Duality and Emergence: When Is Spacetime Not Spacetime?

Spacetime is doomed! At least, so say some physicists. They don’t mean this as a warning, like some comic-book universe-destroying disaster, but rather as a research plan. These physicists believe that what we think of as space and time aren’t the full story, but that they emerge from something more fundamental, so that an ultimate theory of nature might not use space or time at all. Other, grumpier physicists are skeptical. Joined by a few philosophers, they think the “spacetime is doomed” crowd are over-excited and exaggerating the implications of their discoveries. At the heart of the argument is the distinction between two related concepts: duality and emergence.

In physics, sometimes we find that two theories are actually dual: despite seeming different, the patterns of observations they predict are the same. Some of the more popular examples are what we call holographic theories. In these situations, a theory of quantum gravity in some space-time is dual to a theory without gravity describing the edges of that space-time, sort of like how a hologram is a 2D image that looks 3D when you move it. For any question you can ask about the gravitational “bulk” space, there is a matching question on the “boundary”. No matter what you observe, neither description will fail.

If theories with gravity can be described by theories without gravity, does that mean gravity doesn’t really exist? If you’re asking that question, you’re asking whether gravity is emergent. An emergent theory is one that isn’t really fundamental, but instead a result of the interaction of more fundamental parts. For example, hydrodynamics, the theory of fluids like water, emerges from more fundamental theories that describe the motion of atoms and molecules.

(For the experts: I, like most physicists, am talking about “weak emergence” here, not “strong emergence”.)

The “spacetime is doomed” crowd think that not just gravity, but space-time itself is emergent. They expect that distances and times aren’t really fundamental, but a result of relationships that will turn out to be more fundamental, like entanglement between different parts of quantum fields. As evidence, they like to bring up dualities where the dual theories have different concepts of gravity, number of dimensions, or space-time. Using those theories, they argue that space and time might “break down”, and not be really fundamental.

(I’ve made arguments like that in the past too.)

The skeptics, though, bring up an important point. If two theories are really dual, then no observation can distinguish them: they make exactly the same predictions. In that case, say the skeptics, what right do you have to call one theory more fundamental than the other? You can say that gravity emerges from a boundary theory without gravity, but you could just as easily say that the boundary theory emerges from the gravity theory. The whole point of duality is that no theory is “more true” than the other: one might be more or less convenient, but both describe the same world. If you want to really argue for emergence, then your “more fundamental” theory needs to do something extra: to predict something that your emergent theory doesn’t predict.

Sometimes this is a fair objection. There are members of the “spacetime is doomed” crowd who are genuinely reckless about this, who’ll tell a journalist about emergence when they really mean duality. But many of these people are more careful, and have thought more deeply about the question. They tend to have some mix of these two perspectives:

First, if two descriptions give the same results, then do the descriptions matter? As physicists, we have a history of treating theories as the same if they make the same predictions. Space-time itself is a result of this policy: in the theory of relativity, two people might disagree on which one of two events happened first or second, but they will agree on the overall distance in space-time between the two. From this perspective, a duality between a bulk theory and a boundary theory isn’t evidence that the bulk theory emerges from the boundary, but it is evidence that both the bulk and boundary theories should be replaced by an “overall theory”, one that treats bulk and boundary as irrelevant descriptions of the same physical reality. This perspective is similar to an old philosophical theory called positivism: that statements are meaningless if they cannot be derived from something measurable. That theory wasn’t very useful for philosophers, which is probably part of why some philosophers are skeptics of “space-time is doomed”. The perspective has been quite useful to physicists, though, so we’re likely to stick with it.

Second, some will say that it’s true that a dual theory is not an emergent theory…but it can be the first step to discover one. In this perspective, dualities are suggestive evidence that a deeper theory is waiting in the wings. The idea would be that one would first discover a duality, then discover situations that break that duality: examples on one side that don’t correspond to anything sensible on the other. Maybe some patterns of quantum entanglement are dual to a picture of space-time, but some are not. (Closer to my sub-field, maybe there’s an object like the amplituhedron that doesn’t respect locality or unitarity.) If you’re lucky, maybe there are situations, or even experiments, that go from one to the other: where the space-time description works until a certain point, then stops working, and only the dual description survives. Some of the models of emergent space-time people study are genuinely of this type, where a dimension emerges in a theory that previously didn’t have one. (For those of you having a hard time imagining this, read my old post about “bubbles of nothing”, then think of one happening in reverse.)

It’s premature to say space-time is doomed, at least as a definite statement. But it is looking like, one way or another, space-time won’t be the right picture for fundamental physics. Maybe that’s because it’s equivalent to another description, redundant embellishment on an essential theoretical core. Maybe instead it breaks down, and a more fundamental theory could describe more situations. We don’t know yet. But physicists are trying to figure it out.

21 thoughts on “Duality and Emergence: When Is Spacetime Not Spacetime?

  1. J Mark Morris

    Duality and emergence are wonderful facets of nature. I am going to make a few statements that if you suspend disbelief for a moment, may help change your perspective on the situation. Please read this with an entirely open mind, unencumbered by the interpretations of physics and cosmology. The observations are fine.
    1. I assert that there is an incredibly parsimonious formulation of nature that has been tragically missed by scientists.
    2. This formulation of nature is 100% isomorphic to the standard model (less faulty interpretations).
    3. A false interpretive prior in the 1800’s had led to a complicated tree of incorrect prior interpretations which is clouding the vision of the scientists studying physics and cosmology.
    4. Here are the ingredients to the Universe : Eucliean void in space and time, a density I of immutable point charges carrying a density II of energy in kinetic and electromagnetic form. That’s it.
    5. But wait, how can this be? Unfortunately, physicists discarded point charges due to concerns over the math as idealized point charges approach infinitely closely and the math blows up.
    6. Point charges were down, but not out. They can be rehabilitated. Let’s explore a natural rule that prevents any two point charges from approaching any closer then a distance near the Planck length I calculate Lp/2 center to center, but try it yourself using the basic formulas. Also, assign the charge magnitude of |e/6| to the two point charge flavors.
    7. What is the way forward? Study orbital systems of immutable point charges. Don’t take my word for it. Examine the research? Can’t find any? That itself is an enormous clue. Why don’t we have a well established body of research for systems of orbiting point charges?
    8. Imagine a nested set of spherical orbital shells at vastly different radii scales. Start with a simple dipole of two equal and oppose point charges. Imagine it has fixed radius and the point charges can, with the right stimulii, roam all over that spherical shell. Then add another shell with another dipole of two point charges. And a third shell. Label the radii something well below our ability to directly observe, say r=10^-32, 10^-28, and 10^24 as an example. I call that the Noether core. It is what inflates, dilates, expands and implements Einstein’s spacetime on a passive Euclidean substrate of absolute space and time. Einstein’s spactime must be considered from this perspective of a three shell orbital structure. Think about why I called it a Noether core. Yep, it does nearly all the accounting for energy and momentum. It’s also a perfect black body. I could go on.
    9. Now add a fourth shell with six point charges. Pick any combination. That is a fermion. Six negative point charges in shell 4 is an electron. You are allowed to think of the fourth shell and the Noether core in terms of wave equations if you like. You can easily imagine the quarks now as a mix of positive and negative point charges in this shell. Noether cores come in pro and anti because there are three angular momentum vectors in a Noether core and they are different magnitudes, so there are two symmetry states (terminology?).
    10. There you have it. Don’t take my word for it. I’m not a scientist and there is no journal that will accept a non-scientist saying there was a false prior interpretation, leading to a tree of false priors, and the present crisis in physics and cosmology. No worries. Now that I understand the architecture, the math and simulations will be forthcoming, hopefully 2022. Or you could suspend disbelief and think about what I wrote and help me accelerate the transition to the next era.

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    1. 4gravitons Post author

      General thing I’ve warned you about before: try to more explicitly connect your comments to the topic of the post if you want them to not be deleted for being off-topic. Here I can tell what “got you going” (you think of your theory as one in which Standard Model fields emerge from dynamics of point charges), so I’m letting it through, but aside from a throwaway sentence at the beginning of your comment you don’t make that connection clear. In general, comments are for a dialogue with the post, so dialogue, don’t monologue!

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  2. J Mark Morris

    Hi. I’m going to unsubscribe because obviously I am not getting through to you or your readers on an intellectual level. My intentions were good, and someday you will understand that. In the meantime let me leave you with a thought that may cause a light bulb to go off in your community. The actual implementation of nature is far easier than amplitudeology itself. Think about that. What does that imply? Cheers and good blogging and good science on you. Bye.

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  3. Jacques Distler

    When people say this, they usually mean something like what happens in Matrix Theory. Space (to be technical, the 9 dimensions transverse to a null plane; even more technically, the positions of N D0-branes in those transverse dimensions) emerges as the simultaneous eigenvalues of 9 NxN matrices in some low-energy limit where the matrices commute (and hence can be simultaneously diagonalized). In some general excited state of the D0-brane matrix quantum mechanics, there’s nothing like spacetime anywhere to be seen.

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    1. 4gravitons Post author

      Yeah, that’s a nice clean example. Someone on twitter pointed out that if you’re the type to view AdS/CFT as a definition of nonperturbative string theory (at least on AdS) then it’s also a pretty clean case: when the string theory is strongly coupled and thus the perturbative picture breaks down, you still have the CFT side.

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      1. Jacques Distler

        Every time you have a “string theory duality”, in which there are two (or more) descriptions of the same physics, the “other” spacetime emerges quantum-mechanically.

        Consider, for instance, maximally-supersymmetric string theory with (8+1)-dimensional Poincaré invariance. One description of this theory is as Type-IIB compactified on a circle of radius R. That string theory has (p,q) strings (for co-prime p,q). If you wrap n (p,q) strings on the circle, it’s a miraculous fact that they form threshold bound states for every n. The spectrum of those (BPS) bound states is precisely the Kaluza-Klein spectrum of a torus whose complex structure is τ (the complexified IIB string coupling) and whose area A goes to infinity when you take R→0 (in Planck units). This is the M-theory torus, emerging quantum-mechanically from the IIB description.

        Conversely, if you start with the M-theory description, of M-theory compactified on a torus of area A, then n M2-branes, wrapped on the torus, also form threshold bound states for every n. The (BPS) spectrum of those bound states is precisely the Kaluza-Klein spectrum of a circle, whose radius R goes to infinity when you take A→0.

        With variation, the same is true for every string duality. At least in this (weak?) sense, emergent spacetimes are ubiquitous in string theory.

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        1. 4gravitons Post author

          Yeah, but as I explained in my post, a lot of those “don’t count” as emergent spacetime in a sense that would satisfy the skeptics, because either description is complete on its own. Because you can start with either description and see the other one emerge, you can’t really say that one of them is emerging from the other: either one could be “correct” and the other would just be an alternate description.

          (Unless your point is that the dualities hold when a dimension is compact, but tells you about emergence of spacetime in the non-compact limit?)

          (Or I suppose you could just say that, if someone insisted on choosing a “side” as “the real one”, then whichever side they choose there would be a regime where the other side emerges? Ok, if that’s what you’re saying I buy that, yeah, though it’s not really “spacetime emerges from non-spacetime” since the other theory also has a spacetime, just a differently-configured one.)

          Your original M theory example and the AdS/CFT example are better, precisely because there is some sense in which the duality is “broken”: there is some regime in which there really isn’t a spacetime on one side, which smoothly interpolates to a regime with a dual spacetime.

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          1. Jacques Distler

            Yeah, but as I explained in my post, a lot of those “don’t count” as emergent spacetime in a sense that would satisfy the skeptics, because either description is complete on its own.

            I’m not sure what I am trying to prove, to whom, but I don’t see how those examples “don’t count”.

            Let’s take the Type-IIB description. What I’m saying is that there’s a particular limit of the IIB description in which an approximate 11-dimensional Poincaré invariance emerges. Where did the “extra” dimensions come from? As I described, they arise as a subtle quantum-mechanical effect (involving threshold bound states of wrapped branes).

            Sure, there’s another description in which that approximate 11-dimensional Poincaré invariance is obvious, geometrical, and not “emergent”. But in that description, the existence of a different limit, in which 10-dimensional chiral Type-IIB supergravity emerges, is again a subtle quantum mechanical effect (involving threshold bound states of a different set of wrapped branes).

            There’s no description in which all of these spacetimes exist on an equal footing. In any given description, some are manifest while others are emergent. Which is which depends on the description.

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            1. 4gravitons Post author

              See the second parenthetical in the comment you’re responding to. (And this is what I get for starting to type before I’ve thought through the comment…probably should have just rewrote the thing when I noticed that part but eh.)

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        2. 4gravitons Post author

          Another thought here is that as physicists we have a sense of a description “breaking down” that isn’t quite the sense others might have in mind. Specifically, the sense of perturbation theory breaking down, of an approximation becoming worse and worse in some regime, so even if “in principle” a description holds it can become much less useful than another description. This is kind of the case for spacetime in these examples: nothing in principle stops you from sticking on one “side” or another of the duality and “not noticing” the emergent spacetime, but it becomes progressively less and less useful to do so, so in a physicisty sense the original spacetime “breaks down” when the other spacetime emerges.

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  4. Chris Bolger

    My gut tells me this is why string theory does not resemble reality. I think it breaks down at much shorter distances since space-time might. Giving space-time a more digital format that emerges from something else may get rid of (or explain) the extra dimensions needed and simplify or eliminate the complex curling of those extra dimensions. Take string theory from analog infinitesimals and integrals and go to very small but finite chucks with huge summations. Just a though anyway.

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    1. 4gravitons Post author

      Not my specialty, but it’s generally hard to introduce a “digital” breakdown of space-time and stay consistent with the evidence, even quite small “pixels” can have observable consequences. Also, there are plenty of contexts in which string/M theory can model space-time breaking down: I think I gave some examples in the post, but also see Jacques Distler’s comment.

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  5. Karl Young

    This is a really interesting post and to the extent I understand it, I tend yo lean towards the people looking to “break duality”. Though out of the game for a while I remember being told as an undergraduate something resembling emergence held for classical mechanics in terms of the more fundamental quantum mechanics. And this was supposed to be justified by the correspondence principle. But after a few difficult calculations I realized that the correspondence principle only held in a couple of convenient text book examples so talk of emergence was actually pretty hollow. Though appreciating what I can understand of the work that theorists do these days, I now lean pretty much towards an empiricist view (sans the positivism !) that theories cleave to “reality” only to some degree and essentially just serve as (usually incommensurable) descriptions of phenomena in some domain, i.e. dreams of theories of everything seem like fantasies.

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  6. Giotis

    In AdS/CFT in particular there is the holographic RG flow. The radial bulk direction is the energy scale of the CFT. At the boundary you are in the UV of CFT. Going deep in AdS you are moving towards the IR of CFT. In this sense the extra dimension of space is emerging from CFT.

    In dS/CFT on the other hand time is an emerging concept in the above sense.

    Off topic, have you seen this?

    https://arxiv.org/abs/2201.11658

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    1. 4gravitons Post author

      Regarding the paper, I’d glanced at it, though in not much depth (for one, I only just noticed Strominger is one of the authors). I’ve seen people talk about error-correcting codes in AdS/CFT before, but I don’t know enough about the topic to know what this paper is adding.

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  7. Pingback: Spacetime, doomed, so to speak – The nth Root

  8. Dimitris Papadimitriou

    Although I can’t tell for sure, I have the impression that holography works well for ” static/ stationary” cases ( e.g. for extremal black holes, or for Ads spacetime ), but not for ” dynamical” ( like, for example, the interior of a physically relevant subextremal black hole, or the region that is outside our ” subjective” cosmological horizon, assuming that our universe is asymptotically deSitter, as the observations indicate).
    Some other related questions:
    Does anybody know if there is some dual description for phenomena like the well known ( at least to GR community) blueshift / mass inflation instability?
    Or the backreaction effect of the influx ( ingoing part ) of the Hawking radiation that is related to that kind of instabilities that are expected to occur inside all, generically, realistic black holes?

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  9. Andrei

    4gravitons,

    You probably remember my proposed experiment where one could in principle measure a distance with sub-Plankian accuracy (a LIGO-type interference experiment with gamma-ray lasers).

    In your article:

    How to Get a “Minimum Scale” Without Pixels

    you say:

    “Since the two pictures are indistinguishable, it doesn’t actually make sense to talk about dimensions smaller than the length of the string. It’s not that they can’t exist, or that they’re smaller than the “pixels of the universe”: it’s just that any description you write down of such a small dimension could just as easily have been of a larger, dual dimension.”

    You also said that you don’t expect anything unusual to happen in the interference experiment because of Lorentz invariance. It seems to me that string theory would predict something unusual after all. What do you think?

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    1. 4gravitons Post author

      Yeah, I think this runs into the same sort of issue I brought up when you mentioned the proposal before. In order to see those kinds of stringy effects from wrapping and so on, you need high enough energies to excite the wrapping states, because the ground state doesn’t tell you anything by itself. So you still need to be probing small scales in a Lorentz-invariant sense, not just small distances in a non-Lorentz invariant sense.

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