# Loop quantum gravity

In loop quantum gravity it is assumed that space is not infinitely divisible. The nodes are not space . Actually they are the infinitely divisible part of a matter. The distance between the nodes are not discrete. The distance between the nodes may be 1.5 Planck's length or 2.5 planck's length and so on. So quantization of space is not allowed even in loop quantum gravity. And the the distance between loops are also not multiples of Planck's lenght. My conclusion is that space is infinitely divisible and matter is not.

In loop quantum gravity it is assumed that space is not infinitely divisible. The nodes are not space . Actually they are the infinitely divisible part of a matter. The distance between the nodes are not discrete. The distance between the nodes may be 1.5 Planck's length or 2.5 planck's length and so on. So quantization of space is not allowed even in loop quantum gravity. And the the distance between loops are also not multiples of Planck's lenght. My conclusion is that space is infinitely divisible and matter is not.
Even in general relativity there really is no notion of a stage with space or even space-time, there are just collections of gravitational fields that interact with each other in a non-linear fashion. It is important to realize that we don't live in space-time and that GR does not operate in space-time. GR is usually called a geometric theory, it is actually more like a chrono-metric theory since the metric represents a proper time interval. The geo- (or chrono) metric aspects are emphasized in GR, historically coming from the space-time model as introduced by Galileo, used by Newton and reinterpreted by Minkowski towards a 4-dimensional curved manifold model. This is not the case in LQG, LQG is an algebraic theory not a geometric theory. Space (or even space-time) by itself does not exist, at most you can say that LQG creates some notion of "space" and "time" for an observer.

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Even in general relativity there really is no notion of a stage with space or even space-time, there are just collections of gravitational fields that interact with each other in a non-linear fashion. It is important to realize that we don't live in space-time and that GR does not operate in space-time. GR is usually called a geometric theory, it is actually more like a chrono-metric theory since the metric represents a proper time interval. The geo- (or chrono) metric aspects are emphasized in GR, historically coming from the space-time model as introduced by Galileo, used by Newton and reinterpreted by Minkowski towards a 4-dimensional curved manifold model. This is not the case in LQG, LQG is an algebraic theory not a geometric theory. Space (or even space-time) by itself does not exist, at most you can say that LQG creates some notion of "space" and "time" for an observer.

Any theory whether geometric or algebric it has to succefully applied to the events that we are observing in real world. And the theory should be interpreted succesfully and should be tested. What I mean in LQG is that the nodes are not actually the ultimatum of space but of matter. during late 20 the century, we found some quarks as the elementary particles. What i mean from LQG is that quarks are not the ultimate elementary particles and quarks are also divisible to the planck's volume. Since most of the scientists are satisfied with quark and standard model the do not want further divide quarks if it is done then the group theory and the geometry and algebraic theory should further be evolved. Standard model scientist are living in the 1970's and they are still searching for Higg's boson. The LHC which will be operational in july 2007 may or may not give Higg's boson. But these bosons and fermions are not the ultimate elementary particles. I predict from LQG that the planck's volume is the volume of a further elementary particle with a charge and magnetic moment. These elementary particles will then collectively form the electron, proton quarks,and the whole universe what we see.

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LPG is a promising theory. Nodes forms loops. Loops forms branes. Branes form the foam. Foams form the fermions and bosons as per my prediction. Matter cannot be formed directly from the space-time curvature. How from nothing you will use GR and get matter. Common sense suggest that mass and space are seperate entities. In LQG, the nodes are masses and the space between them is really the three dimensional space that we are observing in day to day life. This is a serious violation of GR. GR gets matter out of space and time. It is highly impossible. Compared to GR LQG is promising theory and the only thing is interpret its results. This is the right time to take a deviation from GR.

LQG weaves the matter (node) and space (loops) in a nice way to form foams. These foams are nothing but our bosons and fermions. So LQG does not violate the standard model and at the same time if interpret correctly the LQG, then it will form an alternate to GR in macroscopic scale.

These bosons and fermions in turn form the universe that we see.

The need for background field and ghost fields should be eliminated

marcus
Gold Member
Dearly Missed
Hello Ravi, welcome to PF

since you are interested in LQG (which these days covers a variety of different but related approaches to quantum geometry/quantum gravity/cosmology) let me mention a few things happening in the field

Earlier this year there was an important workshop (The Quantum Nature of Spacetime Singularities) at the Kavli ITP at Santa Barbara. It went on for the better part of 3 weeks and video of the main talks is available on line. Abhay Ashtekar was there and a member of his group at Penn State, Martin Bojowald, was a co-organizer of the workshop.

I think it is fairly obvious that the LQG-community (particularly those doing the cosmology spin-off LQC) are at the forefront in dealing with the big bang and black hole singularities, and some of the string-community are evidently interested in trying to understand what's going on in that area. Hence setting up the workshop and inviting major LQG-community people.

You may be interested purely in the theory, and not in the activities of the people, which is fine. But if you are interested in the current LQG "scene", then we could share news and notes.

Another defining event for the LQG-community this year is the two-week school now in progress in Poland. It is called QGQG-1.
"The first quantum gravity quantum geometry school"
A series of 8 or 9 lectures on LQG proper is being given by Thomas Thiemann. There are other series of lectures on related but different approaches.

Another defining event was the European Science Foundation (ESF) setting up last year the QGQG network, which funds such things as this QGQG school and workshops and conferences.
the distinguishing thing about the LQG-community research is the quantum geometrical approach to gravity. Instead of a graviton or something else moving in a fixed background geometry, the geometric ambience is itself a dynamic entity (as in GR itself). So saying QGQG is a way of evoking background independent, non-perturbative, largely non-string approaches to QG. So the ESF is recognizing this and putting money into it.

Another definining event for the LQG-community will be the publication this year (if it goes as planned) by Cambridge U. Press of the book edited by Dan Oriti called "Approaches to Quantum Gravity, Towards a New Understanding of Space Time and Matter".
there are 10 - 20 authors involved, mainly from the LQG-community. Quite a number of different approaches represented.

We have discussion-threads about some of these happenings here at "Beyond" forum. Hope you will contribute your own thoughts or news items. Again welcome.

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marcus
Gold Member
Dearly Missed
I will get some links for these things later as time permits. (also you may also have seen the things on the web that I am talking about)

Oh, also there is the main LQG-community conference Loops '07 in Morelia in July. It will be interesting to see what is on the program of invited talks and how the conference shapes up.

Do you happen to know of Ganashyam Date? He has raised several young LQG researchers but then there is a kind of braindrain that happens where they get drawn to Berlin-Potsdam (Albert Einstein Institute) and to Penn State. Besides G. Date I can't think of anybody in India right now. maybe you know of more.

UPDATE: by a nice coincidence not long after I wrote this mentioning Ganashyam Date I discovered that he has just posted a new paper

http://arxiv.org/abs/0704.0145
Singularity Resolution in Isotropic Loop Quantum Cosmology: Recent Developments
Ghanashyam Date
(Submitted on 2 Apr 2007)

"Since the past Iarge meeting in December 2004, new developments in loop quantum cosmology have taken place, especially with regards to the resolution of the Big Bang singularity in the isotropic models. The singularity resolution issue has been discussed in terms of physical quantities (expectation values of Dirac observables) and there is also an 'improved' quantization of the Hamiltonian constraint. These developments are briefly discussed. This is an expanded version of the review talk given at the 24-th IAGRG meeting in February 2007."

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