Does Spacetime Emerge From Quantum Information?

Quantizing gravity is an important goal of contemporary physics, but after decades of effort it’s proven to be an extremely tough nut to crack. So it’s worth considering a very slight shift of emphasis. What if the right strategy is not “finding the right theory of gravity and quantizing it,” but “finding a quantum theory out of which gravity emerges”?

That’s one way of thinking about a new and exciting approach to the problem known as “tensor networks” or the “AdS/MERA correspondence.” If you want to have the background and basic ideas presented in a digestible way, the talented Jennifer Ouellette has just published an article at Quanta that lays it all out. If you want to dive right into some of the nitty-gritty, my young and energetic collaborators and I have a new paper out:

Consistency Conditions for an AdS/MERA Correspondence
Ning Bao, ChunJun Cao, Sean M. Carroll, Aidan Chatwin-Davies, Nicholas Hunter-Jones, Jason Pollack, Grant N. Remmen

The Multi-scale Entanglement Renormalization Ansatz (MERA) is a tensor network that provides an efficient way of variationally estimating the ground state of a critical quantum system. The network geometry resembles a discretization of spatial slices of an AdS spacetime and “geodesics” in the MERA reproduce the Ryu-Takayanagi formula for the entanglement entropy of a boundary region in terms of bulk properties. It has therefore been suggested that there could be an AdS/MERA correspondence, relating states in the Hilbert space of the boundary quantum system to ones defined on the bulk lattice. Here we investigate this proposal and derive necessary conditions for it to apply, using geometric features and entropy inequalities that we expect to hold in the bulk. We show that, perhaps unsurprisingly, the MERA lattice can only describe physics on length scales larger than the AdS radius. Further, using the covariant entropy bound in the bulk, we show that there are no conventional MERA parameters that completely reproduce bulk physics even on super-AdS scales. We suggest modifications or generalizations of this kind of tensor network that may be able to provide a more robust correspondence.

(And we’re not the only Caltech-flavored group to be thinking about this stuff.)

Between the Quanta article and our paper you should basically be covered, but let me give the basic idea. It started when quantum-information theorists interested in condensed-matter physics, in particular Giufre Vidal and Glen Evenbly, were looking for ways to find the quantum ground state (the wave function with lowest possible energy) of toy-model systems of spins (qubits) arranged on a line. A simple problem, but one that is very hard to solve, even on a computer — Hilbert space is just too big to efficiently search through it. So they turned to the idea of a “tensor network.”

A tensor network is a way of building up a complicated, highly-entangled state of many particles, by starting with a simple initial state. The particular kind of network that Vidal and Evenbly became interested in is called the MERA, for Multiscale Entanglement Renormalization Ansatz (see for example). Details can be found in the links above; what matters here is that the MERA takes the form of a lattice that looks a bit like this.

tensor banner - circle_0

Our initial simple starting point is actually at the center of this diagram. The various links represent tensors acting on that initial state to make something increasingly more complicated, culminating in the many-body state at the circular boundary of the picture.

Here’s the thing: none of this had anything to do with gravity. It was a just a cute calculational trick to find quantum states of interacting electron spins. But this kind of picture can’t help but remind certain theoretical physicists of a very famous kind of spacetime: Anti-de Sitter space (AdS), the maximally symmetric solution to Einstein’s equation in the presence of a negative cosmological constant. (Or at least the “spatial” part thereof, which is simply a hyperbolic plane.)


Of course, someone has to be the first to actually do the noticing, and in this case it was a young physicist named Brian Swingle. Brian is a condensed-matter physicist himself, but he was intellectually curious enough to take courses on string theory as a grad student. There he learned that string theorists love AdS — it’s the natural home of Maldacena’s celebrated gauge/gravity duality, with a gauge theory living on the flat-space “boundary” and gravity lurking in the AdS “bulk.” Swingle wondered whether the superficial similarity between the MERA tensor network and AdS geometry wasn’t actually a sign of something deeper — an AdS/MERA correspondence?

And the answer is — maybe! Some of the features of AdS gravity are certainly captured by the MERA, so the whole thing kind of smells right. But, as we say in the paper above with the expansive list of authors, it doesn’t all just fall together right away. Some things you would like to be true in AdS don’t happen automatically in the MERA interpretation. Which isn’t a deal-killer — it’s just a sign that we have to, at the very least, work a bit harder. Perhaps there’s a generalization of the simple MERA that must be considered, or a slightly more subtle version of the purported correspondence.

The possibility is well worth pursuing. As amazing (and thoroughly checked) as the traditional AdS/CFT correspondence is, there are still questions about it that we haven’t satisfactorily answered. The tensor networks, on the other hand, are extremely concrete, well-defined objects, for which you should in principle be able to answer any question you might have. Perhaps more intriguingly, the idea of “string theory” never really enters the game. The “bulk” where gravity lives emerges directly from a set of interacting spins, in a context where the original investigators weren’t thinking about gravity at all. The starting point doesn’t even necessarily have anything to do with “spacetime,” and certainly not with the dynamics of spacetime geometry. So I certainly hope that people remain excited and keep thinking in this direction — it would be revolutionary if you could build a complete theory of quantum gravity directly from some interacting qubits.

This entry was posted in arxiv, Science. Bookmark the permalink.

42 Responses to Does Spacetime Emerge From Quantum Information?

  1. Jonathan Langdale says:

    If spacetime emerges from entanglement, does that suggest Hawking’s virtual micro black holes exist forming Planck EPR=ER?

    Is Jacob Bekenstein’s experiment to test for virtual micro black holes plausible? Is this a space-based experiment?

  2. Jim says:

    The one question I would ask, is what sort of curvature does this suggest? What we see seems generally very close to Euclidian, but we know it probably wasn’t always that way, whether locally (ekpyrotic) or globally (unitary big bang) so I don’t have an intuition about whether “very slightly non-Euclidian” is a reasonable range to expect the curvature of a spacetime arising from tensor network configurations. I am enthusiastic about this approach in general.

  3. kashyap vasavada says:

    Interesting post! Without understanding any details, I have two questions:
    (1) Isn’t entanglement supposed to be *monogamous*? So the degree of entanglement would fall rapidly as you go beyond two particle entanglement. Is that why gravity is weak? But then there are three interactions before you get to gravity!
    (2) It seems one can get GR equations with negative cosmological constant. How would you convert them to positive CC?

  4. physics and quantum+consciousness= the answers you are looking for. You already know that the small particles of existence respond to observation for measurement. The large particles like us and the stars respond to the mass of consciousness that we create as a consensus allowing us to exist in this agreed upon hologram. Look for internal answers to this conundrum. The external answers are only confirmations for what we universally want to believe. We are now on the precipice of awakening and the truth will likely blow all of our minds.

  5. Rick says:

    Too bad our universe isn’t an Ads universe. So none of this actually applies to our universe.

  6. Latverian Diplomat says:

    This is a nitpick of a popularization, which is almost always a bad idea. I fully understand why certain explanatory shortcuts are necessary. But it is perhaps useful to remind ourselves from time to time that those shortcuts are there.

    The Poincare disk that inspired Escher is not just a projection of a hyperbolic plane, it is a hyperbolic plane. You just have to use the correct metric. As measured by that metric, the “small” figures that appear near the edge are the same size as the “large” figures near the center.

    The discrepancy is from the misapplication of the Euclidean metric (by our eyes and brains) not a limitation of the model itself.

  7. platohagel says:

    Quickly it came to mind that your efforts and those of your colleagues reminded me of Garrett Lisi’s example to describe a “whole” network of relations. The complexity of E8 is enormous , and to see such an development to include all those things such as spin by example, and reduce it to a lattice construction, is to simplify our understanding.

  8. bostontola says:

    It would be satisfying if gravity emerged from a quantum theory. There does seem to be a lot happening in that direction. It would be nice if it connects up.

  9. John Barrett says:

    The whole thing really sounds far fetched, but it would be interesting if entanglement and gravity where really related to each other in some way. After reading The Particle and the End of the Universe (that I had mistaken for as a book about particles at the edge of black holes, since the universe can be considered a grey hole), I was almost certain that quantum gravity would have to come from overlapping particle waves or possibly their unknown component particles. The main reason being that the idea came to me that during a particle jump, a particle would lose its mass along with the particle itself. Also, the particle waves would mismatch during a particle jump of an electron around the atom. It would seem like it would explain a lot as to why virtual particles have different mass, if there were unknown component particles.

    If you thought of there being a FTL component particle controlling entanglement, it would seem like it’s particle waves could increase or decrease the mass of those particles. One of the biggest problems in developing a theory of quantum gravity is just being able to detect a difference in mass of a particle, but if you could increase the mass of particles substantially by creating a large entanglement network, then it seems like you could possibly be able to then detect a difference in mass through experimentation to derive or test a quantum theory of gravity.

  10. Patrick says:

    “it would be revolutionary if you could build a complete theory of quantum gravity directly from some interacting qubits.”

    I read that quanta article a week or so ago and it really struck a chord with me. I’m happy to see a lot of ideas that are a bit more practical (and functional) than string theory popping up. And since I’m such a freak for boundaries… naturally I’m attracted to this. Pretty excited, even if I don’t fully understand.

  11. Daniel Kerr says:

    Cool stuff but it seems like to me to be an instance of forcing in model theory. Not sure you could say gravity ontologically “emerges” from a quantum theory. I’d sooner buy the claim that gravity as modeled in a quantum formalism of flat space (or whatever non-geometric topological space) is computationally more convenient than starting with a purely gravitational theory.

  12. Rim says:

    Sean, I’m a bit confused about the MERA lattice diagram, perhaps you could be so kind as to enlighten me. I’m completely green in quantum physics, but as I understand this, it’d make more sense to me if it was interpreted inside-out (or outside-in as the case may be). The individual qubits would be the leafs of the diagram, while more interior nodes would be the entangled pairs of the previous level. Does that make sense? If so, would the lattice still capture sufficiently useful properties if it’d be completely tree-like in nature, ie if paired qubits (and pairs of pairs etc) only interact with the next interior level, not laterally within a given level?

  13. Ajay saini says:

    Spacetime is emerged out from singularity at the beginning of universe.Singularity at that moment was banged and stretched apart by extremely powerful source of Dark energy present in the vacuum at all times.
    Any information related to moment of beginning & subsequent existence of universe,must be contained by dark energy present in the vacuum at all times.
    Fundamental particles crushed into the state of singularity can not decide about emerging of spacetime but needs the intervention of dark energy which is full of information & infinte source of energy.

  14. Marc Geddes says:

    Simple definitive answer to your header question: Definitely, definitely not!

    You can separate out physics into 3 different levels based on levels of abstraction – the more abstract, the more fundamental, because more abstract concepts have greater explanatory power.

    Space-Time (Field) level – Deepest level of physics (meta-meta level), because its the basic communication medium (or ‘interface’) between objects.

    Transform (Quantum) level – Functional level (meta-level)

    Symmetry level – Stable objects (object level).

    No, the space-time level is fundamental, QM is derivative. QM effects are a side-effect of space-time, not visa versa. And ‘information’ is a property of minds, not reality.

  15. Amrit Sorli says:

    Space-time has onl a math existence.

  16. Jimmy Boy says:

    While Sean’s wife nicely introduces the idea to everyone, Sean and his colleagues show the idea needs significant retooling to work. Am I wrong?

  17. Rock Brentwood says:

    In this or any approach to the Quantum Gravity, the same question has to be asked: what are the coherent states? Since these are parameterized by the classical states (i.e. the manifolds and their matter/energy content), this leads to the next question: what is the overlap between any two coherent states that represent different light cone configurations? And can any two coherent states with different Weyl tensors have non-zero overlap? If there is non-zero overlap, then you have causality violation.

  18. Marc Geddes says:

    I strongly doubt you can wish geometry away so easily. The math of general relativity is continuous, not discrete. Quantum information can’t be fundamental, because ‘information’ needs to be instantiated in something physical, and you’re back to geometry again.

  19. Tom Andersen says:

    With the thousands of PhDs, Post docs and careers piled in the general direction of quantizing gravity, and zero hard results, its a fairly obvious dead end.

    If you want a job however – its the only game in town. Unlike a century ago, the internet has made the entire world into the same town, so physics is at a standstill.

  20. shuyt says:

    ‘No Empty Space in the Universe –Dark Matter Discovered to Fill Intergalactic Space’

    “A long standing mystery on where the missing dark matter is has been solved by the research. There is no empty space in the universe. The intergalactic space is filled with dark matter.”

  21. shuyt says:

    With the notion the intergalactic space is filled with dark matter, some physicists are using the term ‘dark mass’ in order to allow for a fresh perspective.

    ‘Dark Energy/Dark Mass: The Slient Truth’

    “That is, all that we are certain about [is] the dark mass, not dark matter, let alone to say about the dark ‘particle’.”

  22. Ray Gedaly says:

    So much to comment on here, yet so little time:

    1. Friends think it funny (peculiar, not ha ha) that my wife and I talk physics and astronomy over morning coffee. Assuming the universe is indeed infinite, then there must be other marriages where this common interest is shared. But it’s nice to have some evidence.

    2. Wasn’t aware of the publication Quanta. I’m an instant fan.

    3. Although intuition can be misleading for matters of the quantum world, I will still say that I feel we’re on the path to a deeper truth here.

    4. I have long speculated a tie between a holographic universe and quantum entanglement. This is based on how information in a conventional hologram is spread out in something analogous to a wave function (I think). I’ve even commented about this previously on your blog, albeit in my usual muddled style. (Good title for a future autobiography: “A Cluttered Mind.”)

    5. Late for work again … did I forget to take my medicines?

  23. Buck Field says:

    The assumption a “real” spacetime violates the Copernican Principle, entailing some issue flags that could be called fairly bright shades of red.

    If physics is an information system, then we can certainly mitigate risk of dead-end research with questions & hypotheses framed in terms of “our observations of spacetime”, etc.

    This would be consistent not only with good project management practices, but also with history and philosophy of science focused on these kinds of inquiries, and how they have been successfully resolved in the past.

  24. Richard Kriske says:

    The biggest problem with Physics, is that no one understands the whole of it, and that is causing a lot of problems with the theories. Even if you did understand it all it would probably be wrong for any of the big questions. I believe that the Magnetic field is the same field as the Electric, but viewed from the opposite side of the Space-Time membrane (or more correctly the space membrane with time perpendicular to both sides of it. Normally we view time as only being perpendicular to one side of the membrane, so when we view the Horizon at a distance we see many diverging history lines, much like the Electric field from Maxwell and we call this type of field Parabolic. When we view the other side of the membrane time lines converge, we call this type of time and field Hyperbolic. Hyperbolic time is really confusing, as you are seeing many time lines leading to the same result, many time lines adding up, and this happens in QED (a particle does everything, goes everywhere, etc.). You see the dual viewing of this Time, in the Twins Paradox, where one of the Twins turns around and returns on the wrong side of the membrane–he experience no time passing and is the same age as when he left. Hyperbolic time has that property, since it doesn’t form a time line, it isn’t ordered. Now every QM bracket has the property that (Hyperbolic time) x (Parabolic time) is not equal to (Parabolic time) x (Hyperbolic time), and you can see this with the Twins paradox, as one of the Twins is asymmetric to the other. Now in the Maxwell equations, The Electric field (which can traverse with no time delay) and the Magnetic field (which can traverse with no time delay) have a product which is the photon, which because it has two time elements, one being hyperbolic and one being parabolic can only travel the speed of light and carries information, because only things that contain a product of the two times can be real (the other things can only be Imaginary, but in the case of the Magnetic field, and the Electric field they only enter into experiments when one or both have a time variation (in either type of time), so you see how easily particles and reals are formed in my theory. Anyway, from my theory you can see this whole Information giving rise to the Universe is largely irrelevant as a new particle is formed when the two Twins meet, so the Universe is constantly generating new particles.
    Please prove me wrong, as I would be interested in where it would lead. As far as I have seen Physics is a bunch of half baked theories, with no single person knowing enough about the whole of it to get the truth, yet.
    Richard Kriske,