# I Is spacetime emergent - and in which theories?

#### S Beck

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.

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#### martinbn

I personally have never understood what it mean for spacetime to be emergent!

#### MathematicalPhysicist

Gold Member
I personally have never understood what it mean for spacetime to be emergent!
That there's something more fundamental than space-time.
I don't see it either.

#### romsofia

It's just an idea people have. What it means to have an emergent spacetime, is that the fundamental structure of quantum gravity is not that of spacetime i.e it somehow pops up later.

One paper to get into the subject is: https://arxiv.org/abs/1503.08207

#### MathematicalPhysicist

Gold Member
It's just an idea people have. What it means to have an emergent spacetime, is that the fundamental structure of quantum gravity is not that of spacetime i.e it somehow pops up later.

One paper to get into the subject is: https://arxiv.org/abs/1503.08207
Space-time pops from what?
From another mathematical space?

#### S Beck

LQG treats space and time as discrete, and in the future, possibly emergent from something more fundamental. String theorists also say spacetime is emergent. Nima Arkani-Hamed is vocal about "spacetime is doomed." But as of now I don't have a single clue what gives rise to spacetime.

#### MathematicalPhysicist

Gold Member
LQG treats space and time as discrete, and in the future, possibly emergent from something more fundamental. String theorists also say spacetime is emergent. Nima Arkani-Hamed is vocal about "spacetime is doomed." But as of now I don't have a single clue what gives rise to spacetime.
What they may refer to mathematically, is the Lorentzian manifold $\mathbb{R}^{3+1}$, which might be embedded inside a larger space, perhaps graph-manifolds...
I dunno, there's infinitude of mathematical spaces we can pick from.

#### Haelfix

I personally have never understood what it mean for spacetime to be emergent!
As you might have guessed, the idea is a bit vague. Nevertheless the canonical motivating example is the AdS/CFT correspondance. The technical statement of the correspondance is given by eg
2.29 and 2.30 (and subsequent generalizations) in these lectures:
(Which I recommend reading if people are interested, b/c its quite technically complete, if a bit advanced)

The 'emergence' part is really related to how you define operators in the CFT that are far from the boundary of spacetime. In a sense, the closer you can get to filling out the ADS cylinder, the more things 'look' like semiclassical gravity. This is termed bulk reconstruction.

#### romsofia

Space-time pops from what?
From another mathematical space?
It depends on who you ask. The issue comes down to in quantum gravity you can't have a fixed background spacetime, which is what you assume in quantum mechanics. In QM, you have a fixed background spacetime, and from here you have a notion of a "moment of time". But, now let's say we have a quantum mechanically varying spacetime (i.e not fixed, and now we're invoking quantum mechanics). So, we can't really assign values until measured, and those points don't have fixed values. If these points don't have fixed values, then what does it mean to be spacelike, timelike, or nulllike seperated anymore?

This is known as the "problem of time"! We no longer have the structure we need. Hence, people think that the concept of a classical spacetime falls out here. (Note: this is a very simplified way to explain this).

Now, I'll be talking from my heart here, so you can tune out if you want: it's not very fun to get into this field. You have to read so many papers, some dating back to the 70s just to see how some of these ideas originate. And they build off some random paper form the 70s, so you attempt to read some of there papers from 2018, and they're expecting you to have followed their journey up to this point! Just like some of the others in this thread, I'm a relativist at heart, so I never understood why these groups expect a spacetime emergence. So I read papers, I talked to people, all trying to see what I was missing. The reality was just people have fallen in love with quantum fields more than they have with classical spacetime. There is no mathematical reason for spacetime to be emergent, it's just a hunch they have. But, it's a hunch that a lot of researchers in the field have...

#### mitchell porter

"The Thing cannot be described—there is no language for such abysms of shrieking and immemorial lunacy, such eldritch contradictions of all matter, force, and cosmic order"... Oh, sorry, that's Lovecraft describing the emergence of Cthulhu, not the emergence of space-time.

#### S Beck

"The Thing cannot be described—there is no language for such abysms of shrieking and immemorial lunacy, such eldritch contradictions of all matter, force, and cosmic order"... Oh, sorry, that's Lovecraft describing the emergence of Cthulhu, not the emergence of space-time.
Uh, sorry but I don't know what you're talking about.

OT: There is also a superfluid vacuum theory that treats space as a superfluid.

#### MathematicalPhysicist

Gold Member
Now, I'll be talking from my heart here, so you can tune out if you want: it's not very fun to get into this field. You have to read so many papers, some dating back to the 70s just to see how some of these ideas originate. And they build off some random paper form the 70s, so you attempt to read some of there papers from 2018, and they're expecting you to have followed their journey up to this point! Just like some of the others in this thread, I'm a relativist at heart, so I never understood why these groups expect a spacetime emergence. So I read papers, I talked to people, all trying to see what I was missing. The reality was just people have fallen in love with quantum fields more than they have with classical spacetime. There is no mathematical reason for spacetime to be emergent, it's just a hunch they have. But, it's a hunch that a lot of researchers in the field have...
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.

#### martinbn

Is there a relatively simple toy example of any physical theory (doesn't have to be quantum), which doesn't use spacetime in any way for its formulation?

#### Haelfix

Is there a relatively simple toy example of any physical theory (doesn't have to be quantum), which doesn't use spacetime in any way for its formulation?
I suppose it depends what you mean by spacetime. Would a lattice model be an appropriate answer. What about something like the Ising model?

In the aforementioned AdS/CFT correspondance, you essentially define the gravitational part (fluctuating spacetime etc) by the large N gauge theory CFT (defined on a different Minkowski space).

#### jal

The Big Bang created the 3 dimensions of space plus the dimension of time and all the particles..
Space can be bent. The maximum that it can bend is a bubble.
Before the big bang, there were space-time bubbles packed together in the cosmo.
The universe did not exist before the big bang.
If there are any space-time bubbles existing in our 3+1 dimensions they would be smaller than any particles.

#### martinbn

I suppose it depends what you mean by spacetime. Would a lattice model be an appropriate answer. What about something like the Ising model?

In the aforementioned AdS/CFT correspondance, you essentially define the gravitational part (fluctuating spacetime etc) by the large N gauge theory CFT (defined on a different Minkowski space).
OK, but what are they? I am asking for an oversimplified example, not hundreds of pages.

#### Haelfix

OK, but what are they? I am asking for an oversimplified example, not hundreds of pages.
Just to be clear, you are asking for an oversimplified model of what exactly? Any example of a physical system that doesnt involve clocks and rulers? Well, I don't know how to eliminate clocks (the dynamics) without rendering everything trivial. If you mean rulers, then I suppose a lattice model removes most of the asssumptions of having a pseudo Riemanian manifold so that technically would answer your question. Again something like the Ising model is a physical example of a system that only has emergent Galilean or Lorentz invariance (in specific examples where amongst other things the limit of lattice spacing goes to zero). Perhaps something you are more familiar with might be Regge gravity, a triangulation of GR, which only recovers the spacetime symmetries in the appropriate limits. The triangulation itself picks out a preferred frame, so at best the local poincare symmetry is emergent in some limit.

If you are asking for the much more challenging question of what emergent spacetime is like in so far as what our best ideas of quantum gravity are, then I don't have something that I can give you that's not difficult.

#### romsofia

Is there a relatively simple toy example of any physical theory (doesn't have to be quantum), which doesn't use spacetime in any way for its formulation?
When I was younger, I tried to follow Smolin's work on Causal sets. The one paper I have saved is this one: https://arxiv.org/abs/1308.2206v1 which comes from https://arxiv.org/abs/1307.6167

These aren't hundreds of pages, but it does start with a concept of time. I'm not sure if that's what you're looking for.

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#### martinbn

If you are asking for the much more challenging question of what emergent spacetime is like in so far as what our best ideas of quantum gravity are, then I don't have something that I can give you that's not difficult.
Difficult is ok as long as it isn't hundreds of pages. It should be possible to give a summary of how spacetime emerges.
These aren't hundreds of pages, but it does start with a concept of time. I'm not sure if that's what you're looking for.
If it starts with time, how can spacetime be emergent?

#### PAllen

The Big Bang created the 3 dimensions of space plus the dimension of time and all the particles..
Space can be bent. The maximum that it can bend is a bubble,
Before the big bang, there were space-time bubbles packed together in the cosmo.
The universe did not exist before the big bang.
If there are any space-time bubbles existing in our 3+1 dimensions they would be smaller than any particles.
Note, in the classical Big Bang theory, the whole manifold is 3+1 dimensions, with no emergence of any kind. The singularity is nothing but the fact geodesics of that manifold cannot have an affine parameter ranging from -∞ to ∞

#### jal

Note, in the classical Big Bang theory, the whole manifold is 3+1 dimensions, with no emergence of any kind. The singularity is nothing but the fact geodesics of that manifold cannot have an affine parameter ranging from -∞ to ∞
You raise contentious points.
emergence, singularity, and infinity

Do you have space-time in your "point of view"?

ps I'm only an amateur looking at what the experts are saying.

#### Haelfix

Difficult is ok as long as it isn't hundreds of pages. It should be possible to give a summary of how spacetime emerges.
If you don't like the TASI lectures I mentioned and the level and length they were presented at, its going to be a bit difficult. Are you familiar with the Ryu-Takayanagi formula, and some of the geometry through entanglement programs that are currently underway (Mark Van Raamsdonk et al eg something like:
)

So I don't know quite what to give you. Actual calculations, even in the simplest known examples (eg AdS3) are going to be lengthy, but the statements and the outline of the calculations likely can be made with considerably less effort (eg p22 in the above lecture or read the introduction to the original R-T paper).

#### king vitamin

Gold Member
Is there a relatively simple toy example of any physical theory (doesn't have to be quantum), which doesn't use spacetime in any way for its formulation?
It depends a bit on what you mean by not using spacetime in any way as a formulation. I think Haelfix's holographic examples are using the idea that a quantum mechanical model without gravity in $d$ spatial dimensions may describe a quantum gravity theory in $d+2$ spacetime dimensions. If you're asking for a "simple" model of this sort, I'm tempted to point you to the Sachdev-Ye-Kitaev model, partially because Kitaev's original lectures (which can be watched here and here) were entitled "A simple model of quantum holography." A good intro to this model can be read here, where Section 6 focuses on how this effectively $(0+1)$-dimensional quantum model of interacting fermions leads to some (not entirely understood) quantum gravity theory in $(1+1)$-dimensional space. This microscopic model still has some notion of time in it, but the idea is that the space and time variables of the bulk theory are in general nonlocally related to the time variable of the microscopic model. In this sense, the spacetime in the bulk theory is emergent.

I get the feeling Nima Arkani-Hamed has something more drastic in mind when he says spacetime is doomed. But I don't really understand what sort of theory he is thinking of.

#### martinbn

If you don't like the TASI lectures I mentioned and the level and length they were presented at, its going to be a bit difficult. Are you familiar with the Ryu-Takayanagi formula, and some of the geometry through entanglement programs that are currently underway (Mark Van Raamsdonk et al eg something like:
)

So I don't know quite what to give you. Actual calculations, even in the simplest known examples (eg AdS3) are going to be lengthy, but the statements and the outline of the calculations likely can be made with considerably less effort (eg p22 in the above lecture or read the introduction to the original R-T paper).
Ok, here is a specific question. In the lecture the rough statement of the correspondence is stated as

"The basic statement of AdS/CFT is that any conformal field theory in $d$-dimensional spacetime
is equivalent to a quantum theory of gravity in a family of spacetimes which are asymptotically
$AdS_d\times M$, where $M$ is some compact manifold."

I am puzzled already, how can spacetime be emergent if it is needed before one can even state the conjecture?

"Is spacetime emergent - and in which theories?"

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