View Full Version : quantizing gravity
<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>\n"Urs Schreiber" <Urs.Schreiber@uni-essen.de> wrote in message news:<40b476b6\\$1@news.sentex.net>...\n\n> What I find fascinating is that, while it is not clear that we have found\n> any theory that describes the observed world including its gravitational and\n> quantum aspects, we know that there are consistent quantizations of _some_\n> gravitational theories of sorts - not necessarily of the gravitational\n> theory describing our world, but certainly of some theories containing (some\n> approximation to) Einstein-Hilbert gravity. If you don\'t want to trust in\n> the higher loop finiteness of the superstring think of the regularized\n> supermembrane/BFSS model at finite N, for instance, or of AdS/CFT. This are\n> examples of quantum theories which undoubtly do contain (nontrivial)\n> gravity - plus other stuff, including possibly higher dimensions, etc, of\n> course.\n\nI\'m not sure this is fair to say. The "quantization" of certain asymptotically\nMinkwosky and asymptotically AdS SUGRAs provided by matrix theory and\nAdS/CFT appears to be "a quantization" due to superstring theory, i.e. due\nto the fact we have serious evidence these models have a perturbative\nexpansion in terms of strings moving through Minkowski / AdS space and\nthere is evidence for the later reducing to the appropriate SUGRA in the low\nenergy limit, in some sense. The trouble is, it is difficult to give an exact physical\nexplanation of this sense. In fact, the sole "gauge invariant" observable in\nstringy quantization of asymptotically Minkowsky SUGRA is the S-matrix\n(though as far as I understand there are certain complications in the way of\nproducing it in matrix theory which hasn\'t been completely resolved). The sole\n"gauge invariant" observable in stringy quantization of asymptotically AdS\nSUGRA is the set of n-point functions on the boundary of spacetime. In the\nformer case I don\'t completely understand the physical meaning of this\nobservable, since the S-matrix usually implies turning off the coupling constant\nin past and future infinity. However, for instance in type IIA superstring theory\nthe coupling constant is the compactification radius of M-theory and I don\'t see\nhow it can be artificially enforced to become zero in future and past infinity. At\nany rate, these observables are hardly sufficient to describe what the processes\ngoing on around us, which happen both in finite time and finite space. So while\nwe have clues we are onto something, it is far-fetched to claim we have found\nquantizations of gravity (for spacetime dimension > 3).\n\n\nBest regards,\nSquark\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>"Urs Schreiber" <Urs.Schreiber@uni-essen.de> wrote in message news:<40b476b6$1@news.sentex.net>...
> What I find fascinating is that, while it is not clear that we have found
> any theory that describes the observed world including its gravitational and
> quantum aspects, we know that there are consistent quantizations of _some_
> gravitational theories of sorts - not necessarily of the gravitational
> theory describing our world, but certainly of some theories containing (some
> approximation to) Einstein-Hilbert gravity. If you don't want to trust in
> the higher loop finiteness of the superstring think of the regularized
> supermembrane/BFSS model at finite N, for instance, or of AdS/CFT. This are
> examples of quantum theories which undoubtly do contain (nontrivial)
> gravity - plus other stuff, including possibly higher dimensions, etc, of
> course.
I'm not sure this is fair to say. The "quantization" of certain asymptotically
Minkwosky and asymptotically AdS SUGRAs provided by matrix theory and
AdS/CFT appears to be "a quantization" due to superstring theory, i.e. due
to the fact we have serious evidence these models have a perturbative
expansion in terms of strings moving through Minkowski / AdS space and
there is evidence for the later reducing to the appropriate SUGRA in the low
energy limit, in some sense. The trouble is, it is difficult to give an exact physical
explanation of this sense. In fact, the sole "gauge invariant" observable in
stringy quantization of asymptotically Minkowsky SUGRA is the S-matrix
(though as far as I understand there are certain complications in the way of
producing it in matrix theory which hasn't been completely resolved). The sole
"gauge invariant" observable in stringy quantization of asymptotically AdS
SUGRA is the set of n-point functions on the boundary of spacetime. In the
former case I don't completely understand the physical meaning of this
observable, since the S-matrix usually implies turning off the coupling constant
in past and future infinity. However, for instance in type IIA superstring theory
the coupling constant is the compactification radius of M-theory and I don't see
how it can be artificially enforced to become zero in future and past infinity. At
any rate, these observables are hardly sufficient to describe what the processes
going on around us, which happen both in finite time and finite space. So while
we have clues we are onto something, it is far-fetched to claim we have found
quantizations of gravity (for spacetime dimension > 3).
Best regards,
Squark
Doug Sweetser
May31-04, 04:20 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>Hello Alistair:\n\nThis is a great quote:\n\n> Therefore, as was mentioned by Einstein (1954b), "electro-magnetic\n> waves can be put into a container, gravitational waves cannot."\n\nIt shows why Eistein focused so much effort on a classical unification\nof gravity and EM. He did not succeed, but this quote indicates why\nthere is a deep, non-trivial problem. At one point in his efforts, he\ntried to use an asymmetric tensor, with general relaitivity as the\nmodel (rank 2 tesnor equations). I play a similar game, but at the\nrank 1 level. Thanks again for this quote.\n\ndoug\nquaternions.com\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>Hello Alistair:
This is a great quote:
> Therefore, as was mentioned by Einstein (1954b), "electro-magnetic
> waves can be put into a container, gravitational waves cannot."
It shows why Eistein focused so much effort on a classical unification
of gravity and EM. He did not succeed, but this quote indicates why
there is a deep, non-trivial problem. At one point in his efforts, he
tried to use an asymmetric tensor, with general relaitivity as the
model (rank 2 tesnor equations). I play a similar game, but at the
rank 1 level. Thanks again for this quote.
doug
quaternions.com
Lubos Motl
May31-04, 04:21 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 Sun, 30 May 2004, Squark wrote:\n\n> I\'m not sure this is fair to say. The "quantization" of certain asymptotically\n> Minkwosky and asymptotically AdS SUGRAs provided by matrix theory and\n> AdS/CFT appears to be "a quantization" due to superstring theory, i.e. due\n> to the fact we have serious evidence these models have a perturbative\n> expansion in terms of strings moving through Minkowski / AdS space and\n\nWell, the quantization of gravity in the 11D (and similar) flat space and\nin anti de Sitter space is "only" due to string theory because string\ntheory is the only known consistent way to quantize gravity.\n\n> there is evidence for the later reducing to the appropriate SUGRA in the low\n> energy limit, in some sense.\n\nThere is more than just evidence; we can simply calculate what does CFT in\nAdS/CFT predict about the low energy gravity, for example, and it agrees\nwith SUGRA and gives us a lot of information beyond it.\n\n> The trouble is, it is difficult to give an exact physical\n> explanation of this sense.\n\nIt is not so difficult. The exact sense is that string theory in the\nappropriate background is exactly equivalent to the conformal (gauge)\ntheory that describes it holographically. The low-energy spectrum of\nstring theory is exactly what SUGRA predicts, and the interactions between\nthese objects are exactly what you get from classical SUGRA plus\ncorrections that (relatively) go to zero at low energies. What are you\nexactly dissatisfied with?\n\n> In fact, the sole "gauge invariant" observable in stringy quantization\n> of asymptotically Minkowsky SUGRA is the S-matrix (though as far as I\n> understand there are certain complications in the way of producing it\n> in matrix theory which hasn\'t been completely resolved).\n\nThe reason why current string theory only allows to calculate the S-matrix\nis that the S-matrix is the only known gauge-invariant observable in flat\nspace.\n\n> The sole\n> "gauge invariant" observable in stringy quantization of asymptotically AdS\n> SUGRA is the set of n-point functions on the boundary of spacetime.\n\nAlso, the only reason why current string theory in AdS/CFT space can, as\nfar as dynamics goes, only calculate the boundary correlators - except for\nthe light-cone gauge treatment that can go beyond it - is that the\nboundary correlators (scattering from the AdS boundaries) are the only\nknown covariant gauge-invariant observables in this background.\n\nIf you know some other nice enough and generally neglected gauge-invariant\nobservable in gravity that should be calculable, I am eager to hear about\nit! ;-)\n\n> In the former case I don\'t completely understand the physical meaning\n> of this observable, since the S-matrix usually implies turning off the\n> coupling constant in past and future infinity.\n\nThe interactions are effectively turned off near the AdS boundary, too -\nsimply because the physical space becomes infinitely large due to the warp\nfactor and the gravitons etc. are "infinitely diluted". Your intuition\nthat it is only the usual coupling constant that can make things decoupled\nis correct in flat space, but it breaks in the curved e.g. AdS space. It\nis not hard to see by explicit calculations that all the correlators that\nyou are disputing have a well-defined interpretation on both sides, and\ntherefore your criticism is simply incorrect.\n\n> However, for instance in type IIA superstring theory the coupling\n> constant is the compactification radius of M-theory and I don\'t see\n> how it can be artificially enforced to become zero in future and past\n> infinity. At any rate, these observables are hardly sufficient to\n> describe what the processes going on around us, which happen both in\n> finite time and finite space. So while we have clues we are onto\n> something, it is far-fetched to claim we have found quantizations of\n> gravity (for spacetime dimension > 3).\n\nIt is difficult to define phenomena at finite time - and finite space - in\nsuch a way that these quantities are both exact as well as covariant and\ngauge-invariant (under general diffeomorphisms). If you want to talk about\nphenomena taking place in some "finite piece of spacetime", you must first\ndefine where the "finite piece of spacetime" ends. But coordinates are not\ngood enough - they are transformed to different coordinates by the gauge\ntransformations. Proper distances etc. would be better, but many\nquantities like that become divergent once quantum corrections are added.\n\nOnce we gauge-fix general covariance, for example by imposing the light\ncone gauge, we can calculate finite (light-cone) time evolution, too. All\nsuch ways to fix general covariance are necessarily non-covariant.\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 Sun, 30 May 2004, Squark wrote:
> I'm not sure this is fair to say. The "quantization" of certain asymptotically
> Minkwosky and asymptotically AdS SUGRAs provided by matrix theory and
> AdS/CFT appears to be "a quantization" due to superstring theory, i.e. due
> to the fact we have serious evidence these models have a perturbative
> expansion in terms of strings moving through Minkowski / AdS space and
Well, the quantization of gravity in the 11D (and similar) flat space and
in anti de Sitter space is "only" due to string theory because string
theory is the only known consistent way to quantize gravity.
> there is evidence for the later reducing to the appropriate SUGRA in the low
> energy limit, in some sense.
There is more than just evidence; we can simply calculate what does CFT in
AdS/CFT predict about the low energy gravity, for example, and it agrees
with SUGRA and gives us a lot of information beyond it.
> The trouble is, it is difficult to give an exact physical
> explanation of this sense.
It is not so difficult. The exact sense is that string theory in the
appropriate background is exactly equivalent to the conformal (gauge)
theory that describes it holographically. The low-energy spectrum of
string theory is exactly what SUGRA predicts, and the interactions between
these objects are exactly what you get from classical SUGRA plus
corrections that (relatively) go to zero at low energies. What are you
exactly dissatisfied with?
> In fact, the sole "gauge invariant" observable in stringy quantization
> of asymptotically Minkowsky SUGRA is the S-matrix (though as far as I
> understand there are certain complications in the way of producing it
> in matrix theory which hasn't been completely resolved).
The reason why current string theory only allows to calculate the S-matrix
is that the S-matrix is the only known gauge-invariant observable in flat
space.
> The sole
> "gauge invariant" observable in stringy quantization of asymptotically AdS
> SUGRA is the set of n-point functions on the boundary of spacetime.
Also, the only reason why current string theory in AdS/CFT space can, as
far as dynamics goes, only calculate the boundary correlators - except for
the light-cone gauge treatment that can go beyond it - is that the
boundary correlators (scattering from the AdS boundaries) are the only
known covariant gauge-invariant observables in this background.
If you know some other nice enough and generally neglected gauge-invariant
observable in gravity that should be calculable, I am eager to hear about
it! ;-)
> In the former case I don't completely understand the physical meaning
> of this observable, since the S-matrix usually implies turning off the
> coupling constant in past and future infinity.
The interactions are effectively turned off near the AdS boundary, too -
simply because the physical space becomes infinitely large due to the warp
factor and the gravitons etc. are "infinitely diluted". Your intuition
that it is only the usual coupling constant that can make things decoupled
is correct in flat space, but it breaks in the curved e.g. AdS space. It
is not hard to see by explicit calculations that all the correlators that
you are disputing have a well-defined interpretation on both sides, and
therefore your criticism is simply incorrect.
> However, for instance in type IIA superstring theory the coupling
> constant is the compactification radius of M-theory and I don't see
> how it can be artificially enforced to become zero in future and past
> infinity. At any rate, these observables are hardly sufficient to
> describe what the processes going on around us, which happen both in
> finite time and finite space. So while we have clues we are onto
> something, it is far-fetched to claim we have found quantizations of
> gravity (for spacetime dimension > 3).
It is difficult to define phenomena at finite time - and finite space - in
such a way that these quantities are both exact as well as covariant and
gauge-invariant (under general diffeomorphisms). If you want to talk about
phenomena taking place in some "finite piece of spacetime", you must first
define where the "finite piece of spacetime" ends. But coordinates are not
good enough - they are transformed to different coordinates by the gauge
transformations. Proper distances etc. would be better, but many
quantities like that become divergent once quantum corrections are added.
Once we gauge-fix general covariance, for example by imposing the light
cone gauge, we can calculate finite (light-cone) time evolution, too. All
such ways to fix general covariance are necessarily non-covariant.
__{_______________________________________________ _____________________________}
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)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
<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>\n"Lubos Motl" <motl@feynman.harvard.edu> wrote in message news:Pine.LNX.4.31.0405301432410.10458-100000@feynman.harvard.edu...\n> There is more than just evidence; we can simply calculate what does CFT in\n> AdS/CFT predict about the low energy gravity, for example, and it agrees\n> with SUGRA and gives us a lot of information beyond it.\n\nThe way you calculate is is via the AdS/CFT conjecture, via replacing the CFT\nby a string expansion. Or is there a way to compute things directly in the CFT?\nThis would have to be a method that works in the high coupling regime! At any\nrate the only entirely physical (gauge invariant) information we can compute\ntoday is the n-point functions on the spacetime boundary.\n\n> It is not so difficult. The exact sense is that string theory in the\n> appropriate background is exactly equivalent to the conformal (gauge)\n> theory that describes it holographically. The low-energy spectrum of\n> string theory is exactly what SUGRA predicts, and the interactions between\n> these objects are exactly what you get from classical SUGRA plus\n> corrections that (relatively) go to zero at low energies. What are you\n> exactly dissatisfied with?\n\nThat in SUGRA you can discuss processes occuring in a finite patch of\nspacetime whereas in string theory you cannot (or don\'t know how).\n\n> The reason why current string theory only allows to calculate the S-matrix\n> is that the S-matrix is the only known gauge-invariant observable in flat\n> space.\n> ...\n> Also, the only reason why current string theory in AdS/CFT space can, as\n> far as dynamics goes, only calculate the boundary correlators - except for\n> the light-cone gauge treatment that can go beyond it - is that the\n> boundary correlators (scattering from the AdS boundaries) are the only\n> known covariant gauge-invariant observables in this background.\n\nThis is clear to me. It also appears to me that Edward Witten (page 7,\n"Quantum Gravity in de Sitter Space", hep-th/0106109) believes this\nis the only observable that can or need to be defined in principle.\n\n> If you know some other nice enough and generally neglected gauge-invariant\n> observable in gravity that should be calculable, I am eager to hear about\n> it! ;-)\n\nI don\'t know the solution but I claim there is definitely a problem. Btw, after\nreading Lenny Susskind\'s "The World as a Hologram" (hep-th/9409089) it\nappears to me such an observable exists. Consider asymptotically AdS\ngravity for instance. Choose a point on the asymptotic boundary and a\npositive real number. For any classical solution one may construct a\nspacelike geodesic beginning from the chosen point on the boundary and\northogonal to it. A natural parameter exists on the geodesic (proper length\nstarting from the boundary) - lets call it "depth". The observables are then\nvarious scalars constructed out of fields in the theory at the point on the\ngeodesic for which the depth is the chosen real number. One may construct\nmore observables using derivatives w.r.t. depth and the location of the\nbasepoint on the boundary. Did anyone try defining such observables in\nAdS/CFT? Or maybe it can be shown they are not "nice enough"?\n\n> > In the former case I don\'t completely understand the physical meaning\n> > of this observable, since the S-matrix usually implies turning off the\n> > coupling constant in past and future infinity.\n>\n> The interactions are effectively turned off near the AdS boundary, too -\n> simply because the physical space becomes infinitely large due to the warp\n> factor and the gravitons etc. are "infinitely diluted".\n\nPossibly I formulated myself badly. I have no problem with the AdS\nboundary n-point functions as observables. I have a problem with the\nS-matrix as an observable of superstring theory in asymptotically\nflat spacetime. The usual definition of the S-matrix in QFT includes\nturning off the coupling constant in past and future infinity but I don\'t\nunderstand how can it be consistently then in superstring theory:\n\n> > However, for instance in type IIA superstring theory the coupling\n> > constant is the compactification radius of M-theory and I don\'t see\n> > how it can be artificially enforced to become zero in future and past\n> > infinity.\n\n> It is difficult to define phenomena at finite time - and finite space - in\n> such a way that these quantities are both exact as well as covariant and\n> gauge-invariant (under general diffeomorphisms). If you want to talk about\n> phenomena taking place in some "finite piece of spacetime", you must first\n> define where the "finite piece of spacetime" ends. But coordinates are not\n> good enough - they are transformed to different coordinates by the gauge\n> transformations.\n\nI realize all that completely well. The thing is, these problems are solvable\nin classical gravity. It appears to me that to quantize gravity implies providing\na way to solve this problems for quantum gravity as well, within the setting of\nyour quantization.\n\n> Proper distances etc. would be better, but many\n> quantities like that become divergent once quantum corrections are added.\n\nDoes it include the thingies I mentioned above? How do you know they\nbecome divergent?\n\n\nBest regards,\nSquark\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 in message news:Pine.LNX.4.31.0405301432410.10458-100000@feynman.harvard.edu...
> There is more than just evidence; we can simply calculate what does CFT in
> AdS/CFT predict about the low energy gravity, for example, and it agrees
> with SUGRA and gives us a lot of information beyond it.
The way you calculate is is via the AdS/CFT conjecture, via replacing the CFT
by a string expansion. Or is there a way to compute things directly in the CFT?
This would have to be a method that works in the high coupling regime! At any
rate the only entirely physical (gauge invariant) information we can compute
today is the n-point functions on the spacetime boundary.
> It is not so difficult. The exact sense is that string theory in the
> appropriate background is exactly equivalent to the conformal (gauge)
> theory that describes it holographically. The low-energy spectrum of
> string theory is exactly what SUGRA predicts, and the interactions between
> these objects are exactly what you get from classical SUGRA plus
> corrections that (relatively) go to zero at low energies. What are you
> exactly dissatisfied with?
That in SUGRA you can discuss processes occuring in a finite patch of
spacetime whereas in string theory you cannot (or don't know how).
> The reason why current string theory only allows to calculate the S-matrix
> is that the S-matrix is the only known gauge-invariant observable in flat
> space.
> ...
> Also, the only reason why current string theory in AdS/CFT space can, as
> far as dynamics goes, only calculate the boundary correlators - except for
> the light-cone gauge treatment that can go beyond it - is that the
> boundary correlators (scattering from the AdS boundaries) are the only
> known covariant gauge-invariant observables in this background.
This is clear to me. It also appears to me that Edward Witten (page 7,
"Quantum Gravity in de Sitter Space", http://www.arxiv.org/abs/hep-th/0106109) believes this
is the only observable that can or need to be defined in principle.
> If you know some other nice enough and generally neglected gauge-invariant
> observable in gravity that should be calculable, I am eager to hear about
> it! ;-)
I don't know the solution but I claim there is definitely a problem. Btw, after
reading Lenny Susskind's "The World as a Hologram" (http://www.arxiv.org/abs/hep-th/9409089) it
appears to me such an observable exists. Consider asymptotically AdS
gravity for instance. Choose a point on the asymptotic boundary and a
positive real number. For any classical solution one may construct a
spacelike geodesic beginning from the chosen point on the boundary and
orthogonal to it. A natural parameter exists on the geodesic (proper length
starting from the boundary) - lets call it "depth". The observables are then
various scalars constructed out of fields in the theory at the point on the
geodesic for which the depth is the chosen real number. One may construct
more observables using derivatives w.r.t. depth and the location of the
basepoint on the boundary. Did anyone try defining such observables in
AdS/CFT? Or maybe it can be shown they are not "nice enough"?
> > In the former case I don't completely understand the physical meaning
> > of this observable, since the S-matrix usually implies turning off the
> > coupling constant in past and future infinity.
>
> The interactions are effectively turned off near the AdS boundary, too -
> simply because the physical space becomes infinitely large due to the warp
> factor and the gravitons etc. are "infinitely diluted".
Possibly I formulated myself badly. I have no problem with the AdS
boundary n-point functions as observables. I have a problem with the
S-matrix as an observable of superstring theory in asymptotically
flat spacetime. The usual definition of the S-matrix in QFT includes
turning off the coupling constant in past and future infinity but I don't
understand how can it be consistently then in superstring theory:
> > However, for instance in type IIA superstring theory the coupling
> > constant is the compactification radius of M-theory and I don't see
> > how it can be artificially enforced to become zero in future and past
> > infinity.
> It is difficult to define phenomena at finite time - and finite space - in
> such a way that these quantities are both exact as well as covariant and
> gauge-invariant (under general diffeomorphisms). If you want to talk about
> phenomena taking place in some "finite piece of spacetime", you must first
> define where the "finite piece of spacetime" ends. But coordinates are not
> good enough - they are transformed to different coordinates by the gauge
> transformations.
I realize all that completely well. The thing is, these problems are solvable
in classical gravity. It appears to me that to quantize gravity implies providing
a way to solve this problems for quantum gravity as well, within the setting of
your quantization.
> Proper distances etc. would be better, but many
> quantities like that become divergent once quantum corrections are added.
Does it include the thingies I mentioned above? How do you know they
become divergent?
Best regards,
Squark
alistair
Jun1-04, 02:11 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>ALISTAIR writes:\n\nPhotons with spin 1 can yield two spin 1/2 particles e.g an\nelectron-positron pair, and a photon can result from the quantisation\nof the electric field\nin flat space-time. If a spin 2 graviton can yield a particle pair of\nsome kind,each particle with spin 1, would it then be correct to say\nthat the\ngraviton resulted from a quantisation in a flat space-time?\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>ALISTAIR writes:
Photons with spin 1 can yield two spin 1/2 particles e.g an
electron-positron pair, and a photon can result from the quantisation
of the electric field
in flat space-time. If a spin 2 graviton can yield a particle pair of
some kind,each particle with spin 1, would it then be correct to say
that the
graviton resulted from a quantisation in a flat space-time?
Lubos Motl
Jun7-04, 12:36 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 Wed, 2 Jun 2004, Squark wrote:\n\n> The way you calculate is is via the AdS/CFT conjecture, via replacing\n> the CFT by a string expansion. Or is there a way to compute things\n> directly in the CFT?\n\nYes, that\'s the whole point of the AdS/CFT checks - that you can compute\nmany things on both sides, and they agree for all quantities that are\nexactly calculable on both sides (and people have found many of them). The\ncalculations on the CFT side are being done without string theory - using\nold-fashioned Feynman diagrams in N=4 super Yang-Mills, for example.\nFollowing \'t Hooft, we can reorganize these calculations according to the\ntopology i.e. the genus (and focus on the planar diagrams), but they are\nstill field-theoretical, non-gravitational and "non-stringy" calculations.\n\nMost quantities (the more complicated ones) are however unprotected, and\nthey are difficult to calculate exactly on both sides. It makes the\ncontinuation in either of the two directions difficult, of course, and the\napproximate results then can\'t agree. For example, the entropy density of\nhot D3-branes is known to be renormalized by a factor of 3/4 as you change\nthe \'t Hooft coupling from 0 to infinity.\n\n> This would have to be a method that works in the high coupling regime!\n\nThe SUSY-protected quantities work out correctly in the whole range.\n\n> At any rate the only entirely physical (gauge\n> invariant) information we can compute today is the n-point functions\n> on the spacetime boundary.\n\nAnd according to old-fashioned physics, it is the only exact physical\ninformation that exists. It is a successful consistency check because we\nsee that no wrong and gauge-variant observables can be calculated.\n\n> That in SUGRA you can discuss processes occuring in a finite patch of\n> spacetime whereas in string theory you cannot (or don\'t know how).\n\nYou probably mean classical solutions of SUGRA (defined in a finite patch\nof spacetime) only, don\'t you? Classical SUGRA is a limit of superstring\ntheory in the same sense as it is a limit of any other quantum completion\nof classical supergravity (well, it\'s because string/M-theory is really\nthe only consistent quantum extension of classical SUGRA). You can use\nyour favorite local solutions of classical SUGRA for "finite patches", and\nyou can prove that these solutions are relevant even in string theory, in\nthe limit hbar=0 - at least if the red shifts are bounded and all\ndistances you study are much longer than l_{planck}. But these classical\nsolutions are not quantum-exact observables.\n\nIn a theory of quantum gravity, such as SUGRA, it is just impossible to\ndefine local gauge-invariant operators and compute their correlators or\nanything of this type that we are used to in other quantum theories.\n\nThe difference that you are trying to picture as a difference between\nSUGRA and superstring theory is actually something completely different:\nyou are talking about the things that can be done in classical physics,\nand you seem to complain that they are not meaningful in a quantum theory.\nYour criticism is actually a criticism of (the very framework of) quantum\ntheory, not a specific criticism of string theory. The only problem with\nthis criticism is that quantum theory is proved, beyond any reasonably\ndoubts, to be a feature of reality.\n\nIf one uses a non-stringy framework, one must be very careful to avoid all\nthese potential "quantities" that must be non-physical. String theory does\nit automatically, and it only allows us to calculate physically meaningful\nobservables such as the S-matrix or the boundary correlators.\n\n> > If you know some other nice enough and generally neglected gauge-invariant\n> > observable in gravity that should be calculable, I am eager to hear about\n> > it! ;-)\n>\n> I don\'t know the solution but I claim there is definitely a problem.\n\nHow can you claim that there is "definitely" a problem even if you\'re\nunable to formulate what the problem could be? ;-)\n\n> Btw, after reading Lenny Susskind\'s "The World as a Hologram"\n> (hep-th/9409089) it appears to me such an observable exists. Consider\n> asymptotically AdS gravity for instance. Choose a point on the\n> asymptotic boundary and a positive real number. For any classical\n> solution one may construct a spacelike geodesic beginning from the\n> chosen point on the boundary and orthogonal to it. A natural parameter\n> exists on the geodesic (proper length starting from the boundary) -\n> lets call it "depth".\n\nThe proper length of a line starting from the AdS boundary is infinite\neven in the classical theory. Even if you chose a different geometry where\nthis proper length is finite - or subtracted the divergent piece in some\nway, it would become infinite anyway once you took quantum fluctuations of\nthe geometry into account. In the full theory, geometry *does* fluctuate,\nand your intuition about the finite distances is only valid in the\nclassical, long-distance approximation.\n\nMore generally, there exists absolutely no reason why the notion of\n"distance", "area", and "volume" should have an exact, fundamental meaning\nin a theory of quantum gravity (and string theory is bringing up to\nbelieve that these things can\'t be exact at the Planck scale). It is\nimportant that the Universe roughly behaves as the Minkowski or Euclidean\ngeometry at "long distances" (this usage of the word "distance" is\nself-consistent), because it is a viable framework for Nature to create\nlife. But this does not require the geometric quantities to be\nfundamental. To be honest, we are measuring the distances by sticks,\nlasers, or other gadgets. A physical theory must confirm the existence of\nsticks, lasers, and it must correctly predict their behavior (and masses\nof wrapped branes, or whatever else can physically exist). String theory\ndoes this job, and it does so even though it implies that our notions of\ngeometry are emergent approximate notions that are only valid at low\nenergies.\n\n> The observables are then various scalars constructed out of fields in\n> the theory at the point on the geodesic for which the depth is the\n> chosen real number. One may construct more observables using\n> derivatives w.r.t. depth and the location of the basepoint on the\n> boundary. Did anyone try defining such observables in AdS/CFT? Or\n> maybe it can be shown they are not "nice enough"?\n\nTry it. I won\'t try it because these observables do not seem well\nmotivated and justified to me.\n\n> Possibly I formulated myself badly. I have no problem with the AdS\n> boundary n-point functions as observables. I have a problem with the\n> S-matrix as an observable of superstring theory in asymptotically\n> flat spacetime.\n\nThat\'s about an equally serious objection. ;-)\n\n> The usual definition of the S-matrix in QFT includes\n> turning off the coupling constant in past and future infinity but I don\'t\n> understand how can it be consistently then in superstring theory:\n\nTurning off the interactions is just a trick to define the asymptotic\nscattering states as the adiabatic continuation of the corresponding\nstates at g=0 (even though they exist, as slightly different states, for\nevery value of "g", as long as the particle is stable), and it is equally\nmeaningful in string theory like in a perturbative quantum field theory.\nWhere do you exactly see any difference? In the fact that the stringy\ncoupling constant is the expectation value of the dilaton (exponentiated)?\nWhy would you believe that this could invalidate perturbative expansions?\n\nOn the contrary, it adds more structure and knowledge - not less - because\nthe amplitudes with an extra dilaton in the process can be used to relate\ndifferent orders of "g" contributing to a general amplitude. But otherwise\nbe sure that as long as the dilaton is a modulus, you can tune its value\nto an arbitrarily small positive number. Did you say that you want zero?\nIn field theory, you don\'t need the exact zero to be achieved either; you\njust need the right limit.\n\n> I realize all that completely well. The thing is, these problems are\n> solvable in classical gravity. It appears to me that to quantize\n> gravity implies providing a way to solve this problems for quantum\n> gravity as well, within the setting of your quantization.\n\nIt appears to me that you want to reject basic principles in quantum\nmechanics. In classical physics, the proper length of a geodesic between\ntwo points is a sharply defined number. But in quantum physics, this\nobservable - just like any other observable - becomes an operator whose\nvalues fluctuate, whose values span a probability distribution and they\nhave different amplitudes to take different values in different states.\nThe exceptions are eigenstates, but the eigenstates of such geometric\nquantities can\'t be expected to be close to the energy eigenstates that we\nare more likely to see (states close to the ground state).\n\nMoreover, the uncertainty principle prevents you from having a sharp value\nof g_{ij} and its time-derivative, roughly speaking.\n\nQuantum fluctuations contribute and make these classical quantities - such\nas the proper length - cutoff-dependent, which will prevent you from\ndefining an exact quantity as your cutoff approaches the Planck scale. You\nmight hope that there will be some sharply defined value of the "proper\nlength" where the cutoff is "infinite" - which might be effectively\nequivalent to the Planck scale cutoff - but this logic is misguided\nbecause the classical geometry is simply an incorrect description for\nprocesses that occur at the Planck scale (or shorter).\n\n> Does it include the thingies I mentioned above? How do you know they\n> become divergent?\n\nThe things you mentioned above were divergent even at the classical level.\nMore generally, we can calculate the cutoff-dependence of these quantities\nin effective field theory, and the fluctuations (as well as the mean\nvalue) increases with your cutoff energy. Intuitively this result is\nclear; if you imagine the spacetime geometry to be more foamy, the total\nlength will count all the local features of the foam, and it will grow.\nWell, in Minkowski geometry, you can on the contrary always find a\n*shorter* geodesic, but at any rate, the proper length computed from\n"quantized general relativity" won\'t be finite.\n\nIn string theory, we often compute meaningful "quantum volumes", but their\ndefinition is different. They are counted from masses of the branes\nwrapped on the corresponding cycles, and in a finite theory (with a lot of\nSUSY calculations), these masses (or energies) are finite, of course. But\nonce again, they are not being calculated in the naive classical way as\nthe integral of \\sqrt{g_{mn}dx^m dx^n} with an unlimited UV cutoff\nbecause this prescription is physically misled.\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, 2 Jun 2004, Squark wrote:
> The way you calculate is is via the AdS/CFT conjecture, via replacing
> the CFT by a string expansion. Or is there a way to compute things
> directly in the CFT?
Yes, that's the whole point of the AdS/CFT checks - that you can compute
many things on both sides, and they agree for all quantities that are
exactly calculable on both sides (and people have found many of them). The
calculations on the CFT side are being done without string theory - using
old-fashioned Feynman diagrams in N=4 super Yang-Mills, for example.
Following 't Hooft, we can reorganize these calculations according to the
topology i.e. the genus (and focus on the planar diagrams), but they are
still field-theoretical, non-gravitational and "non-stringy" calculations.
Most quantities (the more complicated ones) are however unprotected, and
they are difficult to calculate exactly on both sides. It makes the
continuation in either of the two directions difficult, of course, and the
approximate results then can't agree. For example, the entropy density of
hot D3-branes is known to be renormalized by a factor of 3/4 as you change
the 't Hooft coupling from to infinity.
> This would have to be a method that works in the high coupling regime!
The SUSY-protected quantities work out correctly in the whole range.
> At any rate the only entirely physical (gauge
> invariant) information we can compute today is the n-point functions
> on the spacetime boundary.
And according to old-fashioned physics, it is the only exact physical
information that exists. It is a successful consistency check because we
see that no wrong and gauge-variant observables can be calculated.
> That in SUGRA you can discuss processes occuring in a finite patch of
> spacetime whereas in string theory you cannot (or don't know how).
You probably mean classical solutions of SUGRA (defined in a finite patch
of spacetime) only, don't you? Classical SUGRA is a limit of superstring
theory in the same sense as it is a limit of any other quantum completion
of classical supergravity (well, it's because string/M-theory is really
the only consistent quantum extension of classical SUGRA). You can use
your favorite local solutions of classical SUGRA for "finite patches", and
you can prove that these solutions are relevant even in string theory, in
the limit \hbar=0 - at least if the red shifts are bounded and all
distances you study are much longer than l_{planck}. But these classical
solutions are not quantum-exact observables.
In a theory of quantum gravity, such as SUGRA, it is just impossible to
define local gauge-invariant operators and compute their correlators or
anything of this type that we are used to in other quantum theories.
The difference that you are trying to picture as a difference between
SUGRA and superstring theory is actually something completely different:
you are talking about the things that can be done in classical physics,
and you seem to complain that they are not meaningful in a quantum theory.
Your criticism is actually a criticism of (the very framework of) quantum
theory, not a specific criticism of string theory. The only problem with
this criticism is that quantum theory is proved, beyond any reasonably
doubts, to be a feature of reality.
If one uses a non-stringy framework, one must be very careful to avoid all
these potential "quantities" that must be non-physical. String theory does
it automatically, and it only allows us to calculate physically meaningful
observables such as the S-matrix or the boundary correlators.
> > If you know some other nice enough and generally neglected gauge-invariant
> > observable in gravity that should be calculable, I am eager to hear about
> > it! ;-)
>
> I don't know the solution but I claim there is definitely a problem.
How can you claim that there is "definitely" a problem even if you're
unable to formulate what the problem could be? ;-)
> Btw, after reading Lenny Susskind's "The World as a Hologram"
> (http://www.arxiv.org/abs/hep-th/9409089) it appears to me such an observable exists. Consider
> asymptotically AdS gravity for instance. Choose a point on the
> asymptotic boundary and a positive real number. For any classical
> solution one may construct a spacelike geodesic beginning from the
> chosen point on the boundary and orthogonal to it. A natural parameter
> exists on the geodesic (proper length starting from the boundary) -
> lets call it "depth".
The proper length of a line starting from the AdS boundary is infinite
even in the classical theory. Even if you chose a different geometry where
this proper length is finite - or subtracted the divergent piece in some
way, it would become infinite anyway once you took quantum fluctuations of
the geometry into account. In the full theory, geometry *does* fluctuate,
and your intuition about the finite distances is only valid in the
classical, long-distance approximation.
More generally, there exists absolutely no reason why the notion of
"distance", "area", and "volume" should have an exact, fundamental meaning
in a theory of quantum gravity (and string theory is bringing up to
believe that these things can't be exact at the Planck scale). It is
important that the Universe roughly behaves as the Minkowski or Euclidean
geometry at "long distances" (this usage of the word "distance" is
self-consistent), because it is a viable framework for Nature to create
life. But this does not require the geometric quantities to be
fundamental. To be honest, we are measuring the distances by sticks,
lasers, or other gadgets. A physical theory must confirm the existence of
sticks, lasers, and it must correctly predict their behavior (and masses
of wrapped branes, or whatever else can physically exist). String theory
does this job, and it does so even though it implies that our notions of
geometry are emergent approximate notions that are only valid at low
energies.
> The observables are then various scalars constructed out of fields in
> the theory at the point on the geodesic for which the depth is the
> chosen real number. One may construct more observables using
> derivatives w.r.t. depth and the location of the basepoint on the
> boundary. Did anyone try defining such observables in AdS/CFT? Or
> maybe it can be shown they are not "nice enough"?
Try it. I won't try it because these observables do not seem well
motivated and justified to me.
> Possibly I formulated myself badly. I have no problem with the AdS
> boundary n-point functions as observables. I have a problem with the
> S-matrix as an observable of superstring theory in asymptotically
> flat spacetime.
That's about an equally serious objection. ;-)
> The usual definition of the S-matrix in QFT includes
> turning off the coupling constant in past and future infinity but I don't
> understand how can it be consistently then in superstring theory:
Turning off the interactions is just a trick to define the asymptotic
scattering states as the adiabatic continuation of the corresponding
states at g=0 (even though they exist, as slightly different states, for
every value of "g", as long as the particle is stable), and it is equally
meaningful in string theory like in a perturbative quantum field theory.
Where do you exactly see any difference? In the fact that the stringy
coupling constant is the expectation value of the dilaton (exponentiated)?
Why would you believe that this could invalidate perturbative expansions?
On the contrary, it adds more structure and knowledge - not less - because
the amplitudes with an extra dilaton in the process can be used to relate
different orders of "g" contributing to a general amplitude. But otherwise
be sure that as long as the dilaton is a modulus, you can tune its value
to an arbitrarily small positive number. Did you say that you want zero?
In field theory, you don't need the exact zero to be achieved either; you
just need the right limit.
> I realize all that completely well. The thing is, these problems are
> solvable in classical gravity. It appears to me that to quantize
> gravity implies providing a way to solve this problems for quantum
> gravity as well, within the setting of your quantization.
It appears to me that you want to reject basic principles in quantum
mechanics. In classical physics, the proper length of a geodesic between
two points is a sharply defined number. But in quantum physics, this
observable - just like any other observable - becomes an operator whose
values fluctuate, whose values span a probability distribution and they
have different amplitudes to take different values in different states.
The exceptions are eigenstates, but the eigenstates of such geometric
quantities can't be expected to be close to the energy eigenstates that we
are more likely to see (states close to the ground state).
Moreover, the uncertainty principle prevents you from having a sharp value
of g_{ij} and its time-derivative, roughly speaking.
Quantum fluctuations contribute and make these classical quantities - such
as the proper length - cutoff-dependent, which will prevent you from
defining an exact quantity as your cutoff approaches the Planck scale. You
might hope that there will be some sharply defined value of the "proper
length" where the cutoff is "infinite" - which might be effectively
equivalent to the Planck scale cutoff - but this logic is misguided
because the classical geometry is simply an incorrect description for
processes that occur at the Planck scale (or shorter).
> Does it include the thingies I mentioned above? How do you know they
> become divergent?
The things you mentioned above were divergent even at the classical level.
More generally, we can calculate the cutoff-dependence of these quantities
in effective field theory, and the fluctuations (as well as the mean
value) increases with your cutoff energy. Intuitively this result is
clear; if you imagine the spacetime geometry to be more foamy, the total
length will count all the local features of the foam, and it will grow.
Well, in Minkowski geometry, you can on the contrary always find a
*shorter* geodesic, but at any rate, the proper length computed from
"quantized general relativity" won't be finite.
In string theory, we often compute meaningful "quantum volumes", but their
definition is different. They are counted from masses of the branes
wrapped on the corresponding cycles, and in a finite theory (with a lot of
SUSY calculations), these masses (or energies) are finite, of course. But
once again, they are not being calculated in the naive classical way as
the integral of \sqrt{g_{mn}dx^m dx^n} with an unlimited UV cutoff
because this prescription is physically misled.
__{_______________________________________________ _____________________________}
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)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
<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>\nLubos Motl <motl@feynman.harvard.edu> wrote in message news:<20040607043417.S2574@mail.kolej.mff.cuni.cz> ...\n> Yes, that\'s the whole point of the AdS/CFT checks - that you can compute\n> many things on both sides, and they agree for all quantities that are\n> exactly calculable on both sides (and people have found many of them).\n\nThat is OK, however, it is still unclear to me in precisely in what sense\ndo you get SUGRA as the classical limit.\n\n> You can use your\n> favorite local solutions of classical SUGRA for "finite patches", and you\n> can prove that these solutions are relevant even in string theory, in the\n> limit hbar=0 - at least if the red shifts are bounded and all distances\n> you study are much longer than l_{planck}. But these classical solutions\n> are not quantum exact observables.\n\nWhat precisely is the meaning of the word "relevant" as you use it here?\n\n> The difference that you are trying to picture as a difference between\n> SUGRA and superstring theory is actually something completely different:\n> you are talking about the things that can be done in classical physics,\n> and you seem to complain that they are not meaningful in a quantum theory.\n> Your criticism is actually a criticism of (the very framework of) quantum\n> theory, not a specific criticism of string theory. The only problem with\n> this criticism is that quantum theory is proved to be a feature of\n> reality.\n\nYou are missing a very simple point though. My own existence, your\nexistence and all of our experiences are things occuring in finite\nspace and through finite times. In previous models of reality such\nas general relativity and QFT it is possible, at least in principle,\nto derive these experiences from the theory. However, it appears to\nme no way is known to do this (even in principle) in string theory.\nIf that is impossible string theory is meaningless as a model of\nreality. Therefore, the things I\'m not about are not things that\n"can be done in classical physics", they are things that have to be\npossible to do in any meaningful model of reality.\n\n> If one uses a non-stringy framework, one must be very careful to avoid all\n> these potential "quantities" that must be non-physical. String theory does\n> it automatically, and it only allows us to calculate physically meaningful\n> observables such as the S-matrix or the boundary correlators.\n\nYou call them "physically meaningful" but I don\'t know any experimentalist\nwho knows how to travel infinite distances and measure the boundary\ncorrelators, not speaking of living from time -infinity to time +infinity\nand controlling the coupling constant in the process.\n\n> How can you claim that there is "definitely" a problem even if you\'re\n> unable to formulate what the problem could be? ;-)\n\nI am able to formulate the _problem_, but not the _solution_.\n\n> The proper length of a line starting from the AdS boundary is infinite\n> even in the classical theory.\n\nI know, I indicated in a recent reposting of this post how to solve\nthis problem. You have to choose a certain offset for the proper\nlength in the corresponding geodesic for genuine AdS and then match\nyour parameter with the AdS one in the asymptotics.\n\n> Try it. I won\'t try it because these observables do not seem well\n> motivated and justified to me.\n\nI think I explained the motivation, though possibly\nmy suggested solution is not a good one.\n\n> Turning off the interactions is just a trick to define the asymptotic\n> scattering states as the adiabatic continuation of the corresponding\n> states at g=0 (even though they exist, as slightly different states, for\n> every value of "g", as long as the particle is stable), and it is equally\n> meaningful in string theory like in a perturbative quantum field theory.\n> Where do you exactly see any difference? In the fact that the stringy\n> coupling constant is the expectation value of the dilaton (exponentiated)?\n> Why would you believe that this could invalidate perturbative expansions?\n\nIn string theory the perturbative expansion is meaningful when\nthe spacetime you\'re expanding around is a solution of the\nclassical equations of motion (possibly with alpha\' corrections)\nand this makes perfect sense. However, I don\'t see how to\nconstruct a classical solution in which the dilaton goes to\n-infinity both in the past and the future but is finite at\nfinite times.\n\n> More generally, we can calculate the cutoff-dependence of these quantities\n> in effective field theory, and the fluctuations (as well as the mean\n> value) increases with your cutoff energy. Intuitively this result is\n> clear; if you imagine the spacetime geometry to be more foamy, the total\n> length will count all the local features of the foam, and it will grow.\n> Well, in Minkowski geometry, you can on the contrary always find a\n> *shorter* geodesic, but at any rate, the proper length computed from\n> "quantized general relativity" won\'t be finite.\n\nYet it is possible the e.v. of the scalar evaluated at the\nfluctuating point will be finite. Also, an alternative\nsuggestion: consider an n-dimensional spacelike subspace\nof the boundary. Define for any classical asymptotically\nAdS spacetime the minimal volume n+1-dimensional spacelike\nsubspace ending on the given one. You might also attempt\nto fix its toplogy. Now take the integral of some\ncovariantly defined n+1-form over this subspace.\n\nBest regards,\nSquark.\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 in message news:<20040607043417.S2574@mail.kolej.mff.cuni.cz>...
> Yes, that's the whole point of the AdS/CFT checks - that you can compute
> many things on both sides, and they agree for all quantities that are
> exactly calculable on both sides (and people have found many of them).
That is OK, however, it is still unclear to me in precisely in what sense
do you get SUGRA as the classical limit.
> You can use your
> favorite local solutions of classical SUGRA for "finite patches", and you
> can prove that these solutions are relevant even in string theory, in the
> limit \hbar=0 - at least if the red shifts are bounded and all distances
> you study are much longer than l_{planck}. But these classical solutions
> are not quantum exact observables.
What precisely is the meaning of the word "relevant" as you use it here?
> The difference that you are trying to picture as a difference between
> SUGRA and superstring theory is actually something completely different:
> you are talking about the things that can be done in classical physics,
> and you seem to complain that they are not meaningful in a quantum theory.
> Your criticism is actually a criticism of (the very framework of) quantum
> theory, not a specific criticism of string theory. The only problem with
> this criticism is that quantum theory is proved to be a feature of
> reality.
You are missing a very simple point though. My own existence, your
existence and all of our experiences are things occuring in finite
space and through finite times. In previous models of reality such
as general relativity and QFT it is possible, at least in principle,
to derive these experiences from the theory. However, it appears to
me no way is known to do this (even in principle) in string theory.
If that is impossible string theory is meaningless as a model of
reality. Therefore, the things I'm not about are not things that
"can be done in classical physics", they are things that have to be
possible to do in any meaningful model of reality.
> If one uses a non-stringy framework, one must be very careful to avoid all
> these potential "quantities" that must be non-physical. String theory does
> it automatically, and it only allows us to calculate physically meaningful
> observables such as the S-matrix or the boundary correlators.
You call them "physically meaningful" but I don't know any experimentalist
who knows how to travel infinite distances and measure the boundary
correlators, not speaking of living from time -infinity to time +infinity
and controlling the coupling constant in the process.
> How can you claim that there is "definitely" a problem even if you're
> unable to formulate what the problem could be? ;-)
I am able to formulate the _problem_, but not the _solution_.
> The proper length of a line starting from the AdS boundary is infinite
> even in the classical theory.
I know, I indicated in a recent reposting of this post how to solve
this problem. You have to choose a certain offset for the proper
length in the corresponding geodesic for genuine AdS and then match
your parameter with the AdS one in the asymptotics.
> Try it. I won't try it because these observables do not seem well
> motivated and justified to me.
I think I explained the motivation, though possibly
my suggested solution is not a good one.
> Turning off the interactions is just a trick to define the asymptotic
> scattering states as the adiabatic continuation of the corresponding
> states at g=0 (even though they exist, as slightly different states, for
> every value of "g", as long as the particle is stable), and it is equally
> meaningful in string theory like in a perturbative quantum field theory.
> Where do you exactly see any difference? In the fact that the stringy
> coupling constant is the expectation value of the dilaton (exponentiated)?
> Why would you believe that this could invalidate perturbative expansions?
In string theory the perturbative expansion is meaningful when
the spacetime you're expanding around is a solution of the
classical equations of motion (possibly with \alpha' corrections)
and this makes perfect sense. However, I don't see how to
construct a classical solution in which the dilaton goes to
-infinity both in the past and the future but is finite at
finite times.
> More generally, we can calculate the cutoff-dependence of these quantities
> in effective field theory, and the fluctuations (as well as the mean
> value) increases with your cutoff energy. Intuitively this result is
> clear; if you imagine the spacetime geometry to be more foamy, the total
> length will count all the local features of the foam, and it will grow.
> Well, in Minkowski geometry, you can on the contrary always find a
> *shorter* geodesic, but at any rate, the proper length computed from
> "quantized general relativity" won't be finite.
Yet it is possible the e.v. of the scalar evaluated at the
fluctuating point will be finite. Also, an alternative
suggestion: consider an n-dimensional spacelike subspace
of the boundary. Define for any classical asymptotically
AdS spacetime the minimal volume n+1-dimensional spacelike
subspace ending on the given one. You might also attempt
to fix its toplogy. Now take the integral of some
covariantly defined n+1-form over this subspace.
Best regards,
Squark.
Ralph Hartley
Jun12-04, 07:15 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>Squark wrote:\n> Lubos Motl <motl@feynman.harvard.edu> wrote:\n\n>>If one uses a non-stringy framework, one must be very careful to avoid all\n>>these potential "quantities" that must be non-physical. String theory does\n>>it automatically, and it only allows us to calculate physically meaningful\n>>observables such as the S-matrix or the boundary correlators.\n>\n> You call them "physically meaningful" but I don\'t know any experimentalist\n> who knows how to travel infinite distances and measure the boundary\n> correlators, not speaking of living from time -infinity to time +infinity\n> and controlling the coupling constant in the process.\n\nWorse than that, in *our* universe, with lambda>0, those observables may\nnot even exist. The universe does *not* appear to resemble ADS or Minkowski\nSpace, but DeSitter Space (asymptotically as the density of matter goes to\n0 bla bla bla ...).\n\nThe S-matrix is defined in terms of a observer at infinity, after infinite\ntime, but such an observer crosses a cosmological horizon and sees nothing.\n\nFor any experiment you can do at Fermi lab, that horizon is far away, so\nthe S-matrix is a very *very* good approximation. When you start talking\nabout black holes forming and evaporating, that\'s another matter.\n\nIf string theory only has observables in ADS and Minkowski Space, then it\nhas no observables at all.\n\nThis is not *necessarily* a fatal problem. Sometimes approximations are\nenough. Also, so far as I know there is nothing that says string theory\ncan\'t *eventually* give predictions with a positive cosmological constant,\nit\'s just that no one knows how to do it.\n\nIf string theory *really* is incompatible with a positive cosmological\nconstant, then it conflicts with experiment and is dead. I assume no one\nthinks this is so, because I haven\'t been hearing eulogies.\n\nRalph Hartley\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>Squark wrote:
> Lubos Motl <motl@feynman.harvard.edu> wrote:
>>If one uses a non-stringy framework, one must be very careful to avoid all
>>these potential "quantities" that must be non-physical. String theory does
>>it automatically, and it only allows us to calculate physically meaningful
>>observables such as the S-matrix or the boundary correlators.
>
> You call them "physically meaningful" but I don't know any experimentalist
> who knows how to travel infinite distances and measure the boundary
> correlators, not speaking of living from time -infinity to time +infinity
> and controlling the coupling constant in the process.
Worse than that, in *our* universe, with \lambda>0, those observables may
not even exist. The universe does *not* appear to resemble ADS or Minkowski
Space, but DeSitter Space (asymptotically as the density of matter goes to
bla bla bla ...).
The S-matrix is defined in terms of a observer at infinity, after infinite
time, but such an observer crosses a cosmological horizon and sees nothing.
For any experiment you can do at Fermi lab, that horizon is far away, so
the S-matrix is a very *very* good approximation. When you start talking
about black holes forming and evaporating, that's another matter.
If string theory only has observables in ADS and Minkowski Space, then it
has no observables at all.
This is not *necessarily* a fatal problem. Sometimes approximations are
enough. Also, so far as I know there is nothing that says string theory
can't *eventually* give predictions with a positive cosmological constant,
it's just that no one knows how to do it.
If string theory *really* is incompatible with a positive cosmological
constant, then it conflicts with experiment and is dead. I assume no one
thinks this is so, because I haven't been hearing eulogies.
Ralph Hartley
Alfred Einstead
Jun13-04, 09:39 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>\nNakanishi and Ojima\nCovariant Operator Formulation of Gauge Theory and Quantum Gravity\n\nLubos Motl <motl@feynman.harvard.edu> wrote:\n> Well, the quantization of gravity in the 11D (and similar) flat space and\n> in anti de Sitter space is "only" due to string theory because string\n> theory is the only known consistent way to quantize gravity.\n\nThere is no known consistent way to quantize gravity, and probably\nnone at all. There is no such thing as a causal structure at the\noperator level, whereas an operator algebra in any known quantization\nrecipe requires an already defined causal structure be there at the\noutset as a prerequisite.\n\nThis is a very fundamental incompatibility that goes beneath everything.\nIn particular, the issue of the viability of any approach to perturbation\ntheory has no bearing on it. Even for a "successful" or "convergent"\nperturbation scheme or "operator definition" scheme, regardless of\nwhat that may mean, the inconsistency is still present.\n\nThis is an issue that has been discussed in more depth by\nNakanishi and Ojima, for instance, in their "Covariant Operator\nFormulation of Gauge Theory and Quantum Gravity".\n\nA more concrete example that illustrates the mutual contradiction:\nfor the metric in states W1, W2 one may have\ngi = Wi[g], i = 1, 2\nwith u, v points in the underlying manifold such that\nu <-> v spacelike with respect to g1\nu <-> v timelike with respect to g2\nand a local observable A(u) with\n[A(u), A(v)] = 0 with respect to g1, by Microcausality\nbut\n[A(u), A(v)] != 0 with respect to g2.\n\nThe very definition of A depends on which state you\'re in; whereas\nstate spaces are defined only in reference to an already-defined\nalgebra of observables.\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>Nakanishi and Ojima
Covariant Operator Formulation of Gauge Theory and Quantum Gravity
Lubos Motl <motl@feynman.harvard.edu> wrote:
> Well, the quantization of gravity in the 11D (and similar) flat space and
> in anti de Sitter space is "only" due to string theory because string
> theory is the only known consistent way to quantize gravity.
There is no known consistent way to quantize gravity, and probably
none at all. There is no such thing as a causal structure at the
operator level, whereas an operator algebra in any known quantization
recipe requires an already defined causal structure be there at the
outset as a prerequisite.
This is a very fundamental incompatibility that goes beneath everything.
In particular, the issue of the viability of any approach to perturbation
theory has no bearing on it. Even for a "successful" or "convergent"
perturbation scheme or "operator definition" scheme, regardless of
what that may mean, the inconsistency is still present.
This is an issue that has been discussed in more depth by
Nakanishi and Ojima, for instance, in their "Covariant Operator
Formulation of Gauge Theory and Quantum Gravity".
A more concrete example that illustrates the mutual contradiction:
for the metric in states W1, W2 one may have
gi = Wi[g], i = 1, 2
with u, v points in the underlying manifold such that
u <-> v spacelike with respect to g1
u <-> v timelike with respect to g2
and a local observable A(u) with
[A(u), A(v)] = with respect to g1, by Microcausality
but
[A(u), A(v)] != with respect to g2.
The very definition of A depends on which state you're in; whereas
state spaces are defined only in reference to an already-defined
algebra of observables.
<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 12/06/2004 1:15 pm, Ralph Hartley at hartley@aic.nrl.navy.mil wrote:\n\n> Squark wrote:\n>> Lubos Motl <motl@feynman.harvard.edu> wrote:\n>\n>>> If one uses a non-stringy framework, one must be very careful to avoid all\n>>> these potential "quantities" that must be non-physical. String theory does\n>>> it automatically, and it only allows us to calculate physically meaningful\n>>> observables such as the S-matrix or the boundary correlators.\n>>\n>> You call them "physically meaningful" but I don\'t know any experimentalist\n>> who knows how to travel infinite distances and measure the boundary\n>> correlators, not speaking of living from time -infinity to time +infinity\n>> and controlling the coupling constant in the process.\n>\n> Worse than that, in *our* universe, with lambda>0, those observables may\n> not even exist. The universe does *not* appear to resemble ADS or Minkowski\n> Space, but DeSitter Space (asymptotically as the density of matter goes to\n> 0 bla bla bla ...).\n>\n> The S-matrix is defined in terms of a observer at infinity, after infinite\n> time, but such an observer crosses a cosmological horizon and sees nothing.\n>\n> For any experiment you can do at Fermi lab, that horizon is far away, so\n> the S-matrix is a very *very* good approximation.\n\nThis is something I don\'t understand. My incomprehension is a bit vague, but\nI guess can be summed up as: "How can part of the bulk be _approximately_ a\nboundary?"\n\nWhy don\'t all the diffeomorphism problems/problem of time/etc apply to the\nscattering experiment together with its surrounding spacetime? Or, going the\nother way round, if this approximation is so good, why can\'t the bulk be\nbuilt up out of boundaries like this?\n\nTim\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 12/06/2004 1:15 pm, Ralph Hartley at hartley@aic.nrl.navy.mil wrote:
> Squark wrote:
>> Lubos Motl <motl@feynman.harvard.edu> wrote:
>
>>> If one uses a non-stringy framework, one must be very careful to avoid all
>>> these potential "quantities" that must be non-physical. String theory does
>>> it automatically, and it only allows us to calculate physically meaningful
>>> observables such as the S-matrix or the boundary correlators.
>>
>> You call them "physically meaningful" but I don't know any experimentalist
>> who knows how to travel infinite distances and measure the boundary
>> correlators, not speaking of living from time -infinity to time +infinity
>> and controlling the coupling constant in the process.
>
> Worse than that, in *our* universe, with \lambda>0, those observables may
> not even exist. The universe does *not* appear to resemble ADS or Minkowski
> Space, but DeSitter Space (asymptotically as the density of matter goes to
> bla bla bla ...).
>
> The S-matrix is defined in terms of a observer at infinity, after infinite
> time, but such an observer crosses a cosmological horizon and sees nothing.
>
> For any experiment you can do at Fermi lab, that horizon is far away, so
> the S-matrix is a very *very* good approximation.
This is something I don't understand. My incomprehension is a bit vague, but
I guess can be summed up as: "How can part of the bulk be _approximately_ a
boundary?"
Why don't all the diffeomorphism problems/problem of time/etc apply to the
scattering experiment together with its surrounding spacetime? Or, going the
other way round, if this approximation is so good, why can't the bulk be
built up out of boundaries like this?
Tim
vBulletin® v3.8.7, Copyright ©2000-2012, vBulletin Solutions, Inc.