What exactly is loop quantum gravity?

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Discussion Overview

The discussion centers on loop quantum gravity (LQG), exploring its properties, challenges in quantizing gravity, and the current state of research. Participants express varying levels of understanding and seek clarification on technical aspects without delving into mathematical details.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about LQG and requests a non-mathematical explanation, indicating a high school level of understanding.
  • Another participant explains that traditional methods of quantizing gravity fail, necessitating a fundamental change in approach, and outlines various approaches including LQG.
  • It is proposed that LQG introduces new variables that replace the spacetime metric, leading to a description of spacetime as emerging from spin networks rather than being fundamental.
  • Participants discuss the analogy of spin networks to a water surface, emphasizing that classical spacetime is an emergent property rather than a fundamental entity.
  • One participant suggests that the classical picture of spacetime becomes inconsistent near singularities, highlighting the need for a new mathematical model that remains valid in extreme conditions.
  • A later reply corrects a minor terminology issue regarding "nodes" versus "knots" in the context of spin networks.
  • Another participant inquires about the current status of LQG regarding its quantization and whether it has a semi-classical description.
  • Responses indicate that while LQG is fully quantized in certain respects, there are ongoing efforts to establish a semi-classical limit and address various technical challenges.
  • Specific challenges mentioned include the construction of coherent states, absence of infrared divergence, and the equivalence of different quantization approaches.

Areas of Agreement / Disagreement

Participants express differing views on the completeness of LQG and its quantization status. While some assert that LQG is fully quantized, others highlight that significant work remains to achieve a semi-classical description and address various technical issues.

Contextual Notes

Participants acknowledge the complexity of LQG and the need for further research to clarify its implications, particularly in extreme conditions like black holes and the early universe. There are unresolved questions regarding the nature of the cosmological constant and the relationship between different quantization methods.

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I don't quite understand the properties of loop quantum gravity. I have searched around and have not come up with anything very helpful. I'm pretty good when it comes to understanding quantum mechanics and string theory, but please, NO MATH! I'm only in high school!

thanks
 
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It's difficult w/o math.

The problem with quantum gravity is that naive mechanisms to quantize gravity (which have been applied successfully to other fields) fail for gravity. That means that something fundamental has to be changed for quantum gravity.

There are different approaches to solve these problems, e.g.
a) string theory
b) asymptotic safety
c) loop quantum gravity (LQG)

I don't want to comment on a) and b) here.

Essentially LQG does the following: it introduces new variables which replace the (in GR) well-known metric that describes spacetime + curvature. This is pure math, so I don't want to go into details here, but what happens is that these new variables are rather close to fields that we know from gauge theory like QED and QCD. Indeed in a certain sense gravity looks rather similar to QCD, but there is one additional property of gravity that allows one to apply a second mathematical trick which essentially replaces the fundamental fields with something like "fluxes through surfaces" or "fluxes along circles". These surfaces and circles are embedded into spacetime.

The next step is again rather technical and it becomes possible due to so-called diffeomorphism invariance: one can get rid of the the embedding of circles and surfaces into spacetime. Instead one replaces these entities with a so-called spin network, i.e. a graph with nodes and links between nodes where each link and each node carries some numbers which represent abstract entities from which certain properies of spacetime can be reconstructed. You can think about spacetime as made of cells (I will soon tell you that you can't :-); each cell has a certain volume carried by a node; each cell has certain surfaces and the link between different nodes (sitting inside these cells) carry the areas of the surfcaes.

The problem with this picture is that one might think about these cells as sitting in spacetime - but this is fundamentally wrong: this picture is only due to the construction, but basically there is no spacetime anymore; all there is are nodes and links (and certain numbers attributed to nodes and links). Spacetime is no longer fundamental but becomes an entity emerging from the more fundamental graphs with their nodes and links. The graphs are called spin networks b/c the numbers they are carrying have properties well-known from spins. But this is a mathematical property only, it does not means that there are real spinning objects.

Compare this emerging spacetime to a water surface of a lake. We know that it consists of atoms, and as soon as we get this picture it is clear that there is no water between the atoms; the surface is only an emerging phenomenon, the true fundamental objects are the atoms. In the same sense the spin networks are the fundametal entities from which spacetime, surfaces etc. and their properties like volume, area, curvature etc. can be constructed. Dynamics of spacetime (which was curvature, gravitational waves etc. in GR) is replaced by dynamics of spin networks: within a given graph new nodes with new links can appear (there are mathematical rules, but I don't want to go into detail here).

The last puzzle I have for you is the fact that such a spin network is not a mechanical object which "is" spacetime. Instead quantized spacetime is a superposition of (infinitly many) spin networks. This is well-known in quantum mechanics; there is no reason why an atom should be in a certain state; we can achieve that via preparation or measurement, but in principle a single atom can be in an arbitrary complex quantum state which is a superposition of "an atom sitting here, an atom moving in a certain direction over there, an atom moving in this or that direction, ...".

So classical spacetime is recovered by two averaging process: first there seems to be a regime were this superposition of spin networks is peaked around a single classical spacetime, i.e. were one networks dominates the superposition of infinitly many spin networks; second from this single spin network one can reconstruct spacetime in the same sense as one can reconstruct the water surface from the individual atoms. But there may be different regimes (e.g. in black holes or closed to the big bang) where is classical picture and this averaging does no longer work. It may be that in these regimes all there is are spin networks w/o any classical property like smooth spacetime, areas, volume etc. It's like looking at a single atom: there is no water surface anymore.

Eventually this is why one started with this stuff: the classical picture of spacetime seems to become inconsistent when one tries to quantize it, i.e. when one defines these superpositins etc. These inconsistencies do not bother us as long as we talk about spacetime here, in the solar system etc. But they become a pain in the a... when we talk about spacetime near a singularity like a black hole or like the big bang. In order to understand these new non-classical regimes of spacetime a fundamentally new picture is required. This is what LQG (and other approaches) are aiming for: construct a new mathematical model from which well-known classical spacetime (like in GR) can be reconstrcuted, but which does not break down in certain regimes but remains well-defined and consistent.

He must so to speak throw away the ladder, after he has climbed up on it - Ludwig Wittgenstein
 
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This is a really good introductory summary. I suggest proposing it for a BTSM forum FAQ. The only minor "typo" is that the usual term is "node" where you have said "knot".
(The two words come from the same etymological root and originally meant the same, but in normal technical language one says that a spin network consists of nodes and links.)
Otherwise this is great. Clearly and concisely giving just the essentials.
 
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Thanks a lot - and sorry for the "knots", of course it must read "node"!

If you like we can discuss and improve the text, so instead of writing new posts I can change the original text (new color).
 
tom.stoer said:
... (new color).

I would suggest you not bother with new color. It's a minor typo of no consequence. If the mentors like the idea of FAQ for BTSM they will (I expect) do a final edit and move the text to wherever it needs to be.

As far as substantive changes, I can't think of anything to add or alter! We are lucky to have something both careful, relaxed, and readable like this is.

Say! maybe I will move the text to SA forum so people can discuss quietly.
 
Nice introduction but what I really want to know is how close LQG is to becoming fully quantized? Does it even have a semi-classical description yet?
 
Aren't these two completely different questions?

Of course LQG is fully quantized ... Hilbert space, operator algebra, inner product, path integral ... what is missing?

Yes, there are attempts for semiclassical / smooth / large-j limit and construction of coherent states; there are results regarding the graviton propagator; ...; but this is (afaik) work in progress and (at least for me) it seems to be too early to present physical results.
 
Aha, yes they are different questions. That was my fault. Thanks for the response. What else is left for LQG to do?
 
semiclassical limit for reasonable smooth spacetimes like BHs, FRW, ...
n-point functions for gravitons (on top of these spacetimes)
absence of infrared divergence
renormalization group
equivalence of canonical and covariant / spin foam quantization
matter degrees of freedom (gauge fields)
nature of cosmological constant (and Immirzi parameter)
phenomenology, experimental tests (*)

Everything but (*) is currently under investigation and I think for all topics the different research groups make good progress. There seems to be no major obstacle, no road block.

For (*) only very indirect results are to be expected, but I think LQG shares this with all other QG approaches, unfortunately.
 
  • #10
So they're not even close.
 
  • #11
close to what?
 
  • #12
To having a full and complete description of LQG.
 
  • #13
tom.stoer said:
semiclassical limit for reasonable smooth spacetimes like BHs, FRW, ...
n-point functions for gravitons (on top of these spacetimes)
absence of infrared divergence
renormalization group
equivalence of canonical and covariant / spin foam quantization
matter degrees of freedom (gauge fields)
nature of cosmological constant (and Immirzi parameter)
phenomenology, experimental tests (*)

Everything but (*) is currently under investigation and I think for all topics the different research groups make good progress. There seems to be no major obstacle, no road block.

For (*) only very indirect results are to be expected, but I think LQG shares this with all other QG approaches, unfortunately.


Also:

consistency of the infinite refinement limit (discussed eg. in http://arxiv.org/abs/1010.5437 and http://arxiv.org/abs/1010.5437 )
 
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  • #14
Kevin_Axion said:
To having a full and complete description of LQG.

They could be close. String theory says that theories without gravity have gravity, so if LQG doesn't have gravity it could have gravity. (More seriously, some lattice gauge theories have a dual formulation as spin foams, and string theory famously says some gauge theories contain gravity).

However, for LQG as pure gravity, they are far. Eg. even the same authors can't decide how to interpret the semiclassical limit. Contrast http://arxiv.org/abs/1004.4550 and http://arxiv.org/abs/1105.0216v5 - these are not just any authors, but people who established the state of the art on the interpretation of the semiclassical limit http://arxiv.org/abs/0905.4082
 
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  • #15
Yes but doesn't AdS/CFT require that the gauge theory be an N = 4 supersymmetric Yang-Mills theory i.e LQG isn't supersymmetric.
 
  • #16
Do 'they' have a full and complete description of QCD?

I mean they have a complete and consistent theory at hand, though much work has to be done to complete the details, to consolidate the proofs, to work out new tools. They address their open issues - that's what science is.

In QCD color confinement has opposed a theoretical justification, but hints and indications are available; nevertheless we believe in QCD as the correct theory of strong interactions.

The main issue is a lack of (*) b/c afaik no prediction (not post-diction) of LQG is available that could falsify LQG or decide between LQG and other QG approaches.
 
  • #17
Kevin_Axion said:
Yes but doesn't AdS/CFT require that the gauge theory be an N = 4 supersymmetric Yang-Mills theory i.e LQG isn't supersymmetric.
In the string / m-theory context this is a rather striking result, but LQG uses a completely different quantization procedure and therefore you can't conclude that AdS/CFT results must apply to LQG; it could very well be that the asymptotic safety program tells us that even standard but non-perturbative quantization of GR is UV complete and fully consistent; it could even be that in a couple of years we have more than obe fully consistent theory of QG at hand.
 
  • #18
Kevin_Axion said:
Yes but doesn't AdS/CFT require that the gauge theory be an N = 4 supersymmetric Yang-Mills theory i.e LQG isn't supersymmetric.

AdS/CFT is thought to be braoder than that. However, that is the most celebrated case. Supersymmetric spin foams are studied in http://arxiv.org/abs/0710.3540 and http://arxiv.org/abs/1004.0672 .
 
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  • #19
tom.stoer said:
In the string / m-theory context this is a rather striking result, but LQG uses a completely different quantization procedure and therefore you can't conclude that AdS/CFT results must apply to LQG; it could very well be that the asymptotic safety program tells us that even standard but non-perturbative quantization of GR is UV complete and fully consistent; it could even be that in a couple of years we have more than obe fully consistent theory of QG at hand.

Yes, but how about the duality between spin foams and lattice gauge theory? I don't know the exact restrictions for such a duality, but I know there's some correspondence.

Also, LQG is capable of quantizing 3D lattice BF theory (in some cases with additional stuff) , which reminds me of the 3D Chern-Simons (with supersymmetry and matter) ABJM case of AdS/CFT.
 
  • #20
atyy said:
AdS/CFT is thought to be braoder than that. However, that is the most celebrated case. Supersymmetric spin foams are studied in http://arxiv.org/abs/0710.3540 and http://arxiv.org/abs/1004.0672 .

That doesn't seem natural in terms of LQG. LQG is generally celebrated for not containing SUSY and other new parameters i.e extra-dimensions. So what is this Asymptotic Safety you and tom.stoer are talking about, has it had any reasonable progress?
 
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  • #21
Kevin_Axion said:
That doesn't seem natural in terms of LQG. LQG is generally celebrated for not containing SUSY and other new parameters i.e extra-dimensions. So what is this Asymptotic Safety you and tom.stoer are talking about, has it had any reasonable progress?

It could be natural - eg. http://arxiv.org/abs/1103.6264 mentions emergent gravity.

I don't know about Asymptotic Safety. The state of the art is, I believe, still http://arxiv.org/abs/0805.2909 and the beautiful results of CDT. It is of course unclear what exactly CDT is connected to, except for gut feeling. I think the recent directions that are interesting are http://arxiv.org/abs/1012.3081 and http://arxiv.org/abs/1012.4280
 
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  • #22
I think we are far away from understanding the relation between AdS/CFT / strings and LQG / spin networks / foams. Strings are both broader (matter degrees of freedom, ...) and narrower (gravity requires strings / swampland - no b/c LQG comes w/o strings but with gravity).

Thiemann published some new papers regarding "SUGRA-LQG"; I just started reading his n-dim LQG papers but had no time to check the SUGRA stuff.

All what we can say is that there seems to be a miraculous relation between classical gravity + QFT, LQG and strings. All these theories predict a fundametal relation regarding black holes, but none of them is complete (classical gravity + QFT is inconsistent, LQG cannot fix the Immirz parameter, strings only talk about BPS BHs).

The main problem for all these theories is that they lack experimental input and falsifiability (in practice, not in principle). We live in an age confronted with a paradigm shift in theoretical physics.
 
  • #23
It seems that both string theory and LQG will turn into theory-producing machineries (instead of theories). There seems to be no reason why not
- construct LQG-like theories in n dimensions (n>2 arbitrary)
- incorporate SUSY / SUGRA / gauge fields
- use higher spin / SU(n) groups
- use qantum deformation

The main difference is that all these theory-producing machines in string theory (they call it 'vacua') are related via dualities and relations like that, whereas in LQG you would do "ordinary construction of theories" w/o any relation between them.
 
  • #24
I see, thanks for the input. I really like LQG for it's simple geometrical solution but dislike it because of the Immirizi parameter (kind of seems like cheating). I also like string theory for it's success but I believe it's tackling way too many problems at once, I mean we don't even know the full extent of physics and String Theory doesn't really go far beyond the SM to be a TOE let alone a QG theory. How does string theory treat space-time anyways? Does it just add new dualities and degrees of freedom to construct a theory of QG?
 
  • #25
tom.stoer said:
The main problem for all these theories is that they lack experimental input and falsifiability (in practice, not in principle). We live in an age confronted with a paradigm shift in theoretical physics.

Oh, I hope not. That would be the end of physics. I think there's plenty of theory outside of quantum gravity, and also LQG already applies to condensed matter, and there is hope that strings will too. After all the renormalization group came via high energy, was truly understood in condensed matter, and then fed back into HEP for no longer being worried about sweeping infinities under the rug, and ideas of asymptotic safety.
 
  • #26
OK; I'll change my wording:

The main problem for all these theories is that they lack experimental input and falsifiability (in practice, not in principle). We live in an age confronted with a paradigm shift in (certain areas of) theoretical physics.
 
  • #27
I didn't understand a thing...thanks for trying!
 
  • #28
We can't leave you unsatisfied! What didn't you understand?
 
  • #29
the whole thing...im no physicist haha just an average high school student who happens to enjoy reading about physics!
 
  • #30
Well, do you firstly know concepts in Quantum Mechanics/Quantum Field Theory or General Relativity? These are essential to understanding Quantum Gravity i.e loop quantum gravity or string theory
 

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