complementarity and firewalls The black hole information paradox
Hawking radiation: strong gravitational field causes more pair production... sometimes one particle falls past the event horizon while the other particle escapes Outgoing radiation seemingly random... so in a mixed state Unitarity broken!
Jonathan Shi Physics 486 Black hole complementarity and firewalls State of Hawking radiation determined by ripples Unitarity saved? Not so fast! Since an infalling observer sees the inside of a black hole, there are now two copies of the information: one inside and one outside!
Solution(?) via the holographic principle
Holographic principle: all information inside the black hole encoded in gravitational ripples around the surface!
Jonathan Shi Physics 486 Black hole complementarity and firewalls Unitarity saved? Not so fast! Since an infalling observer sees the inside of a black hole, there are now two copies of the information: one inside and one outside!
Solution(?) via the holographic principle
Holographic principle: all information inside the black hole encoded in gravitational ripples around the surface! State of Hawking radiation determined by ripples
Jonathan Shi Physics 486 Black hole complementarity and firewalls Not so fast! Since an infalling observer sees the inside of a black hole, there are now two copies of the information: one inside and one outside!
Solution(?) via the holographic principle
Holographic principle: all information inside the black hole encoded in gravitational ripples around the surface! State of Hawking radiation determined by ripples Unitarity saved?
Jonathan Shi Physics 486 Black hole complementarity and firewalls Solution(?) via the holographic principle
Holographic principle: all information inside the black hole encoded in gravitational ripples around the surface! State of Hawking radiation determined by ripples Unitarity saved? Not so fast! Since an infalling observer sees the inside of a black hole, there are now two copies of the information: one inside and one outside!
Jonathan Shi Physics 486 Black hole complementarity and firewalls Infalling and external observables complementary, like how position and momentum of the same particle are complementary. Posit that the information is not cloned, just the same information embodied at two different places. Then no contradiction! Although maybe counterintuitive.
Black hole complementarity
Infalling observer and external observer causally separated.
Jonathan Shi Physics 486 Black hole complementarity and firewalls Posit that the information is not cloned, just the same information embodied at two different places. Then no contradiction! Although maybe counterintuitive.
Black hole complementarity
Infalling observer and external observer causally separated. Infalling and external observables complementary, like how position and momentum of the same particle are complementary.
Jonathan Shi Physics 486 Black hole complementarity and firewalls Then no contradiction! Although maybe counterintuitive.
Black hole complementarity
Infalling observer and external observer causally separated. Infalling and external observables complementary, like how position and momentum of the same particle are complementary. Posit that the information is not cloned, just the same information embodied at two different places.
Jonathan Shi Physics 486 Black hole complementarity and firewalls Black hole complementarity
Infalling observer and external observer causally separated. Infalling and external observables complementary, like how position and momentum of the same particle are complementary. Posit that the information is not cloned, just the same information embodied at two different places. Then no contradiction! Although maybe counterintuitive.
Jonathan Shi Physics 486 Black hole complementarity and firewalls AMPS team: Almheiri, Marolf, Polchinski, Sully AMPS team found that unitarity and semiclassical approximation for an external observer implies general relativity fails for infalling observer.
Problems with complementarity?
Introducing a large number of scalar fields (”Large N limit”) causes some observer to see a causality paradox
Jonathan Shi Physics 486 Black hole complementarity and firewalls AMPS team found that unitarity and semiclassical approximation for an external observer implies general relativity fails for infalling observer.
Problems with complementarity?
Introducing a large number of scalar fields (”Large N limit”) causes some observer to see a causality paradox AMPS team: Almheiri, Marolf, Polchinski, Sully
Jonathan Shi Physics 486 Black hole complementarity and firewalls Problems with complementarity?
Introducing a large number of scalar fields (”Large N limit”) causes some observer to see a causality paradox AMPS team: Almheiri, Marolf, Polchinski, Sully AMPS team found that unitarity and semiclassical approximation for an external observer implies general relativity fails for infalling observer.
Jonathan Shi Physics 486 Black hole complementarity and firewalls Firewall maybe salvages complementarity by obliterating the infalling observer? Susskind suggested firewall is the singularity? Problem: Firewall becomes externally observable in some circumstances
The firewall
AMPS derived a ”firewall” of high-energy modes for infalling observer
Jonathan Shi Physics 486 Black hole complementarity and firewalls Susskind suggested firewall is the singularity? Problem: Firewall becomes externally observable in some circumstances
The firewall
AMPS derived a ”firewall” of high-energy modes for infalling observer Firewall maybe salvages complementarity by obliterating the infalling observer?
Jonathan Shi Physics 486 Black hole complementarity and firewalls Problem: Firewall becomes externally observable in some circumstances
The firewall
AMPS derived a ”firewall” of high-energy modes for infalling observer Firewall maybe salvages complementarity by obliterating the infalling observer? Susskind suggested firewall is the singularity?
Jonathan Shi Physics 486 Black hole complementarity and firewalls The firewall
AMPS derived a ”firewall” of high-energy modes for infalling observer Firewall maybe salvages complementarity by obliterating the infalling observer? Susskind suggested firewall is the singularity? Problem: Firewall becomes externally observable in some circumstances
Jonathan Shi Physics 486 Black hole complementarity and firewalls Black hole complementarity a proposed solution Causality and QM paradoxes for complementarity Firewalls possibly fix paradoxes? Firewalls have paradoxes of their own. More paradoxes! No end in sight!
Review
Black hole information paradox
Jonathan Shi Physics 486 Black hole complementarity and firewalls Causality and QM paradoxes for complementarity Firewalls possibly fix paradoxes? Firewalls have paradoxes of their own. More paradoxes! No end in sight!
Review
Black hole information paradox Black hole complementarity a proposed solution
Jonathan Shi Physics 486 Black hole complementarity and firewalls Firewalls possibly fix paradoxes? Firewalls have paradoxes of their own. More paradoxes! No end in sight!
Review
Black hole information paradox Black hole complementarity a proposed solution Causality and QM paradoxes for complementarity
Jonathan Shi Physics 486 Black hole complementarity and firewalls Firewalls have paradoxes of their own. More paradoxes! No end in sight!
Review
Black hole information paradox Black hole complementarity a proposed solution Causality and QM paradoxes for complementarity Firewalls possibly fix paradoxes?
Jonathan Shi Physics 486 Black hole complementarity and firewalls More paradoxes! No end in sight!
Review
Black hole information paradox Black hole complementarity a proposed solution Causality and QM paradoxes for complementarity Firewalls possibly fix paradoxes? Firewalls have paradoxes of their own.
Jonathan Shi Physics 486 Black hole complementarity and firewalls Review
Black hole information paradox Black hole complementarity a proposed solution Causality and QM paradoxes for complementarity Firewalls possibly fix paradoxes? Firewalls have paradoxes of their own. More paradoxes! No end in sight!
Jonathan Shi Physics 486 Black hole complementarity and firewalls References
D. Hwang, B. Lee, and D. Yeom, “Is the firewall consistent? Gedanken experiments on black hole complementarity and firewall proposal”, J. of Cosmology and Astroparticle Physics. 01(2013)005.
A. Almheiri, D. Marolf, J. Polchinski, and J. Sully, “Black Holes: Complementarity or Firewalls?”, preprint (2012): arXiv:hep-ph/1207.3123v2.
E. Verlinde and H. Verlinde. “Black Hole Entanglement and Quantum Error Correction”, preprint (2012): arXiv:hep-th/1211.6913.
L. Susskind. “The Transfer of Entanglement: The Case for Firewalls”, preprint (2012): arXiv:hep-th/1210.2098.
L. Susskind. “Complementarity And Firewalls”, preprint (2012): arXiv:hep-th/1207.4090.
L. Susskind. “Singularities, Firewalls, and Complementarity’, preprint (2012): arXiv:hep-th/1208.3445.
Jonathan Shi Physics 486 Black hole complementarity and firewalls