Firewalls, Singularities, and the Unibabe Question

[marcus]

Here's the abstract of Jorge Pullin's talk at GR20 in July. It was the first talk of the main Loop session. He presented the February paper by Gambini and Pullin, here is what he had to say about it:

Complete quantization of vacuum spherically symmetric gravity
Pullin J
We find a rescaling of the Hamiltonian constraint for vacuum spherically symmetric gravity that makes the constraint algebra a true Lie algebra. We can implement the Dirac quantization procedure finding in closed form the space of physical states. New observables without classical counterpart arise. The metric can be understood as an evolving constant of the motion defined as a quantum operator on the space of physical states. For it to be self adjoint its range needs to be restricted, which in turn implies that the singularity is eliminated. One is left with a region of high curvature that tunnels into another portion of space-time. The results may have implications for the current discussion of ”firewalls” in black hole evaporation.

Here is the link to the GR20 abstracts. It includes abstracts from the joint (Loop+String+Pheno) session on Quantum Mechanics of BH Evaporation
http://gr20-amaldi10.edu.pl/userfiles/book_07_07_2013.pdf

 

[marcus]

Lee Smolin has a carefully written comment on Woit's blog that I think has several points requiring study.
http://www.math.columbia.edu/~woit/wordpress/?p=6208&cpage=2#comment-159323
Rather than excerpt portions, since it isn't long and is pretty much all thought-provoking, I'll copy so as to have it in front of us
==quote Lee post of 26 August==

Dear Scott,

The issues you raise are subtle, partly because there is not a formulation of QFT on curved spacetime that shares the coordinate and diffeomorphism invariance of classical GR. So at the very least beware of claims and intuitions based on one choice of coordinates. The thermalization of Hawking radiation appears to be fully explained by projecting out a subsystem of an entangled pure state. Remember these are free fields-there are no interactions of the modes at the horizon with each other-so there is no physical basis for rapid mixing. The other system the Hawking photons are entangled with are modes that fall through the horizon and are approaching another boundary–-the singularity in Hawking’s original calculation and whatever is post-singularity when the singularity is resolved. That is the physics as we best understand it.

I’d like then to address your statement: “ Namely, I would like the laws of physics to uphold the holographic entropy bound, that the total number of qubits in any bounded region should be upper-bounded by the region’s surface area in Planck units.”

That is a statement of what we can call the “strong holographic bound”. We can distinguish it from a weak form of the holographic bound (hep-th/0003056) which might be stated, “the total number of qubits measurable on any surface should be upper-bounded by the region’s surface area in Planck units.”

I would argue that all the evidence we have is that the weak form is correct. I give several arguments in hep-th/0003056 for the weak form over the strong form as best explaining the evidence we have from Bekenstein and Hawking’s original arguments as well as since. Moreover, recent work deriving black hole thermodynamics from quantum gravity by Bianchi, both perturbative (arXiv:1211.0522) and non-perturbative (arXiv:1204.5122) shows that the black hole entropy is best understood as an entanglement entropy. I would suggest that this be taken seriously as it is the only calculation of the BH entropy that gets the 1/4 right without any parameter fixing for a generic non-extremal black hole.

Thanks,

Lee
====endquote====
Regarding the orange highlight, live links to the two papers by Eugenio are:
http://arxiv.org/abs/1211.0522
and
http://arxiv.org/abs/1204.5122

The point of the blue highlight, I guess, is that whatever is thru the hole, beyond the phony "singularity" is also part of the region---and there has to be a new piece of the boundary out there.
It could be an asymptotic-type boundary (a separate piece of "future observer" land) or it could be an hypothetically designated boundary of the sort used in Oeckl GBF.
That would be in a thought experiment when one extends Oeckl general boundary formalism to include when a BH occurs in the bulk region.

The magenta highlight makes the operationally crucial distinction between where you imagine qubits to be "located" and where you actually MEASURE them. There may indeed BE more qubits down there in the hole past the erstwhile classic breakdown, but the number you can MEASURE at the event horizon is bounded by the AREA of the event horizon, OK?

 

[atyy]

And also there's a beautifully-written paper by Jacobson which precisely identifies the point of tension in the "firewall"situation.
==quote Jacobson December 2012==
Even if the AdS/CFT argument held only in that specific setting, it would be enough to consider the AMPS question. But in fact Marolf [5] has argued that the essential reason for the AdS/CFT result carries over more generally to any diffeomorphism invariant theory with an asymptotic region in which an algebra of observables can be defined. His point is that in such a theory, the Hamiltonian is a surface integral in the asymptotic region, which I will call “the boundary”. More precisely, the Hamiltonian also contains a volume integral of combinations of the diffeomorphism constraints, but those act trivially1 on any physical state in the Hilbert space (according to Dirac quantization of a constrained system). Hence the algebra of boundary observables evolves unitarily in time into itself, and this means that no boundary information can ever be lost. In the asymptotically flat case, the boundary algebra would ...
==endquote==
I cannot recommend this paper too highly.

arxiv.org/abs/1212.6944
Boundary unitarity without firewalls
Ted Jacobson
(Submitted on 31 Dec 2012)
Both AdS/CFT duality and more general reasoning from quantum gravity point to a rich collection of boundary observables that always evolve unitarily. The physical quantum gravity states described by these observables must be solutions of the spatial diffeomorphism and Wheeler-deWitt constraints, which implies that the state space does not factorize into a tensor product of localized degrees of freedom. The recent "firewall" argument that unitarity of black hole S-matrix implies the presence of a highly excited quantum state near the horizon is based on such a factorization, hence is not applicable in quantum gravity.
7 pages

Topology change in the bulk can break the monogamous relation of bulk to the previous "asymptotic region" and cause the appearance of a new component of the "asymptotic region".

This happens as soon as a hole forms leading to re-expanding unibabe space-time.

In nature of course we already have a complex boundary because we already have many astrophysical black holes. In reality the boundary cannot be a single connected piece as in the simplified approximate AdS/CFT. picture. One should never have imagined the real world was so simple that it had a single unique connected asymptotic region. Instead, down thru every astro BH there is an expanding unibabe with its own separate component of the "boundary".

This December Jacobson paper is exquisitely logical in the clean way it identifies the assumption that is causing the "firewall" tension. And it also shows the importance of Don Marolf's generalization of the AdS/CFT idea to any diffy invariant setup with "asymptotic region in which an algebra of observables can be defined."

Interesting, Jacobson http://arxiv.org/abs/1212.6944 endorses the Papadodimas and Raju argument http://arxiv.org/abs/1211.6767.

 

[atyy]

Actually Marolf, Polchinksi and Sully seem to agree with Jacobson that the state space does not factor. In http://arxiv.org/abs/1201.3664 they write (with Heemskerk), "The interior and exterior Hilbert spaces are both embedded in this, but not as a product, so the interior and exterior operators do not commute. In this strong form, the framework of quantum mechanics remains fully intact, but locality is badly broken down.".

The paper seems to argue against firewalls before Page time, since they propose to reconstruct from the boundary what's behind the horizon at early times.

 

[atyy]

I'm going to vote with Ted Jacobson and Lubos Motl that Papadodimas and Raju http://arxiv.org/abs/1211.6767 have the right idea to construct coarse grained operators. Their work seems very much in the spirit of Mathur's earlier but vaguer conception http://arxiv.org/abs/1012.2101, where he gave the first AMPS argument, and also stated that the infall problem "asks for a coarse grained effective description of the infall of heavy observers into the degrees of freedom of the hole."

Mathur's http://arxiv.org/abs/1201.2079 has a nice analogy. "For example if we stick a thermometer in a beaker of water, then the rise of mercury can be computed using the actual state |ψ_k> of the water, or by using the ensemble average over such states; the result is expected to be the same to leading order. Here the state of water is assumed to be a generic state, and the operator measuring temperature is of the ‘appropriate’ type mentioned above."

One thing that Mathur mentions which is not obvious to me in Papadodimas and Raju's construction is whether the coarse grained density matrix and operators are generic. It'd be nice if these could come out after renormalization or entanglement renormalization.

 

[atyy]

Hmm, Erik and Herman Verlinde http://arxiv.org/abs/1306.0515 do mention Papadodimas and Raju as well as entanglement renormalization. In Verlinde and Verlinde's paper the entanglement renormalization performs coarse graining, which is a concept that Papadodimas and Raju also tried to implement.

 

[Physics Monkey]

When I heard Raju talk about his work, it came out that there is something breaking down in their construction right at the event horizon. Assuming this hasn't changed, I think one needed to average over or coarse grain in time the mode functions in a neighborhood of when the horizon is crossed.

On the one hand, this seems quite reasonable to me. My clock doesn't keep time perfectly. On the other hand, it seems like the perfect place for issues of recurrence to creep. E.g. is the system really thermal at infinite time or does it recur? In particular, the large N and long time limits don't commute.

 

[marcus]

more on the "firewall" kerfluffle:
http://arxiv.org/abs/1309.7977
The Membrane Paradigm and Firewalls
Tom Banks, Willy Fischler, Sandipan Kundu, Juan F. Pedraza
(Submitted on 30 Sep 2013)
Following the Membrane Paradigm, we show that the stretched horizon of a black hole retains information about particles thrown into the hole for a time of order the scrambling time m ln(m/M_P), after the particles cross the horizon. One can, for example, read off the proper time at which a particle anti-particle pair thrown into the hole, annihilates behind the horizon, if this time is less than the scrambling time. If we believe that the Schwarzschild geometry exterior to the horizon is a robust thermodynamic feature of the quantum black hole, independent of whether it is newly formed, or has undergone a long period of Hawking decay, then this classical computation shows that the "firewall" resolution of the AMPS paradox is not valid.
16 pages, 10 figures

==quote Banks et al conclusions==
4 Conclusion

We have shown that particles dropped into a black hole, leave traces of their trajectory behind the horizon, over time scales of order the scrambling time, after horizon crossing. We believe that this is definitive evidence that the firewall scenario for the resolution of the paradox proposed by AMPS, is not correct.

The paradox is nonetheless real, so what could its resolution be? We believe that the issues were stated most clearly by Marolf, in his talk at the Santa Barbara Fuzz or Fire conference[11]. Black hole thermodynamics tells us that the black hole has an exponentially large number of states, concentrated in the vicinity of the stretched horizon. If we consider a causal diamond straddling the stretched horizon, whose size is much smaller than the Schwarzschild radius, but much larger than the Planck scale, then we expect e^A/4 almost degenerate states, where A is the area in Planck units of the piece of the horizon inside of the diamond. On the other hand, QUEFT gives us only a single low energy state, the adiabatic vacuum, in this region.

To the authors, this strongly suggests that any sensible quantum theory of the black hole must contain a huge number of very low energy states, which are not contained in effective quantum field theory. On the other hand, since a causal diamond of size much smaller than the Schwarzschild radius is very close to flat Minkowski space, these states must also be there in empty space. Indeed, in the theory of Holographic Space Time, just such a collection of states has been postulated for some time. These states decouple from Minkowski scattering amplitudes, but are responsible for the entropy of de Sitter space [9]. Two of the present authors (TB,WF) will soon present an updated version of the description of black hole evaporation [12] in this formalism.

FOOTNOTE: 3 In fact, several authors have argued that non-locality is indeed an essential property of fast scramblers [14], a feature that is not present in QUEFT. This is further supported by the fact that non-local interactions increase the level of entanglement among the different degrees of freedom of the theory [15].
==endquote==