From: jos.bergervoet@xs4all.nl   
      
   On 1/5/2018 11:25 PM, Lawrence Crowell wrote:   
   > I answered an outstanding question on the physics stack exchange on page   
   > time and information scrambling. Below are the first three paragraphs of   
   > the answer.   
   >   
   > The Page time comes about because of the nature of entanglement. For a   
   > cavity emitter of black body radiation a photon emitted early on is   
   > entangled with atomic states in the cavity. However, once half the   
   > energy in the cavity is emitted subsequent radiation emitted is   
   > entangled with radiation emitted earlier. As a result the entanglement   
   > entropy increases to some maximum, at about half the energy emitted, and   
   > then declines. The entangled states are towards the end in the form of   
   > emitted radiation.   
   >   
   > A black hole is similar in that Hawking radiation is emitted from an   
   > entangled pair of photons or electron positron pairs. One enters the   
   > black hole and the other escapes to infinity. At the half way mark,   
   > where the black hole has emitted half its mass a conundrum becomes   
   > apparent. The black hole continues to build up entanglement entropy by   
   > this process. It will exceed the Bekenstein entropy bound. If this is   
   > prevented by assuming entanglement of later Hawking radiation is   
   > entangled with early Hawking radiation this force bipartite   
   > entanglements to evolve into tripartite states, which is not possible by   
   > unitary evolution. This is said to violate the monogamy rule. This   
   > generally occurs at the so called Page time.   
   >   
   > The idea then is that something catastrophic happens where either   
   > unitary evolution or the equivalence principle fails. Preference is   
   > given to unitarity, so the equivalence principle is said to fail at the   
   > so called firewall.   
      
   Where does this analysis change if we allow "Soft Hair on Black   
   Holes" as introduced by Hawking, Perry, Strominger, and others?   
      
   This was supposed to give one way out of the paradox! Presumably   
   much more work has been done since then..   
      
   [1] Hawking, Perry and Strominger    
   [2]   
      
   [3] Kapec, Raclariu and Strominger .   
      
   --   
   Jos   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)