This is not about open in terms of flowing matter and energy. This openness is a quantum mechanical openness and the nature of entanglements. This is seen in the analysis on pages 3 and 4. This is where the new physics lies. Here the difference in the qubit content between the inner and out horizon results in the action for topological states. This topological physics emerges because of the two spatial surfaces that an observer in region I may identify data. The observer in region I can't distinguish between them and this leads to a limit on the ability to identify qubit entanglements. This has some analogy with open thermodynamics, where there is a flow of energy in and a dissipation mechanism for the removal of entropy.
Think of a black body, say the interior of a hot cavity made of oscillators. The radiation is emitted out the small opening, and each photon emitted comes as an entanglement from atom* --> atom plus photon, and this is an entanglement between the atom and the photon. The entanglement entropy of the cavity increases as bipartite entanglements are generated. However, at the half way point, the Page time, most of the atoms are now emitting their second photon that is entangled with previously emitted photons. The entanglement entropy of the cavity starts to decline as a gas of entangled photons has now been emitted to I^+.
The black hole is different. At first Hawking radiation is emitted in this process and the BH becomes increasingly entangled with the Hawking radiation. However, at the half way point something happens. The the entangled states composing the BH that are EPR pairs with Hawking radiation, which from the perspective of the exterior observer are on the horizon, must now entangle further with more Hawking radiation. This is what is problematic, for it requires a unitary transformation to convert a bipartite entanglement into a tripartite entanglement. That can't be done. Unitary evolution does not create entanglements or destroy them. As a result if the BH continues to emit Hawking radiation it must violate quantum monogamy and further this will lead to the BH exceeding the Bekenstein bound. This is the firewall issue, and AMPS claims the stretched horizon must now have maximal entanglement and will no longer permit anything to quantum radiate or to pass through. The stretched horizon have been converted into a boundary of spacetime or equivalently into a singularity.
There are then clearly something wrong here. We have in physics the three quantities length, time and mass. With c = 1 we constrain length and time together and with 徴 = 1 we constrain mass with length. So we have one fundamental parameter left, call it length or if we want to work in the Fourier transform space then mass. There is an intertwiner between mass and length however that is a coupling constant. This is Newton's gravitational constant G ~ Area or sqrt{G} ~ length and which we see in the Schwarzschild horizon length r = 2GM/c^2. However, with the firewall something odd happens in that the BH after the page time is an end to spacetime geometry, or equivalently the end of possible entanglement, but yet we have gravitation.
My essay is in part a possible solution to this. Briefly it is a way of looking at Susskind's ER = EPR according to quantum hair and BMS symmetry. It is a complementary relationship between the EP and UP of GR and QM respectively. It means that an exterior observer looking at a BH will observe Hawking radiation being emitted and conclude that the BH will be a firewall once it has emitted half its mass. However, this BH observed later at half its mass by an observer will have the same assessment made. The firewall is not a signature of the end of physics, but it is the inability to make future predictions on BHs because the universe is fundamentally open. A portion of the RN or Kerr conformal diagram makes this evident as seen in the attachment. The Hawking radiation observed in region I has an ambiguity with respect to the topology of quantum states since the two spatial regions here are not topologically equivalent. There is no homomorphism between the two. Quantum hair or BMS symmetry in supergravity means there is no local method for determining the quantum late state of a BH.
I would have included more, but the size limit of the contest prevented that. The last section is somewhat speculative, but it is there to advance the idea that an open world system sets up an open system of qubits. The hyperTuring machine is an idealization, and I argue that a real physical system of this sort is finite and limited. This is then argued to carry over to the world at large, not just black holes. There is fundamentally a sort of pink noise to the structure of spectra, and the Fourier transform of this is the autocorrelation function for the structure of signals. I do not go into how this translates into the properties of complex molecules and life, though complexity is woven into this
LCAttachment #1: Penrose_diagram_for_RN_with_2_spatial_surfaces.png
