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 j"i and chance of j#i 2 Z 2 Z 1 = chance of (j"iX + j#iX ) = j"iX 2 1 and chance of (j"i − j#i ) 2 X X 1 1 =) chance of j"i and chance of j#i 2 X 2 X Pure and mixed states Mixed states Pure states Example: Example: 1 p (j"i + j#i ) 2 Z Z Jonathan Shi Physics 486 Black hole complementarity and firewalls 1 1 chance of j"i and chance of j#i 2 Z 2 Z 1 = chance of (j"i + j#i ) 2 X X 1 and chance of (j"i − j#i ) 2 X X 1 1 =) chance of j"i and chance of j#i 2 X 2 X Pure and mixed states Mixed states Pure states Example: Example: 1 p (j"i + j#i ) 2 Z Z = j"iX Jonathan Shi Physics 486 Black hole complementarity and firewalls 1 = chance of (j"i + j#i ) 2 X X 1 and chance of (j"i − j#i ) 2 X X 1 1 =) chance of j"i and chance of j#i 2 X 2 X Pure and mixed states Mixed states Pure states Example: Example: 1 1 1 chance of j"i and chance of j#i p (j"i + j#i ) 2 Z 2 Z 2 Z Z = j"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 j"i and chance of j#i 2 Z 2 Z p (j"iZ + j#iZ ) 2 1 = chance of (j"iX + j#iX ) = j"iX 2 1 and chance of (j"i − j#i ) 2 X X 1 1 =) chance of j"i and chance of j#i 2 X 2 X Jonathan Shi Physics 486 Black hole complementarity and firewalls State evolution: j (t)i = U(t) j (0)i Rotations: j i jφi ! jφi j i or j iZ jφiZ ! j iX jφiX No-cloning theorem: j i j0i 6! j i j i No information loss: j i 6! j0i No evolution to mixed states: j i 6! mixed state Unitarity Unitary transformation: UyU = I Jonathan Shi Physics 486 Black hole complementarity and firewalls Rotations: j i jφi ! jφi j i or j iZ jφiZ ! j iX jφiX No-cloning theorem: j i j0i 6! j i j i No information loss: j i 6! j0i No evolution to mixed states: j i 6! mixed state Unitarity Unitary transformation: UyU = I State evolution: j (t)i = U(t) j (0)i Jonathan Shi Physics 486 Black hole complementarity and firewalls No-cloning theorem: j i j0i 6! j i j i No information loss: j i 6! j0i No evolution to mixed states: j i 6! mixed state Unitarity Unitary transformation: UyU = I State evolution: j (t)i = U(t) j (0)i Rotations: j i jφi ! jφi j i or j iZ jφiZ ! j iX jφiX Jonathan Shi Physics 486 Black hole complementarity and firewalls No information loss: j i 6! j0i No evolution to mixed states: j i 6! mixed state Unitarity Unitary transformation: UyU = I State evolution: j (t)i = U(t) j (0)i Rotations: j i jφi ! jφi j i or j iZ jφiZ ! j iX jφiX No-cloning theorem: j i j0i 6! j i j i Jonathan Shi Physics 486 Black hole complementarity and firewalls No evolution to mixed states: j i 6! mixed state Unitarity Unitary transformation: UyU = I State evolution: j (t)i = U(t) j (0)i Rotations: j i jφi ! jφi j i or j iZ jφiZ ! j iX jφiX No-cloning theorem: j i j0i 6! j i j i No information loss: j i 6! j0i Jonathan Shi Physics 486 Black hole complementarity and firewalls Unitarity Unitary transformation: UyU = I State evolution: j (t)i = U(t) j (0)i Rotations: j i jφi ! jφi j i or j iZ jφiZ ! j iX jφiX No-cloning theorem: j i j0i 6! j i j i No information loss: j i 6! j0i No evolution to mixed states: j i 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