- #1
S.Daedalus
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Gravity as "Entanglement Thermodynamics"
The recent paper by Lashkari, McDermott and Van Raamsdonk, Gravitational Dynamics from Entanglement "Thermodynamics", has prompted me to consider this approach (which I think I've posted about once or twice on here) once again, and to gather some opinions on this approach to quantum gravity.
Briefly, I see it essentially as originating from Sakharov's ideas on induced gravity, mainly because that was what Ted Jacobson was working on before writing his seminal paper, on the Einstein equation of state. There were, however, some earlier bids to get spacetime and gravity starting from the quantum, e.g. von Weizsäcker's ur-theory, Penrose's spin networks (which in their original formulation referred more directly to 'exchanges' of units of spin between larger systems, from which he was able to derive the structure of three dimensional space), and Finkelstein's space-time code; the former two (in a sense) have found a modern information theoretic successor in the arguments by Müller and Masanes, who show that exchanging qubits in order to accumulate direction information necessarily leads to the appearance of three dimensional space.
More generally, extensions of quantum mechanics based on the quaternion and octonion algebras have been investigated, leading to 5+1 and 9+1 dimensional spacetimes respectively, which seems to point to the fact that at the heart of this relationship is the simple fact that the SLOCC group of single qubits in these cases are just [itex]SL(2,\mathbb{C})[/itex] for standard QM, and [itex]SL(2,\mathbb{H})[/itex] and [itex]SL(2,\mathbb{O})[/itex] for the quaternionic and octonionic cases respectively, which are in turn isomorphic to the Lorentz groups [itex]SO(3,1)[/itex], [itex]SO(5,1)[/itex] and [itex]SO(9,1)[/itex].
Thus, getting spacetime from the quantum is an old idea, that seems to be cashed out now thanks to the termodynamic wrinkle introduced by Jacobson, and refined by (among others) Padmanabhan and most intriguingly Van Raamsdonk (there's also, of course, Verlinde's 'entropic gravity', but I tend to see this more as a toy model of the more developed ideas). The basic idea of this is that if the Bekenstein-Hawking area-entropy relation holds, Einstein's equations can be deduced from simple thermodynamics, making gravity effectively an emergent rather than fundamental force (which is only natural, since spacetime itself is not fundamental in this approach).
The added wrinkle here is that the origin of BH entropy is supposed to lie in quantum mechanical entanglement. One of the first to realize that entanglement entropy, like BH entropy, follows an area law was Srednicki; however, unless you impose a cutoff, the entanglement entropy is divergent. Last year, though, Jacobson has argued that the emergence of gravity effectively renders the entropy finite.
Of late, this picture has become important in the discussion of the black hole firewall problem, with the Maldacena/Susskind ("ER=EPR") conjecture that entangled particles should be connected by a wormhole in the gravitational dual; the recent 'fuzz or fire'-conference even featured a special session on spacetime from entanglement.
All this seems like it should have connections to holography as it is more usually understood, i.e. in the AdS/CFT context, per e.g. Swingle's work on conceptualizing entanglement renormalization as a discrete version of the correspondence (I'm not clear on the details here, and would love some pointers, though). At some point, the words 'Ryu-Takayanagi formula' should probably be used.
The picture that's developing, to my eyes, is roughly the following: spacetime is a fundamentally quantum mechanical object, with separate quantum states yielding separate spacetime pieces, which can be connected by entanglement ('entanglement as glue', Lubos has called it somewhere). Gravity is nothing but the dynamics of this entanglement, governed by thermodynamics. It's then not a fundamental force; rather, you get it extra, if you start with the right quantum (field) theory.
This obviously raises some intriguing questions. First of all, as already Jacobson remarked in his '95 paper, quantizing gravity may then be just kind of a category error, unable to yield the true microscopic degrees of freedom, like quantizing water waves does not yield H2O atoms. That might alleviate some worries about the nonrenormalizability of quantum gravity (if it's useful as a theory at all, it's certainly an effective theory, so there's no real need for it to be renormalizable), and the areas of conflict between QM and GR might just be those where the effective theory no longer describes the situation well---i.e. the 'out of equilibrium'-situations (singularities in black holes, the big bang etc.).
Another interesting question is precisely what is needed for quantum theory to yield gravity in this way. The arguments pointing towards 3+1 dimensional spacetime from quantum theory seem to be quite generic, as you really only need two level quantum systems for that. But when does gravity fall out as entanglement thermodynamics? Do you need a QFT, or even a CFT?
Of course (and the main reason for my starting this thread), it's also possible that I've gotten this whole thing wrong, and am thinking about it in a completely muddle-headed way---because frankly, I'm a bit surprised at the relative lack of discussion regarding what seems (to me, anyway) to be a real shot at getting around the problems of combining quantum theory and relativity in a consistent manner. So if all of this is just wrong (or 'not even'), I'd humbly ask to be educated.
Otherwise, what are your thoughts on the matter? Merely a theoretical curiosity, or some genuine new (I don't want to say 'paradigm changing') development? What does it mean in relation to established quantum gravity proposals, be they stringy, loopy, or something else-y? (One thing I remember from Penrose is the remark that essentially, quantum systems come with their own three-geometry, regardless of what other geometry they may be embedded in; I've sometimes thought that maybe this could be a good alternative way of thinking about dimensional reduction in strings.)
----------------
(Apologies for the length, and thanks if you've stuck it out 'till here...)
The recent paper by Lashkari, McDermott and Van Raamsdonk, Gravitational Dynamics from Entanglement "Thermodynamics", has prompted me to consider this approach (which I think I've posted about once or twice on here) once again, and to gather some opinions on this approach to quantum gravity.
Briefly, I see it essentially as originating from Sakharov's ideas on induced gravity, mainly because that was what Ted Jacobson was working on before writing his seminal paper, on the Einstein equation of state. There were, however, some earlier bids to get spacetime and gravity starting from the quantum, e.g. von Weizsäcker's ur-theory, Penrose's spin networks (which in their original formulation referred more directly to 'exchanges' of units of spin between larger systems, from which he was able to derive the structure of three dimensional space), and Finkelstein's space-time code; the former two (in a sense) have found a modern information theoretic successor in the arguments by Müller and Masanes, who show that exchanging qubits in order to accumulate direction information necessarily leads to the appearance of three dimensional space.
More generally, extensions of quantum mechanics based on the quaternion and octonion algebras have been investigated, leading to 5+1 and 9+1 dimensional spacetimes respectively, which seems to point to the fact that at the heart of this relationship is the simple fact that the SLOCC group of single qubits in these cases are just [itex]SL(2,\mathbb{C})[/itex] for standard QM, and [itex]SL(2,\mathbb{H})[/itex] and [itex]SL(2,\mathbb{O})[/itex] for the quaternionic and octonionic cases respectively, which are in turn isomorphic to the Lorentz groups [itex]SO(3,1)[/itex], [itex]SO(5,1)[/itex] and [itex]SO(9,1)[/itex].
Thus, getting spacetime from the quantum is an old idea, that seems to be cashed out now thanks to the termodynamic wrinkle introduced by Jacobson, and refined by (among others) Padmanabhan and most intriguingly Van Raamsdonk (there's also, of course, Verlinde's 'entropic gravity', but I tend to see this more as a toy model of the more developed ideas). The basic idea of this is that if the Bekenstein-Hawking area-entropy relation holds, Einstein's equations can be deduced from simple thermodynamics, making gravity effectively an emergent rather than fundamental force (which is only natural, since spacetime itself is not fundamental in this approach).
The added wrinkle here is that the origin of BH entropy is supposed to lie in quantum mechanical entanglement. One of the first to realize that entanglement entropy, like BH entropy, follows an area law was Srednicki; however, unless you impose a cutoff, the entanglement entropy is divergent. Last year, though, Jacobson has argued that the emergence of gravity effectively renders the entropy finite.
Of late, this picture has become important in the discussion of the black hole firewall problem, with the Maldacena/Susskind ("ER=EPR") conjecture that entangled particles should be connected by a wormhole in the gravitational dual; the recent 'fuzz or fire'-conference even featured a special session on spacetime from entanglement.
All this seems like it should have connections to holography as it is more usually understood, i.e. in the AdS/CFT context, per e.g. Swingle's work on conceptualizing entanglement renormalization as a discrete version of the correspondence (I'm not clear on the details here, and would love some pointers, though). At some point, the words 'Ryu-Takayanagi formula' should probably be used.
The picture that's developing, to my eyes, is roughly the following: spacetime is a fundamentally quantum mechanical object, with separate quantum states yielding separate spacetime pieces, which can be connected by entanglement ('entanglement as glue', Lubos has called it somewhere). Gravity is nothing but the dynamics of this entanglement, governed by thermodynamics. It's then not a fundamental force; rather, you get it extra, if you start with the right quantum (field) theory.
This obviously raises some intriguing questions. First of all, as already Jacobson remarked in his '95 paper, quantizing gravity may then be just kind of a category error, unable to yield the true microscopic degrees of freedom, like quantizing water waves does not yield H2O atoms. That might alleviate some worries about the nonrenormalizability of quantum gravity (if it's useful as a theory at all, it's certainly an effective theory, so there's no real need for it to be renormalizable), and the areas of conflict between QM and GR might just be those where the effective theory no longer describes the situation well---i.e. the 'out of equilibrium'-situations (singularities in black holes, the big bang etc.).
Another interesting question is precisely what is needed for quantum theory to yield gravity in this way. The arguments pointing towards 3+1 dimensional spacetime from quantum theory seem to be quite generic, as you really only need two level quantum systems for that. But when does gravity fall out as entanglement thermodynamics? Do you need a QFT, or even a CFT?
Of course (and the main reason for my starting this thread), it's also possible that I've gotten this whole thing wrong, and am thinking about it in a completely muddle-headed way---because frankly, I'm a bit surprised at the relative lack of discussion regarding what seems (to me, anyway) to be a real shot at getting around the problems of combining quantum theory and relativity in a consistent manner. So if all of this is just wrong (or 'not even'), I'd humbly ask to be educated.
Otherwise, what are your thoughts on the matter? Merely a theoretical curiosity, or some genuine new (I don't want to say 'paradigm changing') development? What does it mean in relation to established quantum gravity proposals, be they stringy, loopy, or something else-y? (One thing I remember from Penrose is the remark that essentially, quantum systems come with their own three-geometry, regardless of what other geometry they may be embedded in; I've sometimes thought that maybe this could be a good alternative way of thinking about dimensional reduction in strings.)
----------------
(Apologies for the length, and thanks if you've stuck it out 'till here...)