Wednesday, January 11, 2006

Black hole final state

If you're more interested in the illusion of Intelligent Design, you can read this interview with Lenny Susskind who has his predecessor on his T-shirt. ;-) As the reviewer of the Cosmic Landscape at amazon.com wrote, this book has certainly energized God.

Eva Silverstein and Gary Horowitz have submitted an interesting paper that extends the research of the tachyons in cosmology and their impact on topology of spacetime. We talked about these things in the article about the theory of nothing.

One of the potentially far-reaching consequences of Eva's and Gary's paper is that they seem to have found some stringy realization of the black hole final state by Horowitz and Maldacena. Recall that Horowitz and Maldacena try to explain the information loss paradox semiclassically by saying that the information is not lost in the Schwarzschild singularity because all matter converges to a unique state near the singularity - the black hole final state. This is why no information really "crosses" the spacelike singularity inside the Schwarzschild.




In some sense, the matter propagates outside the black hole before it falls in. Then it continues inside the black hole to the singularity, bounces off the singularity because the unique black hole final state translates the incoming states into outgoing states. Then the matter propagates backward in time inside the black hole before it reaches the horizon and transforms into Hawking radiation that escapes to infinity. As you can see, the arrow of time is heavily violated near the singularity because normally we are only allowed to define initial states, not final states. Unitarity is preserved in the picture above because everything evolves with "time" in a unitary way except that this "time" goes back and forth in the real time, in some sense.

Preskill and Gottesman argued that once the interactions are taken into account, unitarity will be lost in the Horowitz-Maldacena picture anyway because the two Hilbert spaces of matter inside the black hole - that are used for the incoming and reflected matter, respectively - are no longer decoupled. These interpretations of the picture are due to your humble correspondent, but I believe that they capture the points of both papers.

Horowitz and Silverstein now argue that in perturbative CFTs with some tachyons, the black hole final state can be given quite an explicit form.

Because we talked about the information loss issues, I should also mention that tonight, David Lowe and Larus Thorlacius propose a plausible description of non-local effects in gravity that are small enough not to violate causality measurably but sufficient to preserve the information.

2 comments:

  1. From a layman point of view I have been trying to follow this, and it is very difficult. But it seems I have come to recognize that if the vitality of extra-dimensional scenrio is ever given credence, then this would be very hard not to accept when the views of what manifests from the collision process in RHIC and LHC......

    Any thoughts here.

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  2. Lubos:

    You are discussing concepts of quantum mechanics: particles, wavefunctions, states, quantum entanglement, near locations where it's highly relativistic (highly GR). Such a discussion is not very meaning because we still don't have a theory where you can put QM and GR together consistently. So your discussion under such scenary is inheritantly inconsistent logically, we just do not know where the inconsistency precisely is. But clearly in GR it requires strict locality: You need to know your precise position to determine where you are insider the event horizon, or just outside, if you are nearby. But QM does not give you that certainty of position.

    The mathematical forms of both GR and QM are exactly time reversible. So if you worry about information loss, you should equally worry about the time reversed effect, i.e., information expansion.

    The correct solution is recognize that and make it a fundamental principle that quantum information shall never be lost nor be created, and shall remain invariant. Once you set that rule up, you then figure out how GR or QM, or both, can be modified to satisfy that requirement. That's is the correct approach I am taking in developing my QUITAR theory, and it's proven to be very successful in both reconciling QM and GR, as well as give out precise and accurate numerical results.

    Quantoken

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