I thought that the acronyms are sort of funny
Two contrasting papers on the Papadodimas-Raju theory of the black hole interior and the Maldacena-Susskind ER-EPR (Einstein-Rosen/Einstein-Podolsky-Rosen) correspondence have been posted to the hep-th arXiv today:
PR and ER-EPR are not quite equivalent although the acronyms may be combined to a rather nice triangle. ;-) But I think that they are ultimately compatible. Both of them are right and complementary. PR tells us something about the freedom we have when we extrapolate dynamics of quantum gravity into the black hole interior; ER-EPR teaches us about the behavior of the Hilbert space in topologically nontrivial situations with an ER bridge (not really studied by PR at all, at least so far). Harlow's paper is against PR; Andreas Karch et al. argue in favor of ER-EPR maximally positively – so positively, in fact, that they (rightfully?) demand a part of the credit for the streamlined interpretation of the ER-EPR correspondence. But even though they focus on "different theories" of the black hole interior, you may see that PR and ER-EPR are "allies" because pretty much the same point that causes so much discomfort to Daniel Harlow is also what Andreas Karch et al. – which will be referred to as Jensen et al., to respect the alphabetical order – embrace so enthusiastically!
What is the point that may describe the "key" to both papers? I think that the point says that PR and ER-EPR may be interpreted as new dualities that allow several equally correct descriptions of the same degrees of freedom and their physical fate. Andreas Karch et al. are big friends of dualities so like your humble correspondent, they think it's cool to discover a new important duality and it's perfectly consistent.
On the other hand, Daniel Harlow seems to have a psychological problem with the very notion that there may be different ways to describe the same Hilbert space.
Let me clarify what I mean a little bit. I have to assume that the reader is mostly familiar with the basics of the ER-EPR correspondence and the PR picture of the black hole interior that have been discussed many times on this blog.
The new Jensen-Karch-Robinson paper builds on the Karch-Jensen followup to the ER-EPR correspondence in which Karch and Jensen argued that the world sheet of the QCD-like quark-antiquark string in the AdS/CFT correspondence has an Einstein-Rosen bridge on it, too. Because the quark and antiquark are entangled, the observations seem to confirm the picture that the entanglement is equivalent to a wormhole.
OK, the new Jensen-Karch-Robinson paper first "extends" the AdS/CFT picture to a Randall-Sundrum model. In the CFT language, this is represented by coupling the quantum field theory to gravity; in the AdS bulk description, the extension looks like a brane ending/cutting the bulk geometry. Things still work. The other point that they make is that the entangled Hawking particle pairs may be seen to be entangled; and may also be seen to be two sides of a wormhole, thus producing another confirmation of the ER-EPR paradigm.
If you're interested in their paper, you should read it and I won't try to reproduce everything they say. But I want to add a few more words of mine about a general philosophical theme that Jensen, Karch, and Robinson describe in their paper and that I fully agree with.
They want the ER-EPR link to be treated as another duality. Some degrees of freedom may be either thought of as living in two isolated places of the spacetime and being entangled; or they may be thought of as being geometrically connected by a wormhole. Moreover, the entanglement-like (EPR) description is more typical in the CFT side of the AdS/CFT correspondence while the wormhole-like (ER) description arises if you consider the bulk, too. In this sense, ER-EPR applied to states in the AdS space may be considered a special case case of the AdS/CFT correspondence, with the identification ER=AdS, EPR=CFT.
I've been defending the same interpretation of the ER-EPR correspondence as another duality for quite some time, namely from the birth of ER-EPR; see e.g. this October 2013 text, especially the section "Possibility to fix the gauge (light-cone gauge) in string theory & allowed topology change & ER-EPR". The point is that in a consistent theory of quantum gravity, the spacetime topology is not only dynamical but it even fails to be a "good quantum number". There is no operator that would count some invariants describing the topology (e.g. the number of Einstein-Rosen bridges in the spacetime). Instead, the same states in the Hilbert space may be built as excitations of a background with no bridges; one bridge; or many bridges. Some of these descriptions of the states may be "more weakly coupled" or "smoother" or "less excited", and therefore "less awkward", but in principle, all the descriptions – descriptions assigning the spacetime with any topology – are allowed.
This "new kind of a duality" seems very profound to me and I think that Jensen, Karch, and Robinson have the same feelings. There is no inconsistency in this paradigm. Incidentally, the first sentences of their new paper say that "entanglement is [just] correlation but the entangled states can't be measured by themselves". It's exactly something that's been claimed in many older TRF blog posts.
Daniel Harlow's dissatisfaction
On the other hand, Daniel Harlow writes something about the \(1/N\) corrections in the PR picture – the general theory of the black hole interior that he reviews – and sort of agrees with PR that it works and has the potential to resolve all puzzles that were promoted in the context of the firewall paradox etc. However, the main point of Harlow's paper is some skepticism. The PR picture is "ambiguous", he thinks. Surprisingly, the people's disagreements about the "interpretation" of quantum mechanics began to play a prominent role in papers such as Harlow's. Until the middle 1990s, the epoch of the Duality Revolution, people would apparently agree what quantum mechanics was. So no stringy paper would ever talk about "interpretations of quantum mechanics". Only confused people were doing so. Suddenly, this business has penetrated to the quantum gravity research and it is turning out that at least someone must be understanding what quantum mechanics actually is.
The first skeptical sentence in the abstract of Harlow's paper says:
\ket\chi = A_\alpha \ket\psi = A_\beta \ket{\psi'}
\] for some equilibrium states \(\ket\psi, \ket{\psi'}\) and \(A_\alpha,A_\beta\in {\mathcal A}\) in various ways. Well, it's just a matter of trivial linear algebra that a vector in the Hilbert space may be obtained as an action by an operator on another state in infinitely many ways. It's true for every quantum mechanical system. What's causing discomfort to Daniel Harlow is clearly his assumption that the question "which equilibrium state or vacuum background is associated with \(\ket\chi\)" should be a well-posed question connected with a good quantum number, with some Hermitian operator(s). In other words, he assumes that it should be possible to measure "the equilibrium state \(\ket\psi\) upon which \(\ket\chi\) is built" by a measurement process.
He's wrong. He could figure out that he's wrong if he actually tried to defend his (indefensible) position, something he didn't bother to do – by describing what the hypothetical process that "measures the background or 'the' equilibrium state underlying a general state" actually is. He would find out that no such experimental algorithm exists and none may exist.
Even though we're talking about PR and not ER-EPR here, you see that it is pretty much the same question as the question discussed above, in the context of the Jensen et al. paper. Their – and my – answer is obviously that "the right equilibrium state" underlying a state \(\ket\chi\) isn't uniquely associated with \(\ket\chi\), and it's a good thing. Whenever we have a duality, and the ER-EPR correspondence is a duality, in fact, in some sense, a manifestation of the AdS/CFT holographic duality (at least some special cases of AdS/CFT and special cases of ER-EPR are the same thing), then we also have many ways to imagine "by what operators" we had to excite a ground state to get to the required state \(\ket\chi\), and so on. In a general field theory (it's enough to imagine a QFT on a curved spacetime background; or a QFT with moduli), there is no single "universally preferred ground state" that should serve as the basis to build the rest of the Hilbert space. A ground state – or, in this case, an equilibrium state – is non-unique. All states in the Hilbert space are actually equally real and equally allowed; that's what the linearity postulate of quantum mechanics demands. One description in the case of S-dualities may describe the same state as an excitation of a D-brane added upon a background; the other, S-dual description may see it as a complicated state of many fundamental strings, and so on. The ground state of one Hamiltonian may be obtained by a Bogoliubov transformation i.e. by an action of some creation operators on the ground state of another Hamiltonian (particle production). None of the descriptions is better than the other(s). They're exactly equivalent.
To localize the problem with Harlow's reasoning from a slightly different angle, let me copy some sentences from page 18:
In other words, and I have been explaining the very same point in dozens of blog posts about the foundations of quantum mechanics, a quantum mechanical theory (probabilistically) answers questions about observables, but it doesn't tell us what the questions should be. There may be different questions – about different observables building the Hilbert space by their action on different ground states or equilibrium states – and once we formulate the question well enough, we may find the corresponding operators in the quantum theory and the quantum mechanical apparatus allows us to calculate the probabilities of different answers according to the Born rule.
But there can't be a universal recipe by which a quantum mechanical theory would tell us which questions we should be asking! The existence of dualities – S-dualities, T-dualities, U-dualities, mirror symmetry, AdS/CFT correspondence, the identification of a 2nd quantized background with a coherent state of gravitons etc. on another background, but even the ER-EPR correspondence, or ambiguities by which we may assign an equilibrium state to a state \(\ket\chi\) in the PR proposal – tells us that there may be different sets of observables, or field operators on different backgrounds, that are equally potent tools to describe a given Hilbert space and its dynamics.
These dualities are not even some "revolutionary additions" made by the stringy physics. The most ordinary quantum-mechanical models have this feature, too. The very fact that there exist operators that don't commute with others guarantees that there is some freedom in the choice of the questions. In non-relativistic quantum mechanics, a wave function \(\ket\psi\) may be written as a function in the position representation or one in the momentum representation. They are Fourier transforms of one another. You may measure \(x\); but you may measure \(p\), too. You can't do both at the same moment. Quantum mechanics doesn't tell you that you should always measure \(x\). It doesn't tell you that you should always measure \(p\), either. There are no fundamentally privileged observables (Hermitian operators) acting on the Hilbert space! Again, it's a point explained in dozens of older TRF posts.
Dualities in string theory only differ from the \(x\)-\(p\) complementarity in the simplest models of quantum mechanics by having numerous, much richer systems of (competing) observables that are describing a much more complicated system. But it's always true that a state may be interpreted in many ways. Even in simple QM models, a state may be interpreted as a superposition of \(x\) eigenstates, or a superposition of \(p\) eigenstates. Or using one of infinitely many other decompositions. None of these decompositions is fundamentally better than the others! This is nothing else than saying that there are many questions that may be asked and the knowledge of the state vector provides us with the answer. In other words, Harlow's words, there are many "interpretations" of the state vector.
I believe that to disagree with this trivial point means to deny the basic postulates of quantum mechanics that have been known for almost 90 years.
In the case of the black hole interior, if an observer is able to parameterize the Hilbert space as a space of fields and objects living on a background geometry and if she can define and calculate the Heisenberg equations of motion for the operators, how they evolve towards the black hole interior, she may probabilistically predict her perceptions in the black hole interior. So yes, she may survive unless something "mundane" kills her. There is no firewall. But one may also get lost in the sea of some completely different operators whose values become singular and quantum mechanics will imply that they're singular, indeed. The absence of the firewall only means – and PR show – that the quantum gravity Hilbert space with all the known constraints allows the life and business-as-usual predictions to continue for an observer that has just entered the black hole interior (unless she wants to measure too complicated correlators with too many excitations, and so on). If she chooses to ask different questions than the questions about observables that are Heisenberg continuations of those from the black hole exterior, there will be different (and possibly singular) answers. If she chooses to ask no questions, there will be no answers. Her survival subjectively (or from the viewpoint of another infalling observer) means that she (or he) is able to continue to ask questions about local fields (including fields inside her body) and QM keeps on answering them in a way that was similar outside the black hole. That's it. We may also talk about her survival from the viewpoint of observers outside the black hole. The answers to all these questions is that nothing inside the event horizon is measurable and the ultimate state is a nearly thermal state of the Hawking radiation into which the infalling observer was transformed (apparently in a process including the death). The internal and external observers are allowed to ask different questions and they are actually doing so. It's no contradiction. A priori, all questions in a quantum mechanical framework are subjective. It's important to specify a question – an operator etc. – before quantum mechanics is supposed to produce the answers.
Harlow also has trouble with the state-dependence of the operators in the PR approach. It is really the very same problem as one above but I don't want to reformulate all these things in yet another language, especially because I have explained why the state-dependence is OK, consistent, and unavoidable in the quantum physics of black holes in August 2013.
I would say that Daniel Harlow who has written a dozen of papers related to quantum gravity isn't a string theorist and this vice seems to be correlated with the confusions about quantum mechanics. It doesn't mean that string theorists never write papers building on confused and deeply deluded "interpretations" of quantum mechanics which are drowning in the popular misleading buzzwords (the word "measurement" or a variation of it appears 45 times in Harlow's paper! All Harlow's comments about "the measurement's being given by a unitary non-Schr̦dinger transformation" are wrong; the measurement is no real process and if there were a nontrivial one, it would never be unitary). After all, Lenny Susskind, a co-father and giant of string theory, has done it several times, too. But I still think that the degree of acceptance of quantum mechanics Рeven in contexts where quantum mechanics look counter-intuitive to others Рis much higher among the string theorists than it is among other physicists.
This correlation may arguably be interpreted in the opposite way, too. A big portion of the difficulties that some physicists face when they are trying to embrace string theory is their inability to fully accept something much simpler and more fundamental, namely quantum mechanics. String theory – and its picture of quantum gravity – is really nothing else than taking the lessons of quantum mechanics seriously even when we are talking about the spacetime geometry.
And that's the memo.
Two contrasting papers on the Papadodimas-Raju theory of the black hole interior and the Maldacena-Susskind ER-EPR (Einstein-Rosen/Einstein-Podolsky-Rosen) correspondence have been posted to the hep-th arXiv today:
Daniel Harlow (Princeton): Aspects of the Papadodimas-Raju [PR] Proposal for the Black Hole Interior(TRF guest blogger) Andreas Karch et al. takes the positive attitude that the newest picture, ER-EPR, works, while Harlow sees a serious problem with another, related yet inequivalent, picture of the black hole interior, the Papadodimas-Raju (PR) theory.
Kristan Jensen, Andreas Karch, Brandon Robinson (Seattle+SUNY): The holographic dual of a Hawking pair has a wormhole
PR and ER-EPR are not quite equivalent although the acronyms may be combined to a rather nice triangle. ;-) But I think that they are ultimately compatible. Both of them are right and complementary. PR tells us something about the freedom we have when we extrapolate dynamics of quantum gravity into the black hole interior; ER-EPR teaches us about the behavior of the Hilbert space in topologically nontrivial situations with an ER bridge (not really studied by PR at all, at least so far). Harlow's paper is against PR; Andreas Karch et al. argue in favor of ER-EPR maximally positively – so positively, in fact, that they (rightfully?) demand a part of the credit for the streamlined interpretation of the ER-EPR correspondence. But even though they focus on "different theories" of the black hole interior, you may see that PR and ER-EPR are "allies" because pretty much the same point that causes so much discomfort to Daniel Harlow is also what Andreas Karch et al. – which will be referred to as Jensen et al., to respect the alphabetical order – embrace so enthusiastically!
What is the point that may describe the "key" to both papers? I think that the point says that PR and ER-EPR may be interpreted as new dualities that allow several equally correct descriptions of the same degrees of freedom and their physical fate. Andreas Karch et al. are big friends of dualities so like your humble correspondent, they think it's cool to discover a new important duality and it's perfectly consistent.
On the other hand, Daniel Harlow seems to have a psychological problem with the very notion that there may be different ways to describe the same Hilbert space.
Let me clarify what I mean a little bit. I have to assume that the reader is mostly familiar with the basics of the ER-EPR correspondence and the PR picture of the black hole interior that have been discussed many times on this blog.
The new Jensen-Karch-Robinson paper builds on the Karch-Jensen followup to the ER-EPR correspondence in which Karch and Jensen argued that the world sheet of the QCD-like quark-antiquark string in the AdS/CFT correspondence has an Einstein-Rosen bridge on it, too. Because the quark and antiquark are entangled, the observations seem to confirm the picture that the entanglement is equivalent to a wormhole.
OK, the new Jensen-Karch-Robinson paper first "extends" the AdS/CFT picture to a Randall-Sundrum model. In the CFT language, this is represented by coupling the quantum field theory to gravity; in the AdS bulk description, the extension looks like a brane ending/cutting the bulk geometry. Things still work. The other point that they make is that the entangled Hawking particle pairs may be seen to be entangled; and may also be seen to be two sides of a wormhole, thus producing another confirmation of the ER-EPR paradigm.
If you're interested in their paper, you should read it and I won't try to reproduce everything they say. But I want to add a few more words of mine about a general philosophical theme that Jensen, Karch, and Robinson describe in their paper and that I fully agree with.
They want the ER-EPR link to be treated as another duality. Some degrees of freedom may be either thought of as living in two isolated places of the spacetime and being entangled; or they may be thought of as being geometrically connected by a wormhole. Moreover, the entanglement-like (EPR) description is more typical in the CFT side of the AdS/CFT correspondence while the wormhole-like (ER) description arises if you consider the bulk, too. In this sense, ER-EPR applied to states in the AdS space may be considered a special case case of the AdS/CFT correspondence, with the identification ER=AdS, EPR=CFT.
I've been defending the same interpretation of the ER-EPR correspondence as another duality for quite some time, namely from the birth of ER-EPR; see e.g. this October 2013 text, especially the section "Possibility to fix the gauge (light-cone gauge) in string theory & allowed topology change & ER-EPR". The point is that in a consistent theory of quantum gravity, the spacetime topology is not only dynamical but it even fails to be a "good quantum number". There is no operator that would count some invariants describing the topology (e.g. the number of Einstein-Rosen bridges in the spacetime). Instead, the same states in the Hilbert space may be built as excitations of a background with no bridges; one bridge; or many bridges. Some of these descriptions of the states may be "more weakly coupled" or "smoother" or "less excited", and therefore "less awkward", but in principle, all the descriptions – descriptions assigning the spacetime with any topology – are allowed.
This "new kind of a duality" seems very profound to me and I think that Jensen, Karch, and Robinson have the same feelings. There is no inconsistency in this paradigm. Incidentally, the first sentences of their new paper say that "entanglement is [just] correlation but the entangled states can't be measured by themselves". It's exactly something that's been claimed in many older TRF blog posts.
Daniel Harlow's dissatisfaction
On the other hand, Daniel Harlow writes something about the \(1/N\) corrections in the PR picture – the general theory of the black hole interior that he reviews – and sort of agrees with PR that it works and has the potential to resolve all puzzles that were promoted in the context of the firewall paradox etc. However, the main point of Harlow's paper is some skepticism. The PR picture is "ambiguous", he thinks. Surprisingly, the people's disagreements about the "interpretation" of quantum mechanics began to play a prominent role in papers such as Harlow's. Until the middle 1990s, the epoch of the Duality Revolution, people would apparently agree what quantum mechanics was. So no stringy paper would ever talk about "interpretations of quantum mechanics". Only confused people were doing so. Suddenly, this business has penetrated to the quantum gravity research and it is turning out that at least someone must be understanding what quantum mechanics actually is.
The first skeptical sentence in the abstract of Harlow's paper says:
I argue however that the proposal has the uncomfortable property that states in the CFT Hilbert space do not have definite physical interpretations, unlike in ordinary quantum mechanics.This sentiment of the author is elaborated upon in Section 3, "Do States Have Unique Interpretations?" on pages 15-18. Harlow is troubled by the fact that a black hole microstate \(\ket \chi\) may be written as\[
\ket\chi = A_\alpha \ket\psi = A_\beta \ket{\psi'}
\] for some equilibrium states \(\ket\psi, \ket{\psi'}\) and \(A_\alpha,A_\beta\in {\mathcal A}\) in various ways. Well, it's just a matter of trivial linear algebra that a vector in the Hilbert space may be obtained as an action by an operator on another state in infinitely many ways. It's true for every quantum mechanical system. What's causing discomfort to Daniel Harlow is clearly his assumption that the question "which equilibrium state or vacuum background is associated with \(\ket\chi\)" should be a well-posed question connected with a good quantum number, with some Hermitian operator(s). In other words, he assumes that it should be possible to measure "the equilibrium state \(\ket\psi\) upon which \(\ket\chi\) is built" by a measurement process.
He's wrong. He could figure out that he's wrong if he actually tried to defend his (indefensible) position, something he didn't bother to do – by describing what the hypothetical process that "measures the background or 'the' equilibrium state underlying a general state" actually is. He would find out that no such experimental algorithm exists and none may exist.
Even though we're talking about PR and not ER-EPR here, you see that it is pretty much the same question as the question discussed above, in the context of the Jensen et al. paper. Their – and my – answer is obviously that "the right equilibrium state" underlying a state \(\ket\chi\) isn't uniquely associated with \(\ket\chi\), and it's a good thing. Whenever we have a duality, and the ER-EPR correspondence is a duality, in fact, in some sense, a manifestation of the AdS/CFT holographic duality (at least some special cases of AdS/CFT and special cases of ER-EPR are the same thing), then we also have many ways to imagine "by what operators" we had to excite a ground state to get to the required state \(\ket\chi\), and so on. In a general field theory (it's enough to imagine a QFT on a curved spacetime background; or a QFT with moduli), there is no single "universally preferred ground state" that should serve as the basis to build the rest of the Hilbert space. A ground state – or, in this case, an equilibrium state – is non-unique. All states in the Hilbert space are actually equally real and equally allowed; that's what the linearity postulate of quantum mechanics demands. One description in the case of S-dualities may describe the same state as an excitation of a D-brane added upon a background; the other, S-dual description may see it as a complicated state of many fundamental strings, and so on. The ground state of one Hamiltonian may be obtained by a Bogoliubov transformation i.e. by an action of some creation operators on the ground state of another Hamiltonian (particle production). None of the descriptions is better than the other(s). They're exactly equivalent.
To localize the problem with Harlow's reasoning from a slightly different angle, let me copy some sentences from page 18:
We thus appear to have found a problem for the PR proposal; what is the bulk interpretation of the state \(V\ket\psi\)? Is the horizon excited or is it not?The bug of Harlow's complaint is that a valid, predictive quantum theory isn't supposed to answer such unphysical questions. A valid, predictive quantum theory is supposed to (probabilistically) predict the results of measurements that may actually be done, and the quote above doesn't describe one!
In other words, and I have been explaining the very same point in dozens of blog posts about the foundations of quantum mechanics, a quantum mechanical theory (probabilistically) answers questions about observables, but it doesn't tell us what the questions should be. There may be different questions – about different observables building the Hilbert space by their action on different ground states or equilibrium states – and once we formulate the question well enough, we may find the corresponding operators in the quantum theory and the quantum mechanical apparatus allows us to calculate the probabilities of different answers according to the Born rule.
But there can't be a universal recipe by which a quantum mechanical theory would tell us which questions we should be asking! The existence of dualities – S-dualities, T-dualities, U-dualities, mirror symmetry, AdS/CFT correspondence, the identification of a 2nd quantized background with a coherent state of gravitons etc. on another background, but even the ER-EPR correspondence, or ambiguities by which we may assign an equilibrium state to a state \(\ket\chi\) in the PR proposal – tells us that there may be different sets of observables, or field operators on different backgrounds, that are equally potent tools to describe a given Hilbert space and its dynamics.
These dualities are not even some "revolutionary additions" made by the stringy physics. The most ordinary quantum-mechanical models have this feature, too. The very fact that there exist operators that don't commute with others guarantees that there is some freedom in the choice of the questions. In non-relativistic quantum mechanics, a wave function \(\ket\psi\) may be written as a function in the position representation or one in the momentum representation. They are Fourier transforms of one another. You may measure \(x\); but you may measure \(p\), too. You can't do both at the same moment. Quantum mechanics doesn't tell you that you should always measure \(x\). It doesn't tell you that you should always measure \(p\), either. There are no fundamentally privileged observables (Hermitian operators) acting on the Hilbert space! Again, it's a point explained in dozens of older TRF posts.
Dualities in string theory only differ from the \(x\)-\(p\) complementarity in the simplest models of quantum mechanics by having numerous, much richer systems of (competing) observables that are describing a much more complicated system. But it's always true that a state may be interpreted in many ways. Even in simple QM models, a state may be interpreted as a superposition of \(x\) eigenstates, or a superposition of \(p\) eigenstates. Or using one of infinitely many other decompositions. None of these decompositions is fundamentally better than the others! This is nothing else than saying that there are many questions that may be asked and the knowledge of the state vector provides us with the answer. In other words, Harlow's words, there are many "interpretations" of the state vector.
I believe that to disagree with this trivial point means to deny the basic postulates of quantum mechanics that have been known for almost 90 years.
In the case of the black hole interior, if an observer is able to parameterize the Hilbert space as a space of fields and objects living on a background geometry and if she can define and calculate the Heisenberg equations of motion for the operators, how they evolve towards the black hole interior, she may probabilistically predict her perceptions in the black hole interior. So yes, she may survive unless something "mundane" kills her. There is no firewall. But one may also get lost in the sea of some completely different operators whose values become singular and quantum mechanics will imply that they're singular, indeed. The absence of the firewall only means – and PR show – that the quantum gravity Hilbert space with all the known constraints allows the life and business-as-usual predictions to continue for an observer that has just entered the black hole interior (unless she wants to measure too complicated correlators with too many excitations, and so on). If she chooses to ask different questions than the questions about observables that are Heisenberg continuations of those from the black hole exterior, there will be different (and possibly singular) answers. If she chooses to ask no questions, there will be no answers. Her survival subjectively (or from the viewpoint of another infalling observer) means that she (or he) is able to continue to ask questions about local fields (including fields inside her body) and QM keeps on answering them in a way that was similar outside the black hole. That's it. We may also talk about her survival from the viewpoint of observers outside the black hole. The answers to all these questions is that nothing inside the event horizon is measurable and the ultimate state is a nearly thermal state of the Hawking radiation into which the infalling observer was transformed (apparently in a process including the death). The internal and external observers are allowed to ask different questions and they are actually doing so. It's no contradiction. A priori, all questions in a quantum mechanical framework are subjective. It's important to specify a question – an operator etc. – before quantum mechanics is supposed to produce the answers.
Harlow also has trouble with the state-dependence of the operators in the PR approach. It is really the very same problem as one above but I don't want to reformulate all these things in yet another language, especially because I have explained why the state-dependence is OK, consistent, and unavoidable in the quantum physics of black holes in August 2013.
I would say that Daniel Harlow who has written a dozen of papers related to quantum gravity isn't a string theorist and this vice seems to be correlated with the confusions about quantum mechanics. It doesn't mean that string theorists never write papers building on confused and deeply deluded "interpretations" of quantum mechanics which are drowning in the popular misleading buzzwords (the word "measurement" or a variation of it appears 45 times in Harlow's paper! All Harlow's comments about "the measurement's being given by a unitary non-Schr̦dinger transformation" are wrong; the measurement is no real process and if there were a nontrivial one, it would never be unitary). After all, Lenny Susskind, a co-father and giant of string theory, has done it several times, too. But I still think that the degree of acceptance of quantum mechanics Рeven in contexts where quantum mechanics look counter-intuitive to others Рis much higher among the string theorists than it is among other physicists.
This correlation may arguably be interpreted in the opposite way, too. A big portion of the difficulties that some physicists face when they are trying to embrace string theory is their inability to fully accept something much simpler and more fundamental, namely quantum mechanics. String theory – and its picture of quantum gravity – is really nothing else than taking the lessons of quantum mechanics seriously even when we are talking about the spacetime geometry.
And that's the memo.
Two very different PR, ER-EPR papers
![Two very different PR, ER-EPR papers]()
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May 09, 2014
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