<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>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:<Pine.LNX.4.31.0405261029590.20392-100000@kaluza.harvard.edu>...\n> Yes, after posting that message I had this idea, too, that the autor is\n> probably thinking of the fact that the _Hamiltomnian constraint_ vanishes.\n> That\'s why he says "at least classically", being aware of the well\n> understood case of 1+1 dimensions where the Hamiltonian constraint (L0 +\n> \\bar L_0) is "0" only up a quantum shift.\n>\n> But if that\'s what the author is thinking of in that paragraph it really\n> makes me feel uneasy, because, as you indicated\n>\n> 1) the fact that the Hamiltonian constraint vanishes says little about the\n> energy content of the universe (much like (L_0-1)|psi>=0 alone tells me\n> nothing about the mass of a string state psi)\n>\n> 2) the statement does not have anything to do with the figure that\n> accompanies it and the conclusions drawn from it (please anyone correct\n> me if I am wrong about this!)\n>\n> > (matter) energy-momentum tensor, which is exactly the\n> > "non-vanishing energy content" you are talking about. It is the\n> > Hamiltonian, though, which is the relevant quantity for\n> > thermodynamical considerations.\n>\n> Yes, that\'s what I would think. And this Hamiltonian does not vanish.\n\nI tend to disagree with you. The only properly defined Hamiltonian\nhere is the Hamiltonian constraint (since we are in bounded space)\nand it _does_ vanish. I.e., instead of the usual Gibbs ensemble\nexp(-beta H) we get just the identity density matrix. Now, since\nentropy is monotonously decreasing with the cosmological constant\n(see equation 2.7 on page 7; note R is monotonously decreasing\nwith the cosmological constant) fluctuations from the metastable\nvacuum at phi_0 (see figure 1) will indeed be suppressed by pure\nentropy considerations.\n\n> It\'s\n>\n> Kachru & Kallosh & Linde & Trivedi:\n> de Sitter vacua in string theory\n> hep-th/0301240\n>\n> which started most of the landscape discussion, as far as I am aware. For\n> a nice summary of some of the effects discussed in there see J. Distler\'s\n>\n> "Digging up the landscape"\n> http://golem.ph.utexas.edu/~distler/blog/archives/000359.html\n>\n> and\n>\n> "The discretium"\n> http://golem.ph.utexas.edu/~distler/blog/archives/000348.html.\n>\n> Also see the sci.physics.strings archive for the thread\n>\n> "Conceptual question"\n>\n> where Shamit Kachru himself, together with J. Polchinski and W. Lerche, L.\n> Motl and A. Rajaraman discuss this issue.\n\nThx!\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:<Pine.LNX.4.31.0405261029590.20...arvard.edu>...
> Yes, after posting that message I had this idea, too, that the autor is
> probably thinking of the fact that the _Hamiltomnian constraint_ vanishes.
> That's why he says "at least classically", being aware of the well
> understood case of 1+1 dimensions where the Hamiltonian constraint (L0 +
> [itex]\bar L_0)[/itex] is "" only up a quantum shift.
>
> But if that's what the author is thinking of in that paragraph it really
> makes me feel uneasy, because, as you indicated
>
> 1) the fact that the Hamiltonian constraint vanishes says little about the
> energy content of the universe (much like [itex](L_0-1)|\psi>=0[/itex] alone tells me
> nothing about the mass of a string state [itex]\psi)[/itex]
>
> 2) the statement does not have anything to do with the figure that
> accompanies it and the conclusions drawn from it (please anyone correct
> me if I am wrong about this!)
>
> > (matter) energy-momentum tensor, which is exactly the
> > "non-vanishing energy content" you are talking about. It is the
> > Hamiltonian, though, which is the relevant quantity for
> > thermodynamical considerations.
>
> Yes, that's what I would think. And this Hamiltonian does not vanish.
I tend to disagree with you. The only properly defined Hamiltonian
here is the Hamiltonian constraint (since we are in bounded space)
and [itex]it _does_[/itex] vanish. I.e., instead of the usual Gibbs ensemble
[itex]\exp(-\beta H) we[/itex] get just the identity density matrix. Now, since
entropy is monotonously decreasing with the cosmological constant
(see equation 2.7 on page 7; note R is monotonously decreasing
with the cosmological constant) fluctuations from the metastable
vacuum [itex]at \phi_0[/itex] (see figure 1) will indeed be suppressed by pure
entropy considerations.
> It's
>
> Kachru & Kallosh & Linde & Trivedi:
> de Sitter vacua in string theory
> http://www.arxiv.org/abs/hep-th/0301240
>
> which started most of the landscape discussion, as far as I am aware. For
> a nice summary of some of the effects discussed in there see J. Distler's
>
> "Digging up the landscape"
> http://golem.ph.utexas.edu/~distler/...es/000359.html
>
> and
>
> "The discretium"
> http://golem.ph.utexas.edu/~distler/...s/000348.html.
>
> Also see the sci.physics.strings archive for the thread
>
> "Conceptual question"
>
> where Shamit Kachru himself, together with J. Polchinski and W. Lerche, L.
> Motl and A. Rajaraman discuss this issue.
Thx!
Best regards,
Squark.