sage
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question for loop quantum gravity
it seems that several people here are interested in loop quantum gravity. Let me ask you a couple of questions,
1) what is the ground state of your theory? is it flat space? or, is flat space a solution of your theory?
2) quantization using gauge invariant variables only has been attempted by people like polyakov in the gauge theories. The main problems are: the theory is regularization dependent, and related, they can not reproduce the anomalies which we know must be there. I imagine loop quantum gravity will have the same problem?
3) the calculation of blackhole entropy seems to be cheating. if you carve out a void in a spin network, of course the entropy is proportional to the area of that void. I heard that loop quantum gravity does not even the coefficient right. is that true? is there something non-trivial that I have missed?
4) how is your quantization procedure apllied to a much simpler system like harmonic oscillator? does it get the right answer?
| 发表时间：2005-10-16, 20:01:39 |
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HPC
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Re: question for loop quantum gravity
Although I am not interested in LQG, here I would like to give you some of my answers.
1, you know, LQG is a background independent theory, which is the fundamental difference from string theory. So there is no much meaning when you ask some issues on the ground state. But flat space can result from semiclassical effect: there exist some quantum states(pure or mixed) which makes the metric expected value is flat.
2, I want to point that the gauge dependent variable called Ashtekar new variable has been employed to quantization rather than gauge independent variable.
3. The procedure for quantization of LQG resort to the lattice gauge theory, but it is background independent. When you said the ossillator, it has a background spacetime at first, which is trivial and of course has the equivalent result to other methods.
4. the entropy of black hole obtained is not trivial. it employed the chern-simon theory. the immirzi parameter is not obtained in theory itself, but could be fixed by semiclassical approach: such as BH thermodynamics and quasinormal modes etc. the fact that the parameter is not fixed seems reasonable, because we do not know the exact form for quantum gravity, perhaps different parameter corresponds to different universe....
Faith, Fashion and Fancy.
| 发表时间：2005-10-16, 20:38:46 |
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sage
发表文章数: 1125
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Re: question for loop quantum gravity
>1, you know, LQG is a background independent theory, which is the fundamental
>difference from string theory. So there is no much meaning when you ask some issues
>on the ground state. But flat space can result from semiclassical effect: there exist
>some quantum states(pure or mixed) which makes the metric expected value is flat.
you are making some claims that even Lee Smolin would not say. What is the ground state of loop quantum gravity? it must be annihilated by the diffeomorphism. however, flat space is not. therefore, flat space is not the ground state of the theory. Nobody has even succeeded in constructing a flat space solution in loop quantum gravity yet.
Every well behaved quantum system has a ground state. Contrary to your claim, loop quantum gravity has a very well defined ground state. it is the state annhilated by diffeomorphism. The trouble is, it is not flat space. It is probably not something that useful.
>2, I want to point that the gauge dependent variable called Ashtekar new variable has >been employed to quantization rather than gauge independent variable.
whatever mathematics and fancy variable you use, you must reprodcue the well-know result of anomalies. It is well established in field theory. the approach that loop quantum gravity uses determines that it could not reprduce the result of anomalies. It is therefore inconsistent with low energy field theory, or anormaly matching.
>3. The procedure for quantization of LQG resort to the lattice gauge theory, but it is >background independent. When you said the ossillator, it has a background spacetime
>at first, which is trivial and of course has the equivalent result to other methods.
Actually, contrary to your claim, people have applied LQG to harmonic oscillators. it gives absurd reuslt like the eigenstate is the eigenstate of the creation operator. such a state does not exist.
>4. the entropy of black hole obtained is not trivial. it employed the chern-simon theory. >the immirzi parameter is not obtained in theory itself, but could be fixed by
>semiclassical approach: such as BH thermodynamics and quasinormal modes etc.
>the fact that the parameter is not fixed seems reasonable, because we do not know
>the exact form for quantum gravity, perhaps different parameter corresponds to
>different universe....
Again, the blackhole entropy puzzle is about why it is proportional to its area, not volume. it has nothing to do whatever mathematical tool you use, chern-simons or not. when you carve out a void in a spin network(or lattice), it is trivial to get the fact that degrees of freedom is on the surface of the void. therefore, it is put in from the beginning in the loop quantum gravity 'calculation'. The non-trivial thing will be the coefficient, which LQG does not get it right.
Please do not say again it is background independent, as if it is a big improvement. IT is not hard to write something down that does not depend on the background, such as wilson-loop in gauge theory (or averaging over diffeomorphism orbits in LQG). the question is whether one can write something down that makes sense, by reproducing well know physics in well-defined limit and not contradicting something that is well-known.
Actually, my questions are more directed to Xuan Xuan, since he is doing loop quantum gravity now.
| 发表时间：2005-10-16, 21:48:19 |
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轩轩
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Re: question for loop quantum gravity
HPC 好象也很懂loop啊,我也不是很懂得,随便说说,可能是错的
1) what is the ground state of your theory? is it flat space? or, is flat space a solution of your theory?
现在loop只处理真空爱因斯坦方程.他们考虑量子爱因斯坦方程的解空间的结构.你说的flat时空可能是半经典分析的内容.他们找一个semi-classical态去看看是不是逼近平坦空间吧
.这里现在已经兴起了loop宇宙学.
总的来说,你的问题是在说loop能不能会到经典物理,答案是大家正在寻找中.
2) quantization using gauge invariant variables only has been attempted by people like polyakov in the gauge theories. The main problems are: the theory is regularization dependent, and related, they can not reproduce the anomalies which we know must be there. I imagine loop quantum gravity will have the same problem?
我感觉好象确实是 regularization dependent, 这背后的事情我搞不清楚,得查查书.
3) the calculation of blackhole entropy seems to be cheating. if you carve out a void in a spin network, of course the entropy is proportional to the area of that void. I heard that loop quantum gravity does not even the coefficient right. is that true? is there something non-trivial that I have missed?
系数不对,这不说明系数一定是1/4.好象那里的immir参数是可以调节的.但我也看不懂得他们用什么chern-simons的u(1)规范理论来得到黑洞熵.据说证明过程中还有错误.等我 下一段时间看看他们到底是什么意思.但总的感觉是,在计算黑洞熵上面,可能是很扯的
4) how is your quantization procedure apllied to a much simpler system like harmonic oscillator? does it get the right answer?
这个当然可以,thiemann有一个复化子的方法.很多很多其他的方法可以得到harmonic oscillator.因为harmonic oscillator完全不是loop量子引力.
引力是非局部的，量子力学也是非局部的。《相对论通俗演义》
i will love you till the null infinity.
| 发表时间：2005-10-16, 22:51:59 |
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sage
发表文章数: 1125
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Re: question for loop quantum gravity
>总的来说,你的问题是在说loop能不能会到经典物理,答案是大家正在
>寻找中.
It seems the answer is no. OR, not obious why it is not NO.
Anyway, see my second post after HPC reply for further comments.
By the way, if you don't mind, ask you a somewhat personal question. Are you doing loop quantum gravity by yourself or with your advisor? I am not aware of who is doing LQG in china, just curious.
| 发表时间：2005-10-16, 23:06:26 |
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HPC
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Re: question for loop quantum gravity
I must stress my answer is perhaps not even wrong:)
but I would like to give more comments.
1. On the ground state, I only stress unlike other theory such as string theory and lattice theory, we need not assume a background spacetime which is generally called ground states at first. I have not said flat space is the ground state, onhow flat space results from quantum geometry, I would like to suggest you to review hep-th/9203079: Weaving a classical geometry with quantum threads, it is not the end of the whole story.
2 I have never said background independent is an improvement, I only stress it is the fundamental difference between LQG and other theory.
3 In the sense, as you said , spin network will give the area theorem trivially, but I want to say spin network itself is the result from LQG. It is not the assumption but derived result. Could you obtain spin network from string theory:)
4 LQG has never claimed that it will give a unified description of our universe like string theorists. immirzi parameter need input from experiment or semiclassical consideration, such as the velocity of phton or Planck constant.
5 From my personal viewpoint, LQG is more modest, cautious than so called M theory.
Faith, Fashion and Fancy.
| 发表时间：2005-10-17, 00:23:21 |
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HPC
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Re: question for loop quantum gravity
more comments:
I do not know how you know the ossillator is bad when LQG approaches is employed. But here I would like to suggest you to scan hep-th/9202063
:A Loop Representation for the Quantum Maxwell Field
you know, the Quantum Maxwell Field is many ossillators, but it seems to behave well.
Finally, I would like to say: as xuanxuan said, ossillators and Maxell field is not LQG for ever:)
Faith, Fashion and Fancy.
| 发表时间：2005-10-17, 00:28:30 |
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轩轩
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Re: question for loop quantum gravity
i work with my advisor ,however i can not put on his name here.
the loop team in china is still very young.
说中文吧,我想loop需要数学家的参与,就可以与string抗衡了.
现在的loop远离物理学.但将来一定有很多人搞.它不会die的.lee smolin曾经说loop已经死亡,但他的意见嘛,不用太认真.他是一个有很多念头的人,他所以出名也是因为他的科普.很奇怪的是他的那本loop科普好象也没有讲loop,而是在讲他自己的一些小故事.
真正的loop高手不能是他.
引力是非局部的，量子力学也是非局部的。《相对论通俗演义》
i will love you till the null infinity.
| 发表时间：2005-10-17, 02:21:34 |
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萍踪浪迹
发表文章数: 1983
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Re: question for loop quantum gravity
loop前景暗淡
漫漫长夜不知晓 日落云寒苦终宵
痴心未悟拈花笑 梦魂飞度同心桥|
-------------------------------------------------
红叶晚萧萧，长亭酒一瓢
残云归太华，疏雨过中条
树色随山迥，河声入海遥
帝乡明日到，犹自梦渔樵
| 发表时间：2005-10-17, 03:42:38 |
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sage
发表文章数: 1125
武功等级: 天山六阳掌
(第六重)
内力值: 535/535
Re: question for loop quantum gravity
>i work with my advisor ,however i can not put on his name here.
>the loop team in china is still very young.
>说中文吧,我想loop需要数学家的参与,就可以与string抗衡了.
well, looking at the history, something in physics never become real physics just because mathematicians' participation. Loop probably has almost as long history as string theory. It has not been picked up by the rest of the physics community, not because they are stupid, but because loop has not meet the threshold of being serious yet.
>现在的loop远离物理学.但将来一定有很多人搞.它不会die的.
as long as you are sure about it. It has been going nowhere for many years. Of course, they always claim they have just made the breakthrough last week.
again, as long as you are sure about that.
I will be very suspicious about something that does not even have the correct things to begin with. as I said, there is a ground state in LQG. however, it is not flat space. On the other hand, although we know very little about gravity, we know its ground state. it is flat space.
so, if you are really interested in LQG, I would say working on flat space first.
lee smolin曾经说loop已经死亡,但他的意见嘛,不用太认真.他是一个有很多念头的人,他所以出名也是因为他的科普.很奇怪的是他的那本loop科普好象也没有讲loop,而是在讲他自己的一些小故事.
真正的loop高手不能是他.
| 发表时间：2005-10-17, 09:21:56 |
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轩轩
发表文章数: 1352
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Re: question for loop quantum gravity
loop 在发展中，确实有不严格的地方，比如它在3空间上的联络场是4-联络的规范固定。号称的spin foam正在发展之中，我不知道这算不算严肃的学问。
so, if you are really interested in LQG, I would say working on flat space first.
loop里的激发态不是3维的，而是一维的。polymer-like的时空图象。如何得到平坦时空这是一个问题，但这背后有一个对称约化的过程。但这些问题会漫漫澄清的。
大家全在说knot和loop的时候，loop的微分同胚不变性等价于knot的jones多项式。那显然需要数学家来处理背后更加高深的关系。
因为对于一个物理学家来说，微分同胚不变性是什么？？？所以物理学家多数不懂得广义相对论。
我现在还是一个新手，还不是忠实的loop defender。当然我希望loop会成功起来
引力是非局部的，量子力学也是非局部的。《相对论通俗演义》
i will love you till the null infinity.
| 发表时间：2005-10-17, 10:09:16 |
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萍踪浪迹
发表文章数: 1983
武功等级: 深不可测
内力值: 645/645
Re: question for loop quantum gravity
所以物理学家多数不懂得广义相对论。
==============================
应了当年Hilbert的狂言：
物理学，对于物理学家已经是太难了
漫漫长夜不知晓 日落云寒苦终宵
痴心未悟拈花笑 梦魂飞度同心桥|
-------------------------------------------------
红叶晚萧萧，长亭酒一瓢
残云归太华，疏雨过中条
树色随山迥，河声入海遥
帝乡明日到，犹自梦渔樵
| 发表时间：2005-10-17, 10:39:32 |
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sage
发表文章数: 1125
武功等级: 天山六阳掌
(第六重)
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Re: question for loop quantum gravity
> On the ground state, I only stress unlike other theory such as
> string theory and lattice theory, we need not assume a background
> spacetime which is generally called ground states at first. I have
> not said flat space is the ground state,
The trouble is, flat space IS the ground state of nature, we know it.
It IS the ground state of Einstein's equation, which loop qunatum gravity tried to quantize.
Loop quantum gravity, apart random guesses (inclduing that paper you quote and many its later followers), still have not demonstrated that flat space will emerge as a ground state. In fact, like I said, there are reasons to believe it will not.
>2 I have never said background independent is an improvement, I only
>stress it is the fundamental difference between LQG and other theory.
I am sure no loop quantum gravity people will agree with you on this point. Try send this to Rovelli see how he replies.
>In the sense, as you said , spin network will give the area theorem
>trivially, but I want to say spin network itself is the result from
>LQG. It is not the assumption but derived result. Could you obtain
>spin network from string theory:)
This is not what I said. Area law does NOT follow from spin network. It follows after one put in by hand the truncation of all the degrees of freedom inside. There is no justification for such a truncation at all.
Since one decide to truncate the inside, of course the entropy will be on the surface. this is trivial. this can be done in ANY theory. After that, the only non-trivial thing for LQG to calculate is the coeffient 1/4. and, LQG got this wrong, or claim that they cannot calculate it. By the way, string theory could only calculate the entropy in very special cases. on the other hand, when they do, they do not need any truncation, and they got the coefficient right.
> LQG has never claimed that it will give a unified description of our
>universe like string theorists. immirzi parameter need input from
>experiment or semiclassical consideration, such as the velocity of
>phton or Planck constant.
=========================================================
actually, it is worse than that. I will do another post on this point.
>I do not know how you know the ossillator is bad when LQG approaches
>is employed. But here I would like to suggest you to scan
>hep-th/9202063
>:A Loop Representation for the Quantum Maxwell Field
>you know, the Quantum Maxwell Field is many ossillators, but it seems
>to behave well.
>Finally, I would like to say: as xuanxuan said, ossillators and Maxell
>field is not LQG for ever:)
==============================================================
Well, you need to read Ashtekar's paper more, because he DOES NOT agree with you.
He thought harmonic oscillator is a very serious problem even in 2002, so he wrote a paper gr-qc/0207106 trying to solve it. His solution is so strange that I think no one outside LQG is impressed with it.
Nevertheless, if you read that paper, you will also see that he consider the classical limit a very serious and unresolved problem.
| 发表时间：2005-10-17, 20:18:28 |
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sage
发表文章数: 1125
武功等级: 天山六阳掌
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Re: question for loop quantum gravity
>loop里的激发态不是3维的，而是一维的。polymer-like的时空图象。如何得到平坦时
>空这是一个问题，但这背后有一个对称约化的过程。但这些问题会漫漫澄清的。
Since you are serious about working on loop, i think you should read
hep-th/0501114. it really clearly defines all the problem about LQG.
大家全在说knot和loop的时候，loop的微分同胚不变性等价于knot的jones多项式。那显然需要数学家来处理背后更加高深的关系。
因为对于一个物理学家来说，微分同胚不变性是什么？？？所以物理学家多数不懂得广义相对论。
it does not take mathematician to develop general relativity. Physically, diffeomorphism is nothing deep.
| 发表时间：2005-10-17, 20:22:03 |
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zzzwp917
发表文章数: 27
武功等级: 野球拳
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Re: question for loop quantum gravity
我懂得不多瞎说一下，圈量子引力中的真空是度规g=(0,0,0,0)的时空不存在任何自旋结网圈，圈量子引力中基态应该是指满足哈密顿，微分同胚，高斯约束的最简单的自旋结网圈把。最简单的自旋结网圈是“颜色”数为一的单圈（不知道满不满高斯约束）把，这种态体积为零而面积不为零是一个二维空间吧。
| 发表时间：2005-10-22, 06:32:49 |
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