sage
发表文章数: 1125
武功等级: 天山六阳掌
(第六重)
内力值: 535/535
The brave new world of LQG
The usual way physics is developed is based on the things we know,
avoid the things we know to be wrong and develop gradually. We get
convinced of a approach if it starts to get something right. We are
discouraged if there is some wrong.
LQG people are really really brave. For them, the last 100 years of
physics development means very little. They are very free to invent
new rules. if some of them are seriously wrong, they still keep going,
hoping that more radical changes could fix it.
Here are some examples
1) We all know at large distance that Einstein equation is
right. However, at very short distance, we know nothing
experimentally. It is prudent to treat GR as effective theory.
However, in LQG, the claim is that GR is exactly right, even at
very short distance 16 orders magnitude beyond our
experiment. Moreover, they claim they know the correct variable at
that scale, it is the SAME as the low energy one, the metric.
2) One would think that a quantum gravity would have to say something
about the dimension of the space-time. LQG could not. THis is no problem
for them. They just assume it is 4 and move on.
3) We know, by looking around or solving Einstein equation, flat space
is and must be the ground state of any sensible quantum gravity. It
does not show up in LQG. There are even many evidence that it will
not. For the LQG people, this is not a place for them to stop. They
assume someday, there will be a flat space emerging from LQG, and
move on.
4) The whole thing about classical limit got even weirder. If one just
apply LQG rules to harmonic oscillator, there is no normal coherent
state! They claim it is the state which is the eigenstate of the
creation operator. Well, that does not exist in ordinary quantum
mechanics. They say, let's change the rules. Let's assume it exists
in some hyperthetical Hilbert space, and move on.
5) The whole spin network business smells really like the old ether
idea. That's fine 100 years ago, except we know that it breaks
lorentz invariance, which is essential to diffeomorphism
invariance that they cherish so much. They say no problem, let's
invent some new rules called doubly special relativity.
6) The quantization is for the pure gravity Einstein term
alone. Matter play no role. Matter can couple anyway they want
to. However, we know that matter interactions will change a lot of
the physics at quantum gravity scale. This is not a problem for
them. They just decide to ignore the question of matter all
together, assuming it plays no role at all.
There are many many other problems, such as regularization dependence,
not reproducing the continuum, no anomalies, non-separable Hilbert
space, huge arbiturainess of the choice of Hamiltonian, non-existence
of the action of the spin network, and so on.
Even the most cherished principle of diffeomrophism has not been
checked to survive their quantization procedure.
However, all these do not make them slow down and think.
And, they are asking the rest of physics community treat them as a
matured science.
| 发表时间：2005-10-17, 20:47:44 |
 作者资料
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轩轩
发表文章数: 1352
武功等级: 易筋经
(第二重)
内力值: 567/567
Re: The brave new world of LQG
所有这些问题确实存在 有的看起来确实很大胆 解出矢量约束 在diff不变的空间里 理论应该就是diff不变的
loop有的时候的做法 的确让人不能信服 所以 要漫漫地整理一下 需要出一两个象witten那样的牛人来做loop的数学物理 sage兄对loop很熟悉啊
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, 21:34:19 |
作者资料
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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: The brave new world of LQG
解出矢量约束 在diff不变的空间里 理论应该就是diff不变的
This statement is not correct.
Classical symmetries in the theory do not usually survived after quantization. This is the essence of anomalies.
Loop quantum gravity so far has not been able to show the diff survives their quantization method.
| 发表时间：2005-10-18, 00:14:57 |
作者资料
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轩轩
发表文章数: 1352
武功等级: 易筋经
(第二重)
内力值: 567/567
Re: The brave new world of LQG
解出矢量约束 在diff不变的空间里 理论应该就是diff不变的
This statement is not correct.
Classical symmetries in the theory do not usually survived after quantization. This is the essence of anomalies.
Loop quantum gravity so far has not been able to show the diff survives their quantization method.
不对,量子矢量约束已经解出,用群平均的办法,解在运动学hilbert空间的对偶空间之中,
不能定义内积,这不奇怪,dirac的delta函数也没有内积
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：2005-10-18, 04:21:14 |
作者资料
|
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: The brave new world of LQG
不对,量子矢量约束已经解出,用群平均的办法,解在运动学hilbert空间的对偶空间之中,
不能定义内积,这不奇怪,dirac的delta函数也没有内积
I am not even talking about internal product yet.
The Hamiltonian+contraint, as the starting point of LQG is diff invariant. However, there is no guarantee that such a symmetry survives the qunatization. This is the spirit of anomaly.
The closure of LQG constraint algebra has never been proved in the full quantum sense, ie., not by using equation of motion. Until the off-shell operator algebra fully worked out, the quantum constraint is NOT sovled.
Otherwise, using the same method, you will not see anomalies in the gauge theory.
Spin network violate special relativity, which is another sign that it is not consistent with diff invariance..
A word on the interanl product,
delta function is well-defined in the sense of distributions. IT is very very different from a
non-separable Hiltbert space. Dual hilbert space has never been explicitly constructed. it is just assumed to exist, like in that paper by Ashtekar.
| 发表时间：2005-10-18, 09:15:35 |
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