# Emergent Gravity / Spacetime

1. Apr 8, 2010

### C_Dawg

I've recently heard for the first time about the topics of Emergent Gravity and Emergent Spacetime.

But I cannot find any resource that explains these ideas in a way that lay people can understand.

If you know of one, please post the link, or write an explanation in simple terms.
I've read a lot about Einstein's work, so I know the broad principles of SR and GR.

Thanks!

2. Apr 8, 2010

### ordered_chaos

Yah, I'm highly interested as well. It'd be nice to have some laymen's explanation while I'm on journey of mastering the math behind it.

3. Apr 8, 2010

### tom.stoer

There are a couple of rather different mechanims which could be summarized as emergent spacetime. The basic idea is the following: one starts with a theory w/o any spacetime structure and calculates (e.g.) a low-energy limit. Then one observes that spacetime and its symmetry emerges from the fundamental symmetry.

You can compare this to (weakly interacting) quasi particles in solid state physics. The quasi particles like phonons, excitons, magnons, ..., Cooper pairs, ... are not fundamental degrees of freedom but are discovered once one eliminates, neglects, "integrates out", ... some fundamental degrees of freedom. The effective theory is valid in some regime, e.g. for some phenomena within a specific energy range; beyond that regime the theory breaks down, e.g. due to the fact that the quasi particles are no longer stable.

In quantum gravity there are a couple of ideas that may be interesting:
1) AdS/CFT or more generally speaking gauge/gravity duality starts with a conformal gauge theory on a fixed spacetime manifold = w/o dynamical spacetime degrees of fredom. Then the theory with spacetime is discovered as a dual description.
2) Truncation of discrete matrix models may lead to something like smooth spacetime structures
3) in Loop Quantum Gravity (LQG) one starts with the quantization of a spacetime manifold end ends up with a discrete spin network from which smooth spacetime should emerge in an appropriate low-energy limit. If one forgets about the history = the construction of the theory and and instead starts directly from a spin network (or a general class of spin foam models) then spacetime is again an emergent phenomenon.

I think there are more ideas on the market.

Hope this helps as a starting point.

4. Apr 8, 2010

### atyy

Yes, why can one forget about the history? Did they mean to construct a non-emergent theory, and by mistake construct an emergent one?

5. Apr 8, 2010

### tom.stoer

It's rather simple, but nevertheless I would like to discuss some details in order to discuss how quantization works.

The quantization of any classical theory is unfortunately not a well-posed problem. You need intuition, gut feeling etc. to make the right decisions. Why do you take the free-particle Hamiltonian p²/2m, replace p with a differential operator and apply this new H as a differential operator to wave functions? Simply because it works! You cannot dervive the quantization rules, you can guess these rules, apply them and check if the results fit to experimental findings (we know it works for the well-known rules of QM).

Constructing a quantum theory based on a classical theory is like constructing a building from an architectural drawing. You always need additional skills to do that job because the drawing is not complete - it is only a drawing, not the building itself. In the same sense the classical theory is not complete and you need additional guesswork to quantize it. We are not aware of this fact as this guesswork was done a few decades ago and now we find it as "fixed ethernal rules" in QM or QFT textbooks. But these rules are neither fixed nor ethernal! Especially in the contect of quantum gravity we currently see a process of guessing new rules which deviate (must deviate!) from the QFT rules. We know that in a certain sense the ordinary QFT rules a plainly wrong when applied to gravity.

But this is "history". The reason is clear: our all-days experience is based on classical entities(stones, chairs, ..., the earth, the moon - and space and time, of course). So mankind is not able to put forward a quantum theory w/o any roots in classical physics. But because it's history one must not take this history too seriously. Using classical spacetime as a guidline to construct a theory of quantum gravity, throw away classical spacetime and eventually reconstruct it from full quantum gravity is a non-trivial consistency check. That's the reason I would say that even Loop Quantum Gravity which is rooted in smooth spacetime is a theory where eventually spacetime is emergent. Btw.: up to now there are hints but no proof that classical 4D spacetime is indeed the correct low-energy limit of LQG!

6. Apr 8, 2010

### atyy

So LQG may be the right theory, even though it was motivated the wrong way? (Yes, nothing wrong with that, but part of the history I would like to forget is "background independence" and "Everything is relational").

7. Apr 8, 2010

8. Apr 8, 2010

### tom.stoer

Of course LQG may be the right theory - and strictky speaking all quantum (field) theories are motivated the wrong way:-)

Why?

Most physicists agree that background independence is key to understand quantum gravity.

9. Apr 8, 2010

### atyy

Well, GR is background independent in the sense that the metric is dynamic. Any theory of quantum gravity must produce have some classical limit whose solutions are those of general relativity. However, GR has elements that are not background independent in the larger sense of the term, for example, the signature. Personally, I would like a theory in which the signature can change, which would argue in favor of enlarging background independence. However, it also shows that background independence is ill-defined, and a successful theory of gravity can have elements of the metric which are in fact fixed. AdS/CFT and GFT both have fixed metrics - just not fixed spacetime metrics. So the diffeomorphism symmetry of spacetime is emergent (well, yet to be proven, but it is hoped).

10. Apr 8, 2010

### tom.stoer

So it's not that you want to get rid of background independence but that you want to enlarge it.

You are right, there are aspects like the signature, boundary conditions and topology that are fixed. If you eliminate spacetime from the setup of your theory (like you do it in LQG) you automatically get rid of some of these fixed aspects (they may still be hidden in the theory).

In LQG there is no obvious meaning of "dimension". Nevertheless there is still an SU(2) symmetry structure (even if local symmetries have been fixed). This "residual" SU(2) structure is related to the fact that spacetime is four-dimensional. So the dimension is somehow fixed (or at least it shows up in certain aspects of the symmetry structure; with more than 3 space dimensions Spin(3) would have to be enlarged accordingly).

But that is an interesting point, as you know enlarge the meaning of "background" in the direction of "overall setup". In this sense background independence would mean to talk about all possible symmetry structures, i.e. about all SU, SO, Sp, E, ... symmetries ... but why only about Lie groups ...

11. Apr 8, 2010

### Finbar

I think that the idea of emergent gravity makes more sense if you understand a very important historical point. That is that general relativity as originally conceived by Einstein was an attempt to rid us of the concepts of space and time. The only thing that matters are the relations betweens physical events. The geometrical interpretation of general relativity was more of an after thought. In a sense classical general relativity's geometrical form is a failure of it being truly relative. However it is apparent that this failure is only 'skin deep' since hidden in the equations of general relativity are hints that space-time is in fact only some large scale approximation.

LQG is an attempt to create a truly relativistic theory where we rid ourselves completely of the notions of space and time. Of coarse the main problem of this is that once we have gotten rid of space-time it is very hard to find the 'classical limit' of LQG that reintroduces these notions.

I'll summarise

1) A truly "generally relativistic", "relational", "background independent" theory seems to be philosophically pleasing to many bright physicists.

2) To construct such a theory involves removing notions of space and time from our understanding of reality.

3 )This was Einstein's original motivation

4) classical GR is expressed in a language that still refers to "space-time" even though it is based on the principle that space-time are not absolute.

5) As such the principle that space-time is not fundamental is in
embedded deeply into the Einstein equations which can be derived from a thermodynamical equation of state. This implies that there is some microstructure that underlies GR.

12. Apr 8, 2010

### LukeD

Even if we get rid of external geometry, there is still intrinsic geometry in the mathematical description of the relations between objects... We can describe this as a manifold (or at least as some properties that a manifold would have to satisfy)

We can then embed this manifold in R^n for some large enough n with a bunch of "charts".

The geometric pictures of GR are really just like that. All of the external geometry is gone, but we've replaced it with a new, completely arbitrary external geometry that lets us draw it on paper and come up with a coordinate system. This new external geometry doesn't matter though. It's just for visualization purposes.

So I'm not really sure what your problem with geometry in GR is... there's no fake geometry being put in except in the coordinate systems (unless you are referring to us putting in the metric of flat space by hand)

My problem with GR is that it's wrong. We write the curvature as being related to the stress-energy tensor, but the stress energy tensor is a big quantum mechanical object. Therefore, our curvature is a big quantum mechanical object, not just a number. Big quantum mechanical objects tend to mix their properties. A big quantum mechanical object of space and time curvature could certainly get all mixed up. But I'd think we still have to put in some parts, like the number of space and time dimensions and the signature of flat space. I know you'd probably think those are big things to put in, but I don't see any reason to believe that quantum mechanics needs to provide the explanation for those (maybe it does, but I don't see it from here)

Last edited: Apr 8, 2010
13. Apr 8, 2010

### atyy

BTW, do you think background independence (in the broader "motivational" sense) is tied to diffeomorphism invariance? For example, what do you think of Thiemann's latest thing where the diff invariance is only on shell (I didn't understand how he got that part, but let's say he's right, would that be in line with background independence or not)?

14. Apr 9, 2010

### Fra

This broader sense of background independence is a key question but it's tricky. I've expressed my opinon on this before but this is how I view it, and characterize the key problems.

If we first look at relativity, both SR and GR, IMO the conceptually sound, clean and understandable reason for the invariance is really simple. It's that idea that the laws of physics must be the same for all observers. In SR we required that the laws of physics must be the same to all intertial observers. To realize that we characterize the lorentz and poincare symmetries which represent this special class of observers, and find the transformation laws that allows us to find covariance of the laws.

In GR, the story is the same except that we extend the class of observers to so that the laws of physics must be the same also to any non-interial observers. Basically to any observer with arbitrary motion.

Still GR only talks about a small subset of observers. Noone would think that diffeomorphisms are enough to generate all traits of an observer. The internal structures is ignored, and conceptually there is no reason to.

I would say the deepest form of rationale common to this, is the idea that the laws of physics must be the same to all observers, and thus the challange, given the obvious that each observer WILL see different things depending on their perspective, is to characterize the relations between these observers, so we can find the transformations laws that restored observer independent physical law.

But

SR and GR are still realist theories, the very transformations and the class of observers are views in a realist sense - in particular they are not subject to measurement or scientific inquire from the physics point of view.

This is why when we seek a proper _measurement theory_ (more proper than QM) that respects the mentioned ideal, things get quite complicated because then it should be formulated to a larger extent in observables only. Otherwise it's still just a "semiclassical" measurement theory, that refers to an system, but with a "classical observer".

The real difficulty is this, that we seem to seek an "observer independent" measurement theory.

To me, the scientific rationale for focusing on observable things only, is more important than a realist type observer independence because a natural non-realist interpretation of the principle that the laws of physics are the same for all observers, is instead an kind of _democracy of observers_ where no observer is more wrong or right than another one, and that in fact the local laws in a community is a result of a democratic process.

If I may allow to use the word "inference" as the generalistation of "measuremnt" to include not only measuring an observable, but also to "measure" symmetries and laws, then the fact that two observers infere inconsistenct laws, need not be an actual "inconsistency" in the sense people usually thing, it might rather be an incentive(force) for each participant to renegotiate, and that objectivity is instead possibly a result of evolution.

This way of seeing it, has IMO a conceptually clean potential to (although in an evolutionary sense rather than realist sense) incorporate the "ultimate" observer indepdendence, including ALL interactions.

The problem of just enlarging the class of observers, and maintain the realist perspective is that no inside observer can RELATE to (encode and process) this information. This is why I think the only way to combined the scientific ideal of a "measurement theory" with the wish that the laws of physics are seen the same to all observers, is to put it in a context of evolution.

Every other attempt at sidestepping this point has IMO lead to terrible realist or weird types of models, with all kinds of other prolbem. The typical realisation of picturing a large class of observers, is that we end up with an unmeasurable landscape, or alternatively unmanagable "choice"-problems. The use of mathematical of "birds view" observers is als a typical trait of these ways of reasonings. By itself, such external observers, are also in violation with the intrinsic ideal also somehow beeing part of GR. But we do not just look for "intrinsic geometry", we look for something much better, we look for an intrinisic measurement theory.

I have a feeling I am in clear minority here.

/Fredrik

15. Apr 9, 2010

### tom.stoer

excellent summary ...

except for the fact that this is afaik not a proven fact but the start of a research program

16. Apr 9, 2010

### tom.stoer

I am not sure. As soon as you talk about diff. inv. you must have a manifold on which it is implemented. In LQG - strictlky speaking - diff. inv. is completely modded out as the spin networks are equivalence classes of diffeos. There is not generator of infinitesimal diffeos!

The fact that the constraint algebra closes only on-shell is known since years and has been criticized e.g. by Nicolai et al.: http://arxiv.org/abs/hep-th/0501114. The problem is that with off-shell non-closure the algebra may have anomalies in the unphysical sector of the Hilbert space. Strictly speaking this need not be a problem as long as you can protect the physical sector from any such anomalous effect. But many physicists don't believe in (gauge or local) symmetry structures if they are anomalous. Attention: the meaning of on-shell in LQG is rather different from the standard meaning in QFT. In LQG on-shell means that you eliminate "gauge or diffeo. copies" due to a constraint C|phys> = 0, whereas in QFT on-shell means that for any state (p²-m²)|phys> = 0 is fulfilled. In QFT we know for sure that off-shell states do propagate whereas in LQG the off-shell sector must decouple completely. The difference is that in LQG the algebra in question is a local or gauge algebra which must be implemented w/o any anomalies whereas in QFT the Lorentz-algebra is a global algebra which is not so crucial; you can always constrain your system by using Lorentz-covariant states as in-and out-states.

To summarize:
if diff. inv. is implemented consistently then LQG is (in this restricted sense) BI as the fundamental objects on which diffeos may act are completely eliminated from the theory; (they simply do no longer exist);
if off-shell closure is required but anomalous and therefore diff. inv.is not implemented consistenly then LQG is not only not BI (in this restricted sense) but simply inconsistent.

Btw.: on-shell closure is studied in SUGRA theories as afaik the proof of the closure of the SUGRA algebra requires the equations of motions to be used; therefore SUGRA may have similar problems. Afaik the approach to show finiteness of SUGRA theories relies on (a larger class of) on-shell symmetries; finiteness is required only for physical amplitudes whereas off-shell the amplitudes may become infinite as long as this does not spoil on-shell properties. In SUGRA on-shell means something similar as in LQG as SYS becomes a local symmetry.

17. Apr 9, 2010

### tom.stoer

I would not refer to any embedding in Rn as this is mathematically not necessary.

Would you agree to call it "incomplete" instead of "wrong"? Is Newtonian phyiscs wrong?

I agree that your call for QG is correct. And I agree that "emergent spacetime" should be a by-product of QG.

At least we must in "something", but I am not so sure what this something is. The signature of the metric is related to causality, so perhaps it's causality that we have to put in; in CDT they found that once causality is used the theory becomes meaningfull and reasonable whereas in the Euclidean domain it's nonsense. I am not so sure about the dimension of spacetime. In LQG spin networks the only residual structure coming from the dimension is the symmetry structure SU(2) of the spin networks; but of cause one could try to construct an LQG-like theory from any SU(N). And as the emergence of spacetime has not been proved, neither has the dimension been derived.

18. Apr 9, 2010

### Naty1

search this forum for emergent spacetime...emergent gravity.......read the threads for references.....the synopsis and introductions to many papers are good non mathematical overviews.

also try terms like causal dynamic triangulation and Verlinde an author of a paper regarding entropic sources.....

Here's one thread discussing entropy and includes some good concepts and possible theories...https://www.physicsforums.com/showthread.php?t=378684&highlight=verlinde