During the days, I had enough time to sort all these issues and I am confident that Raphael Bousso is right and Polchinski and others are wrong.
Here is Raphael's 33-minute talk from Strings 2012
and here is his July 22nd paper:
Observer Complementarity Upholds the Equivalence Principle(The two men who disagree about firewalls were playing accomplices of one another back in 2000 when they were helping to ignite the anthropic coup d'état in string theory by their Bousso-Polchinski landscape (then: discretuum) paper.)
In fact, I would say that the paper is very clear, crisp, and even shows the author's understanding of some basic features of quantum mechanics – features that others unfortunately keep on misunderstanding. That's a very different verdict from my verdict about the nonsensical MWI-inspired Bousso-Susskind hypermultiverse, isn't it?
Bousso defends the complementarity principle. What this principle really means has often been misinterpreted. For example, some people said that the black hole interior contains all the degrees of freedom that one may measure outside the black hole. This is clearly nonsense. The interior contains at most a scrambled version of a part of the exterior degrees of freedom.
Raphael nicely avoids many of the confusions by introducing a refined version of the complementarity principle, the so-called observer complementarity. It's a typically Boussoian concept – and one could argue that he has greatly contributed to this sort of thinking. In the firewall discussion, this Boussoian thinking is extremely natural and arguably right. If I add some "foundations of quantum mechanics" flavor to the principle, it says:
Quantum mechanics is a set of rules that allows an observer to predict, explain, and/or verify observations (and especially their mutual relationships) that he has access to.While the complementarity grew out of technical features of quantum gravity, you may see that this observer complementarity version of it sounds just like some Bohr's (or Heisenberg's) pronouncements. It shouldn't be surprising because it was Bohr who introduced the term "complementarity" into physics and the general idea was really the same as it is here.
An observer has access to a causal diamond – the intersection of the future light cone of the initial moment of his world line and the past light cone of the final moment of his world line (the latter, the final moment before which one must be able to collect the data, is more important in this discussion).
No observer can detect inconsistencies within the causal diamonds. However, inconsistencies between "stories" as told by different observers with different causal diamonds are allowed (and mildly encouraged) in general (as long as there is no observer who could incorporate all the data needed to see an inconsistency).
Bohr has said that physics is about the right things we can say about the real world, not about objective reality, and it has to be internally consistent. However, in the context of general relativity, the internal consistency doesn't imply that there has to be a "global viewpoint" or "objective reality" that is valid for everyone. This is analogous to the statement in ordinary quantum mechanics of the 1920s that a complete physical theory doesn't have to describe the position and momentum (or particle-like and wave-like properties) of a particle at the same moment.
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Polchinski who is the most senior figure behind the recent crazy firewall proposal is not only the father of D-branes and other discoveries but also the author of perhaps the most standardized graduate textbook of string theory.
Bousso shows that AMPS are inconsistently combining the perspectives of different observers in order to deduce their desired contradictions but this is illegal because no observer has access to things outside his causal diamond, and therefore no observer can operationally demonstrate any contradiction. In the Penrose diagrams below, you see that no observer may observe the matter right before it is destroyed by the singularity as well as the late Hawking radiation. You must either sacrifice your life and jump to the black hole or you must stay out: you can't do both things simultaneously.
I recommend you to read the whole Bousso's paper which is just 7-9 pages long, depending on how you count it. However, a sufficient screenshot that explains all his resolutions is Figure 1:
Bousso's caption for Figure 1: The causal diamond of an infalling (outside) observer is shown in red (blue); the overlap region is shown purple. Observer complementarity is the statement that the description of each causal diamond must be self-consistent; but the (operationally meaningless) combination of results from different diamonds can lead to contradictions.
- (a) Unitarity of the Hawking process implies that the original pure state \(\Psi\) is present in the final Hawking radiation. The equivalence principle implies that it is present inside the black hole. If we consider both diamonds simultaneously, then these arguments would lead to quantum xeroxing. However, no observer sees both copies, so no contradiction arises at the level of any one causal diamond.
- (b) Unitarity implies that the late Hawking particle B is maximally entangled with the early radiation A (see text for details). At the earlier time when the mode B is near the horizon, the equivalence principle implies that it is maximally entangled with a mode C inside the black hole. Since B can be maximally entangled only with one other system, this constitutes a paradox. However, no observer can verify both entanglements, so no contradiction arises in any single causal diamond.
LM: Let me repeat those observations again. There are two possible paradoxes we may face but both of them are resolved by a careful application of observer complementarity: the xeroxing paradox and the firewall paradox.
The xeroxing paradox is the observation that the matter that has collapsed into a black hole carries information and the information may get imprinted to two places – somewhere inside the black hole and in the Hawking radiation. These two places may even belong to the same spatial slice through the spacetime. Such a doubling of information is prohibited by the linearity of quantum mechanics. Despite the existence of the "unifying" spatial slice, there is no contradiction because there is no observer who could have access to both copies of the same quantum information, no causal diamond that would include both versions of the same qubit. That's why no particular observer can ever discover a contradiction and this is enough for the consistency of the theory according to the quantum mechanical, "subjective" standards.
The firewall paradox on the right picture was proposed by AMPS. A late Hawking particle B may be shown to be maximally entangled both with some early Hawking radiation's degrees of freedom A as well as with some degrees of freedom inside the black hole C. In quantum mechanics, a system can't be maximally entangled with two other systems. But this is not a problem because no single observer able to access one causal diamond is able to verify both maximal entanglements. In fact, the "old" version of the complementarity could be a legitimate – although less accurate – explanation of the resolution here, too: the degrees of freedom in C aren't really independent from those in A.
You may (approximately or accurately?) say that C is a scrambled subset of A so when you say that B is maximally entangled both with A and C, it is not entangled with two things because the relevant degrees of freedom in A and C are really the same! It's a similar situation as if you considered a "zig-zag" spatial slice of the spacetime that happens to contain 2 or 3 copies of the same object at about the same time. All "xeroxing-like paradoxes" would be artifacts of this slice that pretends the independence of things that aren't independent.
So there is no paradox, one doesn't have to sacrifice the equivalence principle, the infalling observer may still enjoy a life that continues even after he crosses the event horizon of a young or old black hole, and everything makes sense. It really looks to me as though Polchinski et al. have really denied the very essence of the complementarity – whatever precise formulation of it you choose. Maybe they were also misled by some of the usual "realist" misinterpretations of the wave functions and density matrices – for example by the flawed opinion that it must be "objectively and globally decided" whether some system is described by a pure or mixed state, by qubits that are entangled with someone else or not. Such questions can't be answered "objectively and globally": they should be answered relatively to the logic and facts of a particular observer and whether a system is in a pure state or a mixed state is really just a question about the subjective knowledge of this observer, not an "objective question" that must admit a "universally and globally valid answer". In the case of general relativity, especially in spacetimes that are causally nontrivial, this subtlety is very important because individual observers can't transcend their causal diamonds so mutually incompatible perspectives that cannot be "globalized" are not only allowed but, in fact, common.
So applause to Raphael Bousso, ladies and gentlemen.
Update: Polchinski responds to Bousso
Joe Polchinski thinks that Bousso's picture has a bug. A comment on CV:
Bousso (and others) want to say that an infalling observer sees the mode entangled with a mode behind the horizon, and the asymptotic observer sees it entangled with the early radiation. This is an appealing idea, and was what I initially expected. The problem is that the infalling observer can measure the mode and send a signal to infinity, giving a contradiction. Bousso now realizes this, and is trying to find an improved version. The precise entanglement statement in our paper is an inequality known as strong subadditivity of entropy, discussed with references in the wikipedia article on Von Neumann entropy.I would need a picture and details. Where is the measurement taking place? What is the new contradiction? If he measures C inside the black hole, then he clearly can't send it to infinity for causal reasons. If he sends it right before he falls in, in the B phase (old hole's radiation), the information comes out redshifted and hardly readable as a part of the information in the Hawking radiation; it's the same information that we already count as B. If the infalling observer makes the measurement in the stage A, i.e. even earlier than that, then it's irrelevant because that's really the initial state in which the existence of the black hole doesn't play any role yet. If the measurement is done so that it's available to observers near singularity as well as those after the black hole evaporates, it's just a fact that both of these observers share. It makes no sense to say that this piece of information is later entangled with anything else: once a qubit or another piece of quantum information is measured, it's no longer entangled with anything else! When I measure a spin to be up, the state of the whole system is \(\ket{\rm up}\otimes \ket{\psi_{\rm rest}}\) and similarly for the density matrices. No entanglement here.
So whatever method I choose to read Polchinski's reply to Bousso, it makes no sense to me.
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