View Full Version : Quasinormal modes
Urs Schreiber
Aug18-04, 01:25 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Hi Lubos -\n\nas an expert on quasinormal BH modes and the Hod conjecture, what is your\nopinion about today\'s paper\n\nJoanne Kettner, Gabor Kunstatter, A.J.M. Medved:\nQuasinormal modes for single horizon black holes in generic 2-d dilaton\ngravity,\ngr-qc/0408042\n\n?\n\nAnything new and interesting in there?\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hi Lubos -
as an expert on quasinormal BH modes and the Hod conjecture, what is your
opinion about today's paper
Joanne Kettner, Gabor Kunstatter, A.J.M. Medved:
Quasinormal modes for single horizon black holes in generic 2-d dilaton
gravity,
http://www.arxiv.org/abs/gr-qc/0408042
?
Anything new and interesting in there?
Lubos Motl
Aug19-04, 07:33 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Wed, 18 Aug 2004, Urs Schreiber wrote:\n\n> Hi Lubos -\n> as an expert on quasinormal BH modes and the Hod conjecture, what is your\n> opinion about today\'s paper\n> gr-qc/0408042\n\nHi Urs,\n\nthey calculate the QN modes for some black holes in two-dimensional\ngravity with a dilaton. It is slightly non-trivial, I think, that the\nresult again contains log(3). In fact, I am not even sure whether I\nunderstand what component of the fields has a physical polarization. I\nthought that 2D gravity with 1 scalar field has no physical polarizations,\nand therefore no QN modes. But my thinking must be wrong. I have not read\nthe paper in detail.\n\nThe authors join the skeptics who tend to believe that these results are\npurely classical and say nothing about quantum gravity. Well, this is what\nI\'ve have believed since the beginning to be the likely outcome, but this\noutcome is not exciting enough to make me happy if someone joins me. ;-)\nThe number 3 in log(3) in their framework is obtained from a coupling to\nthe dilaton; such a result reflects a specific generalization that they\nstudied. In our broader class, 3 was really 1+cos(2.pi.j) where j is the\nspin of the perturbation, roughly speaking. These are obviously\n"classical" parameters which, on the other hand, does not eliminate the\npossibility that "3" has a dual, deeper explanation. :-)\n\nIt\'s probably a fair paper, but the reason why it might be more\ninteresting for Andy Neitzke is that it sends our paper with Andy among\ntopcite 50+. ;-) The present paper uses our monodromy method.\n\nBut what should I say certainly is that the log(3) business may be now\nreally dead. See\n\nhttp://arxiv.org/abs/gr-qc/0407051\nhttp://arxiv.org/abs/gr-qc/0407052\n\nin which the Polish papers argue that all the previous calculations (of\nLQG black hole entropy) were wrong since the assumption that only the\nlowest spin contributes was not justified. Once they include all the\nspins, log(3) in the LQG entropy changes to log(X) where X is a weird\ntranscendent number. Therefore log(3) is not even wanted right now. ;-) QN\nmodes give a result that is not interesting for LQG anymore. Well, it\'s a\ncollection of failed attempts, wrong coincidences, misguided motivations,\nstupidity, and disagreements, much like LQG itself.\n\nThe controversy whether the LQG result should have log(2), log(3), or\nlog(X) continues. John Baez and others have said that they had no specific\nreason to doubt the new Polish papers. Sergei Alexandrov, on the other\nhand, wrote\n\nhttp://arxiv.org/abs/gr-qc/0408033\n\nwhere he wants to revive log(2) or log(3). As far as I can say, this paper\nis bad even according to the very bad standards from LQG. He claims that\nonly the microstates with the minimal spin should be counted because the\nstates with higher spins are not just different microstates, but\ndifferent *macrostates* blah blah blah. Really, he argues that there is an\nexponentially huge number of macroscopically different states\ncorresponding to the same black hole. What about the no-hair theorem and\nthe conjectured connection between LQG and gravity? I think that SA is\njust terribly confused about some basic physics concepts.\n\nBut this is a stringy group and so this topic probably does not belong\nhere.\n\nAll the best\nLubos\n_____________________________________ _________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 18 Aug 2004, Urs Schreiber wrote:
> Hi Lubos -
> as an expert on quasinormal BH modes and the Hod conjecture, what is your
> opinion about today's paper
> http://www.arxiv.org/abs/gr-qc/0408042
Hi Urs,
they calculate the QN modes for some black holes in two-dimensional
gravity with a dilaton. It is slightly non-trivial, I think, that the
result again contains log(3). In fact, I am not even sure whether I
understand what component of the fields has a physical polarization. I
thought that 2D gravity with 1 scalar field has no physical polarizations,
and therefore no QN modes. But my thinking must be wrong. I have not read
the paper in detail.
The authors join the skeptics who tend to believe that these results are
purely classical and say nothing about quantum gravity. Well, this is what
I've have believed since the beginning to be the likely outcome, but this
outcome is not exciting enough to make me happy if someone joins me. ;-)
The number 3 in log(3) in their framework is obtained from a coupling to
the dilaton; such a result reflects a specific generalization that they
studied. In our broader class, 3 was really 1+cos(2.\pi.j) where j is the
spin of the perturbation, roughly speaking. These are obviously
"classical" parameters which, on the other hand, does not eliminate the
possibility that "3" has a dual, deeper explanation. :-)
It's probably a fair paper, but the reason why it might be more
interesting for Andy Neitzke is that it sends our paper with Andy among
topcite 50+. ;-) The present paper uses our monodromy method.
But what should I say certainly is that the log(3) business may be now
really dead. See
http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0407051
http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0407052
in which the Polish papers argue that all the previous calculations (of
LQG black hole entropy) were wrong since the assumption that only the
lowest spin contributes was not justified. Once they include all the
spins, log(3) in the LQG entropy changes to log(X) where X is a weird
transcendent number. Therefore log(3) is not even wanted right now. ;-) QN
modes give a result that is not interesting for LQG anymore. Well, it's a
collection of failed attempts, wrong coincidences, misguided motivations,
stupidity, and disagreements, much like LQG itself.
The controversy whether the LQG result should have log(2), log(3), or
log(X) continues. John Baez and others have said that they had no specific
reason to doubt the new Polish papers. Sergei Alexandrov, on the other
hand, wrote
http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0408033
where he wants to revive log(2) or log(3). As far as I can say, this paper
is bad even according to the very bad standards from LQG. He claims that
only the microstates with the minimal spin should be counted because the
states with higher spins are not just different microstates, but
different *macrostates* blah blah blah. Really, he argues that there is an
exponentially huge number of macroscopically different states
corresponding to the same black hole. What about the no-hair theorem and
the conjectured connection between LQG and gravity? I think that SA is
just terribly confused about some basic physics concepts.
But this is a stringy group and so this topic probably does not belong
here.
All the best
Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Sergei Alexandrov
Aug20-04, 12:18 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Hi,\n\nMy friend pointed out to me this comment and I feel\nthat I should answer to this criticism.\n\nLubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0408190819380.907-100000@einstein.physics.harvard.edu>...\n\n> The controversy whether the LQG result should have log(2), log(3), or\n> log(X) continues. John Baez and others have said that they had no specific\n> reason to doubt the new Polish papers. Sergei Alexandrov, on the other\n> hand, wrote\n>\n> http://arxiv.org/abs/gr-qc/0408033\n>\n> where he wants to revive log(2) or log(3). As far as I can say, this paper\n> is bad even according to the very bad standards from LQG. He claims that\n> only the microstates with the minimal spin should be counted because the\n> states with higher spins are not just different microstates, but\n> different *macrostates* blah blah blah. Really, he argues that there is an\n> exponentially huge number of macroscopically different states\n> corresponding to the same black hole. What about the no-hair theorem and\n> the conjectured connection between LQG and gravity? I think that SA is\n> just terribly confused about some basic physics concepts.\n\nThe only criticism which I see here is the possible disagreement with\nthe no-hair theorem. But I do not see any contradiction with it\nbecause the macrostates which are mentioned above are not necessarilly\nstationary. Moreover, it was one of the arguments in gr-qc/0408033\nthat the evolution leads to the unique state characterized by the\nmaximal entropy. The no-hair theorem is applied only to this state and\nthus there is no any disagreement.\n\n[Moderator\'s note: Dear Sergei, the number of states with a lower entropy\nis so much smaller that it does not matter whether you count them or not.\nIn other words, if you include all possible perturbations of a black\nhole, you still obtain the same entropy. Virtually the whole entropy\n*always* comes from counting the microstates; the number of\nmacroscopically distinct states may be large, but it is always much\nsmaller than the number of microstates. Even if these comments were\nnot true, it would be hard to justify that if you change a couple of\nspins - a few degrees of freedom changing the area by the Planck area\n- from 1/2 to 1, you obtain a "macroscopically distinct state". Note\nthat the calculation of the entropy always means that one counts all\npossible "tiny" allowed modifications of the state that do not change\nits gross properties - for example the total energy. We can require\nthe energy density in each cubed millimeter to be preserved, but it\ndoes not really matter - the entropy comes out virtually identical.\nChanging a spin from 1/2 to 1, if allowed, is certainly such a\nmicromodification. Baez, Krasnov et al. counted them, but they\nconcluded that the number of such states with nonminimal spins is\nso small that it does not change the leading formula for the entropy.\nMeissner obtained a different result. LM]\n\nI am not struggling for log(2) and for the possible connection to\nquasinormal modes. In my view it was just a coincidence. Moreover, I\neven do not believe in the discrete SU(2) spectrum for the area\noperator. But I wanted to express that if to follow the logic of loop\ngravity the states with higher spins should correspond to different\nNON-STATIONARY macrostates.\n\nAll the best,\nSergei\n\n[Moderator\'s note: Could you please explain why you think that the states\nwith all spins being 1/2 are stationary while the states with higher spins\nare not stationary? This comment about being "stationary" is an addition\nto your paper. ;-) Well, let me say that whatever you follow, I can\'t\ncall it "logic" - perhaps "magic". It seems to me like a person who wants\nto get the result 1917 apples, but he gets, by an explicit counting,\n1991. Well, the remaining 74 are anti-socialist macroaples and they\nshould not be counted, should they? At any rate, we\'re happy that you\ncame here and responded. LM]\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hi,
My friend pointed out to me this comment and I feel
that I should answer to this criticism.
Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0408190819380.907-100000@einstein.physics.harvard.edu>...
> The controversy whether the LQG result should have log(2), log(3), or
> log(X) continues. John Baez and others have said that they had no specific
> reason to doubt the new Polish papers. Sergei Alexandrov, on the other
> hand, wrote
>
> http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0408033
>
> where he wants to revive log(2) or log(3). As far as I can say, this paper
> is bad even according to the very bad standards from LQG. He claims that
> only the microstates with the minimal spin should be counted because the
> states with higher spins are not just different microstates, but
> different *macrostates* blah blah blah. Really, he argues that there is an
> exponentially huge number of macroscopically different states
> corresponding to the same black hole. What about the no-hair theorem and
> the conjectured connection between LQG and gravity? I think that SA is
> just terribly confused about some basic physics concepts.
The only criticism which I see here is the possible disagreement with
the no-hair theorem. But I do not see any contradiction with it
because the macrostates which are mentioned above are not necessarilly
stationary. Moreover, it was one of the arguments in http://www.arxiv.org/abs/gr-qc/0408033
that the evolution leads to the unique state characterized by the
maximal entropy. The no-hair theorem is applied only to this state and
thus there is no any disagreement.
[Moderator's note: Dear Sergei, the number of states with a lower entropy
is so much smaller that it does not matter whether you count them or not.
In other words, if you include all possible perturbations of a black
hole, you still obtain the same entropy. Virtually the whole entropy
*always* comes from counting the microstates; the number of
macroscopically distinct states may be large, but it is always much
smaller than the number of microstates. Even if these comments were
not true, it would be hard to justify that if you change a couple of
spins - a few degrees of freedom changing the area by the Planck area
- from 1/2 to 1, you obtain a "macroscopically distinct state". Note
that the calculation of the entropy always means that one counts all
possible "tiny" allowed modifications of the state that do not change
its gross properties - for example the total energy. We can require
the energy density in each cubed millimeter to be preserved, but it
does not really matter - the entropy comes out virtually identical.
Changing a spin from 1/2 to 1, if allowed, is certainly such a
micromodification. Baez, Krasnov et al. counted them, but they
concluded that the number of such states with nonminimal spins is
so small that it does not change the leading formula for the entropy.
Meissner obtained a different result. LM]
I am not struggling for log(2) and for the possible connection to
quasinormal modes. In my view it was just a coincidence. Moreover, I
even do not believe in the discrete SU(2) spectrum for the area
operator. But I wanted to express that if to follow the logic of loop
gravity the states with higher spins should correspond to different
NON-STATIONARY macrostates.
All the best,
Sergei
[Moderator's note: Could you please explain why you think that the states
with all spins being 1/2 are stationary while the states with higher spins
are not stationary? This comment about being "stationary" is an addition
to your paper. ;-) Well, let me say that whatever you follow, I can't
call it "logic" - perhaps "magic". It seems to me like a person who wants
to get the result 1917 apples, but he gets, by an explicit counting,
1991. Well, the remaining 74 are anti-socialist macroaples and they
should not be counted, should they? At any rate, we're happy that you
came here and responded. LM]
Sergei Alexandrov
Aug31-04, 12:54 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Dear Lubos,\n\nI agree what you wrote that if we allow to change little bit the spins it\nshould not change the entropy. But what is this boundary of how many spins\nwe can change? If we change all spins, is it the same macrostate or a\ndifferent one? I would argue that it is different. Then the calculation\nof Maissner at al. shows that if we take into account such "large"\nmodifications of puncturing of the horizon, it is already significant for\nthe calculation of the entropy.\n\n> Could you please explain why you think that the states\n> with all spins being 1/2 are stationary while the states with higher spins\n> are not stationary? This comment about being "stationary" is an addition\n> to your paper. ;-) Well, let me say that whatever you follow, I can\'t\n> call it "logic" - perhaps "magic".\n\nWhat is "unlogic" for me in the usual counting is that I have to consider\nas the same macrostate, for example, the puncturing with all spins 1/2 and\nthe puncturing consisting only from one puncture with a large spin. I can\nnot agree that they can decribe the same physical situation, the same\nspacetime. Therefore, the only "logic" resolution which I see is to claim\nthat they correspond to different macrostates.\n\nThen the statement that the state with all spins 1/2 is stationary and the\nothers are not should be true if we accept that the different punctures\ngive rise to different macrostates and if we believe that there is a\ncorrespondence between these states and classical GR. In some sence, it is\na consequenece of the "no hair" theorem which you mentioned and which was\nmentioned also in the paper. Of course, this statement can not be proven\ndirectly in this formalism and it is a consequence of these two\nsuggestions.\n\nIn fact, as I wrote previously, I did not try to obtain some desirable\nresult. It was an attempt to solve the problem that we count states which\nobviously have different spacetime geometry outside the horizon. Also,\nsince I think that the discrete area spectrum is not correct, it was an\nattempt to understand how a similar counting can work in the case of a\ncontinuus area spectrum.\n\nBest wishes,\nSergei\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Dear Lubos,
I agree what you wrote that if we allow to change little bit the spins it
should not change the entropy. But what is this boundary of how many spins
we can change? If we change all spins, is it the same macrostate or a
different one? I would argue that it is different. Then the calculation
of Maissner at al. shows that if we take into account such "large"
modifications of puncturing of the horizon, it is already significant for
the calculation of the entropy.
> Could you please explain why you think that the states
> with all spins being 1/2 are stationary while the states with higher spins
> are not stationary? This comment about being "stationary" is an addition
> to your paper. ;-) Well, let me say that whatever you follow, I can't
> call it "logic" - perhaps "magic".
What is "unlogic" for me in the usual counting is that I have to consider
as the same macrostate, for example, the puncturing with all spins 1/2 and
the puncturing consisting only from one puncture with a large spin. I can
not agree that they can decribe the same physical situation, the same
spacetime. Therefore, the only "logic" resolution which I see is to claim
that they correspond to different macrostates.
Then the statement that the state with all spins 1/2 is stationary and the
others are not should be true if we accept that the different punctures
give rise to different macrostates and if we believe that there is a
correspondence between these states and classical GR. In some sence, it is
a consequenece of the "no hair" theorem which you mentioned and which was
mentioned also in the paper. Of course, this statement can not be proven
directly in this formalism and it is a consequence of these two
suggestions.
In fact, as I wrote previously, I did not try to obtain some desirable
result. It was an attempt to solve the problem that we count states which
obviously have different spacetime geometry outside the horizon. Also,
since I think that the discrete area spectrum is not correct, it was an
attempt to understand how a similar counting can work in the case of a
continuus area spectrum.
Best wishes,
Sergei
Lubos Motl
Aug31-04, 05:23 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Dear Sergei,\n\n> I agree what you wrote that if we allow to change little bit the spins it\n> should not change the entropy. But what is this boundary of how many spins\n> we can change? If we change all spins, is it the same macrostate or a\n> different one? I would argue that it is different.\n\nwe completely agree that the question whether a microstate describes the\nsame macroscopic state or not is a matter of convention. It depends how\nfinely we define a macroscopic state. But what I\'ve been trying to say is\nthat there exists no known physical situation in which the chosen\n"resolution" affects the leading term contributing to the entropy. For\nexample, if you specify the total number of atoms in every cubed\ncentimeter of some gas (equal for all these volumes), you obtain entropy\nS. If you only specify the total number of atoms only, you obtain entropy\nthat is just a little bit higher than S. The difference, relatively\nspeaking, disappears in the thermodynamic limit.\n\nIf you consider a Schwarzschild black hole of mass M, then it is also\npossible to focus on "large" deviations from the ideal black hole - for\nexample two black holes with mass M/2 per each. Because the entropy of the\n4D black holes scales like the squared mass, you will see that the entropy\nof the pair of M/2 black holes is (twice) smaller than the entropy of a\nsingle black hole of mass M. The typical states in the ensemble of states\nwith the same total mass *must* look like a single black hole. A similar\ninequality always holds if the spacetime dimension is d>3.\n\nIn other words, if you have an alternative description of d=4 general\nrelativity, it must be true that the number of states which are very\n("classically") different from the spherical black hole must be much\nsmaller (infinitely smaller, if you consider infinitely big black holes)\nthan the number of the states that look almost exactly like the ideal\nspherical black hole. The ideal, single, regular black hole is always\nfavored entropically.\n\nFor example, if the simple picture of the horizon punctured by the spin\nnetwork\'s links (in loop quantum gravity) described physics of black\nholes, then it would have to be true that a typical state still looks more\nor less like the single spherical black hole - simply because one can\nderive this typical state from semiclassical general relativity. It means\nthat if you accept LQG as a dual description of the black holes, then you\nare allowed to choose a finite fraction of the spins to be 3/2 or 5/2, and\nstill claim that the resulting black hole describes a spherical black hole\nwith very small deviations.\n\nMeissner showed that a typical state of the spin networks really *does*\ncontain a finite fraction (a larger number) of higher spin punctures. If\nyou combine this result with the statement that a typical "compact" state\nof mass M in general relativity is a single almost perfectly smooth black\nhole, then you must conclude that\n\n* either a large number of higher spins do not affect\nthe overall "regular" semiclassical shape of the black hole\n\n* or that the spin network with the higher spins is, because of\nsome mysterious reasons, a very delocalized state (such as\nthe Hawking radiation from a black hole whose entropy is\neven larger)\n\n* or that LQG has just been proved to disagree with gravity\n\nIn other words, there is no known physical system - not even in gravity -\nwhere the number of macroscopically distinct states is larger than the\nnumber of the microstates. In all known systems, including gravity, most\nof the entropy - counted as the logarithm of *any* states - always comes\nfrom the microscopic states. Although quantum gravity may require us to\ncall these states by a different word from "microscopic", it should still\nbe true that if we count *all* conceivable states, the logarithm of their\nnumber will equal the entropy, up to some corrections that relatively go\nto zero for large objects (black holes). These rules are violated in your\ntreatment of LQG, and therefore your treatment of LQG cannot be a dual\ndescription of any physical system.\n\n> What is "unlogic" for me in the usual counting is that I have to consider\n> as the same macrostate, for example, the puncturing with all spins 1/2 and\n> the puncturing consisting only from one puncture with a large spin. I can\n> not agree that they can decribe the same physical situation, the same\n> spacetime.\n\nThese particular states that you describe do not have to matter because\nthey\'re not typical in the ensemble. Maybe they should be viewed as a\nspherical black hole, maybe not. The typical states in the ensemble matter\nand they contain a specific finite percentage of the spin 1/2 punctures\n(determined with a rather good accuracy), a different finite percentage of\nthe spin 1 punctures, and so on, and if this picture has anything to do\nwith gravity, all these typical states must describe the typical members\nof the quantum gravity ensemble - and it is known that a typical compact\nstate with a given mass *is* a single black hole, one that is classically\nindistinguishable from the exact stationary classical solution.\n\nIncidentally, the spin networks are eigenstates of the area operators, but\nthey never look directly like smooth geometries (well, smooth geometries\ndo not have quantized areas). I think that your discussion "I cannot agree\nthat different punctures describe the same [classical] spacetime" leads\nnowhere because so far, you do not have any dictionary how to decide this\nquestion and/or define the best "classical" spacetime corresponding to a\ngiven spin network.\n\nOf course, I don\'t believe that LQG has anything to do with gravity, and\ntherefore the existence of *any* dictionary translating spin networks to\nclassical geometries seems very unlikely to me. But it seems clear to me\nthat even those who want to propose that LQG is related to gravity would\nnot claim that there is a direct one-to-one map between the specific\ncolored spin networks one one side, and classical geometries on the other\nside. A classical geometry is rather a superposition of a large number of\nspin networks, and it is only determined approximately - so that\ndifferent spin networks (microstates) may lead to the same classical\ngeometry, even if they contain higher spin punctures.\n\n> Therefore, the only "logic" resolution which I see is to claim\n> that they correspond to different macrostates.\n\nUnfortunately, this statement implies that LQG cannot have anything to do\nwith physics of gravity because a typical microstate in gravity simply\n*does* belong to the *same* macroscopic state, and the number of very\ndifferent macroscopic states of mass M is much smaller than the number of\nthe microstates of a black hole with the same mass.\n\n> Then the statement that the state with all spins 1/2 is stationary and the\n> others are not should be true if we accept that the different punctures\n> give rise to different macrostates and if we believe that there is a\n> correspondence between these states and classical GR.\n\nI just have a feeling that you are linguistically manipulating with some\nwords whose meaning you don\'t want to take seriously. The entropy is\ndefined as the logarithm of macroscopically indistinguishable microstates,\nand because a legitimate calculation has given a different entropy than\nyou like, you try to challenge various words in the sentence - logarithm;\nmacroscopically indistinguishable, and so on. This is linguistics, not\nphysics.\n\nIt is just clear on physical grounds that the statements you say are\nabsurd - for example elementary statistical physics is enough to know that\nthe "resolution" in defining the ensemble (which divides the microstates\ninto groups) cannot affect the leading value of the entropy as long as the\nresolution is macroscopic - while according to your proposal, the choice\nof the resolution would dramatically affect the resulting entropy.\n\nAlso, the question whether a state is stationary or not is not just a\nmatter of assigning abstract labels to some abstract objects. It can be\nstudied scientifically. Even though LQG is a not quite well-defined model,\none can take their semi-well-defined Hamiltonian and act with it on a spin\nnetwork. It seems pretty clear that it can\'t be true that the\nspin-1/2-only spin networks are exactly stationary while those with some\nhigher spin punctures are not stationary. For example, if you wanted to\nclaim that the spin networks with j>1/2 spins are non-stationary because\nthe higher spins "decay" to j=1/2 components, a similar arguments would\nimply that the j=1/2 components can join to j>1/2 blocks, and therefore\nare non-stationary, too.\n\nThe only special value of the spin that may play some role is j=0, but it\ncontributes no entropy and no area. All other spins are either stationary,\nor - which is much more likely - all other spins lead to non-stationary\nstates (not eigenstates of the Hamiltonian). I think that the whole\nLQG literature is likely to agree that the spin networks are never\nHamiltonian eigenstates.\n\nYou can\'t expect an answer from me - I not only believe that the spin\nnetworks don\'t describe systems in quantum gravity, but I also believe\nthat there exists no meaningful Hamiltonian in LQG to talk about. All of\nthem have UV problems and so on. LQG is not string theory, and therefore\nit can\'t describe gravity. Consequently it is a randomly chosen discrete\nmodel, and any Hamiltonian is equally good for such models. But even if we\nforget about these problems, I guess that it is clear that it is *you* who\nshould present some evidence for your statements. You have not presented a\nsingle glimpse of an argument in favor of any statement similar to your\nclaim that your preferred subclass of the spin networks is stationary\nwhile the rest is not.\n\nI just feel that a proposal of this quality can be presented for *any*\ndiscrepancy in the whole science, and can be used to change any result C\nto D. If we don\'t like the result C for a quantity XY and prefer D=C-25\ninstead, we say that some 25 objects in the ensemble of C objects are\nwrong and do not satisfy one of the adjective in the definition of C - and\nwe don\'t care about the fact that we have no argument for this "wrong 25"\ntheory and we introduced new serious contradictions. Sorry, I just see no\nrationality in such an approach. The number of things that you solve is\nnegative.\n\n> In some sence, it is a consequenece of the "no hair" theorem which you\n> mentioned and which was mentioned also in the paper.\n\nI agree that it is a consequence, but if you think for a few extra\nseconds, you can derive not only the conclusion about non-stationary\nstates, but you can also derive a contradiction with gravity.\n\n> Of course, this statement can not be proven directly in this formalism\n> and it is a consequence of these two suggestions.\n\nThen LQG is not a scientific theory. I don\'t understand how a physical\nstatement cannot be proven (or disproven) in a formalism. I thought that\nyou\'ve made a conjecture about the nature of some states in LQG (a highly\nunreasonably sounding conjecture, I would say) - whose corrolary about the\nnon-stationary states can be tested once the dynamics of LQG is\nwell-defined. Do you now agree that LQG cannot be used to study any\ndynamical questions?\n\n> In fact, as I wrote previously, I did not try to obtain some desirable\n> result.\n\nYou have obtained no result whatsoever. You just randomly picked a random\nnumber (one that has been picked by some other people in the past who\nhappened to have calculated a combinatorial problem incorrectly) and\nconstructed an illogical pseudoargument that this number is the correct\nanswer to a physical question. Anyone else can pick any other number and\nclaim that it is the correct black hole entropy - for example someone can\nclaim that only the spin networks with at most 19.73 per cent of spin j=1\npunctures (and no higher spins) are allowed as extra microstates and\nothers are macroscopically distinguishable. This leads to 0.931415926\ntimes Meissner\'s entropy - which is the correct result which also implies\nthat the states with j>1 punctures or more than 19.73 per cent of the j=1\npunctures are non-stationary. I think that this is a less contrived\n"calculation" than yours because 1973 is, at least, the year of my birth.\n;-) OK, honestly, let\'s end up with a peaceful, polite, and democratic\nconclusion: both of them - mine and yours - are equally big stupidities.\n\n> It was an attempt to solve the problem that we count states which\n> obviously have different spacetime geometry outside the horizon.\n\nAs I\'ve explained, this problem does not exist in quantum gravity. One can\ncount all localized states with a fixed mass, and one always obtains the\nsame entropy up to corrections that go to zero for large black holes.\nMoreover, even if this problem existed, you have not solved anything - you\njust randomly postulated a new selection criterion, one of an\nexponentially huge number of similar criteria that explain absolutely\nnothing and have absolutely no justification.\n\nBest\nLubos\n___________________ __________________________________________________ _________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Dear Sergei,
> I agree what you wrote that if we allow to change little bit the spins it
> should not change the entropy. But what is this boundary of how many spins
> we can change? If we change all spins, is it the same macrostate or a
> different one? I would argue that it is different.
we completely agree that the question whether a microstate describes the
same macroscopic state or not is a matter of convention. It depends how
finely we define a macroscopic state. But what I've been trying to say is
that there exists no known physical situation in which the chosen
"resolution" affects the leading term contributing to the entropy. For
example, if you specify the total number of atoms in every cubed
centimeter of some gas (equal for all these volumes), you obtain entropy
S. If you only specify the total number of atoms only, you obtain entropy
that is just a little bit higher than S. The difference, relatively
speaking, disappears in the thermodynamic limit.
If you consider a Schwarzschild black hole of mass M, then it is also
possible to focus on "large" deviations from the ideal black hole - for
example two black holes with mass M/2 per each. Because the entropy of the
4D black holes scales like the squared mass, you will see that the entropy
of the pair of M/2 black holes is (twice) smaller than the entropy of a
single black hole of mass M. The typical states in the ensemble of states
with the same total mass *must* look like a single black hole. A similar
inequality always holds if the spacetime dimension is d>3.
In other words, if you have an alternative description of d=4 general
relativity, it must be true that the number of states which are very
("classically") different from the spherical black hole must be much
smaller (infinitely smaller, if you consider infinitely big black holes)
than the number of the states that look almost exactly like the ideal
spherical black hole. The ideal, single, regular black hole is always
favored entropically.
For example, if the simple picture of the horizon punctured by the spin
network's links (in loop quantum gravity) described physics of black
holes, then it would have to be true that a typical state still looks more
or less like the single spherical black hole - simply because one can
derive this typical state from semiclassical general relativity. It means
that if you accept LQG as a dual description of the black holes, then you
are allowed to choose a finite fraction of the spins to be 3/2 or 5/2, and
still claim that the resulting black hole describes a spherical black hole
with very small deviations.
Meissner showed that a typical state of the spin networks really *does*
contain a finite fraction (a larger number) of higher spin punctures. If
you combine this result with the statement that a typical "compact" state
of mass M in general relativity is a single almost perfectly smooth black
hole, then you must conclude that
* either a large number of higher spins do not affect
the overall "regular" semiclassical shape of the black hole
* or that the spin network with the higher spins is, because of
some mysterious reasons, a very delocalized state (such as
the Hawking radiation from a black hole whose entropy is
even larger)
* or that LQG has just been proved to disagree with gravity
In other words, there is no known physical system - not even in gravity -
where the number of macroscopically distinct states is larger than the
number of the microstates. In all known systems, including gravity, most
of the entropy - counted as the logarithm of *any* states - always comes
from the microscopic states. Although quantum gravity may require us to
call these states by a different word from "microscopic", it should still
be true that if we count *all* conceivable states, the logarithm of their
number will equal the entropy, up to some corrections that relatively go
to zero for large objects (black holes). These rules are violated in your
treatment of LQG, and therefore your treatment of LQG cannot be a dual
description of any physical system.
> What is "unlogic" for me in the usual counting is that I have to consider
> as the same macrostate, for example, the puncturing with all spins 1/2 and
> the puncturing consisting only from one puncture with a large spin. I can
> not agree that they can decribe the same physical situation, the same
> spacetime.
These particular states that you describe do not have to matter because
they're not typical in the ensemble. Maybe they should be viewed as a
spherical black hole, maybe not. The typical states in the ensemble matter
and they contain a specific finite percentage of the spin 1/2 punctures
(determined with a rather good accuracy), a different finite percentage of
the spin 1 punctures, and so on, and if this picture has anything to do
with gravity, all these typical states must describe the typical members
of the quantum gravity ensemble - and it is known that a typical compact
state with a given mass *is* a single black hole, one that is classically
indistinguishable from the exact stationary classical solution.
Incidentally, the spin networks are eigenstates of the area operators, but
they never look directly like smooth geometries (well, smooth geometries
do not have quantized areas). I think that your discussion "I cannot agree
that different punctures describe the same [classical] spacetime" leads
nowhere because so far, you do not have any dictionary how to decide this
question and/or define the best "classical" spacetime corresponding to a
given spin network.
Of course, I don't believe that LQG has anything to do with gravity, and
therefore the existence of *any* dictionary translating spin networks to
classical geometries seems very unlikely to me. But it seems clear to me
that even those who want to propose that LQG is related to gravity would
not claim that there is a direct one-to-one map between the specific
colored spin networks one one side, and classical geometries on the other
side. A classical geometry is rather a superposition of a large number of
spin networks, and it is only determined approximately - so that
different spin networks (microstates) may lead to the same classical
geometry, even if they contain higher spin punctures.
> Therefore, the only "logic" resolution which I see is to claim
> that they correspond to different macrostates.
Unfortunately, this statement implies that LQG cannot have anything to do
with physics of gravity because a typical microstate in gravity simply
*does* belong to the *same* macroscopic state, and the number of very
different macroscopic states of mass M is much smaller than the number of
the microstates of a black hole with the same mass.
> Then the statement that the state with all spins 1/2 is stationary and the
> others are not should be true if we accept that the different punctures
> give rise to different macrostates and if we believe that there is a
> correspondence between these states and classical GR.
I just have a feeling that you are linguistically manipulating with some
words whose meaning you don't want to take seriously. The entropy is
defined as the logarithm of macroscopically indistinguishable microstates,
and because a legitimate calculation has given a different entropy than
you like, you try to challenge various words in the sentence - logarithm;
macroscopically indistinguishable, and so on. This is linguistics, not
physics.
It is just clear on physical grounds that the statements you say are
absurd - for example elementary statistical physics is enough to know that
the "resolution" in defining the ensemble (which divides the microstates
into groups) cannot affect the leading value of the entropy as long as the
resolution is macroscopic - while according to your proposal, the choice
of the resolution would dramatically affect the resulting entropy.
Also, the question whether a state is stationary or not is not just a
matter of assigning abstract labels to some abstract objects. It can be
studied scientifically. Even though LQG is a not quite well-defined model,
one can take their semi-well-defined Hamiltonian and act with it on a spin
network. It seems pretty clear that it can't be true that the
spin-1/2-only spin networks are exactly stationary while those with some
higher spin punctures are not stationary. For example, if you wanted to
claim that the spin networks with j>1/2 spins are non-stationary because
the higher spins "decay" to j=1/2 components, a similar arguments would
imply that the j=1/2 components can join to j>1/2 blocks, and therefore
are non-stationary, too.
The only special value of the spin that may play some role is j=0, but it
contributes no entropy and no area. All other spins are either stationary,
or - which is much more likely - all other spins lead to non-stationary
states (not eigenstates of the Hamiltonian). I think that the whole
LQG literature is likely to agree that the spin networks are never
Hamiltonian eigenstates.
You can't expect an answer from me - I not only believe that the spin
networks don't describe systems in quantum gravity, but I also believe
that there exists no meaningful Hamiltonian in LQG to talk about. All of
them have UV problems and so on. LQG is not string theory, and therefore
it can't describe gravity. Consequently it is a randomly chosen discrete
model, and any Hamiltonian is equally good for such models. But even if we
forget about these problems, I guess that it is clear that it is *you* who
should present some evidence for your statements. You have not presented a
single glimpse of an argument in favor of any statement similar to your
claim that your preferred subclass of the spin networks is stationary
while the rest is not.
I just feel that a proposal of this quality can be presented for *any*
discrepancy in the whole science, and can be used to change any result C
to D. If we don't like the result C for a quantity XY and prefer D=C-25
instead, we say that some 25 objects in the ensemble of C objects are
wrong and do not satisfy one of the adjective in the definition of C - and
we don't care about the fact that we have no argument for this "wrong 25"
theory and we introduced new serious contradictions. Sorry, I just see no
rationality in such an approach. The number of things that you solve is
negative.
> In some sence, it is a consequenece of the "no hair" theorem which you
> mentioned and which was mentioned also in the paper.
I agree that it is a consequence, but if you think for a few extra
seconds, you can derive not only the conclusion about non-stationary
states, but you can also derive a contradiction with gravity.
> Of course, this statement can not be proven directly in this formalism
> and it is a consequence of these two suggestions.
Then LQG is not a scientific theory. I don't understand how a physical
statement cannot be proven (or disproven) in a formalism. I thought that
you've made a conjecture about the nature of some states in LQG (a highly
unreasonably sounding conjecture, I would say) - whose corrolary about the
non-stationary states can be tested once the dynamics of LQG is
well-defined. Do you now agree that LQG cannot be used to study any
dynamical questions?
> In fact, as I wrote previously, I did not try to obtain some desirable
> result.
You have obtained no result whatsoever. You just randomly picked a random
number (one that has been picked by some other people in the past who
happened to have calculated a combinatorial problem incorrectly) and
constructed an illogical pseudoargument that this number is the correct
answer to a physical question. Anyone else can pick any other number and
claim that it is the correct black hole entropy - for example someone can
claim that only the spin networks with at most 19.73 per cent of spin j=1
punctures (and no higher spins) are allowed as extra microstates and
others are macroscopically distinguishable. This leads to .931415926
times Meissner's entropy - which is the correct result which also implies
that the states with j>1 punctures or more than 19.73 per cent of the j=1
punctures are non-stationary. I think that this is a less contrived
"calculation" than yours because 1973 is, at least, the year of my birth.
;-) OK, honestly, let's end up with a peaceful, polite, and democratic
conclusion: both of them - mine and yours - are equally big stupidities.
> It was an attempt to solve the problem that we count states which
> obviously have different spacetime geometry outside the horizon.
As I've explained, this problem does not exist in quantum gravity. One can
count all localized states with a fixed mass, and one always obtains the
same entropy up to corrections that go to zero for large black holes.
Moreover, even if this problem existed, you have not solved anything - you
just randomly postulated a new selection criterion, one of an
exponentially huge number of similar criteria that explain absolutely
nothing and have absolutely no justification.
Best
Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Arun Gupta
Sep1-04, 08:25 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Is physics reverting to religion?\n\n[Moderator\'s note: This is the only off-topic message in this thread that\nwill be tolerated. Please find a newsgroup about religion if you\nwant to continue with this sort of non-string-theoretical discussion. LM]\n\nLubos Motl <motl@feynman.harvard.edu> wrote\n\n> LQG is not string theory, and therefore it can\'t describe gravity.\n\nNewton and Einstein have done fairly good jobs so far, describing\ngravity without string theory. Yes, I know you mean a quantum theory.\n\n[Moderator\'s note: Yes and no. I meant what I wrote. I wrote that LQG\ncan\'t describe gravity. LQG may be a quantum theory, but it is not a theory\nof gravity. Yes, of course the constraint is that string theory is\nthe unique *quantum* theory of gravity. LM]\n\nBut then demonstrate that there are no other routes to a quantum\ntheory of gravity, not mistaking mathematical difficulty for impossibility.\n\n[Moderator\'s note: It may be mathematically *difficult* to prove that\nstring theory is the unique solution, but it does not mean that it is not\nunique. This uniqueness may be hard to see for someone who knows very\nlittle about string theory, but the more you will know about theoretical\nphysics and the possible inconsistencies in various candidate theories -\nand the miraculous ways how string theory avoids these inconsistencies -\nthe more you will realize how true and deep my statement is and how\nfalse and shallow is yours. LM]\n\nOr, following the usual route of physics, demonstrate experimental\nresults so distinct and compelling that possible competing theories are\nof little interest.\n\nSince neither of the above are available,\n\n[Moderator\'s note: The strategy that you propose is unscientific. It is\nnot necessary to disprove all conceivable alternatives to string theory\nif we want to rule out LQG. It was enough to rule out LQG which was a\nmuch easier task. LM]\n\nI can only interpret the attacks on people who seek gravity outside of\nstring theory as quasi-religious fervor.\n\n[Moderator\'s note: if you learned some technical stuff instead of your\ncurrent philosophical/religious words, you might become able to do\nbetter and find a better interpretation. LM]\n\nIt seems obvious that if you don\'t look, you can\'t find.\n\n[Moderator\'s note: I assure you that I look. Conversely, if you don\'t\nlook, you can\'t see the problems with *any* inconsistent theory. LM]\n\nAnd ultimately, if the search fails, it will be a compelling argument in\nfavor of string theory, so why fear it?\n\n[Moderator\'s note: I don\'t fear anything. I just stated a rather\nwell-known insight about uniqueness of string theory among the known\nquantum theories of gravity. It seems to me that it is *you* who fears\nit. LM]\n\nIf the search succeeds, it won\'t be a disaster for physics, as someone has\nclaimed.\n\n[Moderator\'s note: Anyone is allowed to search for anything, which does\nnot mean that all searches are equally justified and reasonable. LM]\n\n-Arun\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Is physics reverting to religion?
[Moderator's note: This is the only off-topic message in this thread that
will be tolerated. Please find a newsgroup about religion if you
want to continue with this sort of non-string-theoretical discussion. LM]
Lubos Motl <motl@feynman.harvard.edu> wrote
> LQG is not string theory, and therefore it can't describe gravity.
Newton and Einstein have done fairly good jobs so far, describing
gravity without string theory. Yes, I know you mean a quantum theory.
[Moderator's note: Yes and no. I meant what I wrote. I wrote that LQG
can't describe gravity. LQG may be a quantum theory, but it is not a theory
of gravity. Yes, of course the constraint is that string theory is
the unique *quantum* theory of gravity. LM]
But then demonstrate that there are no other routes to a quantum
theory of gravity, not mistaking mathematical difficulty for impossibility.
[Moderator's note: It may be mathematically *difficult* to prove that
string theory is the unique solution, but it does not mean that it is not
unique. This uniqueness may be hard to see for someone who knows very
little about string theory, but the more you will know about theoretical
physics and the possible inconsistencies in various candidate theories -
and the miraculous ways how string theory avoids these inconsistencies -
the more you will realize how true and deep my statement is and how
false and shallow is yours. LM]
Or, following the usual route of physics, demonstrate experimental
results so distinct and compelling that possible competing theories are
of little interest.
Since neither of the above are available,
[Moderator's note: The strategy that you propose is unscientific. It is
not necessary to disprove all conceivable alternatives to string theory
if we want to rule out LQG. It was enough to rule out LQG which was a
much easier task. LM]
I can only interpret the attacks on people who seek gravity outside of
string theory as quasi-religious fervor.
[Moderator's note: if you learned some technical stuff instead of your
current philosophical/religious words, you might become able to do
better and find a better interpretation. LM]
It seems obvious that if you don't look, you can't find.
[Moderator's note: I assure you that I look. Conversely, if you don't
look, you can't see the problems with *any* inconsistent theory. LM]
And ultimately, if the search fails, it will be a compelling argument in
favor of string theory, so why fear it?
[Moderator's note: I don't fear anything. I just stated a rather
well-known insight about uniqueness of string theory among the known
quantum theories of gravity. It seems to me that it is *you* who fears
it. LM]
If the search succeeds, it won't be a disaster for physics, as someone has
claimed.
[Moderator's note: Anyone is allowed to search for anything, which does
not mean that all searches are equally justified and reasonable. LM]
-Arun
Urs Schreiber
Sep1-04, 06:04 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On 1 Sep 2004, Rufus Anton wrote:\n\n> It is nothing short of bizarre that you direct this question to the\n> moderator, who argues for the scientific method, rather than to the\n> loop quantum gravitist, who refuses to count the "antisocialist\n> macro-apples".\n\nDear Rufus,\n\nyour opinion is appreciated, but this comment must be returned you as an\noff-topic contribution. I hope that it won\'t discourage you.\n\nLubos\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On 1 Sep 2004, Rufus Anton wrote:
> It is nothing short of bizarre that you direct this question to the
> moderator, who argues for the scientific method, rather than to the
> loop quantum gravitist, who refuses to count the "antisocialist
> macro-apples".
Dear Rufus,
your opinion is appreciated, but this comment must be returned you as an
off-topic contribution. I hope that it won't discourage you.
Lubos
Lubos Motl
Sep6-04, 07:51 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Dear Sergei A.,\n\nyou are not the only one anymore. Andy Neitzke predicted that there would\nbe lots of papers explaining why log(3) is relevant even though the Poles\nshowed that the correct LQG result is different, and Andy Neitzke was\napparently right. The new paper of this type is\n\nhttp://www.arxiv.org/abs/hep-th/0409056\n\nIf I had not seen this paper, I would not believe that it can appear on\nhep-th except for April 1st. They argue that the subset of LQG states that\nlead to the incorrect entropy proportional to log(3) is nice because it\ndescribes a "noiseless subsystem".\n\nGiven the fact that the very meaning of entropy is to count how much\ninformation can be encoded in (any kind of) noise, it is a really\nentertaining argument. It\'s like if one counts the entropy of golden gas,\nand only allows the gas to contain protons because the electrons would be\na noise and gold cannot have any noise in it.\n\nThe goal of this game is to return to the apparently wrong result for the\nLQG entropy involving log(3). Even if this could work, there would still\nbe no explanation why the real part of QN frequencies should be related to\nthe area spectrum, and why the log(3) is only found in one black hole\'s QN\nmodes and all other black holes apparently lead to different results as\nmany recent papers quantitatively show.\n\nProbably the cutest sentence of the article is the following one:\n\n"On the other hand, if [the Hilbert space with all spins] is the right\nHilbert space for the horizon of a Schwarzschild black hole, loop quantum\ngravity is in deep trouble, because there is no choice of \\gamma that will\nagree with both the Hawking entropy and the quasi-normal mode spectrum."\n\nWell, this happens if Paul Ginsparg becomes a highly tollerant person. ;-)\nThe authors will probably keep on deriving amazing results from loop\nquantum gravity, its modern ramifications, and the assumption of their\nmutual consistency, but I think that most readers will conclude that the\ncontent of these papers really shows, without too many serious doubts,\nthat loop quantum gravity *is* in deep trouble.\n\nBy the way, our LQG colleagues do not quite agree how the name of\nSchwarzschild should be spelled. While Carlo Rovelli in his book talks\nabout "Schwarzshild", Olaf, Lee, and Fotini mostly write about\n"Schwarzchild" or even "Schwartzchild".\n\nAll the best\nLubos\n_____________________________________ _________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Dear Sergei A.,
you are not the only one anymore. Andy Neitzke predicted that there would
be lots of papers explaining why log(3) is relevant even though the Poles
showed that the correct LQG result is different, and Andy Neitzke was
apparently right. The new paper of this type is
http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0409056
If I had not seen this paper, I would not believe that it can appear on
hep-th except for April 1st. They argue that the subset of LQG states that
lead to the incorrect entropy proportional to log(3) is nice because it
describes a "noiseless subsystem".
Given the fact that the very meaning of entropy is to count how much
information can be encoded in (any kind of) noise, it is a really
entertaining argument. It's like if one counts the entropy of golden gas,
and only allows the gas to contain protons because the electrons would be
a noise and gold cannot have any noise in it.
The goal of this game is to return to the apparently wrong result for the
LQG entropy involving log(3). Even if this could work, there would still
be no explanation why the real part of QN frequencies should be related to
the area spectrum, and why the log(3) is only found in one black hole's QN
modes and all other black holes apparently lead to different results as
many recent papers quantitatively show.
Probably the cutest sentence of the article is the following one:
"On the other hand, if [the Hilbert space with all spins] is the right
Hilbert space for the horizon of a Schwarzschild black hole, loop quantum
gravity is in deep trouble, because there is no choice of \gamma that will
agree with both the Hawking entropy and the quasi-normal mode spectrum."
Well, this happens if Paul Ginsparg becomes a highly tollerant person. ;-)
The authors will probably keep on deriving amazing results from loop
quantum gravity, its modern ramifications, and the assumption of their
mutual consistency, but I think that most readers will conclude that the
content of these papers really shows, without too many serious doubts,
that loop quantum gravity *is* in deep trouble.
By the way, our LQG colleagues do not quite agree how the name of
Schwarzschild should be spelled. While Carlo Rovelli in his book talks
about "Schwarzshild", Olaf, Lee, and Fotini mostly write about
"Schwarzchild" or even "Schwartzchild".
All the best
Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Thomas Dent
Sep7-04, 07:11 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Lubos Motl <motl@feynman.harvard.edu> wrote\n\n\n> By the way, our LQG colleagues do not quite agree how the name of\n> Schwarzschild should be spelled. While Carlo Rovelli in his book talks\n> about "Schwarzshild", Olaf, Lee, and Fotini mostly write about\n> "Schwarzchild" or even "Schwartzchild".\n>\n\nOut of all the previous discussion, this is one thing I know, since it\nis very trivial and self-consistent within the framework of German\nlanguage:\n\n"Schwarz" = black\n\n"Schild" = shield\n\nGerman words do not begin with Sh or Ch, only Sch.\n\nWhen the German Schwarz\'s moved to America some of them became\nSchwartz\'s to keep the same pronunciation, ... so when they move to\nCanada, logically they might also change spelling??\n\nHowever, Karl himself remained in old Europe, and with rather bad\njudgement volunteered to go and fight the Russians, during which he\nmanaged also to obtain two solutions of GR.\n\nThomas\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lubos Motl <motl@feynman.harvard.edu> wrote
> By the way, our LQG colleagues do not quite agree how the name of
> Schwarzschild should be spelled. While Carlo Rovelli in his book talks
> about "Schwarzshild", Olaf, Lee, and Fotini mostly write about
> "Schwarzchild" or even "Schwartzchild".
>
Out of all the previous discussion, this is one thing I know, since it
is very trivial and self-consistent within the framework of German
language:
"Schwarz" = black
"Schild" = shield
German words do not begin with Sh or Ch, only Sch.
When the German Schwarz's moved to America some of them became
Schwartz's to keep the same pronunciation, ... so when they move to
Canada, logically they might also change spelling??
However, Karl himself remained in old Europe, and with rather bad
judgement volunteered to go and fight the Russians, during which he
managed also to obtain two solutions of GR.
Thomas
Sergei Alexandrov
Sep12-04, 04:26 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Dear Lubos,\n\nFirst of all, let me give some comments concerning your critics of the paper\nfrom which we started the discussion. From what you wrote,\nit seems to me that you overlooked one of the main arguments.\nNamely, it is a simple mathematical fact that the dimension of the\nHilbert space associated with a given puncturing of the horizon\nis maximal for the puncturing consisting only from spins 1/2.\nTherefore, IF we consider each puncturing as a different macrostate\nthan this particular puncturing has the maximal entropy.\nThis is the reason why it is preferable and neither yours nor\nmy year of birth have nothing to do with its choice.\n\nConcerning other issues of loop gravity that you mentioned, some of them\n(like necessity to work with linear combinations of spin networks)\nwere actually explained already in the original papers by Ashtekar et al.,\nand some issues (like Hamiltonian operator) I am not going to defend\nbecause as you I think they give an indication that LQG, at least in its\npresent formulation, is not correct. And I have a concrete argument why.\n(Your statement "LQG is not string theory, and therefore it can\'t\ndescribe gravity" cannot be a serious argument because\n1) there are no experimental evidences in favor of string theory;\n2) there is no theorem showing that this is the only consistent\nquantization of GR. One can believe that such theorem exists, but\nup to now nobody proved it and I do not think it is possible.)\nRoughly speaking, I have evidences that the usual loop quantization\nbreaks the diffeomorphism invariance. Therefore, some problems with\nthe quasiclassical limit are quite expected.\n\nSo the actual motivation for this work, I wrote this already but\nlet me repeat, was to understand how a similar counting can work\nin the case of a continuous area spectrum, where as I believe at least\nsome problems of the usual loop quantization are absent.\nThe standard counting procedure gives in this case just a stupid infinity,\nwhereas when we restrict to a particular puncturing, it may give\na meaningful result. But since a boundary theory (as well as many\nother things) for the case of the continuum spectrum is not\ndeveloped yet, I had to work with the standard discrete spectrum.\n\nSince from my point of view the discrete spectrum is wrong and the Immirzi\nparameter has no physical meaning, the whole story with the relation\nto quasinormal modes also does not seem to be correct.\nSo, please, do not consider the paper as one in the series\ntrying to "restore" the log(3) story and, if you do not know\nthe original motivation, please, do not extrapolate your guesses.\n\nNevertheless, I think your critics of the recent paper by\nLee, Fotini and Olaf was presented in an unfair way. It seems to me you\nwere playing words and cutting sentences out of the context.\nFor example, are you sure that the "noise" which you mentioned and\nwhich is relevant for the entropy counting is the same as the notion appeared\nin their paper? Also the sentence which you cited has nothing to do with\ntheir argumentation which is contained in the main body of\nthe paper and not in the introduction.\n\nIn fact, their argument is similar to mine. They ask:\n"How do we find the subspace corresponding to the spherically\nsymmetric black hole, as opposed to a general surface of a given area?"\nThis is exactly the question which I was trying to address.\nAlso they use essentially a similar argument involving the spherical\nsymmetry and come to a similar conclusion that only the puncturing by spins\n1/2 corresponds in the low energy limit to a stable configuration.\nTheir argumentation contains more details and relies on some additional\nconsiderations, although of course nothing is rigorous at this stage.\n\nRegards\nSergei\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Dear Lubos,
First of all, let me give some comments concerning your critics of the paper
from which we started the discussion. From what you wrote,
it seems to me that you overlooked one of the main arguments.
Namely, it is a simple mathematical fact that the dimension of the
Hilbert space associated with a given puncturing of the horizon
is maximal for the puncturing consisting only from spins 1/2.
Therefore, IF we consider each puncturing as a different macrostate
than this particular puncturing has the maximal entropy.
This is the reason why it is preferable and neither yours nor
my year of birth have nothing to do with its choice.
Concerning other issues of loop gravity that you mentioned, some of them
(like necessity to work with linear combinations of spin networks)
were actually explained already in the original papers by Ashtekar et al.,
and some issues (like Hamiltonian operator) I am not going to defend
because as you I think they give an indication that LQG, at least in its
present formulation, is not correct. And I have a concrete argument why.
(Your statement "LQG is not string theory, and therefore it can't
describe gravity" cannot be a serious argument because
1) there are no experimental evidences in favor of string theory;
2) there is no theorem showing that this is the only consistent
quantization of GR. One can believe that such theorem exists, but
up to now nobody proved it and I do not think it is possible.)
Roughly speaking, I have evidences that the usual loop quantization
breaks the diffeomorphism invariance. Therefore, some problems with
the quasiclassical limit are quite expected.
So the actual motivation for this work, I wrote this already but
let me repeat, was to understand how a similar counting can work
in the case of a continuous area spectrum, where as I believe at least
some problems of the usual loop quantization are absent.
The standard counting procedure gives in this case just a stupid infinity,
whereas when we restrict to a particular puncturing, it may give
a meaningful result. But since a boundary theory (as well as many
other things) for the case of the continuum spectrum is not
developed yet, I had to work with the standard discrete spectrum.
Since from my point of view the discrete spectrum is wrong and the Immirzi
parameter has no physical meaning, the whole story with the relation
to quasinormal modes also does not seem to be correct.
So, please, do not consider the paper as one in the series
trying to "restore" the log(3) story and, if you do not know
the original motivation, please, do not extrapolate your guesses.
Nevertheless, I think your critics of the recent paper by
Lee, Fotini and Olaf was presented in an unfair way. It seems to me you
were playing words and cutting sentences out of the context.
For example, are you sure that the "noise" which you mentioned and
which is relevant for the entropy counting is the same as the notion appeared
in their paper? Also the sentence which you cited has nothing to do with
their argumentation which is contained in the main body of
the paper and not in the introduction.
In fact, their argument is similar to mine. They ask:
"How do we find the subspace corresponding to the spherically
symmetric black hole, as opposed to a general surface of a given area?"
This is exactly the question which I was trying to address.
Also they use essentially a similar argument involving the spherical
symmetry and come to a similar conclusion that only the puncturing by spins
1/2 corresponds in the low energy limit to a stable configuration.
Their argumentation contains more details and relies on some additional
considerations, although of course nothing is rigorous at this stage.
Regards
Sergei
Lubos Motl
Sep13-04, 12:03 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Dear Sergei,\n\n> Namely, it is a simple mathematical fact that the dimension of the\n> Hilbert space associated with a given puncturing of the horizon\n> is maximal for the puncturing consisting only from spins 1/2.\n\nbut if you add the number of states coming from all different puncturings,\nyou will obtain - as Meissner showed - a comparable contribution to the\nentropy. The puncturings with higher spins in it simply cannot be\nneglected if one computes the entropy.\n\n> Therefore, IF we consider each puncturing as a different macrostate\n> than this particular puncturing has the maximal entropy.\n\nDifferent puncturings cannot be different macrostates because you would\nhave an exponentially huge number of macrostates. Moreover, it is pretty\nclear on physical grounds that a single modified puncture is not what\nchanges a given state macroscopically.\n\n> This is the reason why it is preferable and neither yours nor\n> my year of birth have nothing to do with its choice.\n\nYou can *prefer* something if you wish, but it does not allow you to\nneglect other existing contributions to the entropy. Once again,\npreferring such a subset of states is equally justified as preferring\nstates associated with a year of birth. You can prefer quarks because they\nare colorful and different from leptons, but if you eliminate leptons\'\ncontribution to the gauge anomaly, you will obtain a wrong result.\n\n> Concerning other issues of loop gravity that you mentioned, some of them\n> (like necessity to work with linear combinations of spin networks)\n> were actually explained already in the original papers by Ashtekar et al.,\n\nHappy to agree with them that this would be the only hope for a consistent\npicture.\n\n> (Your statement "LQG is not string theory, and therefore it can\'t\n> describe gravity" cannot be a serious argument because\n> 1) there are no experimental evidences in favor of string theory;\n> 2) there is no theorem showing that this is the only consistent\n> quantization of GR. One can believe that such theorem exists, but\n> up to now nobody proved it and I do not think it is possible.)\n\nOnce again, I admit that it is not a theorem, but it has a significant\nbody of evidence that underlies this statement - and saying "it\'s only a\nnonsense because it is not a theorem [yet]" is not the sort of fair\njudgement of a physical principle.\n\n> Roughly speaking, I have evidences that the usual loop quantization\n> breaks the diffeomorphism invariance.\n\nInteresting - I am afraid that your colleagues won\'t like it too much.\n\n> Since from my point of view the discrete spectrum is wrong and the Immirzi\n> parameter has no physical meaning, the whole story with the relation\n> to quasinormal modes also does not seem to be correct.\n\nThat\'s a rather logical implication.\n\n> So, please, do not consider the paper as one in the series\n> trying to "restore" the log(3) story and, if you do not know\n> the original motivation, please, do not extrapolate your guesses.\n\nI thought that the point of your paper *was* to restore the relevance of\nthe number log(2) or log(3) for the LQG entropy counting. Exactly the\nopposite was the point of Meissner\'s paper.\n\n> Nevertheless, I think your critics of the recent paper by\n> Lee, Fotini and Olaf was presented in an unfair way. It seems to me you\n> were playing words and cutting sentences out of the context.\n> For example, are you sure that the "noise" which you mentioned and\n> which is relevant for the entropy counting is the same as the notion appeared\n> in their paper?\n\nYes, I am. Black holes are the most entropic systems among all objects of\nthe same size. All conceivable degrees of freedom - including\ntransPlanckian degres of freedom - are thermally excited and they must be\nin order to give this huge, maximal possible entropy. Yet, Lee, Fotini,\nand Olaf model black holes as noiseless systems. It does not matter how\nexactly you define noise. The point of their paper definitely agrees with\nthe usual intuition - they want to present the black holes as clean things\nin which most excitations are not allowed because they would be a "noise".\n\nBut the black holes are, in this language, the most noisy objects that\nphysics admits.\n\n> In fact, their argument is similar to mine. They ask:\n> "How do we find the subspace corresponding to the spherically\n> symmetric black hole, as opposed to a general surface of a given area?"\n\nThis very question is already a misunderstanding because virtually *all*\nstates look like the single black hole. The black hole dominates the\nensemble of microstates with any constraint - e.g. the total mass or area\n-, and only if you want to obtain something else and special - a pair of\ntwo black holes with the half-size - you would choose a very special\nsubset of the states whose majority is assigned to the single black hole.\n\nYour question is analogous to the question "which microstates correspond\nto the uniform gas in a bottle" - well, most of them, and with some choice\nof graining, virtually all of them. Both you as well as the three more\nrecent authors have a very different answer.\n\n> This is exactly the question which I was trying to address.\n> Also they use essentially a similar argument involving the spherical\n> symmetry and come to a similar conclusion that only the puncturing by spins\n> 1/2 corresponds in the low energy limit to a stable configuration.\n\nIt\'s neither true that the configurations with spin 1/2 only are more\nspherically symmetric than others (the inevitably irregular distribution\nof the punctures, as well as the fluctuating third component, necessarily\nbreak the symmetry completely), nor it\'s true that the spherically\nsymmetric microstates are closer to the spherically symmetric classical\ngeometry. The argument seems misled at all levels.\n\nWe are starting to repeat ourselves. Whoever thinks that the papers\ncontain a rational argument to single out a specific small subset of the\nmicrostates (and reduce the entropy) - whose only special feture is that\nit is simple and it leads to an incorrect result for the entropy that was\nhowever believed to be correct - is free to keep on believing it...\n\nAll the best\nLubos\n_____________________________________ _________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Dear Sergei,
> Namely, it is a simple mathematical fact that the dimension of the
> Hilbert space associated with a given puncturing of the horizon
> is maximal for the puncturing consisting only from spins 1/2.
but if you add the number of states coming from all different puncturings,
you will obtain - as Meissner showed - a comparable contribution to the
entropy. The puncturings with higher spins in it simply cannot be
neglected if one computes the entropy.
> Therefore, IF we consider each puncturing as a different macrostate
> than this particular puncturing has the maximal entropy.
Different puncturings cannot be different macrostates because you would
have an exponentially huge number of macrostates. Moreover, it is pretty
clear on physical grounds that a single modified puncture is not what
changes a given state macroscopically.
> This is the reason why it is preferable and neither yours nor
> my year of birth have nothing to do with its choice.
You can *prefer* something if you wish, but it does not allow you to
neglect other existing contributions to the entropy. Once again,
preferring such a subset of states is equally justified as preferring
states associated with a year of birth. You can prefer quarks because they
are colorful and different from leptons, but if you eliminate leptons'
contribution to the gauge anomaly, you will obtain a wrong result.
> Concerning other issues of loop gravity that you mentioned, some of them
> (like necessity to work with linear combinations of spin networks)
> were actually explained already in the original papers by Ashtekar et al.,
Happy to agree with them that this would be the only hope for a consistent
picture.
> (Your statement "LQG is not string theory, and therefore it can't
> describe gravity" cannot be a serious argument because
> 1) there are no experimental evidences in favor of string theory;
> 2) there is no theorem showing that this is the only consistent
> quantization of GR. One can believe that such theorem exists, but
> up to now nobody proved it and I do not think it is possible.)
Once again, I admit that it is not a theorem, but it has a significant
body of evidence that underlies this statement - and saying "it's only a
nonsense because it is not a theorem [yet]" is not the sort of fair
judgement of a physical principle.
> Roughly speaking, I have evidences that the usual loop quantization
> breaks the diffeomorphism invariance.
Interesting - I am afraid that your colleagues won't like it too much.
> Since from my point of view the discrete spectrum is wrong and the Immirzi
> parameter has no physical meaning, the whole story with the relation
> to quasinormal modes also does not seem to be correct.
That's a rather logical implication.
> So, please, do not consider the paper as one in the series
> trying to "restore" the log(3) story and, if you do not know
> the original motivation, please, do not extrapolate your guesses.
I thought that the point of your paper *was* to restore the relevance of
the number log(2) or log(3) for the LQG entropy counting. Exactly the
opposite was the point of Meissner's paper.
> Nevertheless, I think your critics of the recent paper by
> Lee, Fotini and Olaf was presented in an unfair way. It seems to me you
> were playing words and cutting sentences out of the context.
> For example, are you sure that the "noise" which you mentioned and
> which is relevant for the entropy counting is the same as the notion appeared
> in their paper?
Yes, I am. Black holes are the most entropic systems among all objects of
the same size. All conceivable degrees of freedom - including
transPlanckian degres of freedom - are thermally excited and they must be
in order to give this huge, maximal possible entropy. Yet, Lee, Fotini,
and Olaf model black holes as noiseless systems. It does not matter how
exactly you define noise. The point of their paper definitely agrees with
the usual intuition - they want to present the black holes as clean things
in which most excitations are not allowed because they would be a "noise".
But the black holes are, in this language, the most noisy objects that
physics admits.
> In fact, their argument is similar to mine. They ask:
> "How do we find the subspace corresponding to the spherically
> symmetric black hole, as opposed to a general surface of a given area?"
This very question is already a misunderstanding because virtually *all*
states look like the single black hole. The black hole dominates the
ensemble of microstates with any constraint - e.g. the total mass or area
-, and only if you want to obtain something else and special - a pair of
two black holes with the half-size - you would choose a very special
subset of the states whose majority is assigned to the single black hole.
Your question is analogous to the question "which microstates correspond
to the uniform gas in a bottle" - well, most of them, and with some choice
of graining, virtually all of them. Both you as well as the three more
recent authors have a very different answer.
> This is exactly the question which I was trying to address.
> Also they use essentially a similar argument involving the spherical
> symmetry and come to a similar conclusion that only the puncturing by spins
> 1/2 corresponds in the low energy limit to a stable configuration.
It's neither true that the configurations with spin 1/2 only are more
spherically symmetric than others (the inevitably irregular distribution
of the punctures, as well as the fluctuating third component, necessarily
break the symmetry completely), nor it's true that the spherically
symmetric microstates are closer to the spherically symmetric classical
geometry. The argument seems misled at all levels.
We are starting to repeat ourselves. Whoever thinks that the papers
contain a rational argument to single out a specific small subset of the
microstates (and reduce the entropy) - whose only special feture is that
it is simple and it leads to an incorrect result for the entropy that was
however believed to be correct - is free to keep on believing it...
All the best
Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
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