I Is spacetime emergent - and in which theories?

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Haelfix

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The only thing that is fixed on the gravitational side are the asymptotics. What takes place in the 'bulk' is an arbitrary solution to the classical field equations subject to those boundary conditions (so you can have black holes, cosmic strings, etc etc), so it is that which 'emerges' within the AdS box. We don't have explicit examples of gravitational holographic dualities that do not share that sort of structure (although see the SYK model that King Vitamin mentioned).

The emergent perspective of the duality comes when you think about the nature of the conformal field theory. Naively, you have what looks like a standard theory of something not very much different than a theory describing a lot of massless quarks. Then despite having those very specific degrees of freedom, somehow encoded within the 'quarks' interactions/entanglement structure and so on, is a completely different theory which not only grows an extra spatial dimension but also somehow knows something about the gravitational force. The duality is believed to go even further now (into something called subregion duality). It's not just an isomorphism of Hilbert spaces for the full theories, but even for a given finite lapse of time in the CFT, it somehow is able to 'see' a wedge of the gravitational bulk.

It's wonderfully nonlocal, but somehow that is what's needed to answer the Bekenstein bound and the R-T generalizations.
 

Haelfix

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For other interested readers. Note that the word 'emergent' is another one of those equivocated words in theoretical physics. We've already described the holographic sense, as well as the lattice sense but in the older literature there were yet other senses. For instance people played with the idea that gravity could 'emerge' much like electromagnetism emerges from the electroweak theory. Namely as the consequence of a broken symmetry.

It turns out for the case of gravity there are theorems forbidding such a thing, but well the story doesn't quite end there either.
 

martinbn

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The only thing that is fixed on the gravitational side are the asymptotics. What takes place in the 'bulk' is an arbitrary solution to the classical field equations subject to those boundary conditions (so you can have black holes, cosmic strings, etc etc), so it is that which 'emerges' within the AdS box. We don't have explicit examples of gravitational holographic dualities that do not share that sort of structure (although see the SYK model that King Vitamin mentioned).
How is this different than classical general relativity? An arbitrary solution to the field equations, subject to boundary conditions, is not an emergent spacetime!
 
Time might seem fundamental to emergence, as being fundamental to events (how can you have events without time etc? How can you even speak of "before" without time being taken for granted?) but it is conceivable for a system to do without time and only have a sequence (mesh) of states with rules (call them rules of implication or potential, or something) such as one might have in a Finite (multiple) State Machine graph, in which the transitions are sequence dependent, but time, duration etc are not immediately defined. In that case one could imagine time (duration etc) emerging within such a system (much as numbers could emerge from certain rules of sets, starting from just the empty set).

It might help to think of a movie film strip, either being projected, in which time is defined by the sequence of frames in the projector, or in a reel in a rack; the whole sequence is there, unchanged, fully determined, but time as such is not relevant.

Now the concept of "before" does not apply to the world of the film, because the rack, even the strip, and in fact the projector are not part of anything in the frames. The action is emergent from the audience and the projector and a lot of other stuff outside the frame sequence.

Of course, what I describe is not 1-dimensional like a film frame sequence in our universe, but models are necessarily dimensionally limited.
 
Some physicists, like Nima, Ed. Witten, Gross, and others have said/suggested that space-time is doomed, or emergent from something more fundamental. What ideas would replace space-time? Something similar to a perfect material? A fluid? Geometry? Quantum field theory of some sort? Entanglement?

Is there any evidence that space-time is emergent or is this some idea in the air? String theory and I believe LQG point to the idea of emergent space-time.
In this paper it is suggested that space-time emerges, together with quantum physics, from an underlying geometric theory having to do with fluctuations in the metrics of 2-manifolds:
https://link.springer.com/article/10.1007/s40509-014-0022-6
and a short erratum:
https://link.springer.com/article/10.1007/s40509-015-0032-z
 
Aren't all quantum gravity theories aiming for an emergent spacetime? Those I know of, like LQG, are quantisations of space alone and set in an Hilbert space where the dynamics are governed by a Hamiltonian. The spacetime of GR is then supposed to be emergent in some suitable limit.

Are there any QG theories which don't follow this approach?
 

PAllen

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While not a very active research area, Causal Dynamical Triangulations literally has a notion of spacetime continuum emerging from discrete substructure.

 

Haelfix

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How is this different than classical general relativity? An arbitrary solution to the field equations, subject to boundary conditions, is not an emergent spacetime!
You are right, from that perspective it is not. But that's when i've given you the full CFT.

The 'emergent' point of view arises if you hand me a holographic CFT, and then I put it on my quantum computer to simulate. During time evolution, we literally see spacetime emerging from what would otherwise look like a mess of degrees of freedom that look nothing like gravitational physics. Moreover, you might imagine that under such a time evolution the duality would lead to something like normal ADM/Hamiltonian evolution on the gravity side, but it is known that this does not take place. Instead the reconstruction occurs far more nonlocally.
 

jal

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" ...a notion of spacetime continuum emerging from discrete substructure."

Reading from the above following references I get a question.

Gravity at Planck scale
Lectures on Gravity and Entanglement Mark Van Raamsdonk

Abstract The AdS/CFT correspondence provides quantum theories of gravity in which spacetime and gravitational physics emerge from ordinary non-gravitational quantum systems with many degrees of freedom. Recent work in this context has uncovered fascinating connections between quantum information theory and quantum gravity, suggesting that spacetime geometry is directly related to the entanglement structure of the underlying quantum mechanical degrees of freedom and that aspects of spacetime dynamics (gravitation) can be understood from basic quantum information theoretic constraints

https://arxiv.org/pdf/1609.00026.pdf


p. 54 Example: spherically symmetric geometries
The right side is obtained from the modular Hamiltonian expectation value using the fact that for a translation-invariant stress-tensor on the sphere (which we assume to be of unit radius), we have ∆hT00i = ECF T 4π = Mℓ/ 4π . (125)
The result (124) tells us that there is a limit to how much a certain mass can deform the spacetime from pure AdS. This should restrict the equation of state that matter in a consistent theory of gravity can have.


p. 62 Figure 21. assume planck scale areas then there can only be 12 discrete planck size rays coming from 12 discrete planck size areas that exist on the surface of a planks size sphere of a radius of one planck length.



------
https://link.springer.com/article/10.1007/s40509-014-0022-6#Sec7
" .... our fundamental geometrical object: a circle of radius 1 and perimeter 2π ....
What I seem to be proposing is that the geometrical concept of angle can only be formulated as a limit, where some oscillation’s amplitude tends to zero. EMO theory then deals with the structures created by these infinitesimal oscillations, while placing them against the idealized background of ε=0
ε=0. "


The surface area of a sphere of one planck radius is given by the formula
Area=4πr^2 =12.566
Therefore a sphere can only have/be discrete 12 planck scale areas on the surface. Nothing exist smaller than one planck unit. Therefore, its cannot be a sphere.
That sphere can contain,inside, another ? planck areas ( the radius) connected to the 12 planck scale areas on the surface of the sphere.
That planck sphere is packed/surrounderd by 12 other similar spheres, (kissing number of densest packing), to create one unit of densest packing .
A planck size area on the surface of a sphere, can connect to another planck size area of another sphere.

Therefore, how does Mℓ/ 4π get modified to arrive at consistent theory of gravity at planck scale?
Discreteness seems to exist at planck size. You can't make bubble. When does 4π become a rational number and therefor become capable of making a continuous sphere.
 

Fra

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If it starts with time, how can spacetime be emergent?
I dont have a good reference but for a coherent exposition of this but fwiw, a POSSIBLE principal explanation of this is:?

The rational sense in i think of emergent spacetime starts with a concept of uncertainty, and from this one can consider transitions and then associate a metric from how "far away" something is in hypothesis space, and first dimension is usually time if one parametrises things as per an expected flow, which conserves information.

After that one can consider a chaotical system, where one tries to "index" events in the chaos, and order them. Such dimensions from chaos are created as a way of efficient representation or embedding dimensions.

This is fuzzy, but its roughly how i envisions emergent dimensions, that are DRIVEN by efficient coding. Ie. the driving force for the new dimenstions are efficienty of encoding and also computations.

But to work it out explicitly in a way that reproduces known physics is a massive challenge. But I still think the conceptual vision is clear enough. But its hard to convey it perhaps, unless you already aligned in thinking like this.

So i essential see the starting ingredients, NOT HUGER super space, but the opposite, just chaos, and uncertainty. And in there we have an evolving physical code, that response to the environment. This "code" is then identified with "matter". And its the structure of matter than encodes space (ie relations to other matter). Ie its consistent with the idea that spacetime is a pure relation. But the relation is physicall encoded into sturcture of matter, litteraly speaking.

/Fredrik
 

haushofer

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As I understand it, holography and entanglement entropy suggest that classical spacetime can emerge from something more fundamental, say "spacetime atoms". In that sense classical spacetime emerges from quantum entanglement of these "atoms", like e.g. a continuous fluid description emerges from water molecules.

We don't know the details yet of these spacetime "atoms", just like Maxwell, Boltzmann and others didn't know the precise details and quantum mechanics of atoms.
 
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As I understand it, holography and entanglement entropy suggest that classical spacetime can emerge from something more fundamental, say "spacetime atoms". In that sense classical spacetime emerges from quantum entanglement of these "atoms", like e.g. a continuous fluid description emerges from water molecules.

We don't know the details yet of these spacetime "atoms", just like Maxwell, Boltzmann and others didn't know the precise details and quantum mechanics of atoms.
So for an idea in terms of spacetime atoms, what would you expect spacetime to be? Some analogy of a block or crystal of condensed matter?
 
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I emailed two researchers in this field and here are the responses:
"
There has been a lot of discussion of this, but I don’t know a good place where it is reviewed in print. One reason is that due to quantum effects, we don’t expect spacetime geometry to make sense at very short distances. But there are others as well."

and
"
If there is a quantum theory of gravity, then it describes a quantum spacetime which has the same relation to classical spacetime that the quantum states of an electron have to the classical particle trajectories. We use methods like coherent states or the WKB approximation to show how the classical particle trajectories emerge from the dynamics of quantum states. This is one sense in which we expect classical spacetime to be not fundamental, but to be emergent from a quantum state or quantum path integral description."

Maybe this will help people on their quest to understanding.
 
Some physicists, like Nima, Ed. Witten, Gross, and others have said/suggested that space-time is doomed, or emergent from something more fundamental. What ideas would replace space-time? Something similar to a perfect material? A fluid? Geometry? Quantum field theory of some sort? Entanglement?

Is there any evidence that space-time is emergent or is this some idea in the air? String theory and I believe LQG point to the idea of emergent space-time.
Where did you find it? I've never read about it.
 

haushofer

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So for an idea in terms of spacetime atoms, what would you expect spacetime to be? Some analogy of a block or crystal of condensed matter?
I don't know, but that wouldn't be a huge surprise; high energy physics has more ties to condensed matter physics; think e.g. Higgs mechanism.
 
The essence of the emergent spacetime program of people like Carrol, Verlinde, Raamsdonk, Giddings et cetera is the Ryu-Takayanagi relation. I will focus on the Raamsdonk type of emergence because I am most familiar with it, although I can't promise I didn't get anything wrong (especially regarding how nongeometric a CFT is)...

A conformal field theory (CFT) is not a priori geometric, formally it is all operators and commutators and a spectrum of possible states. A conformal field theory (and indeed, any QFT) has a vacuum state with a very peculiar entanglement structure that prevents factorization of the Hilbert space into (spacetime) local factors. Despite this, we may classify a subset of operators on this space in terms of local regions by demanding that it respects the notion of causality carried by a Lorentzian spacetime. There is a natural definition of entropy in this framework, and since this definition makes reference to a pure vacuum state this entropy is purely due to entanglement. The main point I am trying to make here is that while we use spacetime causality as a guide for constructing the "algrebra of observables" of the quantum theory, the geometry is not explicitly a part of the operators in Hilbert space side of it all.

Raamsdonk et al in for example 1308.3716 and 1705.03026 show that: (I'd like to note that I found the latter paper really difficult, while the first is actually a really approachable, explicit proof by induction for the first order resutl)

There is a unique geometry that correctly computes the entanglement entropy of the boundary CFT to second order via the Ryu-Takayanagi relation, and this geometry satisfies the Einstein Field Equations to second order. (By unique I mean unique in the sense that the equations that determine the geometry are uniquely the Einstein field equations)

The CFT side of their computations has no a priori geometry (especially not a dynamical geometry) but it turns out that the dynamics of entanglement in the CFT are equivalent to graviational dynamics. If we see the entanglement as "more fundamental", we can see the gravitational as "emerging from the more fundamental theory". It is also important to stress that for the second order result, they need to consider a very specific class of CFT states, there are lots of CFT states whose entanglement structure can not be interpreted as describing any classical geometry. In this sense gravity emerges as a particular subspace of possible states in a larger, a priori nongeometric theory.

If you think that CFT/QFT comes equipped with too much "a priori geometry" you may appreciate the speculative part of 1809.01197 . I should also note that there are lots of reasons for why just entanglement is not enough to fully reconstruct spacetime geometry, most notably the interior of black holes. For example, the extremal surfaces used for Ryu-Takayanagi can not pass event horizons, and the eternal AdS wormhole grows in length without this being reflected in any entanglement quantity. For more on this see for example 1411.0690 and maybe the original ER=EPR paper 1306.0533.

Edit: made hyperlinks
 
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You are right, from that perspective it is not. But that's when i've given you the full CFT.

The 'emergent' point of view arises if you hand me a holographic CFT, and then I put it on my quantum computer to simulate. During time evolution, we literally see spacetime emerging from what would otherwise look like a mess of degrees of freedom that look nothing like gravitational physics. Moreover, you might imagine that under such a time evolution the duality would lead to something like normal ADM/Hamiltonian evolution on the gravity side, but it is known that this does not take place. Instead the reconstruction occurs far more nonlocally.
I tend to think along this lines, spacetime seems to be a phase space of all (or a subset of) degrees of freedom in a system.
 
That there's something more fundamental than space-time.
I don't see it either.
Without reference to any proposed theory I can think of a couple of ways that space-time can be emergent:

1) starting with a single point (e.g. big bang) and bud new points off it and others as they form. (These new points are connected to their parents and other closely related points. Imagine lines draw these points together to create a network.) These points are where particles can be positioned. As you gain more and more points space is expanding but the topology of how those points connect will determine the shape of space-time. The simplest version is a single point breaks into two and remains connected to those points either side and to each other and as this continues creates a growing circle (1d line) more complex network topologies such as lattices and diamond like tetrahedral connections give 3d bulk space, etc. Those points don't have to have a real position in anything and just gets one from the relationship to its neighbours only.

2) the other way which is less realistic is if space and time do not exist at all but every particle or wave packet has "coordinates" (maybe just as distances from all other particles) the laws of physics could then be enough to give the impression that a type of space-time exists and that would emergent from the particle interactions and the laws.

These are obviously toy models but should give you an idea of how emergence could work.

Paul Cooper
 

MathematicalPhysicist

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Without reference to any proposed theory I can think of a couple of ways that space-time can be emergent:

1) starting with a single point (e.g. big bang) and bud new points off it and others as they form. (These new points are connected to their parents and other closely related points. Imagine lines draw these points together to create a network.) These points are where particles can be positioned. As you gain more and more points space is expanding but the topology of how those points connect will determine the shape of space-time. The simplest version is a single point breaks into two and remains connected to those points either side and to each other and as this continues creates a growing circle (1d line) more complex network topologies such as lattices and diamond like tetrahedral connections give 3d bulk space, etc. Those points don't have to have a real position in anything and just gets one from the relationship to its neighbours only.

2) the other way which is less realistic is if space and time do not exist at all but every particle or wave packet has "coordinates" (maybe just as distances from all other particles) the laws of physics could then be enough to give the impression that a type of space-time exists and that would emergent from the particle interactions and the laws.

These are obviously toy models but should give you an idea of how emergence could work.

Paul Cooper
As for your 1) I don't see how all of the richness of the universe can pop out of a point.
A point cannot contain in it spheres,planets, humans etc. which are comprised of infinite number of points.
So you actually say that from one point we can have infinite number of points?
How exactly?

I never quite understood the big bang theory, maybe next year I'll take a course in cosmology and the lecturer will explain it (I am not sure it will be explained there).

Or do you mean mathematically we can look at a graph instead of a Lorentzian manifold?
I wasn't referring to the mathematical structure, but to the notion of spatial distances and temporal intervals that is in the experimental way of doing physics which is basically fundamental.

Instead of some structure with properties from analysis we take some structure from combinatorics, namely a graph; but then how do you do analysis on graphs?

I read a few weeks ago a paper about PDEs and graph theory and the interconnections between them (more skimmed over it) perhaps it could work.
But the question is will it solve problems that the analysis construct didn't?

Here's the paper I looked at:
 
My published research with Suresh G. Advani in Physics of Fluids on the Saffman-Taylor Instability (on the radial domain) suggests to me that this low-energy quantum process is one of self-ordering (self-ordered criticality). I saw that someone above spoke of a source as being a single location or point. In my relational philosophy as an offshoot of expanding-universe/fluid-droplet thought, nothing can exist without relationship, meaning a change in the universe of between at least two locations or magnitudes. Both what we sample as space and what we sample as time are CHANGES and therefore, to us, exist explicitly. Are they, as David Bohm suggests, implicit to our universe? More soon.
 

ohwilleke

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LQG basically says that space-time consists of points and connections between points (often three per point). The number of space-time dimensions in emergent from the network of connections between points, and so is locality, which is imperfect since points could have a connection to another point which doesn't have a lot of other connections in common with it, creating a Planck scale non-locality. Smoothness in LQG is just an illusion in what is fundamentally a discrete structure of space-time that is so fine grained that it cannot be experimentally distinguished from a smooth space-time. In LQG and kindred theories the points and connections, or the equivalent, are axiomatic, but not the topological features of space-time.

To understand how dimensionality could be emergent, try using the definition of a fractal dimension or a generalization of that. In LQG, very simple small scale systems could be functionally two dimensional, for example, even though they become four dimensional as the network of connections self-organized (in something a bit like a spontaneous symmetry violation).

LQG also has an elaboration in which matter is basically just a tightly bundled cluster of connected points.

While this is hard to observe, this means that none of the usual axioms relied upon for real analysis or complex analysis in almost every circumstance that intuitively seem like they must be true (like smoothness and continuity) hold, which kicks you out of glorified calculus and into the world of discrete mathematics.

I'm oversimplifying, but that is the basic idea in a nutshell.

An emergent space-time makes a lot less sense in many versions of string theory because those theories often include the number of space-time dimensions as an axiom of the theory, and because some versions of it have both a 10 or 11 dimensional space-time (which phenomenologically explains why gravity is so weak) and a 4 or 5 dimensional brane to which interactions except gravity are confined, with the branes also being axiomatic.
 
What I highlighted is true of so many fields in science and technology, if you decided on being an academic scholar and being good at that you are bound to read quite a lot of papers and books.
So true. I grok what you're saying. But I came by my interests and activities naturally by experimenting (really all my life). I was able to publish my research on the self-organization of a low-energy quantum physical behavior, that shows that our universe of normal space and time behaves like an unstable (Saffman-Taylor Instability) expanding boundary (about 100 years of reference materials (actual experiments)) to go through helped out a lot).
 
As for your 1) I don't see how all of the richness of the universe can pop out of a point.
A point cannot contain in it spheres,planets, humans etc. which are comprised of infinite number of points.
So you actually say that from one point we can have infinite number of points?
How exactly?
I thought it was obvious that 1) was referring to a universe where space-time is granular. If it is not then that type of model isn't applicable for that exact reason. But given that the granularity, if it exists, would likely be on the planck scale so the theories we have which we describe with differentiable manifolds could just be approximations in the same way gas laws are statistical approximations of the behaviour of particles in a gas.

These models are not meant to be taken with any seriousness there is no mathematics or theory behind them, more just didactic examples of the concept of emergence in regards to space-time. This subject is an active area of research so there is no "answer" yet.

I never quite understood the big bang theory, maybe next year I'll take a course in cosmology and the lecturer will explain it (I am not sure it will be explained there).
That should be interesting but if my Gravitation and Cosmology module I did (~25years ago) is anything to go by it will be heavy on the Maths. I also doubt it will cover the emergent spacetime topic.

Or do you mean mathematically we can look at a graph instead of a Lorentzian manifold?
I wasn't referring to the mathematical structure, but to the notion of spatial distances and temporal intervals that is in the experimental way of doing physics which is basically fundamental.
Unfortunately there is no reason to believe spatial distances and temporal intervals are fundamental.

Instead of some structure with properties from analysis we take some structure from combinatorics, namely a graph; but then how do you do analysis on graphs?

I read a few weeks ago a paper about PDEs and graph theory and the interconnections between them (more skimmed over it) perhaps it could work.
But the question is will it solve problems that the analysis construct didn't?

Here's the paper I looked at:
Looks interesting I will dive into that later.

This essay I found might be of interest to you: http://guava.physics.uiuc.edu/~nigel/courses/569/Essays_Spring2018/Files/gupta.pdf
 

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