# The Reference Frame

Our stringy Universe from a conservative viewpoint

## Saturday, September 29, 2012

### Raphael Bousso is right about firewalls

Five days ago, I reviewed the discussions on black hole firewalls, started by AMPS in July 2012. Joe Polchinski wrote a guest blog for Cosmic Variance yesterday.

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.

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).
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.

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.

.....

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.
Therefore, it is not necessary to posit a violation of the equivalence principle for the infalling observer.

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.

#### 33 comments:

1. gradstudent

I'm sorry, but I feel that Busso didn't invent anything at all actually. This principle of complementarity, if I understand it well, always been there since special relativity and generalized (in some sense) with general relativity.
One can think about the uniformly accelerated observer in special relativity, or about the radiation of an infalling electrical charge in general relativity.
In both cases, there are no inconsistencies because all the naive paradoxes one can encounter by qualitative reasonning disappear in a simple way : the creation of an horizon, where all the "bad stuff" turns out to be confined behind it.
So, well, is that legit to say that Susskind, Polchinski & al never got it whereas every decent graduate graduate students did ?

2. Dear grad student, first of all, his name is Bousso.

Second, it's complete nonsense that the complementarity principle was there in (classical) relativity. Complementarity of any form is a feature of quantum mechanics. The old Bohr's complementarity was coined by Niels Bohr in the context of QM. But here we're talking about a more specific complementarity, one related to black holes, and Bousso of course didn't invent this, either. However, he refined the way to formulate it – he invented "observer complementarity" which is actually somewhat closer to the complementarity of Bohr.

Pretty much all your comment implies that you are completely unfamiliar with quantum mechanics – which automatically implies that you are unfamiliar with all issues concerning complementarity etc. – so your breathtaking arrogance isn't justifiable by anything at all. Classical physics assumed objective and unique values of all fields or other degrees of freedom whether or not they were behind the horizon. Only in quantum mechanics, such an assumption became subtle and challenged because of the constraints that quantum mechanics itself imposes, especially the "conservation of information" in the Hawking radiation that follows from unitarity of quantum mechanics.

Before you actually learn at least some basic things in this quantum mechanical discussion, and if possible, also things like the Hawking radiation, information preservation, and so on, could you please exploit your opportunity to shut up? This is surely not a debate that can be resolved by comments about classical physics, which is what you seem to think.

3. gradstudent

Well, maybe I don't understand what is the complementary principle then, but I really feel that its already here in relativity in the sense that the set of accessible events of an observer depends of the observer (and there time order too as everybody knows, still causality holds).

Anyway, fair enough, i'm not familiar with black holes information loss, so maybe I misunderstood what is this complementary principles : any references ? :}

4. Hi, could you please just read the articles and trace to the original references - or textbooks - yourslef? I can't plan learning of all the basic physics for you. at least not if you don't pay me \$100,000 a year for doing this service for you.

5. Dilaton

Dear Lumo, can you put the link to this article into your answer to my SE question too? I'd like to see it included in yout answer there but I'd never in my life dare to touch (edit) anything you have written ... ;-).
Anyway, thanks for this update I've not yet read it but I'll enjoy it very soon?

(At the moment I'm still trying to see what I can get out for myself of the exotic branes article (just for the heck and the fun of it), but for this I'll have to review certain things I have forgotten (darn !) etc ...)

6. Hi Dilaton, I added the link to the SE answer.

7. Vlad

I'm layman when it comes to these things but that firewall zone is ridiculous to me.Black hole is a black hole regardless of its' size and age.

8. Robert Graham

Thank you for this decisively clear summary of Bousso's great contribution to the firewall-debate.
Could not the contradictons incurred by disregarding observor-complementarity be used to establish it
as a fundamental principle in QM?

9. Dilaton

Thanks Lumo :-)

Maybe after having read this article I'll finally be able to give Raphael Bousso's Munich talk a try ...

Cheers

10. lemon

Polchinski has an example in the post on CV where he sends a half of |+->+|-+> into the BH. But this does not come out as a thermal radiation, no? The thermal radiation is a manifestation of how the IN vacuum is seen in the OUT region (considering asymptotic stationary regions). But an initial field with just one particle (from Polchinski's example) gives rise to a non-thermal corrections in the OUT field. This is enough to show that the information comes out unharmed after the BH evaporates.

11. Dear Lemon, if you know something about the initial state, e.g. if you know the pure state of two qubits you mentioned, no one in this discussion has any doubts that the final state after the BH evaporates is pure and encodes the initial state.

More generally, even before the BH evaporates, it has deviations from thermality. It is not maximally mixed - thermal.

As the BH starts to evaporate, the entanglement between the interior and exterior starts to grow but this entanglement is really unphysical because entanglement is correlation and no one can measure both the interior and the whole Hawking radiation.

You could think that you may circumvent this a little bit because you may catch "most of the Hawking radiation" and assume it has "almost all the information" but what you omit is actually essential for the paradox to be absent.

The real debate is whether any of these QM principles imply anything dramatic for the infalling observer crossing the event horizon. Polchinski et al. think that the answer is Yes, Bousso and others think it's No, and so do I.

AMPS say that the interior isn't really allowed for a black hole because the later Hawking radiation B could be maximally entangled with two different systems, which is impossible in QM, namely the interior C and the early Hawking radiation A. But that's a wrong argument because to find a paradox, there must be an observer, and no observe can see A and C simultaneously. Effectively we can't even show that A and C are different degrees of freedom.

12. Borun D. Chowdhury

Observer complementarity is a nice idea by itself. I must thank Harlow for explaining it to me in some detail. If two observers cannot communicate, they do not have to agree on the results of their experiment.

However, I find it hard to believe that the experience of such observers might be so different outside the stretched horizon. I believe this is an ongoing discussion right now and I have nothing to add on that.

However, I would like to point out something somewhat tautological about the statement of observer complementarity. If Alice's experience can be so different while falling in that she might see B maximally entangled with C (instead of A), I don't see the point in asking if she can communicate this to Bob. Communication depends on a predetermined algorithm. However, if the physics is so different and Alice and Bob do not know what it is when they were together, then there is no way to come up with such an algorithm.

13. Lemon

Ok, thanks for the explanation. I was a bit confused what is this discussion all about. At one point it's about what an infalling observer sees but at the same time people talk about the information loss (Polchinski mentions it too). But nobody really disputes these days that the information is preserved. Am I right? Or did this problem crawl back again by the (suspicious) firewal proposal?

14. anony

Bousso is on the right track. There is an additional serious flaw in the Polchinski argument. If the black hole emits radiation before the observer jumps in, you have to allow for the possibility for it to interact with the observer in some way prior to him jumping in. If the radiation that is emitted is maximally entangled with the black hole, the interaction with the observer prior to the observer jumping in allows for mixing of the information for both internal and external degrees of freedom with the observer. The only concern for the observer is whether there is consistency between the measured information from the outgoing radiation with the measured information he finds in the black hole. The only pure system at that point is the combined system of outgoing, observer, and black hole.

IOW, the inconsistency that Polchinski found is because of an arbitrary assertion of separability of the blackhole information and the observer, *even after the blackhole has emitted and before the observer jumps in*.

Basically he is trying to deny the initial interaction terms of the interaction hamiltonian, effectively imposing some sort of arbitrary cutoff in a region where those terms are significant.

15. Peter F.

I think it is a fair assessment (of 'the relevant situation' in much of Science) to conclude that: A carefully conservative attitude [such as Lumo's - and to some extent also one such as mine (that I partly developed because of what I've learned during my many visits to TRF)] can help to keep imaginative and strongly driven (endogenously motivated) intellectual people from foraging too deeply into, and sometimes getting permanently lost in, 'theoretical Fairyland'.

16. Shannon

I find this observer-complementarity absolutely awesome. I think you are holding something here ! It's like we are part of the blackhole picture as well...

17. Ruz

Nice that you believe in Bousso's argument, now we just have to convince him to believe in it too ;)

(He retracted his objections to the Polchinski et al. paper, mostly...)

18. Dear Ruz, I find this kind of "arguing" bizarre. I haven't seen any blunder in that argument so those comments about "retractions" – which I have seen as well – are completely vacuous for me so far.

19. Luke Lea

So even the best of physicists can lose it.

20. cynholt

It seems to me that describing a black hole as though it were behind
some sort of information-based firewall is just a lame excuse for not
figuring out how black holes work and how they fit into the evolution of
the universe. If we didn't know how the Sun was formed and how it gets
its energy, or why the sky is blue and why grass is green, or when Earth
formed and when life formed on Earth, we'd simply say that firewalls
are preventing us from knowing any of these and other sorts of puzzling
things. Once we learn most of the hows, whys, and whens of black holes,
all of this talk of firewalls will disappear. Then again, we'll move on
to describing something else, which has got us collectively scratching
our heads over, as being behind a firewall. Perhaps that something else
will be the world beyond our world in the multi-universe. Death is the
only thing that'll stop us from asking questions, after questions, in
hopes of finding answers to at least some of them.

21. Eugene S

Dear Cynthia, I probably know even less of physics than you but I beg to differ. The uncertainty principle in quantum mechanics is a well-known example where in trying to measure two non-commuting variables simultaneously, we run up against a fundamental limitation of nature: we cannot determine both their values accurately. This is how nature everywhere works on the smallest, the quantum, level. Black holes, on the other hand, are how nature works at its most extreme, where spacetime curvature becomes infinite. From what little I understand of the present topic, I would say that the scientists investigating this "firewall" business want to know if equally fundamental constraints on what can be known are placed by nature in the case of black holes. I do not view this as a "lame excuse" but as a noble endeavor in pursuit of an exciting goal.

22. Dilaton

Ha ha, this interpretation of people hiding behind the firewall to avoid having to properly figure out how (parts of) nature works made me chuckle :-D
(even though I do not exactly agree and, as Eugene, rather think they are trying to find out serious things)

But I always thought people apply the anthropic principle as a lame excuse to avoid properly figuring out how things work :-P

23. Shannon

Cynthia, I guess the main thing is that there are no inconsistencies in this theory on BH. That in itself is a step forward understanding how they work. Death might give us the answer to all this, or it might just freeze our knowledge...

24. Gene

Lubos,
Thanks for yet another crystal-clear explanation. I am still amazed that people as smart as Polchinski can be confused about the very essence of quantum mechanics.
How do you explain this phenomenon? Is the disease contagious?

25. Dear Gene, there are many people confused by QM but so far, I didn't dare to think that Joe could be among them, so I still prefer to think this is just a more technical thing dependent on subtleties of quantum gravity and Joe would give the same answers to non-gravitational QM problems as Bohr - or two of us. ;-)

26. Newman

What was the Dvali's question in the end about? Black hole is large N system? Does someone take his (Dvali's) recent papers seriously?

27. Hi, well, I personally don't...

28. Trimok

This inside/outside observer complementary, seems to be closely related to all the Ads/CFT or Quantum. Gravity/QFT correspondences.
Let me try some speculations.
Maybe, very roughly, one may say that the (free falling) inside observer see Quantum gravity or String theory , while the (accelerated) outside observer see QFT and CFT (with one dimension less, at the (exterior) surface of the horizon).
So, maybe, is some sense, our universe is just a boundary surface where we use standard QFT/CFT. We don't see the inside of the domain whose boudary (and some kind of horizon) is our universe. This inside domain could be described by String theory, and this description should be complementary to the standard CFT/QFT description at the boundary.
But we should not use the two theories at the same time, for instance, to examine some paradox.

29. Dilaton

Hm, I've some place read the argument that our inflating universe could be described as stuff falling towards a black hole horizon with the black hole lying outside the cosmic horizon. Do you mean something like this?

30. Trimok

No, my speculation, was to consider our entire 4-D universe as an horizon/boundary of some higher 5-dimensional space. So CFT/QFT apply to our
4-D universe, and then String theory/Quantum gravity apply to the 5-dimensional space. They are just different expressions of the same physics, which are complementary, but you can't use the 2 theories together to express a paradox.

31. Clayton

Hi Lubos,

Have you seen that Bousso has now recanted his position? The latest version of the paper you link to above has an extremely different tone than the one taken here. Very interested to know what you think!

32. Thanks for telling me. I am going to study it soon.

33. Why are people so loath to give up omniscience?

## Who is Lumo?

Luboš Motl
Pilsen, Czech Republic
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