A clarification of LQG by Lubos Motl

[marcus]

http://www.arxiv.org/abs/gr-qc/0212096

Lubos Motl (at Harvard's Jefferson Phys. Lab.)

this paper is pure gold for what it does on the side
quite apart from what you might expect from the title,
which sounds narrowly focused on a specialized technical issue.

what Motl gives on the side is a *critical* overview of LQG
that cuts thru the underbrush and distinguishes a short list of impressive results---you could say one impressive result

Motl recognizes the landmark importance of Olaf Dreyer's
2002 paper, which seems to have put LQG on a new footing.
Dreyer's paper is less than 4 pages long and has
potentially far-reaching effects on quantum gravity, which
Motl provides perspective on. Here's Dreyer's 4 page paper:

http://www.arxiv.org/abs/gr-qc/0211076

 

[marcus]

One thing Motl does that seems very interesting to me at least is to use " good old-fashioned" methods to come up with a result suggesting that

the quantum of area is 4 ln(3) times the conventional Planck area.

By unexplained coincidence this is also what Dreyer came up with for the quantum of area---using LQG.

But Motl's analysis is neither stringy nor loopy! It has a classical flavor----analysing the vibration frequencies of a vintage 1916 black hole based on the vintage 1916 Schwarzschild model of one! There is no quantum mechanics at all in the basic model. The classical GR model of hole supports vibrations, and the minimal steps in frequency which Motl finds (NOW Planck's constant can come in) correspond to minimal steps in energy and therefore area. So there is a so-to-speak "classical" support for the quantum of area being 4 ln(3) Planck.

As Dreyer got by other (LQG) methods.

Maybe it should be mentioned that Motl is analytically pinning down some results about the vibration frequency of black holes that were gotten four years earlier by (of all things!) a
*computer simulation* of black hole vibrations.

So this number was known to be equal to 4 ln(3) out to 5 decimal places---as far as the computer could get it---but until Motl one did not know that it was exactly 4 ln(3). The next decimal place could have been wrong I only mention this because this is not just the work of one person but a kind of convergence on the quantum of area by a computer simulation by a man named Sachar Hod and by classical analysis of Motl and by LQG of Dreyer and probably help from other people. It is no one person's thing.
But Motl's account of the matter seems unusually clear-sighted to me.

BTW for people like Instanton and Sauron who may already be somewhat familiar with LQG technicalities the corollary of this is that the LQG group changes to SO(3) and the Immirzi parameter becomes ln(3)/(2pi sqrt2) which is 1/8.088 or about 1/8. Motl explains the Immirzi parameter as giving the "bare" value of Newton's gravitational constant G. The bare value at Planck scale is only about one eighth as big as the renormalized largerscale lower energy G that we know and love. For this interesting detail see middle of page 7 of Motl and also the explicit value of Immirzi at top of page 9. These developments may strike one as provocative and worth looking into---hope so anyway.

 

[jeff]

Originally posted by marcus
One thing Motl does that seems very interesting to me at least is to use " good old-fashioned" methods to come up with a result suggesting that

the quantum of area is 4 ln(3) times the conventional Planck area.

By unexplained coincidence this is also what Dreyer came up with for the quantum of area---using LQG.

But Motl's analysis is neither stringy nor loopy! It has a classical flavor----analysing the vibration frequencies of a vintage 1916 black hole based on the vintage 1916 Schwarzschild model of one! There is no quantum mechanics at all in the basic model. The classical GR model of hole supports vibrations, and the minimal steps in frequency which Motl finds (NOW Planck's constant can come in) correspond to minimal steps in energy and therefore area. So there is a so-to-speak "classical" support for the quantum of area being 4 ln(3) Planck.

As Dreyer got by other (LQG) methods.

Maybe it should be mentioned that Motl is analytically pinning down some results about the vibration frequency of black holes that were gotten four years earlier by (of all things!) a
*computer simulation* of black hole vibrations.

So this number was known to be equal to 4 ln(3) out to 5 decimal places---as far as the computer could get it---but until Motl one did not know that it was exactly 4 ln(3). The next decimal place could have been wrong I only mention this because this is not just the work of one person but a kind of convergence on the quantum of area by a computer simulation by a man named Sachar Hod and by classical analysis of Motl and by LQG of Dreyer and probably help from other people. It is no one person's thing.
But Motl's account of the matter seems unusually clear-sighted to me.

BTW for people like Instanton and Sauron who may already be somewhat familiar with LQG technicalities the corollary of this is that the LQG group changes to SO(3) and the Immirzi parameter becomes ln(3)/(2pi sqrt2) which is 1/8.088 or about 1/8. Motl explains the Immirzi parameter as giving the "bare" value of Newton's gravitational constant G. The bare value at Planck scale is only about one eighth as big as the renormalized largerscale lower energy G that we know and love. For this interesting detail see middle of page 7 of Motl and also the explicit value of Immirzi at top of page 9. These developments may strike one as provocative and worth looking into---hope so anyway.

Too many remarks that miss the mark marcus. To explain:

To enforce agreement of the LQG result for black hole entropy with the accepted one, a dimensionless multiplicative factor - the "immirzi" parameter - was introduced without further justification. Later someone observed that the rounded off value of a number cropping up in a certain GR-based black hole related computation equaled the immirzi parameter value needed in a version of LQG previously argued to be more natural than the standard one.

Lubos in his paper strengthened the view that this may not be mere coincidence by showing that the rounded off value was in fact the exact value, though the calculation itself shed little light on the ultimate significance of this result (but about which some speculation is offered anyway).

This result added credence to the view that LQG may have something important to tell us about QG, even if LQG is wrong. Unfortunately, it could also be seen as doing the same for the view that the latter is the case, since it was already known that this alternative arguably more natural version of LQG is inconsistent with the existence of matter. In fact this inconsistency directly reflects the very naturality argument that "there is no reason why a man-made theory like LQG that is meant to reinterpret old physics should know about our desire to incorporate fermions" on which advocacy for this version of LQG was based.

As well, Lubos offers the following critique of LQG:

"LQG has not been able to show that gravity at low energies behaves as it should and instead, it assumes some extremely unlikely conjectures about physics at high energies that we could not have tested: for example, LQG essentially claims that Einsteins equations are exact and uncorrected even at the Planck scale and the bad divergences in the Feynman diagrams only reflect our inappropriate choice of variables and the perturbative character of the calculations rather than new physics that we should learn. LQG formally agrees with Einstein in the regime where we have no reasons to believe that Einstein is correct; at the same moment, it most likely disagrees with Einstein at low energies where General Relativity has been successfully tested by many experiments. Since the LQG dynamics is pure Einstein at the Planck scale and the renormalization group flow is known to generate corrections, the physics at long distances probably does not exist. Many people believe that LQG, much like other discrete approaches to Quantum Gravity, does not contain large flat spacetime as a solution."

Lubos has made it clear in his posts to sci.phys.research that he is no friend of LQG, and I think this paper reflects that to a significantly greater degree than marcus intimated above.

Naturally, other immirzi parameter related ideas have been advanced since this paper. If your into LQG, take a look (even my always enthusiastic friend marcus )

 

[marcus]

Originally posted by steinitz
Too many remarks that miss the mark marcus. To explain:

To enforce agreement of the LQG result for black hole entropy with the accepted one, a dimensionless multiplicative factor - the "immirzi" parameter - was introduced without further justification. Later someone observed that the rounded off value of a number cropping up in a certain GR-based black hole related computation equaled the immirzi parameter value needed in a version of LQG previously argued to be more natural than the standard one.

Lubos in his paper strengthened the view that this may not be mere coincidence by showing that the rounded off value was in fact the exact value, though the calculation itself shed little light on the ultimate significance of this result (but about which some speculation is offered anyway).

This result added credence to the view that LQG may have something important to tell us about QG, even if LQG is wrong. Unfortunately, it could also be seen as doing the same for the view that the latter is the case, since it was already known that this alternative arguably more natural version of LQG is inconsistent with the existence of matter. In fact this inconsistency directly reflects the very naturality argument that "there is no reason why a man-made theory like LQG that is meant to reinterpret old physics should know about our desire to incorporate fermions" on which advocacy for this version of LQG was based.

As well, Lubos offers the following critique of LQG:

"LQG has not been able to show that gravity at low energies behaves as it should and instead, it assumes some extremely unlikely conjectures about physics at high energies that we could not have tested: for example, LQG essentially claims that Einsteins equations are exact and uncorrected even at the Planck scale and the bad divergences in the Feynman diagrams only reflect our inappropriate choice of variables and the perturbative character of the calculations rather than new physics that we should learn. LQG formally agrees with Einstein in the regime where we have no reasons to believe that Einstein is correct; at the same moment, it most likely disagrees with Einstein at low energies where General Relativity has been successfully tested by many experiments. Since the LQG dynamics is pure Einstein at the Planck scale and the renormalization group flow is known to generate corrections, the physics at long distances probably does not exist. Many people believe that LQG, much like other discrete approaches to Quantum Gravity, does not contain large flat spacetime as a solution."

Lubos has made it clear in his posts to sci.phys.research that he is no friend of LQG, and I think this paper reflects that to a significantly greater degree than marcus intimated above.

Naturally, other immirzi parameter related ideas have been advanced since this paper. If your into LQG, take a look (even my always enthusiastic friend marcus )

 

[Sauron]

>>Throughout this paper, we will neglect six or seven dimensions of >>the Universe and
>>discuss four-dimensional Schwarzschild black holes

Oh, what a lack of generality...

Seriously, string theorist´s are bbecoming a bit crazy now adays. They expect for their theory the same respect that the standar model has.

And by no means they deserve it. I could totally ignore string theory (it´s not the case) and still consider i am totally aware of high energy physics.


I consider totally unbeliveable that somehting some exotic as M-theory is considered seriously and people like Myron Evans, who claims to have some experimntal evidence of new behaviours of electromagnetism -and a theory to explain the- would be totally ignored.

 

[Sauron]

BTW, a clarification about my knowledge of LQG, ii hve readed basicaly two intros, the Rovelli´s one in living reports and a a Thieman intro in pDF format of around 90 pages.

I clarify it because i know there is another Thieman intro of 300+ pages which i am beginning to read now. Also i readed the Gambini-pullini book on the subjecto of gauge fields, knot theory and gravity. I have notices that Gambini has written a more recent one, these time in collaboration wiith jonh Baez, but i am not sure aobut it.

 

[jeff]

Originally posted by Sauron
>>Throughout this paper, we will neglect six or seven dimensions of >>the Universe and
>>discuss four-dimensional Schwarzschild black holes

Oh, what a lack of generality...

Seriously, string theorist´s are bbecoming a bit crazy now adays. They expect for their theory the same respect that the standar model has.

And by no means they deserve it. I could totally ignore string theory (it´s not the case) and still consider i am totally aware of high energy physics.


I consider totally unbeliveable that somehting some exotic as M-theory is considered seriously and people like Myron Evans, who claims to have some experimntal evidence of new behaviours of electromagnetism -and a theory to explain the- would be totally ignored.

Has myron evans discussed his ideas with you?

 

[Sauron]

No, he hasn´t.

But i colaborate from time to time with a friend in developing (extending into other areas, for example Yang-Mills) a theory of electromagnetic knots.

And Myron Evans has sometimes cited these theory as favourable to his own work. Even, throught one of his collaborators hasmade to my friend the oportunity to publish the developments of the electromagnetics knot theory in his new incoming book.

 

[marcus]

Hey Sauron,

Motl is kind of outrageous in places----like at the end in the Unsolved Questions section he raises the question "could it be that LQG does not allow for the existence of fermions?"

And his comic side comment you cited "thoughout this paper we neglect 6 or 7 dimensions!"

But I still like his paper. He acknowledges a real advance in LQG even though he has often attacked LQG in the past.
particularly around the issue of the Immirzi parameter.

Now, while he talks critically about LQG, he has actually contributed a significant supporting result.

Originally posted by Sauron
>>Throughout this paper, we will neglect six or seven dimensions of >>the Universe and
>>discuss four-dimensional Schwarzschild black holes

Oh, what a lack of generality...

Seriously, string theorist´s are bbecoming a bit crazy now adays. They expect for their theory the same respect that the standar model has.

And by no means they deserve it. I could totally ignore string theory (it´s not the case) and still consider i am totally aware of high energy physics.


I consider totally unbeliveable that somehting some exotic as M-theory is considered seriously and people like Myron Evans, who claims to have some experimntal evidence of new behaviours of electromagnetism -and a theory to explain the- would be totally ignored.

 

[marcus]

Sauron,

did you notice that steinitz said:

" since it was already known that this alternative arguably more natural version of LQG is inconsistent with the existence of matter. "

It is not what Motl said, either in his footnote (which speculates as to the original motive for using SU(2) instead of SO(3)) or in his "unanswered questions" at the end.

Nobody else I know of says this either. Yet steinitz would
have us think that this is "already known"
.

 

[marcus]

Motl has been a staunch and vocal supporter of strings in the past and has attacked LQG. In this paper he uses a derogatory tone but makes several important contributions to LQG. It is revealing to see what has interested this one-time enemy but now partial collaborator. On page 7 he says:

"The most interesting result of this controversial approach to quantization of gravity is the following area quantization law that results driectly from [the two basic defining equations]

Area = 8piG_Newton x Immirzi x Σ spin network terms

...Immirzi parameter, a pure number that can be interpreted as the finite renormalization of 8piG_Newton between the Planck scale and low energies..."

I cannot easily write this out. It is simple and elegant and I can understand Motl being intrigued by it. The minimal spin network term dominates the sum and is equal to the sqrt 2. The sum is over network links intersecting the surface whose area is to be measured.

The Newtonian gravitational constant occurs as 8piG in the main equation of GR, the Einstein equation. People have often taken 8piG_Newton as the "real" gravitational constant.

Motl (usually a foe of LQG) is telling us in effect that the constant in front of the sum of sqrt 2 terms (one for each crossing of the surface) is the *real, bare* gravitational constant.

Motl is helping in this paper to establish the value of the Immirzi number as about 1/8.088 and in effect establish that the true gravitational constant (at Planck scale) is about 1/8 of our usual
largescale low energy 8piG_Newton

And yes he certainly does his share of grudging quarreling and nit-picking while he is doing this! But Motl is making a substantial contribution and meanwhile recognizing (for all his critical-sounding talk) an impressive development.

Wish I could write out the Σ sum of spin label terms
as he has it in the paper. Very elegant formula for area.

So this area formula is what impresses one of the most vocal critics of this new approach to modeling gravity. Its always important to notice what impresses the enemies of a theory
and even temporarily brings them over to the other camp.

 

[jeff]

Originally posted by marcus
steinitz said:

"since it was already known that this alternative arguably more natural version of LQG is inconsistent with the existence of matter."

It is not what Motl said, either in his footnote (which speculates as to the original motive for using SU(2) instead of SO(3)) or in his "unanswered questions" at the end.

Yep, I think you're right for bringing this up because looking at it again I clearly was cavalier, so thanks (and yes I really do mean that).

But it's not that I was attributing that particular statement to motl or his paper. That statement was purely my own. Like any high energy theorist coming across this, I, and obviously the proponents of SO(3) LQG - of which I'm not one, as you know - immediately understood why - despite it's advantages purely in the context of the LQG program - coupling it to matter was impossible.

What was wrong of me to do was make the unqualified remark that "In fact this inconsistency directly reflects the very naturality argument that "there is no reason why a man-made theory like LQG that is meant to reinterpret old physics should know about our desire to incorporate fermions" on which advocacy for this version of LQG was based." Btw, just in case there's any confusion - and I'm not suggesting there is - all matter is fermionic.

Anyway, I appologize for this (sorry marcus).

Btw, my name is jeff ("steinitz" is a reference to wilhelm steinitz, the father of modern chess)

 

[marcus]

No problemo steinitz,

BTW since you indicate that you are a "professional researcher" (in high energy particle theory one infers from context, or some related area) I would very much like to look over some of your published research. Please post some references so I can look them up----I have ready access to a large academic library of journals and it would be no trouble for me to find pretty much anything you have in print if it is peer-reviewed hard-copy.

Originally posted by steinitz
Yep, I think you're right for bringing this up because looking at it again I clearly was cavalier, so thanks (and yes I really do mean that).

But it's not that I was attributing that particular statement to motl or his paper. That statement was purely my own. Like any high energy theorist coming across this, I, and obviously the proponents of SO(3) LQG - of which I'm not one, as you know - immediately understood why - despite it's advantages purely in the context of the LQG program - coupling it to matter was impossible.

What was wrong of me to do was make the unqualified remark that "In fact this inconsistency directly reflects the very naturality argument that "there is no reason why a man-made theory like LQG that is meant to reinterpret old physics should know about our desire to incorporate fermions" on which advocacy for this version of LQG was based."

I appologize (sorry marcus)

 

[jeff]

Originally posted by marcus
No problemo steinitz,

BTW since you indicate that you are a "professional researcher" (in high energy particle theory one infers from context, or some related area) I would very much like to look over some of your published research. Please post some references so I can look them up----I have ready access to a large academic library of journals and it would be no trouble for me to find pretty much anything you have in print if it is peer-reviewed hard-copy.

I think that revealing identities in online public forums is not necessarily the smartest move people can make. Sorry.

 

[marcus]

For a contrast to your manner, check out this interesting website:

http://www.geocities.com/jefferywinkler

and the many posts by "Jeffery" on Usenet's

sci.physics.research

the guarded reserve of this Jeff (steinitz) sharply
contrasts with the self-revelatory openness shown by
Usenet's Mr. Winkler--a multifaceted
and widely informed individual if there ever was one!

No reflection on you but I think I may prefer the Jeff on Usenet.

 

[marcus]

Jeff Winkler's online (mostly science) resource

Good gracious!

http://www.geocities.com/jefferywinkler/Aristotles_Lyceum_in_Cyberspace.html

Index page for Winkler's online (mostly) Science resource. All these things are links including the "idea for a Shakespearean comedy". A great many science essays on diverse topics. I will quote the page to show the remarkable and wideranging breadth. Some posters may wish to refer to some of these essays
as tutorials or whatnot. At your own risk however, I cannot vouch for them.
--------------------------------------------------------------------------------

Greetings Lifeform. Welcome to my humble page. I'm Jeffery Winkler. I live in Hanford, CA. Here are some things that I've written.

Physics
The Big Bang
Quantum Physics
Physics and Mathematics
Tensors
Lagrangian
The Standard Model
Beyond The Standard Model
Particle Physics
Brane World Cosmology
Special Relativity
Black Holes
Superconductivity
Historical and Current Cosmology
Mach's Principle
Alternative Histories
UFO's
Religion
Cults
Early British History
Stonehenge
Art
Halloween
Christmas
Computers
IBM and the first computers
Political Terminology
Earth's Core
Reproduction
NVFRAM's
CGI
Human Cloning
Martial Arts
Environmentalism
Egyptian Hieroglyphics
Greek Myth Triplets
The Soviet Union
Humor
The Millennium
Wine
Sports
I maintain a Physics Website.

You can also read my posts on a Vietnam board.

I wrote a chart of the ups and downs of Bill Clinton. Read my article explaining why Clinton should have been impeached.

Read my interactive novel.

I wrote a screenplay.

Here is a short story I wrote. Here you can read my idea for a Shakespearean comedy.

I wrote haiku and a sonnet.

Please visit my other homepage.

Here I have yet another homepage.

I draw fantasy art.

Finally, here you can look at various other stuff.
------------------------------------------------------------------------

 

[jeff]

Originally posted by Sauron
No, he hasn´t.

But i colaborate from time to time with a friend in developing (extending into other areas, for example Yang-Mills) a theory of electromagnetic knots.

And Myron Evans has sometimes cited these theory as favourable to his own work. Even, throught one of his collaborators hasmade to my friend the oportunity to publish the developments of the electromagnetics knot theory in his new incoming book.

Electromagnetic knots?

 

[jeff]

Originally posted by marcus
Hey Sauron,

Motl is kind of outrageous in places----like at the end in the Unsolved Questions section he raises the question "could it be that LQG does not allow for the existence of fermions?"

marcus - and I do feel this is a fair question - do you not see the basis for this remark and why lubos ended the paper with it?

 

[Sauron]

I don´t know where the claim aobut LQG unability to incorprate fermionic matter comes from. In fact it surprises me.

In the Thieman paper i readed he has no problem to talk about matter. I guess that if fermionic matter is not allowed he would clarify it.

Also i readed Smollin paper comparing Strings and LQG and his claim is htat LQG can include the standard model without any problem.



And at first glance i don´t see areason for it. The Asthekar forumulation is based in the vielvein which allows the introduction of fermions in gravity, is is in fact the way to include fermions.

I was not criticizing the contribution these article means for LQG at all. It is just that recently i am getting the impression that string theorists try to convince people his theory is as good as standar model physics althought it has no experimental support. And aalso that they are THE WAY to do things.

And i find that a bit stupid. I recognize the erits of string theory, and also i like some of their achievemnts.But to be honest i don´t find it as elegant as some people say. The days in which the use of XX century maths (topology mainly) could givve shine to a theory by themselves are gne.

Electormagnetic knots is a reformulation of classical e-m first created by Antonio Rañeda, and developed by a friend in his doctoral thesis. Ateending a sugestion by Michael Berry they applied it to ball rays (hope the back traslation from spanish to english would be right).

It has no relatiion with LQG, nor even with the application of LQG thecniques to classical e-m.

It is based in a change of variables of the electromagnetic field. Instead of E an dB you use a fields which are related to them by a nonliear relation. These fields permit the use of topological thecniques to find solutions of the Maxwell equations. The can be interpreted as maps from S^3^->S^2 (I use the ^ to indicate supraindice).


These solutions can be classified according the hopf index of the map that the fields represnt. These index is conserved by time evolution. And it can be related to a classical quantities, the electric and magnetic helicities.

A more extensive description of these theory would lead us far from the topic i guess.

 

[jeff]

Originally posted by Sauron
No, he hasn´t.

But i colaborate from time to time with a friend in developing (extending into other areas, for example Yang-Mills) a theory of electromagnetic knots.

And Myron Evans has sometimes cited these theory as favourable to his own work. Even, throught one of his collaborators hasmade to my friend the oportunity to publish the developments of the electromagnetics knot theory in his new incoming book.

Originally posted by Sauron
Electormagnetic knots is a reformulation of classical e-m first created by Antonio Rañeda, and developed by a friend in his doctoral thesis. Ateending a sugestion by Michael Berry they applied it to ball rays (hope the back traslation from spanish to english would be right). It has no relatiion with LQG, nor even with the application of LQG thecniques to classical e-m. It is based in a change of variables of the electromagnetic field. Instead of E an dB you use a fields which are related to them by a nonliear relation. These fields permit the use of topological thecniques to find solutions of the Maxwell equations. The can be interpreted as maps from S^3^->S^2 (I use the ^ to indicate supraindice). These solutions can be classified according the hopf index of the map that the fields represnt. These index is conserved by time evolution. And it can be related to a classical quantities, the electric and magnetic helicities. A more extensive description of these theory would lead us far from the topic i guess.

Originally posted by Sauron
Afther a bit of research i have at last found the right place to learn about the Miron Evans theory.

It is here:
http://www.aias.us/

From the many papers enumerated there i have foudn that these could be one of the most self-contained:

http://www.aias.us/Note05182003/finalwaveeqnms.pdf


As far as i have understood till now (these guy is very disordered and it is hard to guess which are his claims and the order in which they appeared) i believe the history is something like these:

Some experimental facts (inverse farday effect-phase free magnetization by circularly polarized electromagnetic radiaton), other non linear optics fenomenology,and i guess also the sagnac effect) left him to guess classical and quantum U(1) electromagnetism is not the right theory.

Instead there is a O(3) theory which allows further polarization states.


Them gran unified theories wouldn´t result in SU(3)xSU(2)xU(1) but in SU(3)xSU(2)xO(3).

Later he found a way to relate his O(3) theorywith general relativiy resulting in an unified theory of all known interactions. (aparently it overcomes the coleman-mandela therem without supersymmetry)

In a diferent paper he speaks of some kind of antisymmetrized gravity as source of his theory.

As far as i have seen till now he has good ideas and good arguments. Anybody know exactly why he is considered an outsider? and how, beeing an outsider he an publish books in rigurous editorials?

Unhappily i have not

 

[jeff]

Originally posted by marcus
Hey Sauron, Motl is kind of outrageous in places----like at the end in the Unsolved Questions section he raises the question "could it be that LQG does not allow for the existence of fermions?"

Originally posted by Sauron

I don´t know where the claim aobut LQG unability to incorprate fermionic matter comes from. In fact it surprises me. In the Thieman paper i readed he has no problem to talk about matter. I guess that if fermionic matter is not allowed he would clarify it. Also i readed Smollin paper comparing Strings and LQG and his claim is htat LQG can include the standard model without any problem. And at first glance i don´t see areason for it. The Asthekar forumulation is based in the vielvein which allows the introduction of fermions in gravity, is is in fact the way to include fermions.

Okay guys, briefly - as all children learn in kindergarten (maybe you guys skipped?) - particles are defined in terms of their mass and spin which label - and this reflects their deeper significance - the representations of the inhomogeneous lorentz group under which their states must transform to respect invariances related to the geometry of spacetime that give rise by noether's theorem to conservation of mass-energy-momentum. In particular, spin specifies the representation of the rotational subgroup SO(3) of the homogeneous lorentz group SO(3,1). For even and odd spin particles - i.e. bosons and fermions - the reps are tensorial and spinorial respectively. For instance, in the case of spin-1 particles - the photon is an example - the rep is SO(3) itself. On the other hand, states of the spin-1/2 particles out of which all matter in our universe is composed transform under the double cover SU(2) of SO(3).

We'll marcus, you now have the answer to the question "why SU(2)?" I challenged you to answer a while back, which is that the LQG gauge group G is some representation of the rotational subgroup SO(3) of the lorentz group, with the observed existence of matter requiring G=SU(2), the double cover of SO(3), with G=SO(3) being by itself insufficient to incorporate this basic empirical fact.

But cheer-up guys because recently it's been argued - though inconclusively - that restoring SU(2) without invalidating lubos's basic result is possible.

Originally posted by Sauron
i am getting the impression that string theorists try to convince people his theory is as good as standar model physics

We don't.

Originally posted by Sauron
I recognize the erits of string theory, and also i like some of their achievemnts.But to be honest i don´t find it as elegant as some people say.

We think of string theory very much more as beautiful and deep than elegant. I think the reason that hobbiests gravitate towards LQG is their realization that the string theory program is for a whole host of reasons simply too monumentally difficult for them to ever really assimilate.

 

[marcus]

Sauron,

your back-translation is understandable but I could possibly edit parts of the post, if you wish me to try, to make it communicate more immediately in English.

I think "ball rays" may mean spherical wave-fronts----not sure about this.


I have mentioned the double cover of SO(3) by SU(2) several times in recent posts-----Steinitz pretends that I ignored his request out of ignorance, which is insulting. I see nothing wrong with his brief exposition here, however.

Steinitz' problem comes when he says it is "already known" that using SO(3) makes LQG inconsistent with the existence of fermionic matter. Not every part of nature has to use the same group of symmetries. If quantum gravity turns out to use SO(3) fine, we can still have spin 1/2 particles. This is not my personal opinion but evident from the main references----as Sauron points out----such as Thiemann, Rovelli etc.

BTW Sauron you also have been reading Smolin's March 2003 side by side comparison of String and LQG. "How far are we from the quantum theory of gravity"

this seems valuable because it is an up-to-date comparison of what remains unsolved in the two theories, and takes account of the fixing of the Immirzi parameter----which earlier surveys do not since Dreyer's result is so recent.

I am glad someone else here has been looking at that paper!

I am appending a copy of the previous "rant" for I know not what reason----enjoyment?

Originally posted by steinitz
Okay guys, briefly - as all children learn in kindergarten (maybe you guys skipped?) - particles are defined in terms of their mass and spin which label - and this reflects their deeper significance - the representations of the inhomogeneous lorentz group under which their states must transform to respect invariances related to the geometry of spacetime. In particular, spin specifies the representation of the rotational subgroup SO(3) of the lorentz group SO(3,1). For even and odd spin particles - i.e. bosons and fermions - the reps are tensorial and spinorial respectively. For instance, in the case of spin-1 particles - the photon is an example - the rep is SO(3) itself. On the other hand, states of the spin-1/2 particles out of which all matter in our universe is composed transform under the double cover SU(2) of SO(3).

We'll marcus, you now have the answer to the question "why SU(2)?" I challenged you to answer a while back, which is that the LQG gauge group G is some representation of the rotational subgroup SO(3) of the lorentz group, with the observed existence of matter requiring G=SU(2), the choice G=SO(3) being inconsistent with this empirical fact.

 

[jeff]

Originally posted by marcus
I have mentioned the double cover of SO(3) by SU(2) several times in recent posts-----Steinitz pretends that I ignored his request out of ignorance, which is insulting. I see nothing wrong with his brief exposition here, however.

Steinitz' problem comes when he says it is "already known" that using SO(3) makes LQG inconsistent with the existence of fermionic matter. Not every part of nature has to use the same group of symmetries. If quantum gravity turns out to use SO(3) fine, we can still have spin 1/2 particles. This is not my personal opinion but evident from the main references----as Sauron points out----such as Thiemann, Rovelli etc.

When you post a response, be sure to quote the most recent version of my posts because I try to give answers that are precise and detailed, and that requires an editing process.

As you can see by the log, I edited my response long before you posted it, in part because I decided to look through the literature to see if any progress had been made on overcoming the problem crystallized in lubos's paper. It turns out there has been as I was delighted (at the time) to indicate in my post. I didn't do that for my benefit because I don't work on LQG. I did it out of deference to your interest in LQG which I've absolutely no problem with, I mean, why on Earth would I? Now I feel like a complete chump for even wasting my time.

Anyway, what you've written here is utter nonsense; it's wrong period; you simply don't know what you're talking about. Please ask one of the "mentors" to go over yours and my posts with you.

The thing is that we're not talking about any old gauge theory of interactions in which who knows what symmetries might be involved. We're talking about gravity, and like all QG theories, in order to work, LQG - and strings - must be consistent with lorentz invariance. There's simply no escaping this. The limitations of SO(3) LQG are not a matter of conjecture or opinion. No matter what the correct theory looks like, there's simply no escaping the fact that they're low energy effective theories will have to obey the standard invariances of GR, and in the case of LQG this constrains it, as I've with great care indicated.

As I've done with every sensible question I've responded to in this forum, I've given prompt, thoughtful and detailed answers to every single question you've put to me. All you've done is justify your refusals to answer my questions by claiming they're somehow insulting. Unlike some around here, I'm perfectly happy to let the quality of my physics explanations speak for me, and I've had every right to ask you the questions I have, and expect an answer, even if it's that you're not quite sure, in which case I'd just explain it.

Now, is it not part of an explainers role to do what they can to identify where there may be confusion? You do it all the time. In fact you're virtually the only guy here who seems to need to start his own threads to lecture on something you just taught yourself. What's that about? And have you noticed that there really isn't a lot of "hey, how you doin" going on around here? Your dainty style of explanation doesn't mean a damn thing, only the physics does which is why in the long run continuing this can only be to you're great great disadvantage. If you want to critique my posts, have the decency to address me directly.

When you say you mentioned that SU(2) is the double cover of SO(3), I have no problem believing that whatsoever. But that well known fact can be stated without being understood. Do you understand the physical significance of SU(2) doubly covering SO(3)?

 

[marcus]

Originally posted by steinitz
Firstly, as you can see by the log, I edited my response long before you posted it,
Also, when you do post a response, be sure to quote the most recent version of my posts because I try to give answers that are precise and detailed, and that requires an editing process.

Just for the record, at this point, I think you're a petty jerk.

Not sure what you are talking about.
I took your most recent, pressed "quote" which gives a reply with quote.

My post was dated 10:28 and your self-revision was dated
10:36.

As far as I know I used the most recent. But I would be happy to go back to earlier versions of your posts if I wanted to make a point about the author which was essential to the discussion.

You appear to be self-taught, which if fine unless you claim to be a "professional researcher" or to be professionally qualified. PF posters would be deceived if they read you as an authority. But I like the fact that you are obviously intelligent and widely read.

You appear to be a bright "hobbyist" to use your word. I have great respect for talented and even brilliant amateurs. But some of your posts SUGGEST by innuendo (as if to say: I Jeff post on sci.physics.research Usenet which is for professional researchers and we string-theorists or high energy whatnots believe such and such) that you fancy yourself as a member of a professional research community.

And even something of an authority!

Your occasional mistakes belie this. Besides I think in this kind of unstructured environment it may be best to have no rigid idea of an "Explainer" role----your word, which I find a bit confusing. Everybody feels free to explain as best he or she can to anybody else! At least I hope this is the case!

It may be best not to claim or suggest that one has professional qualifications, but to leave all that stuff behind and jump into the swimming pool devoid of status. And one certainly should not try to impose ones pretensions on others and imply non-existent professional standing.

No rancour on my part---despite your frequently insulting tone.

I think you can contribute lot to a board like this as long as you don't think of yourself as God's gift to it----and cut out the professional pretensions.

Regards

 

[jeff]

Originally posted by marcus
Not sure what you are talking about.
I took your most recent, pressed "quote" which gives a reply with quote. My post was dated 10:28 and your self-revision was dated 10:36.As far as I know I used the most recent. But I would be happy to go back to earlier versions of your posts if I wanted to make a point about the author which was essential to the discussion.

Check again. My final edit was made at 11:14a.m. your post was tagged 2hrs and 14 mins later at 1:28p.m.

Originally posted by marcus
You appear to be self-taught, which if fine unless you claim to be a "professional researcher" or to be professionally qualified.

Again you're making assumptions about things you don't know. In this case how theorists learn. I do not know of a single high energy theorist that was not completely self-taught.

Originally posted by marcus
Your occasional mistakes belie this. Besides

I've made no mistakes. And even if I had, you wouldn't know it. In particular, take another look at that apology I made earlier in this thread. It should be easy to remember given it's (purposefully, he he) unequivocal and gracious tone. But what did I actually do wrong? Nothing! It was a test of your character, and you flunked. You fell for it because you don't understand the physics well enough to realize I had in fact done nothing wrong. That horribly "unqualified statement" required no qualification whatsoever! But if someone had made an apology like that to me, I'd be doubled over with new respect. Instead, I got a "no problemo steinitz" and you proceeded to insult me in this really bizarre way and then talk right past me in an unbelievable display of pure pettiness and disrespect.

Originally posted by marcus
It may be best not to claim or suggest that one has professional qualifications, but to leave all that stuff behind and jump into the swimming pool devoid of status. And one certainly should not try to impose ones pretensions on others and imply non-existent professional standing.

I felt that way as well, but only briefly as experience with people who don't understand that they don't understand quickly disabused me of that notion altogether. Letting them have it right from the start is in the long run far more time-efficient for me, and the other guy too. Of course, not everyone reacts well to this, but usually they do. But in the end what do I care, I'm not here to make friends. I'm here to answer the kind of basic questions that keep minds in the right gear for being creative.

Still, I don't want to fight with you. You annoy me, but you clearly love physics. If you can agree with me that we both made mistakes - and we both did - and leave it behind us, I think we can have some good uncritical exchanges. Anyway that's my olive branch. Take it or leave it.

 

[marcus]

Jeff says: "I've made no mistakes. And even if I had, you wouldn't know it." see paragraph three of this rather lengthy post

Originally posted by steinitz
Check again. My final edit was made at 11:14a.m. your post was tagged 2hrs and 14 mins later at 1:28p.m.

Again you're making assumptions about things you don't know. In this case how theorists learn. I do not know of a single high energy theorist that was not completely self-taught.

I've made no mistakes. And even if I had, you wouldn't know it. In particular, take another look at that apology I made earlier in this thread. It should be easy to remember given it's (purposefully, he he) unequivocal and gracious tone. But what did I actually do wrong? Nothing! It was a test of your character, and you flunked. You fell for it because you don't understand the physics well enough to realize I had in fact done nothing wrong. That horribly "unqualified statement" required no qualification whatsoever! But if someone had made an apology like that to me, I'd be doubled over with new respect. Instead, I got a "no problemo steinitz" and you proceeded to insult me in this really bizarre way and then talk right past me in an unbelievable display of pure pettiness and disrespect.



I felt that way as well, but only briefly as experience with people who don't understand that they don't understand quickly disabused me of that notion altogether. Letting them have it right from the start is in the long run far more time-efficient for me, and the other guy too. Of course, not everyone reacts well to this, but usually they do. But in the end what do I care, I'm not here to make friends. I'm here to answer the kind of basic questions that keep minds in the right gear for being creative.

Still, I don't want to fight with you. You annoy me, but you clearly love physics. If you can agree with me that we both made mistakes - and we both did - and leave it behind us, I think we can have some good uncritical exchanges. Anyway that's my olive branch. Take it or leave it.

 

[chroot]

I'm still not sure of the whole amateur vs. professional argument. I'm technically a professional -- or at least am on the way to becoming one -- but I'll be damned if I feel like one. Both of you guys seem to know a great deal more than me. Stop bickering and and insulting one another and try to work together to help people like me understand things more clearly. I, for one, would appreciate it.

- Warren

 

[jeff]

Originally posted by chroot
Stop bickering and insulting one another and try to work together to help people like me understand things more clearly. I, for one, would appreciate it.

- Warren

You're right SB (stanford bookstore) . But my guess is he'll be taking his own parting shot.

 

[chroot]

Originally posted by steinitz
(stanford bookstore)

I don't get it. [?]

- Warren

 

[jeff]

Originally posted by chroot
I don't get it. [?]

- Warren

Oops, someone told me they buy books in the stanford bookstore. I thought it was you. There seems to be no embarrassed smiley. Sorry about that.

 

[chroot]

No, that was me... but I don't understand why you would want to nickname me "stanford bookstore" as a result.

- Warren

 

[jeff]

Originally posted by marcus
Jeff says: "I've made no mistakes. And even if I had, you wouldn't know it." see paragraph three of this rather lengthy post

If you're done, the olive branch is still there.

 

[jeff]

Originally posted by chroot
No, that was me... but I don't understand why you would want to nickname me "stanford bookstore" as a result.

- Warren

I just figured you went to stanford, so I just thought it would be funny to tease you by calling you stanford bookstore instead of stanford. It was just a dumb joke, sorry.

 

[Sauron]

Steinitz, your aptitude classifiying non stringy physicst as "hobbiests" is just was i was referring to.


I dón´t feel particularly worried about learning in deep string theory. I actually know it reasonably well. I readed the Kaku and polchinsky books and also a ew papers in themes i have some interest. In fact I had the intution that the bosonic striing could not be rulled out so easilly before i had any new aobut the actual work in bosonic condensates. If you read the original Feimberg work in tachyons you can see that he stablish that they would haave opposite spin-stattistic behavioulr. that is, spin 0 tachyons would be fermions. That suggested it could be applied something similar to the dirac sea argument to bosonic string that would prevent it from beeing unstable. I didn´t actually read any paper in bosonic condensates but reading comments i got the idea that their arguments hasn´t nothing to do with mine. Anyway, i discarded to pursuit that idea any further

I don´t believe i would have any problem focussing in some prticular aspect of string theory and make research on it.As far as i know it is what most people does. Experts in compactification couldn´t do research in SFT, and viceversa, etc.

The whole thing is that i don´t see a reason for it. With string theory you can spend your whole carrer developing internal aspects of the theory without any possibility to ever address a phsyical problem, and i haven´t any interest in it. Some string physys´t said once "The theory is samrtest than me". Well, i dón´t like that philosophy.


So i prefer to do researh in another alternatives, and LQG is just the best.

And about the pro vs hobbiest debate has a simple solution. noowadays there is no preciseelly lot of money for ressearch so you may do your postgrade sutdies in some area which allows you to be payed for it but it is not your favourite. Afther you have passed it you are (relatively) free to investigate what you want. And in all my experience i ahven´t seen any diference in beeing self-tauched or going throught guided sutdies. In fact i usually advance fastes iin the self study-way.

For example i have sutdied algebraic topology for myself while i was in my phyisic degree. But later i had to do two exams about that self learned stuff in fourth and fitth of my math degree (which i didn´t end, simply i fell to bored about statistic and a few other asignatures). I could pass them without even assisting to any class in the faculty.

Your argument about particle labels don´t totally convince me. In fact it doesn´t convince me at all. You first begin with a 4 manifold provided with an vielbein and an spin connecton. So your departure point allows you to define spin 1/2 particles without any problem. that´s the usuall way it is done in particle physics(with the "curved" dirac matrices and all that).

Ok, later you do the ADM slicing and you pass form lagrngian to hamiltonian and get your constraints and all that. But think these. You initially have L=Lgravity + Lmatter. When you go to the hamiltonian the Lmatter would be transformed In Hmatter. That doesn´t introduce any difficoultie (constraint) for spiin 1/2 particles.

In fact even in mikownsky space i don´t understand why you claim you need to get the SU(2) covering of the SO(3) subgroup of SO(3,1) to get spin 1/2. I studied that topic in the Ramond´s book on field theory (and also i ht kaku book of field theory) and don´t remember to have seen that statement.

Anyway i have an expositure work about Lorentz group and spin of particles that a friend gave in an expositon in the group theory asignature and i´ll look there. BTW, that aspect is not carfully covered in none of the graduate or postgraduate studies on quantum filed theory in my facoulty. So to know it you must self-learn it which makes me wonder which is the advantage of ruled education over self learning (beyond the ability to get payed for doing research).


Last thing. "ray ball" aren not wave-fronts. They are an atmospheric phenomna. My dictionary is not precise enought about it, but maybe a better translation wout be "ball lighthing".

Anywy, in an electric storm you have usuall rays (or lightings,ionized air which becomes plasma, you know). But ocassionally it has been noticed that it appears a luminous ball which keeps stable for a time of 15 seconds to even 5 minut. It seems It can have various colors and temperatures. The hipothesis is that it consit´s of hte same phenomena that the lighthings, i.e. plasma, but it is lacking a precise mechanism which gives them an stability which forbides a fast disipation of temperature, as in usuall lighthings. A topollogically non trivial (knotted) configuration of the magnetic field in the plasma could be the reason.

These hipothesis was publisehd in a 1999 (i belive) article in nature by Rañeda and my friend -Trueba-.

 

[marcus]

"Ball lightning" is a good English phrase and corresponds
to the phenomenon you describe.

It has alway seemed mysterious to me. People I know say they have seen it but I have found it difficult to imagine how it could work.

You say the magnetic field could be knotted and this might
help explain the temporary stability.

[My dictionary is not precise enought about it, but maybe a better translation wout be "ball lighthing".

Anywy, in an electric storm you have usuall rays (or lightings,ionized air which becomes plasma, you know). But ocassionally it has been noticed that it appears a luminous ball which keeps stable for a time of 15 seconds to even 5 minut. It seems It can have various colors and temperatures. The hipothesis is that it consit´s of hte same phenomena that the lighthings, i.e. plasma, but it is lacking a precise mechanism which gives them an stability which forbides a fast disipation of temperature, as in usuall lighthings. A topollogically non trivial (knotted) configuration of the magnetic field in the plasma could be the reason.]

 

[Tyger]

Just plug "ball lightning"

into MSN or Google, you'll get a lot of stuff.

 

[marcus]

Originally posted by Tyger
into MSN or Google, you'll get a lot of stuff.

Thanks Tyger, right now would you believe it
I am trying to review some basic facts about classical
Lie groups and Lie algebras. Otherwise would find out about ball lightning on Google.

I would guess you know some things about O(3)
the real orthogonal group, det = +/- 1 and so on.
Transpose equals inverse etc. etc. At least its real so
you don't have to take complex conjugate all the time
Are you comfortable talking about SO(3) and the algebra so(3)?

And, if comfortable, are you at all interested?
I might start a thread about SO(3) and Loop Quantum Gravity
to go thru the easy facts with others interested in LQG.

 

[jeff]

Originally posted by Sauron
Your argument about particle labels don´t totally convince me. In fact it doesn´t convince me at all. You first begin with a 4 manifold provided with an vielbein and an spin connecton. So your departure point allows you to define spin 1/2 particles without any problem. that´s the usuall way it is done in particle physics(with the "curved" dirac matrices and all that).

Ok, later you do the ADM slicing and you pass form lagrngian to hamiltonian and get your constraints and all that. But think these. You initially have L=Lgravity + Lmatter. When you go to the hamiltonian the Lmatter would be transformed In Hmatter. That doesn´t introduce any difficoultie (constraint) for spiin 1/2 particles.

In fact even in mikownsky space i don´t understand why you claim you need to get the SU(2) covering of the SO(3) subgroup of SO(3,1) to get spin 1/2. I studied that topic in the Ramond´s book on field theory (and also i ht kaku book of field theory) and don´t remember to have seen that statement.

So you disagree, both with the claim that the lowest spin particles allowed in SO(3) and SU(2) LQG are spin-1 and spin-1/2 respectively, and with my attempt to account for this. Correct?

 

[Sauron]

>>So you disagree, both with the claim that the lowest spin >>particles allowed in SO(3) and SU(2) LQG are spin-1 and spin-1/2 >>respectively

Now you say that the lowest allowed particles are spin -1 and spin-1/2. But if spin-1/2 are fermions and your first claim was that fermions were not allowed. Now instead your problem is with the spin-0, i.e. thte hiporthethical and still unobserved Highs bosson (that tachyonic particle in the unbroken symmetry phase...).


I guess that you may explain your change of opinion before i give any answer to these aspect.

 

[jeff]

Originally posted by Sauron
Now you say that the lowest allowed particles are spin -1 and spin-1/2. But if spin-1/2 are fermions and your first claim was that fermions were not allowed. Now instead your problem is with the spin-0, i.e. thte hiporthethical and still unobserved Highs bosson (that tachyonic particle in the unbroken symmetry phase...). I guess that you may explain your change of opinion before i give any answer to these aspect.

Of course you're right about the implication of my statement for spin-0 particles, but that's a problem for the LQG people, not me. Besides, spin-1/2 is more important than spin-0.

Now, I know you're saying that you think I've changed my previously stated position. But I'm having a bit of trouble decoding precisely why. Anyway, I haven't, as the following shows.

Originally posted by marcus
Motl is kind of outrageous in places----like at the end in the Unsolved Questions section he raises the question "could it be that LQG does not allow for the existence of fermions?"

Who's right lubos motl at harvard or marcus? It's clear what marcus thought. Similarly, because of this it was clear to me that marcus didn't understand what was going on. He needed to learn about spin, so I gave a brief overview of this subject in very general terms unrelated to LQG in any specific way. Here's what I said (you can check that I haven't changed a single word)

'Okay guys, briefly - as all children learn in kindergarten (maybe you guys skipped?) - particles are defined in terms of their mass and spin which label - and this reflects their deeper significance - the representations of the inhomogeneous lorentz group under which their states must transform to respect invariances related to the geometry of spacetime that give rise by noether's theorem to conservation of mass-energy-momentum. In particular, spin specifies the representation of the rotational subgroup SO(3) of the homogeneous lorentz group SO(3,1). For even and odd spin particles - i.e. bosons and fermions - the reps are tensorial and spinorial respectively. For instance, in the case of spin-1 particles - the photon is an example - the rep is SO(3) itself. On the other hand, states of the spin-1/2 particles out of which all matter in our universe is composed transform under the double cover SU(2) of SO(3)."

The point is that I've said nothing about LQG in this: This is a lesson on spin, not LQG. Now, what marcus needed to understand to see that lubos motl was in fact not being "outrageous" was why SO(3) LQG doesn't couple to spin-1/2 particles - i.e. to matter, clearly a bad thing - while SU(2) does, the rest is irrelevant. Thus to make my point, it was sufficient to simply give marcus the examples in the last line of my explanation, and with those examples given, I could end with the following conclusion (again you can check that I haven't changed a word)

"We'll marcus, you now have the answer to the question "why SU(2)?" I challenged you to answer a while back, which is that the LQG gauge group G is some representation of the rotational subgroup SO(3) of the lorentz group, with the observed existence of matter requiring G=SU(2), the double cover of SO(3), with G=SO(3) being by itself insufficient to incorporate this basic empirical fact."

Everything I wrote is correct and designed simply to convince marcus of the special import of lubos's result with respect to LQG's consistency with the existence of matter. Pointing out that once G - which can simply be taken as some compact group - is chosen, the complete spectrum (open questions about the precise manner and consistency of couplings to gravity - if they can ever be sensibly defined at all - aside) is given by it's irreducible representations was irrelevant, since it was only the lowest spin reps that were at issue.

But your not marcus. I responded directly to your post in which you voiced general disagreement with the above remarks, but I wasn't completely sure how to respond because you said you hadn't learned about what I'd discussed above, so I simply asked the general question I did to set the compass, and it in no way reflects a change of opinion on my part.

Still, based on this post, I don't know whether you agree with marcus. If you don't agree than I'll simply tell you to keep reading until you come to it. The SO(3) problem is well-known, I didn't make it up.

If you do agree but still aren't convinced that my way of looking at it is correct, then let me know and we'll figure out the right argument if mine turns out to be wrong (though I'm fairly sure this is not the case). In any event, I think it's important to understand the stuff I was saying about spin.

I'm aware that in GR, bosons can live on the spacetime manifold from the start, while fermions require a vierbein. But in LQG there is no fixed background geometry and the gauge group would determine the spectrum (assuming that this idea can ever work).

One last thing. When you post a response, be sure to quote the most recent version of my posts because I'm building an arsenal of explanations so I try to give answers that are precise and detailed, and that requires an editing process.

 

[thermonuclear]

I’m wondering that there is no reply to this question. Is this a trivial, uninteresting point for all who have participated in this thread? For me it is not, but may be this is just due to my ignorance.

I agree that the restriction to SO(3) excludes the fermions from the theory, since spin-1/2 transforms under SU(2) and not under SO(3). Why does L. Motl claim that SO(3) is more “natural” than SU(2) at this place? According L. Motl, SU(2) was chosen by Ashtekar and Baez hoping to overcome the problem of the fermions but not logically derived from the theory, which describes only vacuum solutions.

It would be great if some of you could explain the derivation of this gauge group.

The Lorentz group is SO(3,1) and restricting to a three dimensional vector space (by use of the ADM formalism) it reduces to SO(3). But what is the reason to take only Lorentz symmetries and not to use a representation of the Poincaré group --SO(3,1) and the translation group R^4-- as a gauge group? Or, let’s say better, since we are dealing with a complex manifold in the Ashtekar formulation, we may use SL(2,C) and the translation group R^4 (covering the Poincaré group) as the gauge group...?

If there is indeed no interest may be someone could give me some references anyway.

Regards.

 

[Sauron]

Well, it is not that the thrad would have lost interest for me.

I am just triying to find where the exposition i had about the lorent´z groups representations is.

Also jeff has pointed an aspect i hadn´t realized. I know what a vielbein (n-bein in general) is, but it usually is exposed related to a metric. If we have no metric, as it hapens inLQG i must revisate the detaills.


The complementary thread that marcus created is being very informative about the detais of spin networks, and it consumes time to read it. Most of the literature i had readed in LQG beguined with Wilson loops adn was quickly into topological BF theories, and the detaills of spin networks were not addressed.

Last, but not least, i am studiying some aspects of statitisthical mechanics (not related to LQG, it is just that my basic in that area is very weak and i am triying to remediate that, just for fun)

So let´s say i am being a reader most of time. I am basically new to LQG and i still need to meditate a lot about it.


Jeff, i understand that people eidt it´s messages, but it makes a bit confusing to follow the thread, why not just to indicate your previous mistakes in a new post?

And i still see a self-contradiction in the posts. You say LQG allows particles of spin not minor than 1/2, but that means fermions are allowed, and in other places ou say LQG doesn´t couple to fermionic matter. And your argument says that the absence of SU(2) is forbiding spin 1/2, so ,why are them allowed and only spin 0 particles are not allowed?.


To end these point a clarification. I say i dón´t like too much string theory, but for sure string physicans are great physicians. In fact previous to LQG i defended string physics, that´s why i studied it. But now i see LQG like a most natural creature. I think LQG is the theory to study now, and only when it is proved it failss(if it fails) we would return to strings. Let's say that in my opinion if LQG woule have existed in the 80´s (almost) nobody would have studied strings.

 

[jeff]

Originally posted by Sauron
Jeff, i understand that people eidt it´s messages, but it makes a bit confusing to follow the thread, why not just to indicate your previous mistakes in a new post?

Okay, sorry about that.

Originally posted by Sauron And i still see a self-contradiction in the posts. You say LQG allows particles of spin not minor than 1/2, but that means fermions are allowed, and in other places ou say LQG doesn´t couple to fermionic matter. And your argument says that the absence of SU(2) is forbiding spin 1/2, so ,why are them allowed and only spin 0 particles are not allowed?.

The point was simply that lubos's result strengthened a previous result suggesting that the lowest spin particles that can be coupled to gravity in LQG are spin-1 so that the gauge group should be taken as SO(3) rather than SU(2). Since all matter is composed of spin-1/2 particles this would make LQG inconsistent with the existence of matter. If you continue to feel that I'm contradicting myself, quote the contradictory passages and I'll comment on them.