Sunday, November 23, 2014

quantum field theory - Is the firewall paradox really a paradox?


The firewall paradox is a very hot topic at the moment (1207.3123v4). Everyone who is anybody in theoretical physics seems to be jumping into the action (Maldacena, Polchinski, Susskind to name a few).


However, I am unable to see the paradox. To me Hawking's resolution of the information paradox (hep-th/0507171) also resolves the so called firewall paradox. Hawking never says that the information is not lost on a fixed black hole background. In fact, he says the opposite. He says (page 3): "So in the end everyone was right in a way. Information is lost in topologically non-trivial metrics like black holes. This corresponds to dissipation in which one loses sight of the exact state. On the other hand, information about the exact state is preserved in topologically trivial metrics. The confusion and paradox arose because people thought classically in terms of a single topology for spacetime."


To surmise, in quantum gravity you don't know if you actually have a black hole or not, so you have to include the trivial topologies, including those when there isn't a black hole there, in the amplitude. Only then do recover unitarity.


It seems to me that the error of the AMPS guys is that they use a fixed black hole background and assume conservation of information (i.e., late time radiation is maximally entangled with early time radiation). It is no wonder they are lead to a contradiction. They are simply doing the information paradox yet again.



They give a menu of implications in the abstract: (i) Hawking radiation is in a pure state, (ii) the information carried by the radiation is emitted from the region near the horizon, with low energy effective field theory valid beyond some microscopic distance from the horizon, and (iii) the infalling observer encounters nothing unusual at the horizon.


But the obvious solution is that (i) is wrong. The radiation, within the semi-classical calculation in which they calculate it (i.e., not quantum gravity), is non-unitary.


So my question is, why is this a paradox? Something so obvious surely can not be overlooked by the ``masters'' of physics. Therefore I'd like to hear your opinions.




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