User:Aflemingclt/sandbox

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Black Hole Complementarity and Firewalls
The Hayden-Preskill thought experiment implies that information that falls into a black hole can be recovered via the hawking radiation, which begs the question: does the information that falls into a black hole fall in or radiate out? One approach to this is the concept of black hole complementarity, which claims that an observer orbiting a black hole observes the information radiating out as hawking radiation, while an observer that falls into the black hole observes the information falling inward. This does not seem to violate the no cloning principle of quantum mechanics since you can only measure one or the other; if you fall into a black hole and measure a qubit, you can't leave and then measure the hawking radiation. Black hole complementarity has four basic postulates:


 * 1) Hawking radiation is in a pure state. The black hole can be thought of as a quantum operator, which takes the quantum state of the original mass and converts it into the quantum state of the hawking radiation, as viewed by a distant observer.
 * 2) Outside of the black hole's event horizon, semi-classical field equations remain valid.
 * 3) A black hole is a quantum system with discrete energy levels, as viewed by a distant observer.
 * 4) A free falling observer encounters nothing unique or strange; passing the event horizon is not marked by observable phenomena intrinsic to the horizon itself.

According to Almheiri, Marolf, Polchinski, and Sully, postulates 1, 2, and 4 feature a contradiction. Say we divide the hawking radiation leaving the black hole into two time frames: one "early," and one "late." Because the hawking radiation is a pure state based on the quantum wave function of the original mass, the late hawking radiation must be entangled with the early hawking radiation. However, black hole complementarity also implies that the outgoing hawking radiation is entangled with the information inside the black hole. This violates what is known as "monogamy of entanglement," the idea that a quantum system can only be entangled with one other quantum system. To fix this problem, either postulate 2 or postulate 4 must be false: if postulate 2 is false, then there must be some exotic dynamics extending beyond the event horizon that resolve this conflict; if postulate 4 is false, then the entanglement of the inner and outer information must be broken, leading to the creation of high-energy modes. These high-energy modes create a "firewall" that burns up anything that enters the black hole.