On Saturday, January 13, 2018 at 5:56:01 PM UTC-6, John Clark wrote: > > On Sat, Jan 13, 2018 at 2:35 PM, Lawrence Crowell < > goldenfield...@gmail.com <javascript:>> wrote: > > > >> Go to https://jila.colorado.edu/~ajsh/insidebh/ to look an numerical >> simulations of what falling into a black hole would appear as. In effect >> nothing spectacularly different appears upon crossing the horizon. >> > > I think that would be true if, as in your example, the observer were > freely falling into the Black Hole, but > if I was hovering just outside the Event Horizon in a super powerful > spaceship I could observe the Black Hole evaporating in just a few minutes > even though > to > you > , > who is far away > in a much weaker gravitational field, > that would take many trillions of years; the only problem is > in addition to the Black Hole evaporation > I would also observe many trillions of years worth of Hawking Radiation in > just a few minutes, and that would cook me. However if I had no spaceship > and was just freely falling through the Event Horizon the Hawking Radiation > wouldn't bother me at all > and I couldn't even tell when I reached the Event Horizon. > > > A > t least that was the idea before 5 or 6 years ago when > the idea of a Black Hole Firewall came up: > > http://www.nature.com/news/astrophysics-fire-in-the-hole-1.12726#b8 > > Such a firewall violates Einstein's equivalence principle and claims even a > > freely > falling > m > an > will > > will > cooked at the Event Horizon, but I don't understand Black Hole Firewalls > worth a damn. > > > John K Clark >
The near horizon condition for an accelerated observer is different. If one accelerates in order to remain stationary at some distance d from the horizon this requires an acceleration a = c^2/d. The spacetime this observer witnesses is AdS_2×S^2, which I work out in this page on Stack Exchange <https://physics.stackexchange.com/questions/262735/ads-black-holes/262744#262744>. This vacuum is negative with no lower bound, which is odd for quantum field theory and quantum mechanics with a bounded spectrum, and so quantum field are emitted from near the horizon. This accelerated observer in effect observes Hawking radiation within a frame that is accelerated in time. As the observer is able to accelerate to remain ever closer to the horizon, a null congruence with no time, the duration of the black hole is shortened ever further. Hence Hawking radiation appears to come gushing out rapidly. https://physics.stackexchange.com/questions/262735/ads-black-holes/262744#262744 I wrote a post on a possible way to understand the firewall. This issue tells us there is some relationship between quantum mechanics and general relativity not canonically understood. The initial quantum state of a black hole becomes randomized as Hawking radiation is emitted. Once half the mass of the black hole is lost to Hawking radiation the quantum states on the black hole have been randomized beyond the ability of a quantum error correction code. In some recent work I was motivated by Maryam Mirzakhani's death. She died of breast cancer last July, and the news for various reason made me angry. I had read one of her paper's back in 2014 when she won the Fields medal, and at the time I thought this had something maybe to do with physics. Last spring I studied the Ryu-Takayanagi (RT) formula and for some reason the day I heard of Maryam's death the insight on how her work connects with this hit me. There is this problem with how gravitation and quantum mechanics merge or function in a single system. It is often said we understand nothing of quantum gravity, and this is not quite so. Even with the based canonical quantization of gravity from the 1970s in a weak limit is computable and tells you something. This theoretical understanding is very limited and big open questions remain. Of course since then far more progress has been made. The AdS/CFT correspondence, the Raamsdonk equivalence between entanglement and spacetime and the RT formula are some of the more recent developments. These indicate how spacetime physics has a correspondence or maybe equivalency with quantum mechanics or quantum Yang-Mills fields. However, an obstruction exists that appears very stubborn. The vacuum is filled with virtual pairs of fields. With a black hole the gravity field causes one of these pairs to fall into the black hole and the other to escape. This means the quantum particle or photon that escapes as Hawking radiation is entangled with the pair that falls into the black hole, and so this means Hawking radiation is entangled with the black hole. So at first blush there seems to be no problem. However, if we think of a thermal cavity heated to high temperature photons that escape are entangled with quantum states of atoms composing the cavity. Once the entanglement entropy reaches a maximum at half the energy released the subsequent photons released are entangled with prior photons released. This would hold with black holes as well, but because of the virtual pair nature of this radiation it means Hawking radiation previously emitted in a bipartite entanglement are now entangled not just with the black hole, but with more recently emitted radiation as well. This means a bipartite entanglement is transformed into a tripartite entanglement. Such transformations are not permitted by quantum unitary evolution. This is called quantum monogamy requirement, and what this suggests is unitarity fails. To prevent the failure of quantum mechanics some proposed a firewall that violates the equivalency principle. This is called a firewall. The firewall occurs when half the possible radiation is emitted, which is also the Page time. This also corresponds to the failure of a quantum error correction code. Error correction codes involve some deep mathematics; it is connected with the RT formula and I illustrate in my essay the connection with Mirzakhani's mathematics on the geodesics in hyperbolic spaces. Error correction is also tied with the packing of spheres or how oranges stack at the grocery store, the Kepler problem. This gets into the guts of what my paper is about. However focusing in an error correction corrects the mixing of information. Think of a library, in particular an elementary school library with little kids, and the patrons scramble up the order of books. The distance a books ends up from its right position is the Hamming distance. As the library gets mixed up an algorithm can manage this disordering. However, at about half mixing up things break down. The librarian has to virtually start over. The solution with Susskind and others is to say spacetime variables and quantum states are equivalent. I do not disagree completely, but I think this is a complementarity instead of an equivalency. It means with either spacetime or quantum states you can account for the system, but at the expense of abandoning a description of the system by the other. You can't describe quantum gravity completely by both in the same measurement description. So this is a sort of Heisenberg uncertainty, if you will. Cheers LC -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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