Saturday, June 08, 2013

Maldacena, Susskind: any entanglement is a wormhole of a sort

...more precisely, EPR is equivalent to ER...

Juan Maldacena and Leonard Susskind wrote a cool paper attacking the horizons of our current understanding of quantum gravity which may look convoluted if not entangled to many readers, which may swallow your attention like a black hole, and which is called
Cool horizons for entangled black holes.
I suppose that the paper was created after Juan Maldacena explained to Lenny Susskind why his recent pro-firewall paper was wrong. Both Maldacena and Susskind have thought about similar things for quite some time but there are many reasons – including my knowledge of the genesis of this modest paper – why I think that the active claims and "choices of the right answers" are Juan's, not Lenny's. ;-)
Update: See also John Preskill's enthusiastic review of the paper.
Just very recently, Lenny was very confused about the firewalls and thought that the AMPS arguments have made firewalls inevitable. The new Maldacena-Susskind paper is clearly an anti-firewall paper. Well, they actually conclude that the firewalls don't have to be there but there may, depending on the decision of a female overlord whose identity will be partially clarified below...

Healfix finds the paper controversial, either wrong or the first salvo of a completely new revolution. I don't. The paper is cool but it's a totally natural continuation of the state of the affairs as we have known it for quite some time. It builds on Werner Israel's thermofields (Werner Israel is an ex-collaborator of our Gordon Wilson), Maldacena's 2001 comments about the "pair of CFTs" description of the eternal AdS black hole, and some ideas about "entanglement as a topology change" that I recently associated with Mark Van Raamsdonk although many people, including your humble correspondent, have been thinking about the same paradigm for many years. Ryu and Takayanagi have contributed an influential 2006 paper about the entanglement in the black hole context.

The ideas linked to thermofields and the doubling of degrees of freedom were recently mentioned and exploited by the Raju-Papadodimas paper but again, it's true that a dozen of credible researchers or so has thought about these matters in this way.

I need to mention that Juan Maldacena's image among those who have a clue about theoretical physics is so stellar partly because he has never written a paper – and perhaps a sentence in a paper – that wouldn't be supported by rock-solid evidence. (Well, Horowitz-Maldacena's intriguing yet speculative "black hole final state" may be an exception to the rule but the logic of that paper may get revived due to this Maldacena+Susskind development, too.) And this paper is no different. Comments by folks like Sean Carroll that these authors may afford to write rubbish because they have tenure has nothing to do with the actual reality. These is completely false and sort of disrespectful.

These folks have way too much to lose – their top status in theoretical physics, acquired by having written systematically valid and important contributions to physics. Carroll has never cared about the validity or quality of his papers and claims which is why he's respected as a physicist by the know-nothing popular bullshitters only but Maldacena (in particular) is a genuine scientist, the ultimate cautious researcher who is, despite these tough constraints, still able to ignite revolutions at some points and it's no coincidence that he was among the inaugural recipients of the $3 million Milner Prize.

Both authors are giants of dualities and equivalences so the main idea of the paper may be expressed as a new kind of duality – the existence of two seemingly different but ultimately exactly equivalent descriptions – which may be expressed by their formula\[


\] This equation says that the Einstein-Podolsky-Rosen entanglement is the same thing as the Einstein-Rosen bridge. You may be tempted to cancel ER and disrespectfully deduce that Podolsky is equal to zero. However, you shouldn't forget that the equation above is one of a multiplicative rather than additive sort so the right conclusion is that Podolsky is the number one. ;-)

The new paper starts with some comments you have seen on this blog many times: EPR-style entanglement doesn't represent any genuine non-locality. It doesn't allow you to send any genuine information to spacelike-separated regions of the spacetime i.e. faster than light. Correlation isn't causation; quantum mechanics predicts correlation for EPR-style experiments but the correlation/entanglement is a consequence of the objects' mutual contact in the past when the state of the whole system was prepared, not a consequence of any action at a distance in the moment of the measurement.

There is another concept that doesn't allow you to send the information superluminally although you could naively think that it can: the Einstein-Rosen bridge. This is a technical name for a special wormhole, one that is constructed by gluing and/or maximally extending the vacuum solutions of Einstein's equations of general relativity i.e. things similar to Schwarzschild's solution for an empty and neutral black hole.

Off-topic: Lisa Randall's 19-year-old lookalike, Ms Sabina Křováková of the Northern Bohemian town of Děčín [Dyeh-cheen] won the 2013 Czech and Slovak Superstar.

A reason why this sort of a "non-traversable" wormhole doesn't allow any standard faster-than-light communication (at least not a permanent one) is simply the black-hole-like appearance of the exterior of the wormhole (on both sides): you may only catch the would-be information that has propagated through the wormhole if you actually jump into the black hole but in that case, you de facto commit suicide and give up the right to exchange the information forever. Once you jump to the black hole, you may say that your position with respect to the exterior asymptotic region of the spacetime is "confusing". You are somewhere in between the original two widely separated places, not in the vicinity of either of them, so your perceptions shouldn't affect the question whether the two separated places may exchange the information. They cannot and you don't belong to those places anymore!

So both ER and EPR are concepts that could naively allow you to send the information faster than light; but both of them actually refuse to do so. They share these two properties so they could be the same thing. Of course, it's not a proof that they're the same thing which is why Maldacena's and Susskind's claim that they are actually the same thing both non-obvious and non-vacuous contribution to physics if it is true. And they have some more detailed evidence that it actually is true.

Whenever there are two objects that are entangled, one may view this entanglement as the existence of a wormhole of some kind. However, in most cases, such a wormhole is Planckian, so to say, and it requires the full theory of quantum gravity – going well beyond the effective long-distance theory similar to general relativity – to be properly studied. (I can't resist to think about the thin handles that may be added to M2-branes modeled by Matrix theory without changing the state described by the noncommutative geometry; their spacetime wormholes must be analogous to these "world volume wormholes".) They admit so: they reinterpretation of the entanglement as an Einstein-Rosen wormhole may often be just an academic formality that doesn't allow you to exploit the useful properties we like to associate with large and thick wormholes.

On the other hand, they accumulate quite some evidence that a greater number of examples of entanglement than what you might think may be described in terms of the Einstein-Rosen wormhole that is really large and classical and unquestionably deserves the title.

In particular, they suggest that once a black hole evaporates one-half of the original entropy, i.e. after the Page time when we know the early radiation to be almost maximally entangled with the remaining black hole, one automatically gets the "thermofield-like" doubling of the degrees of freedom – doubling of the number of black holes. The early Hawking radiation may be interpreted as one of the two black holes that is connected (after some transformation of its degrees of freedom) to the remaining, self-evident black hole by the Einstein-Rosen bridge.

The authors claim that this has consequences for the perceptions felt by an observer who jumps into the remaining black hole: his perceptions – which may include the firewall-like death near the horizon – are actually affected by the decision what some other observers do with the early Hawking radiation! After all, manipulating with the early Hawking radiation should be interpreted as processes "somewhere inside the wormhole" so these processes may be thought of as appearing "geometrically close to the black hole interior" because this is where the second exit from the wormhole resides!

Whether or not such an influence of the "experimenter measuring the early Hawking radiation" on the "infalling observer" violates any notion of locality and how strongly is a subtle question that requires you to be careful. Clearly, some locality as defined strictly by classical general relativity (and assuming the non-wormhole relationships between events in spacetime!) has to be violated because the measurements of the early Hawking radiation can't be connected by any time-like trajectory with the events in the remaining black hole interior. However, they are connected in more general ways.

Even if the infalling observer is able to miraculously find out something about the activities done by very distant, seemingly spacelike-separated experimenters who measure the early Hawking radiation, it doesn't imply any real paradox that we may derive from faster-than-light communication simply because the infalling observer has no way of communicating his perceptions to the folks outside the nearby event horizon.

We shouldn't overstate the reasons why we believe principles such as locality. We believe them because in combination with the Lorentz invariance, faster-than-light communication would be equivalent to the changes of the past and closed time-like curves that would lead to contradictions. However, if we consider more general situations with "doomed infalling observers" whose doomed fate allows us to avoid the paradoxes, the original evidence in favor of the strict locality really evaporates.

The observer on one side of the Einstein-Rosen bridge may control the perceptions of the other if she acts quickly enough; a section of the paper is dedicated to the question what this condition means. It seems that they want to apply these considerations to the experimenter who manipulates with the early Hawking radiation, too. She has some power over the poor observer who falls into the remaining black hole after the Page time. Don't forget that while feminism empowers women (yes, all the observers who control others are female in the paper), it comes with a responsibility, too. ;-)

A nice thing about the paper is that it passes all tests of "absence of basic misunderstandings". The authors don't seem to suffer from any confusion such as a misunderstanding of the foundations of quantum mechanics. I have already suggested that this virtue results from Juan Maldacena's genes incorporated into the paper. (Lenny, despite his being so utterly sensible, has already written some papers boiling down to a misinterpretation of the postulates of quantum mechanics.) In fact, I believe that Juan Maldacena is flawless in this respect – he would never write a paper that makes an error in the foundations or interpretation of quantum mechanics or any other topic that one could include among the "standard undergraduate or graduate course material". I believe he suffers from no confusions that are so widespread in the "popular science literature".

To say something stronger, much of the paper seems obviously right. Quantum mechanics is used fully up to the limits and they struggle to interpret any dynamics – including any sort of entanglement – geometrically, as a bridge of a sort. That's right because after all, string theory unifies all forces and matter with gravity so everything may be viewed as a generalized gravity or generalized geometry.

At the same moment, there's quite some potential for this line of reasoning to run much deeper than that. Various folks including Edward Witten and Cumrun Vafa have explicitly said that while they didn't expect any true deformation to be ever made to quantum mechanics, they could imagine a future revolution that will unify the postulates of quantum mechanics with all kinds of geometry that appears in physics (especially the spacetime geometry) in a new, more intimate way. The geometrization (conversion to a bridge) of any entanglement in physics could lead us to a very tangible realizations of those ambitious visions.

And that's the memo.


  1. Does this mean there really was something unclear to many (including Susskind) that was clarified by the firewall discussion?

    You write both "Healfix finds the paper controversial, either wrong or the first salvo of a completely new revolution. I don't. The paper is cool but it's a totally natural continuation of the state of the affairs as we have known it for quite some time." and "The geometrization (conversion to a bridge) of any entanglement in physics could lead us to a very tangible realizations of those ambitious visions."

    Not necessarily a contradiction but a bit hard to interpret.

  2. Dear JollyJoker, the topics of the two quotes are completely different because in the first one, I actually talk about their paper and what they achieved with the usual Maldacena-style of accuracy.

    The second quote refers to visions that are still presented mostly as visions - or they're not presented in this paper at all. It's a very promising line of reasoning but it is not completely new and the ambitious conclusions - that have been dreamed about for many years as well - haven't actually been achieved yet.

    So there is absolutely no contradiction here. One of the things are the actual results; and the other things are dreams. Your confusion suggests that you don't distinguish these two very different things.

  3. Nima Arkani-Hamed has stated that spacetime is doomed. Can you reconcile his prediction with a unification (in a new and more intimate way) of the postulates of QM and spacetime geometry?

  4. Dear Gene, I don't claim that I can actually *do* it i.e. specify all the details and full proofs but I surely do believe that the paradigms may be compatible.

    When spacetime is doomed, it's only a spacetime of some sort that obeys certain conditions, including exact locality, and so on. The spacetime with wormholes that may be relevant for a new description of a singlet state of two spins is a different state. It's not local in the usual sense - it allows one to create distant ER bridges and similar things.

    Physics doesn't run on words or slogans so although the slogans may sound as the opposite ones at the linguistic level, a reinterpretation of all pure or mixed states in terms of exotic geometries may actually be viewed as an explicit proof that the old spacetime is doomed. The new one becomes more important, too.

    Propositions such as "spacetime is doomed" are subtle and one must be cautious about their meaning. But take just quantum mechanics and the phase space. It's noncommutative, px isn't equal to xp. Density matrices are still in one-to-one correspondence with the ordinary functions on the phase space, as in Wigner distributions The noncommutativity is transferred elsewhere.

    It's one of the great lessons of theoretical physics of the last 20 years in particular - but it already began with QM if not much earlier - that the same physics may be formulated using two, several, or many descriptions that are ultimately fully equivalent but that seem to have different "apparent qualitative properties". Whether a spacetime is manifest and more important than ever before or completely lost and emergent may be just a matter of the choice of the description, just like the question whether reality is composed of particles or waves or tons of similar questions.

  5. Brian G ValentineJun 5, 2013, 5:44:00 PM

    Nima Arkani-Hamed has stated that spacetime is doomed.

    Another unfortunate consequence of global warming.

  6. I believe more and more in a principle which would state that physical reality does not depend on observers. For instance, using quantum formalism, physical reality would be described by a state |psi>. But observer-dependent quantities as < t | psi> or or , are only a partial view, or partial representation of the reality, while very useful for concrete calculus. Of course, the paper seems to be at a higher level, equivalence of structures, rather than a basic observer-equivalence.

  7. These people must be really desperate if this is an example of a top hep paper. If it was written by an obscure physicist from Novosibirsk (or a similar hole), nobody would even notice let alone open the preprint (and rightfully IMHO).

    Sussking stopped being relevant for modern physics sometime in the late nineties...

  8. I can't resist to think about the thin handles that may be added to
    M2-branes modeled by Matrix theory without changing the state described
    by the noncommutative geometry; their spacetime wormholes must be
    analogous to these "world volume wormholes".

    The picture might also be interesting in the dyonic case, where one can study the U-duals of the brane configurations.

  9. You have no idea what you're talking about.

    No person from Novosibirsk or the rest of Russia, for that matter, would be able to write a paper that would boast 10% of the solidity or 10% of the originality of this paper.

    If you can't distinguish Maldacena's work from the world of some rank-and-file chap from Siberia, it's a proof of your inadequacy, not Maldacena's.

  10. What about the Alcubierre's-like transversal wormholes? Are they related to what kind of quantum phenomena?

  11. Dear Lubos,
    this interpretation of EPR as wormholes seem to allow a more realistic interpretation of quantum mechanics: The "spooky" action at a distance would be due to a somewhat real communication channel. Do you agree?

  12. I like these very nice explanations :-), since I got once confused by Nima's slogan too

  13. Thanks, Lubos. That is exactly the answer that I was looking for.
    I have really been questioning what Arkani-Hamed was talking about and this helps me a great deal.
    I surely did not think that a seeming linguistic contradiction would be reflected in the mathematical physics. I agree completely with your last paragraph.

  14. I don't think there are many reasonable people that buy into this nonsense. Sorry, Lubos, but there are perhaps dozens of si-fi articles that postulate this kind of speculative (bullshit??). You need a LOT of empirical evidence, and I don't think I will live to see it. Fun thoughts on your part, but nothing more.

    My advice to you morons is to INVENT even more strange words to describe what you have not really described! How about "surprise worm," or "dark worm" or "devil particle?"

    You folks are just a comicalcuriosity to other scientists, I think.

  15. Well, I just woke up ;)

  16. No, of course that I completely disagree. Quite on the contrary, and it is discussed in the first sentences of the paper and at many other places (including this blog entry), the Einstein-Rosen bridge is unable to provide one with any communication channel between two places of the spacetime just like EPR entanglement is unable to do so.

  17. Almost certainly not. It's absolutely critical that the Einstein-Rosen bridge is "irreversible" once you fall into it, it is not traversable. Did you try to understand the paper? It is not just stating it; it is proving that the relationship must be in this way so that an intelligent reader should be able to understand it.

    The womholes you mention seem inconsistent. There may be a loophole and they may be related to something but another, different, clever paper would have to be written that would clarify how it can work. No such a paper or idea exists at this moment so Alcubierre's fast-drive stuff is simply an inconsistency not allowed by a functional theory of QG.

    Clearly, it seems to me that *absolutely* every single commenter on TRF has misunderstood all these things.

  18. Interesting the connection ER=EPR. It
    reminded me of a blog comment I made a couple of years ago at FQXi (among some critical comments I made against a theory which was supposed to violate Bell's theorem, by JC), in which I propose something similar:

    I proposed it for theoretical purposes only, as an example of local explanation of EPR by using ER, which seems to circumvent Bell’s theorem, but I did not consider it such a big deal.

  19. Actually I have not read the paper, maybe I should have done this before. Anyway, I simply asked you because the correspondence wormhole-EPR_like (or a no-go theorem proving the impossibility of that hypothesis) would be a fascinating one! Sorry, but I am not really convinced of the existence of a single proof in QG theories that forbid transversable wormholes: if know that, please, post the reference. Thanks

  20. Mark von Raamsdonk's paper is a fun read. Here is his brief and understandable summary:

    and the arxiv paper, which is also quite transparent:

    Thanks for the mention of myself and Werner Israel--
    a kind and great man and my former supervisor.

  21. Dear Lubos,
    I understand that you cannot send light signals through these wormholes and more generally that the physics doesn't change through this geometrical description. Just what I want to say is that a wormhole "smells" a bit like an "explanation" in the classical sense.

  22. Smells?

    Maybe it's better to use the brain rather than the nose if you want to rationally think. ;-)

    In this paper, they argue that ER and EPR is the very same thing, so if that's true, they smell exactly the same to every rational nose.

  23. Brian G ValentineJun 6, 2013, 9:45:00 PM

    I never got my arms around any aspect of quantum gravity, I don't think I ever will.

    I spent years studying gen relativity, viewing spacetime as the ultimate continuum, now I don't know what to think.

    Like all other dinosaurs my variety will be extinct in short order.

  24. Ok, Lubos, here comes my brain version of the argument
    (taken from Feynman): Different equivalent descriptions of the same physics are important because they may lead to different ways to extend them.

  25. You can fret about about it like a little boy but the fact is that while the 2001 paper is interesting and moderately profound, the current preprint is mediocre. To claim that the states in (2.5) can be described by ER bridges only results in a honorable mention in Nude Socialist (by the way, they are locally unitarily related hard to imagine two different bridges but whatever). The only non-trivial statement is that somehow the entanglement classification might be found in geometry so the math will be the same. Wow, what an insight. At best, it resembles the work of Borsten et al relating BPS BHs and entnaglement measures. So yes, it's trivial, speculative and not really innovative at the same time.

  26. Gene---read the first link I posted above.

  27. ditto my comment to Gene.

  28. Right but realist i.e. classical physics is *not* an extension of the modern i.e. quantum physics. It's the other way around.

  29. I have just proved that states of M2-branes analogous to (2.5) are described by wormhole-like configurations in the matrix model and identified the differences to the geometry made by different relative phases, and so on.

    Such things may be proven rather rigorously.

    I told you that you would be banned after yet another utterly idiotic rant about theoretical physics, the comment you wrote just above this one is the critical one, and you are banned.

  30. Brian G ValentineJun 7, 2013, 7:36:00 AM

    Classical physics are a reduction of observations.

    Quantum physics are a reduction of postulates.

    Sorry if that sounds like I'm being critical.

  31. Dear Lubos, by checking references on arxive it seems me that stable wormholes are a direct consequence of ST and not the other way round as you told: arxiv:1111.4049 ... Thus, maybe there is still some hope for Star Trek fans yet! ;-) Comments?

  32. Very interesting references.

    The fascinating idea is that space-time geometry would be only information, especially mutual information, and interpreted as entanglement states in the boudary CFT dual.

  33. I can see where you would take issue with Mikael's use of
    the terms "communicate" and "classical", and I think most of
    us get that this paper is entirely consistent with the observables of QM, but I
    think the root of Mikael's question is, "does this model offer anything
    new with respect to explaining how entangled particles correlate their states
    across time and space?"

  34. Dear Rsala, new research can't offer us any conceptually new things about predictions of entanglement - what the predictions for experiments actually are and how they're calculated - because we have understood it perfectly since early 1930s and essentially since 1925.

    If you keep on believing that the postulates of quantum mechanics will be shown invalid, your belief is exactly as unscientific as the belief that Jesus Christ, and not Yang-Mills fields, will be shown to hold the nuclei together.

  35. Dear Justin, the situation is exactly the opposite than what you suggest.

    I have always been saying that the Hawking radiation, as a mechanism that gets some detailed microscopic information out of the black hole, violates locality, although by an exponentially tiny amount (the information is "tunneling" from the black hole and temporarily violating the relativity bounds - and temporary violations of laws are possible in quantum mechanics).

    But in an appropriate interpretation, this paper shows exactly the opposite. The information isn't propagated to distant places because, due to the wormhole, the places we considered quite separated aren't that separated, after all.

    Because the wormholes they discuss are non-traversable, the mechanism here doesn't allow one to send information to distant places of the flat space which means that nothing in this paper violates the locality assumption of Bell's theorem, however. This assumption is as obeyed as it is in quantum mechanics - because the theory they talk about is still 100% equivalent to quantum mechanics, including all the interpretational issues. They just say that the quantum entanglement may also be interpreted geometrically in the spacetime but the logic governing all the states, predictions, observatinos, and so on, is still the same quantum mechanics. The state equal to a superposition of two tensor-product states on "ordinary space" is the same thing as the simplest state of a spacetime with the ER bridge.

    I don't believe that there is anything ambiguous about this point and I wonder where this stunning desire of the laymen to liquidate quantum mechanics comes from.

  36. Lubos, largely due to your diligent efforts, I've formed a deep appreciation for how truly revolutionary, profound, and enduring the work of the founders of QM is. And I agree with you that it is an injustice that so many have tried, and continue to try to invalidate their discoveries simply because it conflicts with their naïve intuition. I was trying to make the distinction between description and explanation, because while I am totally convinced that QM fully and satisfactory describes and predicts how particles behave with respect to entanglement, I have never heard an explanation of how it happens that resonates with me.

    Maybe I'm like the student who tells his physics instructor that he is mystified by the thermos bottle. When his instructor asks him "why", he says, "Because it keeps things cold in the summer and hot in the winter … how do it know???"

    But to your analogy, if I ask you, "What holds the nuclei together?" You answer, "The Yang-Mills fields". And if I ask you, "How do entagled paricles correlate their states?" You answer ...

  37. Right, thanks for your kind feedback, rsala.

    Whether there is a difference between an explanation and a description is a subtle question. As we discussed e.g. in the context of Feynman's answer to the question "what's the feeling between magnets", every explanation has to assume some true facts, it has to work with some axioms. So it's just like a description.

    One may only discuss whether the number of axioms that have to be assumed is economic or not; and whether these axioms may explain many diverse phenomena or not. But that's it. There's no qualitative difference between an explanation and a description.

    Thermos bottle keeps the temperature of the confined box with liquid (or anything) because it prevents any flow of energy from or into the box. There's vacuum in between so there's no convection or conduction; and the flow of energy by radiation is prevented by mirrors. Is that a description or an explanation? I think it's both.

    In the same sense, quantum mechanics provides us with both in the context of experiments exhibiting what we call "entanglement".

    Your question "How do entagled paricles correlate their states?" is loaded because it tries to force us into a totally wrong assumption that entanglement isn't a fundamental property of Nature - into the opinion that it needs or admits a "deeper" explanation. But it doesn't. Entanglement is actually deeper and more universal in Nature than the Yang-Mills fields.

    Entanglement is the most general correlation as allowed by the laws of quantum mechanics - the laws of the Universe around us - or, more specifically, a property of a state in the Hilbert space meaning that it can't be factorized into a tensor product of states in two regions,just into some superpositions of two or many such tensor products.

    Entanglement between two subsystems is always created by the two subsystems' contact or common origin in the past and its precise implications and predicted measures of correlations are calculable through the fundamental equations of QM.

    I am absolutely convinced that these words, with the technical bonus if needed, are both a description and and an explanation of what's going on, how it's going on, and why it's going on, and any suggestion that there's something missing is just a tendentious and deeply fundamentally misguided attempt to force us into saying or thinking something that is completely false, e.g. that there exists a classical mechanism underneath quantum mechanics.

    It's wrong to reduce the observations of entanglement into a classical mechanism in exactly the same sense in which it's wrong to reduce the attraction between nucleons to Jesus Christ.

  38. I agree, but one thing that is perhaps not made so clear is just how quantum correlations differ from classical correlations - especially since these recent firewall papers have focused on the idea of 'entanglement monogamy' - ie a third particle can't be fully (maximally) correlated with two existing maximally entangled particles.

    So quantum entanglement isn't just like classical conservation of momentum for example.

    A pretty easy but sensible discussion can be found in

    Overall though, regarding the firewall discussions, my feeling is that are theories are not yet mature enough to make sensible models or predictions in these regimes.

  39. Lubos, that was a nice response to clear up my confusion. I hope you can tolerate, or even appreciate laymen who can't help but be fascinated by physics and tune in to your blog.

  40. Sure, it's pleasure as long as it isn't an overwhelming distortion of the comment threads or an indefinite sucker of my time.

  41. What baffles me of this construction is that it seems to imply that spacetime topology is observer-dependent. Imagine the vacuum state, no ER bridges whatsoever. But to two counter-accelerating observers this looks like a bath of highly entangled particles - hence to them spacetime topology is more like a Swiss cheese.

  42. Does your comment refer to the Rindler space? I think that you're overstating the complexity of the geometry. It's, on the contrary, very smooth as the entanglement links "everything simultaneously". So no Swiss cheese.

    In general, I think that you understate what MS do to topology. Topology becomes an ill-defined "quantum number" even for a single observer, something that isn't new to those of us who have spent some time with M2-branes in Matrix theory.

    The reason is that the "up here, down there" state of two spins which apparently lives on a background without wormholes isn't orthogonal to - isn't mutually exclusive with - the entangled state identified with a configuration that has an ER bridge. So the two spacetime topologies aren't mutually exclusive. In other words, the spacetime topology isn't given by a well-defined operator.

    I find it a rather natural property of the quantum foam in general.

  43. Thanks for the thorough reply Lubos. I understand that topology need not be a well-defined observable in quantum gravity, and that there is no problem with that. Another thing that baffles me is what MS state right above (3.1):

    "Suppose that we take a large number of particles, entangled into separate Bell pairs, and separate them in the same way as the mini-black holes. When we collapse each side to form two distant black holes, the two black holes will be entangled. We make the conjecture that they will also be connected by an Einstein-Rosen bridge."

    If the initial entanglement is maximal, then the ER bridge will be macroscopic. But we can do this with arbitrarily weak fields, etc (at least until we reach the singularity, but the ER throat is much bigger than that). So we should be very well within the domain of validity of classical GR/QFT in curved spacetime, which clearly predicts no ER bridge. How can we explain the presence of strong QG effects in this seemingly innocent regime?

  44. Dear Miguel, it's a good question but your apparent paradox is a consequence of a simple mistake you're doing, essentially overlooking the first sentences of the very same section 3.2 that you quoted.

    The point is that classical communication and local operations (which includes every process that may be described by classical GR) do *not* increase the amount of entanglement inside the physical system. So the many entangled pairs are there only if the members of each pair were entangled from the beginning.

    So you're not really creating new bridges, they're there from the point when you create the Bell pairs.

    You may just move all these many small bridges to a single region. You will find out that they're separated from each other - there are many thin bridges - if you have many small particles in an otherwise nearly empty surrounding space.

    If you want to perfectly entangle all the degrees of freedom in a pair of large black holes, you must appreciate that their entropy is fantastically high - you need to correlated 10^{80} qubit pairs for an astronomical black hole. This makes it infeasible in practice.

    So in reality, the only feasible method to make the two black holes perfectly entangled by all their degrees of freedom is to pair-create them - and indeed, that's the flagship example they mention. When you pair-create e.g. charged black holes in a magnetic field, they will be connected by a bridge because that's what the black-hole-pair-creating instanton says even in the semiclassical treatment of this nonperturbative process.

  45. Hi Lubos,

    Thanks again. I see your point -I assumed that the initial entanglement was maximal without realizing that this might mean we have the ER-bridged BHs from the start-.

    However, there seems to be ways to circumvent this, at least as a gedanken. I can entangle 10^80 qubit pairs and send them apart, one by one. Then carry on with the collapse and the macroscopic ER bridge. All of it (apparently) within the domain of QFT in curved spacetimes. What is failing in this simple construction?

  46. Dear Miguel, what fails is that the black hole actually has a much higher entropy - many more qubits - than any star or another collection of ordinary particles.

    The black hole entropy goes like A^{1} while the star entropy goes like A^{3/4} which is parametrically smaller. So if you create a black hole out of a collapse of anything that resembles a star, ordinary matter, most of the black hole's qubits/degrees of freedom/entropy will be unrelated to the qubits in the original matter - they will belong to the extra entropy that was created during the collapse.

    But even if this complaint against your construction didn't exist, one could say that the effective QFT fails because it's no good for a description of a too high number of excitations. If you have too much information in a small volume, then you simply need to consider quantum gravity because classical or otherwise simplified gravity isn't capable of describing why too much entropy is impossible to be squeezed into a small volume, aside from other limitations.

  47. Lubos - An interesting aspect of elementary entanglement is that, e.g. a system of two entangled qubits may be viewed, by a coordinate transformation, as a system of two unentangled, independent qubits. Can a similar thing occur here?

  48. Sorry, I don't understand how your claim could not be a contradiction.

  49. And here I thought you knew everything!
    No contradiction, in fact quite simple - see and
    for the basics.

  50. Dear Lubos,

    Thanks. I was going to propose one last scenario -two initially independent, uncorrelated BH's which I entangle later on by means of entanglement swapping through a very large reservoir of entangled pairs-. That might overcome the first point of your last answer (do you agree?), as we may have as many entangled pairs as we like, but certainly not the last.

    Thanks again for the enlightening responses, and for TRF in general.

  51. Dear RAF, the papers make no sense. And yes, I did notice a "famous" name of a co-author of one of them.

    Of course that usefulness of a tensor product decomposition depends on the identity of the useful observables. But all these things are being assumed every time we talk about entanglement. Of course that entanglement is relatively to a particular tensor decomposition of a Hilbert space. But this decomposition for separated parts of the system, is by locality independent of the observers as long as the observers keep the same definition of the vacuum outside the two regions with the subsystems that are considered.

  52. Dear Miguel, you may have as large a reservoir as you want but it's still true that during the collapse of ordinary matter to a black hole, the entropy is increasing dramatically and parametrically which means that the overwhelming majority of the qubits encoded in a black hole will be uncorrelated with the qubits of another black hole. Black holes are the best scramblers so they mix the relatively few qubits that were entangled from your bath with the rest so the entangled part of the qubits gets insanely diluted in each black hole.

  53. Lubos - I was not advocating the papers in their entirety but referenced them simply to apprise you of the simple mathematical fact that, as you wrote, "Of course that entanglement is present or absent relatively to a particular tensor decomposition of a Hilbert space." and which you initially viewed as a contradiction.
    I'm quite sure that our opinions of the 'famous author' are in complete agreement.
    It had occurred to me that the presence/absence of an ER bridge and entanglement might be due to observables based on different decompositions.
    Anyhow, thanks for your answer.

  54. Right, except that it's one of the points of locality that the decomposition of the big Hilbert space to a tensor product is unique (in particular, independent of the inertial system).

    After Maldacena+Susskind, one may phrase these things a bit more generally - there is a unique decomposition of the Hilbert space into tensor factors that are maximally far from the bridge-like states.

  55. Thanks again.
    If I could pester you once more -
    I thought this could be related to the notion of observer complementarity and the difference between external and infalling observers.

    Am I off the mark here?

  56. The Maldacena-Susskind paper is surely closely related to - more precisely strongly relevant for - the black hole complementarity and the differences between infalling and external observers.

    It says that their degrees of freedom are overlapping - like in complementarity - but it also invites us to give a clear geometric representation to this relationship that identifies some of their degrees of freedom - the relationship "is" the ER bridge.

  57. I look forward to seeing your more explicit description.
    What puzzles me is that if the decompostion is unique surely this constrains possible observations; and since the ER bridges are essentially superpositions in this basis, how can they be observed or realized?

  58. Sorry, I don't understand your question.

    Every Hermitian linear operator on the Hilbert space is an observable that can be "realized" and measured.

    For a system composed of two subsystems, the Hilbert space is a tensor product. Most operators are observables depending on both subsystems, some special operators only depend on the system A or system B.

  59. But wouldn't such an observable provide a basis given by the bridge states?
    And wouldn't this provide a different decomposition?
    You wrote before that the decomposition was unique.
    I'm still puzzled.

  60. Which observable are you asking about in the 1st sentence?

    Every (pq)-dimensional Hilbert space may be written as a tensor product of p- and q-dimensional Hilbert spaces in infinitely many ways but only the factorization that is respected by the Hamiltonian or evolution amplitudes (at least approximately, in some approximation) is physically useful and that's the decomposition - dictated by locality - we're talking about and this unique useful decomposition is shared by all initial frames.

  61. I see your point now.
    Thanks for bearing with me.

  62. Proof that EPR is the multiplicative sort:

    Firstly, this is equivalent to proving that the set of all physicists, couple with the group law of working on the topic is not a commutative group.

    Whether one physicist (say "Einstein") writes the paper first, and then another physicist (say "Witten" (did I spell that right?)) then works on this paper, is going to be a different result than if Witten writes the paper first and then Einstein works on it, because Einstein is dead, and that would result in no paper, i.e.

    $\hat{W}\hat{E}|\operatorname{Old Physics}\rangle=|\operatorname{New Physics}\langle$

    $\hat{E}\hat{W}|\operatorname{Old Physics}\rangle = 0\rangle$.

    I.e.,; Einstein and Witten aninhilate physics, but Witten and Einstein raise its level.


    $\left[\hat{W},\hat{E}\right]|\operatorname{Old Physics}\rangle = |\operatorname{New Physics}\rangle$

    This means that the magma is not commutative!. So, now, is it even a group? Does every physicist have an inverse? No... Not yet, at least.

    Does closure hold? Yes. Because if two physicists operate on a topic, the result is another (probably the same?) topic. Regardless of whether that topic is physics or not physics, whether it is mainstream or crackpot, etc.

    Does associativity hold? Trivial. Yes, it does...

    What about existence of identity? Yup, there is definitely a physicist "e" such that:

    $e|\operatorname{New Physics}\rangle = eP|\operatorname{Old physics}\rangle = P|\operatorname{Old physics}\rangle=e|\operatorname{New Physics}\rangle.$

    I.e. there exists a physicist who is neither harmful nor harmless to Physics.

    So, conclusion:

    Physicists form a magma.

    Physicists form a semi-group.

    Physicists form a monoid.

    Physicists do not form a group.

    Physicists therefore do not form a commutative group.

    Therefore, "EPR" and "ER" are of the multiplickative sort, and since, EPR = ER, therrefore,

    P = e;

    And therefore, Polydoskiy has had no impact on Physics...

    Wait, what??? That is wrong! Therefore, Maldacena and Susskind must be wrong! (And thus, $M|\operatorname{physics}\rangle = S|\operatorname{physics}\rangle |\operatorname{bad physics}\rangle$


    For all those who didn't understand, the above is simply as joke, and please don't use the argument against the Maldacaena - Susskind paper.

  63. So, if the duality would happen to be a fundamental property of nature, more fundamental than quantum mechanics or lorentz-invariant local space, then it would be interesting to obtain some first order corrections implied by features of the dual

    for instance, a kind of question that could be proposed is: how does the description of quantum entanglement (as a sum of tensor products of subsystems) breaks down when the relevant dual geometry is a wormhole where the width of the throats is large compared to the separation of the throats in asymptotically flat space? or as a different possible question: when the wormhole is not a simple one dimensional curve joining two remote endpoints, but the curve has a more complicated homotopy (i.e: the curve has closed loops)

  64. I am pretty sure that Maldacena and Susskind would agree that according to the current evidence, quantum mechanics is exact and their alternative EPR-bridge description is just another description that is exactly equivalent to QM including its entanglement etc.

    It doesn't look like any deformation of QM is possible.

  65. "It doesn't look like any deformation of QM is possible". So far, QM is inherently linear, which means that amplitudes do not interact directly with other amplitudes. All deterministic processes are unitary, and the only allowed non-unitary processes allowed are non-deterministic (i.e; measurement collapse, or whatever people like to call it these days). I agree that currently there is no observational data to believe that a deformation should be expected, but neither was observational data available before 1915 to expect that gravity would deflect light rays, or that spacetime could be anything but flat. That didn't stop someone giving the idea consideration

    While it may be true that the duality only holds for planckian-thin wormholes and purely vanilla quantum entanglement, I would find if weird if the duality would suddenly utterly break when we move out of those regimes. Maybe a slightly more general versions would hold, that would still make slight corrections that wouldn't break our current observations.

  66. Well, a difference is that the linearity/additiviity of the gravitational forces was an observed accident and it was ultimately false while linearity of quantum mechanics may be proved both by experimental and theoretical considerations and it is ultimately true and exact.

    Because the truth and untruth aren't equivalent, these two cases aren't analogous, either.

    Linearity in QM has the very same reasons to be
    exact why the probability

    P(A or B) = P(A) + P(B) - P(A and B)

    In fact, these two relationships are implied by one another - and in some contexts are equivalent - once one adopts the basic quantum associations between operators and observables.

    So everyone who is expecting or working on a nonlinear deformation of QM is just a sucking or would-be physicist who really has no clue.