If LQG now satisfactory, how to add matter?

In summary: While a direct coupling of gravity and matter on the spin foam has so far proved unsuccessful, it is interesting to note that the coupling is in many ways a natural consequence of the structure of the theory."This completes the definition of the model.So at first sight, and this may be correct as well, the theory is a theory of two-complexes, so if matter is to be added to the picture it must carried by the two complexes.
  • #1
marcus
Science Advisor
Gold Member
Dearly Missed
24,775
792
Currently the two definitive papers are 1004.1780 and 1010.1939, with several others applying spinfoams to cosmology e.g. 1003.3483.

LQG is about where one could have predicted back in Fall 2008, with the merger of the canonical, covariant, and cosmological versions. I think in fact one or more people here at PF did observe that trend and predict that. It unifies the theory and brings it closer to testability, because early-universe cosmology is a potential venue for testing.

The present form of LQG is at the intersection of lines of work by Ooguri, Atiyah, Feynman, Regge, Penrose. The October paper mentions that it follows from 3 separate approaches:
1. Canonical quantization of the conventional phase space of General Relativity
2. Polyhedral quantum geometry
3. Covariant lattice quantization
For details, see 1010.1939

Thus there are signs that the present form of LQG is a satisfactory theory of quantum geometry/gravity without matter. Matter still has to be introduced.
So the question concerns the logical next step. Assuming that what we see will turn out to be satisfactory, how can matter be laid on to the spacetime foundation it provides?

At first sight, in the one-page formulation given in the October paper, you see a list of FEYNMAN RULES GOVERNING TWO-COMPLEXES.
There is a half-page section on page 1 of 1010.1939 called "Feynman Rules" which at the end says "This completes the definition of the model."

The 4 Feynman rules determine how to calculate transition amplitudes, for the two-complexes. That defines LQG.

So at first sight, and this may be correct as well, the theory is a theory of two-complexes, so if matter is to be added to the picture it must carried by the two complexes.

That's one possibility. I'd like to hear any ideas about how this could be done, or about other schemes for including matter.
 
Last edited:
Physics news on Phys.org
  • #2
LQG is not satisfactory. The physical innner product is probably divergent (in addition to the IR divergence). My own guess is that it needs GFT renormalization. And I would prefer if gravity and matter should both emerge together from a GFT.
 
  • #3
atyy said:
The physical innner product is probably divergent
Can you post a reference?

atyy said:
And I would prefer if gravity and matter should both emerge together from a GFT.
Emergence of matter - yes; but from GFT? How?
 
  • #4
As an outsider and total ignoramus about LQG, the statement that LQG is OK except for the need for coupling to matter seems a little implausible. Maybe I'm just an idiot, but to me, this would seem to imply that LQG was currently able to reproduce any result that you could get in the classical limit from the vacuum field equations of GR, and to examine the quantum effects when the classical limit doesn't apply. Is this really true? Do the LQG folks have a Schwarzschild metric with quantum corrections? Do they have plane gravitational waves with appropriate modes of polarization?
 
  • #5
tom.stoer said:
Can you post a reference?

http://arxiv.org/abs/1010.1939 "The second source of divergences is given by the limit (26)."
http://arxiv.org/abs/1010.5437 "We have observed that under certain general conditions, if this limit exist ..."

In a different but related context (GFT, not spinfoam LQG), http://arxiv.org/abs/gr-qc/0607032 "That such a sum can be defined constructively thanks to the simplicial and QFT setting is already quite an achievement, and to ask for it to be finite would be really too much!"


tom.stoer said:
Emergence of matter - yes; but from GFT? How?

I don't know, of course, if I did ... But I am hoping for further developments following
http://arxiv.org/abs/hep-th/0512113
http://arxiv.org/abs/0903.3475
http://arxiv.org/abs/1004.0672

Some background as to whether gravity and matter should be unified is given in the last reference:
"Several approaches to coupling matter within spin foams were embarked upon [2–7]. The most tractable and indeed most successful of these procedures embedded the Feynman diagrams of the field theory into the spin foam. Remarkably, summing over the gravitational degrees of freedom, the effective matter amplitude was seen to arise as the Feynman diagram of a non-commutative field theory [8]. To add to this position, it was shown that an explicit 2nd quantised theory of this gravity matter theory could be provided by group field theory, while later the non-commutative field theory was seen to arise as a phase around a classical solution of a related group field theory [9]. Of course, one may approach the subject with the view that one should discretise the field directly on the spin foam, since in the continuum theory, we expect that the field has a non-trivial energy-momentum tensor, and should affect the state sum globally. This method has yielded to a succinct initial quantisation for Yang-Mills and fermionic theories [4–6], but due to the non-topological nature of the resulting amplitudes, further calculations proved unwieldy. Now, it was not our intention that this work would or should settle this debate, but we find that this theory is more in line with the arguments of the former way."
 
Last edited:
  • #6
bcrowell said:
the statement that LQG is OK except for the need for coupling to matter ...

I am not making that statement. The author of the papers, which provide a kind of current status report, does not. You should look at the two papers, which have carefully qualified statements with a lot of references. I would say there are signs that the current form might be satisfactory----a kind of final version of LQG.

That does not yet mean that it is RIGHT. (One still has to derive predictions, and test.)
But if we are seeing something like a finished version of the theory, then a natural question to ask is how to add matter.

So this is a kind of speculative experiment. If the present form were satisfactory, how would matter be added?

I don't immediately see how,and I would like to get people's ideas of how it could go.
 
  • #7
bcrowell said:
As an outsider and total ignoramus about LQG, the statement that LQG is OK except for the need for coupling to matter seems a little implausible. Maybe I'm just an idiot, but to me, this would seem to imply that LQG was currently able to reproduce any result that you could get in the classical limit from the vacuum field equations of GR, and to examine the quantum effects when the classical limit doesn't apply. Is this really true? Do the LQG folks have a Schwarzschild metric with quantum corrections? Do they have plane gravitational waves with appropriate modes of polarization?

None of this has been achieved. The latest is summarized in http://arxiv.org/abs/1004.4550 . This is not sufficient, because eg. DT started from a similar point, but didn't produce anything sensible until it became CDT. Also, in CDT, although one starts with the Regge action, a continuum limit is supposed to be taken ultimately. Whereas in LQG, the Regge action is the classical limit, but that would seem to imply classical spacetime is discrete? Is another limit missing? Would that limit commute with the classical limit? Or will matching the free parameter in LQG make the discretization sufficiently fine?

The free parameter is discussed http://arxiv.org/abs/1010.1939 "Let's call LPl the unit of length in which all the equations above hold. LPl is a fundamental parameter of the theory, setting the scale at which the theory is defined, namely the scale of the quantum granularity of space"
 
Last edited:
  • #8
tom.stoer said:
Emergence of matter - yes; but from GFT? How?

I'd be interested to hear about that too. The reference Atyy gave, with the quote, was
http://arxiv.org/abs/1004.0672
The particle interpretation of N = 1 supersymmetric spin foams
V. Baccetti, E. R. Livine, J. P. Ryan
(Submitted on 5 Apr 2010)
"We show that N = 1 supersymmetric BF theory in 3d leads to a supersymmetric spin foam amplitude via a lattice discretisation. Furthermore, by analysing the supersymmetric quantum amplitudes, we show that they can be re-interpreted as 3d gravity coupled to embedded fermionic Feynman diagrams."

Here's what was quoted in Atyy's post:

atyy said:
...
Some background as to whether gravity and matter should be unified is given in the last reference:
"Several approaches to coupling matter within spin foams were embarked upon [2–7]. The most tractable and indeed most successful of these procedures embedded the Feynman diagrams of the field theory into the spin foam. Remarkably, summing over the gravitational degrees of freedom, the effective matter amplitude was seen to arise as the Feynman diagram of a non-commutative field theory [8]. To add to this position, it was shown that an explicit 2nd quantised theory of this gravity matter theory could be provided by group field theory, while later the non-commutative field theory was seen to arise as a phase around a classical solution of a related group field theory [9]. Of course, one may approach the subject with the view that one should discretise the field directly on the spin foam, since in the continuum theory, we expect that the field has a non-trivial energy-momentum tensor, and should affect the state sum globally. This method has yielded to a succinct initial quantisation for Yang-Mills and fermionic theories [4–6], but due to the non-topological nature of the resulting amplitudes, further calculations proved unwieldy. Now, it was not our intention that this work would or should settle this debate, but we find that this theory is more in line with the arguments of the former way."

It isn't clear to me, and we are having company so I won't have time soon to try to figure it out. Would be grateful for any hints as to how this might work.
 
Last edited:
  • #9
Should matter emerge from the mismatch of tetrahedra in spin foam?
 
  • #10
Atyy, I looked at the paper you indicated that you were quoting. I found this on page 15, in the conclusions:

==quote 1004.0672==
Finally, the most interesting application to our formalism would be to study the insertion of actual physical non-topological fermionic fields. Starting in 3d, in the present work, we have tracked from the initial continuum action down to the final discretised spinfoam amplitude how the explicit fermionic Feynman diagrams get inserted in the spinfoam amplitude. These fermionic observables come with precise weights (see e.g. eqn. (39)-(40)). These weights are fine-tuned so as to ensure that the full model ‘gravity+fermions’ is topological.

That shows that these spinfoam amplitudes provide the correct quantisation for our supersymmetric theory. As soon as we modify these weights, we would get non-topological amplitudes and it would be interesting to see how we could modify them in order to insert more physical fermionic fields. Then, we hope to apply the same procedure to the four-dimensional case by first deriving the spinfoam quantisation of supersymmetric BF theory and studying how the fermions are coupled to the spinfoam background, and then seeing how this structure is maintained or deformed when we introduce the (simplicity) constraints on the B-field in order to go from the topological BF theory down back to proper gravity.

Another interesting outlook is to push our analysis to N = 2 supersymmetric BF theory, already in three space-time dimensions, following the footsteps of [7]. Indeed, such a theory already include a spin-1 gauge field, and we could study in more detail how the full supersymmetric amplitudes decomposes into Feynman diagrams for the fermions and spin-1 field inserted in the gravitational spinfoam structure. Then we would see how it is possible to deform this structure in such a way that the spin-1 field represents standard gauge fields. This road would provide an alternative way to coupling (Yang-Mills) gauge fields to spinfoam models, which we could then compare to the other approaches developed in this direction [6]...
==endquote==

I am thankful for any indication of how the researchers imagine adding matter to the picture. The LQG literature goes back and forth between Group Field Theory (GFT) and spinfoam and BF theory. It is becoming all one. So whichever way you can get matter in, seems fine.
With this paper, they are working in 3D and so far can just hope to extend the method to 4D.
 
Last edited:
  • #12
bcrowell said:
Do the LQG folks have a Schwarzschild metric with quantum corrections? Do they have plane gravitational waves with appropriate modes of polarization?
Afaik neither Schwarzschild nor de Sitter has been reproduced so far.
The graviton propagator has been constructed over the last couple of years by Rovelli et al. and was shown to have thre correct limit. This is a kind of consistency check b/c one does not know whether the graviton propagator as constructed from standard GR at tree level is of any physical relevenace beyond (!) tree level (as standard GR fails to be consistend beyond tree level).
 
  • #13
bcrowell said:
Do the LQG folks have a Schwarzschild metric with quantum corrections? Do they have plane gravitational waves with appropriate modes of polarization?

Tom responded as relates to plane gravitational waves (at least I think what he mentioned about the LQG graviton applies in that direction.)

In LQG there are BH models which reproduce classical results with quantum corrections. There are many papers and you can judge for yourself how complete the program is in that department by looking at recent ones. I doubt that this is all that relevant to the main topic question of how to add matter.

But here are some papers to glance at, if you are curious:
http://arxiv.org/abs/1007.2768
http://arxiv.org/abs/1006.0634
http://arxiv.org/abs/0905.3168

The first one here, for example:
Generic isolated horizons in loop quantum gravity
Christopher Beetle, Jonathan Engle
(Submitted on 16 Jul 2010)
"Isolated horizons model equilibrium states of classical black holes. A detailed quantization, starting from a classical phase space restricted to spherically symmetric horizons, exists in the literature and has since been extended to axisymmetry. This paper extends the quantum theory to horizons of arbitrary shape. Surprisingly, the Hilbert space obtained by quantizing the full phase space of all generic horizons with a fixed area is identical to that originally found in spherical symmetry. The entropy of a large horizon remains one quarter its area, with the Barbero-Immirzi parameter retaining its value from symmetric analyses. These results suggest a reinterpretation of the intrinsic quantum geometry of the horizon surface."

From my perspective as outside observer, I reckon that matterless LQG is now reaching a satisfactory stable formulation, so that it is time to ask how they are going to include matter. What approaches will be tried?

What makes sense given the kind of "asymptotic" formulation (w/o matter) that we are now seeing emerge?

What I THINK is that the best clues, or hints come from looking at last year's Oberwolfach workshop "Noncommutative Geometry and LQG"

http://owpdb.mfo.de/show_workshop?id=783

What this shows me is a network of people, which includes Alain Connes and Vincent Rivasseau even thought they did not directly participate in the workshop.
So it is a window on a network of potentially fertile ideas. You see there elements of
GFT (group field theory)
Noncommutative field theory (e.g. Richard Nest, Thomas Schücker)
NCG (Marcolli and others).

One of the workshop participants was Thomas Krajewski, a member of Rovelli's QG team at Marseille. I'll list his papers to see what things he has worked on.
 
Last edited:
  • #14
BTW I think it would be naive to start asking if the theory is right or wrong, or to start making bets. :biggrin:

What we see now are more like signs of maturity. What a I called an "asymptotic" version.
The formulation is mathematically extremely nice.
It is at a convergence of several lines of QG research, that I mentioned in the opening post. It is at an intersection, making contact with other things I mentioned (NGC, Ooguri, BF, Feynman diagrams, GFT, Regge).
Notably also we see a strenghtened coherence, it's clear now that canonical=covariant=cosmology. A loose association has fused and taken shape.

This is still happening, which is why I called the formulation asymptotic. But AFAICS it is time to assume that the main outlines (of matterless LQG) will remain as they are and to look ahead. It is how matter is added that could change things now.
================

So, looking for clues as to how that could go, I looked at Krajewski's list of papers. He has 24 on Spires going back to before his 1998 PhD thesis. Look at the network of topics and collaborators:
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=a+Krajewski%2C+Thomas&FORMAT=WWW&SEQUENCE= [Broken]

My sense is that somewhere in that "hotbed" of mathematical topics, that you see in the list, there are the seeds of how to put matter into LQG. And it is not the person (Krajewski in this case) but the web of mathematically fertile ideas that you see. The person or persons could be anybody---someone we have heard of or not heard of. I am trying to comprehend what is comprised in this mathematical "hotbed".

BTW Alain Connes and Vaughn Jones were on Krajewski's 1998 Thesis committee, at Marseille. The more I hear about CPT Luminy at Marseille the more I like it. It seems to enjoy a good intellectual climate.
 
Last edited by a moderator:
  • #15
marcus said:
My sense is that somewhere in that "hotbed" of mathematical topics, that you see in the list, there are the seeds of how to put matter into LQG. And it is not the person (Krajewski in this case) but the web of mathematically fertile ideas that you see. The person or persons could be anybody---someone we have heard of or not heard of. I am trying to comprehend what is comprised in this mathematical "hotbed".

I think this particular cluster is spinfoams-GFT-non commutative field theory and comes from a paper http://arxiv.org/abs/hep-th/0512113 and a manifesto http://arxiv.org/abs/hep-th/0505016 .
 
Last edited by a moderator:
  • #16
Two more graduates of the ENS Lyon! Must be something in the water at the École Normale :-D.

But then tell me if you see: what mathematical form would the matter take?

The basic object here is the set of square-integrable complex-valued functions on a cartesian product of (just any number) K copies of a compact group G.

L2(GK)

(It looks good already: L2 spaces and compact groups are some of the really nice things in mathematics.)

In matterless LQG the group G is SU(2). And K is the number of links in a graph. Afterwards the "graph goes to infinity" but the theory is initially built on finite graphs.

Could it be that one adds matter to the picture simply by enlarging the group G?
This could have been what was happening in the paper you quoted only a few posts back. Baccetti Livine Ryan.
As I recall the group UOSP(1|2) appeared in that paper. I don't know that group.

I suppose there are other possibilities. the L2 space could be a set of functions not from GK to the complex numbers x+iy but to some other number system, or to matrices. That does not immediately make sense to me, so I am inclined to prefer thinking about the first possibility---an enlarged group G manifold---for the time being.
=====================

Here is a 1980 paper about the group UOSP(1|2) by Berezin and Tolstoy
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103908695
Free open access provided by Project Euclid.

To recall the paper that uses UOSP(1|2):
marcus said:
...The reference Atyy gave, with the quote, was
http://arxiv.org/abs/1004.0672
The particle interpretation of N = 1 supersymmetric spin foams
V. Baccetti, E. R. Livine, J. P. Ryan
(Submitted on 5 Apr 2010)
"We show that N = 1 supersymmetric BF theory in 3d leads to a supersymmetric spin foam amplitude via a lattice discretisation. Furthermore, by analysing the supersymmetric quantum amplitudes, we show that they can be re-interpreted as 3d gravity coupled to embedded fermionic Feynman diagrams."
...
 
Last edited:
  • #17
Whatever happened to the idea that matter is already included in LQG (and similar approaches) via the Bilson-Thompson topological preon construction (see, e.g. http://arxiv.org/abs/hep-th/0603022" [Broken])? I seem to recall a claim by Smolin that such models may be 'already unified', and thus, one wouldn't have to add matter as much as to just find it.
 
Last edited by a moderator:
  • #18
Skyrmions have been used to model baryons. It has been predicted that they could be created in a multicomponent Bose–Einstein condensate.
Skyrmion is a particular case of a topological soliton.
Is this theory a mainstream now or something beyond the mainstream ?
 
  • #19
S.Daedalus said:
I seem to recall a claim by Smolin that such models may be 'already unified', and thus, one wouldn't have to add matter as much as to just find it.

And they are. The problem they still lack things like gluons.
 
  • #20
czes said:
Skyrmions have been used to model baryons.
Skyrmions are valid in the context of chiral effective theories using pions (and other mesons) as degrees of freedom. Afaik there is no reason why Skyrmions should be treated as something more fundamental.

But that is certainly not relevant in the LQG context.
 
  • #21
S.Daedalus said:
Whatever happened to the idea that matter is already included in LQG (and similar approaches) via the Bilson-Thompson topological preon construction (see, e.g. http://arxiv.org/abs/hep-th/0603022" [Broken])? I seem to recall a claim by Smolin that such models may be 'already unified', and thus, one wouldn't have to add matter as much as to just find it.
They don't get all particles (I thought gluons are there but no second and third fermion generation). They don't get the (low-energy effective) dynamics, only algebraic rules. For me this approach is "Einstein's dream"; it would be at least as revolutionary as GR and QM. But as of today it's work in progress - with only a small number of players, I am afraid.
 
Last edited by a moderator:
  • #22
Most of this seems pretty much wishful thinking. I see a huge list of "may" , "promising", "future research" in all those papers, with no real concrete demonstration that any of these zillions of vague proposals may actually work. Kicking around ideas is easy, but getting something to work, even approximately, is not a minor detail, but actually the main part of the problem!

I understand that this is work in progress, but to be fair one should note that if string physicists would get much heat for hype of similar caliber; while the theory is much further developed.

I can understand the title of the thread only as ironic - didn't the recent paper of Alexandrov and Roche exhibit that there are serious problems with LQG at a basic level, so before one looses oneself in speculations about how to possibly add matter, shouldn't one first make sure that any of these many different attempts that one may loosely call "LQG" make sense at all?
 
  • #23
This horse is so beaten that even the carcass is waiting for paleontologists.
 
  • #24
tom.stoer said:
Skyrmions are valid in the context of chiral effective theories using pions (and other mesons) as degrees of freedom. Afaik there is no reason why Skyrmions should be treated as something more fundamental.

But that is certainly not relevant in the LQG context.

Are Skyrmions a kind of the mathematical tool then ?
 
  • #25
suprised said:
Most of this seems pretty much wishful thinking.

The other problem is that even if they can finagle their way into making something consistent (eg we can add a scalar here, a vector there, etc), the ultimate problem of QG remains in force. Namely that you have no idea what matter fields to add without actually doing the experiment!

So I would consider it somewhat dissappointing even if the succeeded in showing that their theory was consistent for all arbitrary matter couplings, b/c it would imply a lack of predictivity in nature (eg Nature is consistent even as a superset of itself) and that at best the current constraints on Bysm physics were all that we could get from pure theory.

The alternative, is to add constraints (new physics/symmetries/selection principles) to the mix, which gets right back into supersymmetry, conformal field theory, NCQ and so forth and we're right back to the old 1970s criticism of all the quantization of gravity approaches.. Namely that one way or the other, you have to add stuff to it until you can get control (and ultimately predictions)
 
  • #26
Haelfix said:
The other problem is that ... the ultimate problem of QG remains in force. Namely that you have no idea what matter fields to add without actually doing the experiment!
I don't know to which idea you are referring here (I think LQG + "something"), but the Bilson-Thompson preons are not "added by hand" but are emerging from the quantized geometry itself. Of course tis is a rather speculative idea and by no means maisntream but it should be taken into account as an approach to unify geometry and matter degrees of freedom.
 
  • #27
This horse is so beaten that even the carcass is waiting for paleontologists.
 
  • #28
czes said:
Are Skyrmions a kind of the mathematical tool then ?
Originally Skyrme proposed that nucleons (proton, neutron) can be described in terms pion fields [tex]\pi^a(x)[/tex] where a=1..3 counts the three pions in SU(2)flavour. Now instead of using a linear field theory (Klein-Gordon) he introduced a non-linear field theory (non-linear sigma model with some extra terms) in terms of the SU(2) matrix

[tex]U(x) = e^{i\tau^a\pi^a(x)}[/tex]

Then he showed that the field equations allow for a "radial" static "hedhog" solution

[tex]\pi^a(x) = \hat{r}^a f(r)[/tex]

with a certain profile function f(r).

This solution in a topological soliton (the nucleon) b/c it has a "winding number" one which guarantuees its stability against decays into pions (mathematically this is due to the homotopy group defined by the mapping from compactified space S3 to SU(2)). A simple example is a field living in U(1) on a space defined by a circle S1. As x runs around the circle the field runs around the the U(1).

One can show that these topological Skyrmions plus improved phenomenological models including vector mesons can be used as so-called chiral effective theories to describe
- nucleon masses
- nuclean form factors
- nucleon-nucleon scattering
- pion-nucleon scattering
- photo-pion production

Similar solitons can be constructed whenever there is a field living in a manifold (like the group SU(2)) which allows a topologically non-trivial mapping betwen spacetime and the manifold. In that sense it is by no means restricted to phenomenological models for the strong interactions. But I have never seen that solitons are used in LQG.
 
  • #29
tom.stoer said:
I don't know to which idea you are referring here (I think LQG + "something"), but the Bilson-Thompson preons are not "added by hand" but are emerging from the quantized geometry itself. Of course tis is a rather speculative idea and by no means maisntream but it should be taken into account as an approach to unify geometry and matter degrees of freedom.

When this idea (its really a variant of an old idea by Wheeler) was proposed several years ago, people immediately asked if it put any constraints at all on particle physics. Like for instance, does it enforce chirality? The answer was a vague 'I don't know'! So for now, it seems that if it works at all, its essentially equivalent to matter being added by hand since the exact nature of the geometry is uncertain.
 
  • #31
suprised said:
Most of this seems pretty much wishful thinking. I see a huge list of "may" , "promising", "future research" in all those papers, with no real concrete demonstration that any of these zillions of vague proposals may actually work. Kicking around ideas is easy, but getting something to work, even approximately, is not a minor detail, but actually the main part of the problem!

I understand that this is work in progress, but to be fair one should note that if string physicists would get much heat for hype of similar caliber; while the theory is much further developed.

I can understand the title of the thread only as ironic - didn't the recent paper of Alexandrov and Roche exhibit that there are serious problems with LQG at a basic level, so before one looses oneself in speculations about how to possibly add matter, shouldn't one first make sure that any of these many different attempts that one may loosely call "LQG" make sense at all?


LQG carries matter in the following way from Smolin's paper. It is 99% similar to my own idea coming from a very different angle. I am very astonished that nobody so far has mentioned this idea which he has been working very hard on it, and he even tied it to Lisi's idea.

http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.0977v2.pdf



Consider a graph as in
Figure (1) which is regular and therefor may occur in the superposition of states making
up a semiclassical state associated with a flat metric. There is in loop quantum gravity,
no apparent energy cost to contaminating that lattice-like graph with non-local links as
shown in the figure. Nor is there an incompatibility with the semiclasicality of the state.
As there are many more ways to add a link to a lattice that connects two far away nodes
than two nearby nodes, there is an instability for the formation of such non-local links
as the universe expands from Planck scales. Moreover, once inserted in a graph, nonlocal
links are trapped, as they can only be eliminated if two of them annihilate by the
coincidence of their ends arriving by local moves at neighboring nodes. The proposal
is then that these act as Planck scale wormholes, carrying quantum numbers associated
with gauge fields carried by the non-local link.

Let us consider observations made by a local observer in the neighborhood of x. From
their point of view the edge exy simply comes to an end, that is it appears to connect
to a one valent node. But ends, or one valent nodes in loop quantum gravity represent
matter degrees of freedom. Thus, the dislocations due to disordered locality appear in the semiclassical limit as matter degrees of freedom.
Let us suppose that the gauge group is SU(2)⊗H, where H is an internal gauge symmetry.
Then the edge exy carries representations of these groups, (j, r). Local observers will describe exy as a particle of spin j and charge r.This leads to a picture in which for every generator of G, the gauge symmetry, the
semiclassical limit has a gauge field plus a set of particle excitations given by the representations of G.
 
  • #32
But still "most of this seems pretty much wishful thinking".

In a second paper Smolin tried to explain the cosmological constant via these non-local links. In addition Smolin proposes Bilson-Thompson. And then one can add matter by hand ...

The conclusion is that LQG carries a rich and (to a large extend) unexplored structure. Some known effects may be explained via these structures, some new effects may arise. Some unwanted effects may rule out LQG, ..., everything is possible.
 
  • #33
If I remember correctly, the Bilson-Thompson model is a preon model which is equivalent to Haim Harari's Rishon model. That model had suddendly disappeared many years ago... why? because a smart student of Harari, Nathan Seiberg, had shown that this model is inconsistent due to anomalies. Well, since anomalies seem to be neglected in the LQG community, I am not surprised that they revive the Rishon model. Indeed, back to the 70s...

Incidentally, the question of matter is an interesting one also from the following perspective. If string theory is any right, matter is necessary for internal consistency. Pure gravity would not be consistent. It would be interesting to see whether LQG comes up with a similar consistency constraint. If not, then this would be a clear dividing line between strings and LQG. I guess it is too early to see because LQG seems so far to be plagued by all sorts of problems; but perhaps some day this issue can be sharpened.
 
  • #34
Haven't heard much about braid matter for the past couple of years. :smile: I hope that in this discussion thread we can get back to the main topic---the ways currently being considered to include matter.

It seems fairly obvious that matterless (or simple scalar matter) LQG has matured to the point of being testable with the next generation of CMB spacecraft . The proposed NASA B-Pol mission for example--how soon such steps are taken depends mainly economic and political conditions, there are no technical barriers.
http://www.b-pol.org/index.php

Since there are evidently differing opinions regarding the theory's maturity, I'll copy two recent abstracts bearing on that:

http://arxiv.org/abs/1011.1811
Observing the Big Bounce with Tensor Modes in the Cosmic Microwave Background: Phenomenology and Fundamental LQC Parameters
Julien Grain, A. Barrau, T. Cailleteau, J. Mielczarek
12 pages, 5 figures
(Submitted on 8 Nov 2010)
"Cosmological models where the standard Big Bang is replaced by a bounce have been studied for decades. The situation has however dramatically changed in the last years for two reasons. First, because new ways to probe the early Universe have emerged, in particular thanks to the Cosmic Microwave Background (CMB). Second, because some well grounded theories -- especially Loop Quantum Cosmology -- unambiguously predict a bounce, at least for homogeneous models. In this article, we investigate into the details the phenomenological parameters that could be constrained or measured by next-generation B-mode CMB experiments. We point out that an important observational window could be opened. We then show that those constraints can be converted into very meaningful limits on the fundamental Loop Quantum Cosmology (LQC) parameters. This establishes the early universe as an invaluable quantum gravity laboratory."

http://arxiv.org/abs/1007.2396
Constraints on standard and non-standard early Universe models from CMB B-mode polarization
Yin-Zhe Ma, Wen Zhao, Michael L. Brown
(Submitted on 14 Jul 2010)
"We investigate the observational signatures of three models of the early Universe in the B-mode polarization of the Cosmic Microwave Background (CMB) radiation. In addition to the standard single field inflationary model, we also consider the constraints obtainable on the loop quantum cosmology model (from Loop Quantum Gravity) and on cosmic strings, expected to be copiously produced during the latter stages of Brane inflation. We first examine the observational features of the three models, and then use current B-mode polarization data from the BICEP and QUaD experiments to constrain their parameters. We also examine the detectability of the primordial B-mode signal predicted by these models and forecast the parameter constraints achievable with future CMB polarization experiments. We find that:
(a) these three models of the early Universe predict different features in the CMB B-mode polarization power spectrum, which are potentially distinguishable from the CMB experiments;

(b) since B-mode polarization measurements are mostly unaffected by parameter degeneracies, they provide the cleanest probe of these early Universe models;

(c) using the BICEP and QUaD data we obtain the following parameter constraints:
[tex]r=0.02^{+0.31}_{-0.26}[/tex] (1 sigma for the tensor-to-scalar ratio in the single field inflationary model);

[tex]m < 1.36\times 10^{-8} \text{M}_{\text{pl}}[/tex] and [tex]k_{*} < 2.43 \times 10^{-4} \text{Mpc}^{-1}[/tex] (1 sigma for the mass and scale parameters in the loop quantum cosmology model);

[tex]G\mu < 5.77 \times 10^{-7}[/tex] (1 sigma for the cosmic string tension);

(d) future CMB observations (both satellite missions and forthcoming sub-orbital experiments) will provide much more rigorous tests of these early Universe models."
 
Last edited:
  • #35
tom.stoer said:
But still "most of this seems pretty much wishful thinking".

In a second paper Smolin tried to explain the cosmological constant via these non-local links. In addition Smolin proposes Bilson-Thompson. And then one can add matter by hand ...

The conclusion is that LQG carries a rich and (to a large extend) unexplored structure. Some known effects may be explained via these structures, some new effects may arise. Some unwanted effects may rule out LQG, ..., everything is possible.




1-Consider particles as lines extending from the particle to everywhere in the universe.

2-generate these lines by throwing a random number, make it on a line i.e. 1D as an example
do above for two particles sitting each at the opposite side of a universe of 10^40 in atomic units-size of the proton-(size of our universe). Throw 10^41 times.

3-if you consider gravity as when both lines meet you have a probability of 1 in 10^40

4-if you consider EM force as when these lines cross one another p is close to .99

you can see the ratio, can't you. trust me ,forces are related to these probabilities.

increasing(decreasing) the universe size changes the ratio, EM stays .99. This is Diracs large number hypothesis(Google). Numbers are approximate. I hope I show details soon.

Quantum gravity in four lines.
 
<h2>1. How does Loop Quantum Gravity (LQG) explain the addition of matter?</h2><p>LQG is a theory of quantum gravity that describes the fabric of space-time as a network of interconnected loops. It does not directly explain how matter is added, but rather provides a framework for incorporating matter into the theory.</p><h2>2. Can matter be quantized in LQG?</h2><p>Yes, matter can be quantized in LQG. The theory allows for the quantization of both space-time and matter, providing a more complete understanding of the fundamental building blocks of the universe.</p><h2>3. Are there any challenges in adding matter to LQG?</h2><p>Yes, there are several challenges in adding matter to LQG. One major challenge is reconciling the discreteness of space-time in LQG with the continuous nature of matter. Another challenge is finding a consistent way to incorporate the principles of quantum mechanics into the theory of LQG.</p><h2>4. What is the current progress in adding matter to LQG?</h2><p>There is ongoing research and progress in incorporating matter into LQG. Some approaches involve using mathematical tools such as spin networks and spin foams to describe the interactions between matter and space-time in LQG. However, there is still much work to be done in this area.</p><h2>5. How does the addition of matter affect the predictions of LQG?</h2><p>The addition of matter can have a significant impact on the predictions of LQG. It can lead to a better understanding of the behavior of matter in extreme conditions, such as near black holes or during the early stages of the universe. It can also potentially provide a more complete picture of the fundamental laws of nature.</p>

1. How does Loop Quantum Gravity (LQG) explain the addition of matter?

LQG is a theory of quantum gravity that describes the fabric of space-time as a network of interconnected loops. It does not directly explain how matter is added, but rather provides a framework for incorporating matter into the theory.

2. Can matter be quantized in LQG?

Yes, matter can be quantized in LQG. The theory allows for the quantization of both space-time and matter, providing a more complete understanding of the fundamental building blocks of the universe.

3. Are there any challenges in adding matter to LQG?

Yes, there are several challenges in adding matter to LQG. One major challenge is reconciling the discreteness of space-time in LQG with the continuous nature of matter. Another challenge is finding a consistent way to incorporate the principles of quantum mechanics into the theory of LQG.

4. What is the current progress in adding matter to LQG?

There is ongoing research and progress in incorporating matter into LQG. Some approaches involve using mathematical tools such as spin networks and spin foams to describe the interactions between matter and space-time in LQG. However, there is still much work to be done in this area.

5. How does the addition of matter affect the predictions of LQG?

The addition of matter can have a significant impact on the predictions of LQG. It can lead to a better understanding of the behavior of matter in extreme conditions, such as near black holes or during the early stages of the universe. It can also potentially provide a more complete picture of the fundamental laws of nature.

Similar threads

  • Beyond the Standard Models
Replies
2
Views
2K
  • Beyond the Standard Models
Replies
9
Views
3K
  • Beyond the Standard Models
Replies
2
Views
2K
  • Beyond the Standard Models
Replies
12
Views
5K
  • Beyond the Standard Models
2
Replies
48
Views
14K
  • Beyond the Standard Models
Replies
11
Views
2K
  • Beyond the Standard Models
Replies
5
Views
2K
  • Beyond the Standard Models
Replies
14
Views
4K
  • Beyond the Standard Models
Replies
13
Views
3K
  • Beyond the Standard Models
4
Replies
105
Views
10K
Back
Top