minimum size of a string

alistair

<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>How would string theory be changed if the minimum size of a string wasn\'t\n10^ -34 metres?\nThe current radius of the universe is about 4 x 10^26 metres.\nDoes string theory predict that a string can be this size at the most?\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>How would string theory be changed if the minimum size of a string wasn't
[itex]10^ -34[/itex] metres?
The current radius of the universe is about 4 [itex]x 10^26[/itex] metres.
Does string theory predict that a string can be this size at the most?

Rene Meyer

<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 Mon, 28 Jun 2004 10:40:07 -0400, alistair wrote:\n> How would string theory be changed if the minimum size of a string wasn\'t\n> 10^ -34 metres?\n> The current radius of the universe is about 4 x 10^26 metres.\n> Does string theory predict that a string can be this size at the most?\n\nWhat happens with the string depends on the target space time you\nembedd it into. If the spacetime is something like a closed universe,\nthen I think the string could wrap around it. But actually, the energy\nof a string increases with it\'s length, and you\'d get very very\nmassive objects. So one normally thinks of strings to be very short,\nand even then the energies of the massive excitations are huge.\n\nRene.\n\n--\nRené Meyer\nStudent of Physics & Mathematics\nZhejiang University, Hangzhou, China\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 Mon, 28 Jun 2004 10:40:07 [itex]-0400,[/itex] alistair wrote:
> How would string theory be changed if the minimum size of a string wasn't
> [itex]10^ -34[/itex] metres?
> The current radius of the universe is about 4 [itex]x 10^26[/itex] metres.
> Does string theory predict that a string can be this size at the most?

What happens with the string depends on the target space time you
embedd it into. If the spacetime is something like a closed universe,
then I think the string could wrap around it. But actually, the energy
of a string increases with it's length, and you'd get very very
massive objects. So one normally thinks of strings to be very short,
and even then the energies of the massive excitations are huge.

Rene.

--
René Meyer
Student of Physics & Mathematics
Zhejiang University, Hangzhou, China

mandro

<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>First of all, what do you mean by "the size\nof a string" 1) Do you mean minimum radius\nsized ball which contains the string? 2)Do\nyou mean the length of the string? what do\nyou mean?\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>First of all, what do you mean by "the size
of a string" 1) Do you mean minimum radius
sized ball which contains the string? 2)Do
you mean the length of the string? what do
you mean?

*kurious*

MANDRO:

First of all, what do you mean by "the size
of a string" 1) Do you mean minimum radius
sized ball which contains the string? 2)Do
you mean the length of the string? what do
you mean?

ALISTAIR writes:

I mean the length of an open string.

Ulmo

<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>kurious <alistair@goforit64.fsnet.co.uk> wrote in message news:<kurious.18mu1g-100000@physicsforums.com>...\n> MANDRO:\n>\n> First of all, what do you mean by "the size\n> of a string" 1) Do you mean minimum radius\n> sized ball which contains the string? 2)Do\n> you mean the length of the string? what do\n> you mean?\n>\n>\n> ALISTAIR writes:\n>\n> I mean the length of an open string.\n>\n\nIt would have to be the planck length.\n\nDavid\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>kurious <alistair@goforit64.fsnet.co.uk> wrote in message news:<kurious.18mu1g-100000@physicsforums.com>...
> MANDRO:
>
> First of all, what do you mean by "the size
> of a string" 1) Do you mean minimum radius
> sized ball which contains the string? 2)Do
> you mean the length of the string? what do
> you mean?
>
>
> ALISTAIR writes:
>
> I mean the length of an open string.
>

It would have to be the planck length.

David

mandro

<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>Well, I just made my statement so you\'d\nthink about this. You know, as Lubos informed\nme, the length of the average string is\ninfinity. So what\'s your proposed resolution\nnow?\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>Well, I just made my statement so you'd
think about this. You know, as Lubos informed
me, the length of the average string is
infinity. So what's your proposed resolution
now?

Simon Gladman

<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"Ulmo" <ulmo@cheerful.com> wrote in message\nnews:53ca460a.0407011218.7b191562-100000@posting.google.com...\n> kurious <alistair@goforit64.fsnet.co.uk> wrote in message\nnews:<kurious.18mu1g-100000@physicsforums.com>...\n> > MANDRO:\n\n> >\n> > I mean the length of an open string.\n> >\n>\n> It would have to be the planck length.\n\nIf the mininum length of a string is the Planck length, does that mean the\nwavelength of the string\'s vibrations are sub-Planck length? Can anything of\na sub-Planck length have any meaning?\n\nCheers,\n\nSimon.\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>"Ulmo" <ulmo@cheerful.com> wrote in message
news:53ca460a.0407011218.7b191562-10....google.com...
> kurious <alistair@goforit64.fsnet.co.uk> wrote in message
news:<kurious.18mu1g-100000@physicsforums.com>...
> > MANDRO:

> >
> > I mean the length of an open string.
> >
>
> It would have to be the planck length.

If the mininum length of a string is the Planck length, does that mean the
wavelength of the string's vibrations are sub-Planck length? Can anything of
a sub-Planck length have any meaning?

Cheers,

Simon.

alejandro.rivero

<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>mandro <ultraman2002@hotmail.com> wrote in message news:<dec722c5.0406281525.6aa72b92-100000@posting.google.com>...\n> First of all, what do you mean by "the size\n> of a string" 1) Do you mean minimum radius\n> sized ball which contains the string? 2)Do\n> you mean the length of the string? what do\n> you mean?\n\nBoth questions seem interesting to me, so please go ahead with both.\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>mandro <ultraman2002@hotmail.com> wrote in message news:<dec722c5.0406281525.6aa72b92-1...google.com>...
> First of all, what do you mean by "the size
> of a string" 1) Do you mean minimum radius
> sized ball which contains the string? 2)Do
> you mean the length of the string? what do
> you mean?

Both questions seem interesting to me, so please go ahead with both.

mandro

<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>Well, I already said, that I\'d been\ninformed that the average length of\na string is infinity. So, one may be\nable to try the other way of looking\nat it i.e., to catch it in a ball of\na certain constrainig radius. I was/am\nconfused about this for a long time and\nseveral people told me stuff I didn\'t\nunderstad. The main reason for this is that\nI was looking at it as wavefunctions on\nthe space of smooth loops (I think that\'s)\nwhat most amateurs have in mind when they\nthik of a string. However, over time, I have\ncome to believe that what these guys are\nactually doing is that they as looking at\nit as a QFT in 2d space time (which I\'ve\nknown for years)but what I didnt know well\nwas what the configuration space was for\nthat theory and "how" to apply it to decide\nquestions like this for string theory. I now\nbelieve that what these guys do, is to take\nthe space of field configs on a one-dimenstional\nspace say [0, pi] (2-d space time) to be a space\nthat, at least, contains C[0, pi]. Now, there\'s\nsome spiel about most functions in C[0,pi]\nhaving infinite length, where the length is\ndefined via some suitable limit of smooth functions.\nSo, evidently the length of most objects in\nthe string configuration space is infinite. Thus\nit\'s foolish to say that a string state has\nfinite length (unless you allow delta functions\nin your space of wavefunctions).\n\nNow, the argument for the conataining in a ball\npart I don\'t know, but I\'m sure how the experts\nview this is to ask the question "Can I have states\nwhere the value of the fields in configuration space\nare all contained in a certain ball" e.g., analize\nthe case of a scalar field and ask this question.\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>Well, I already said, that I'd been
informed that the average length of
a string is infinity. So, one may be
able to try the other way of looking
at it i.e., to catch it in a ball of
a certain constrainig radius. [itex]I was/am[/itex]
confused about this for a long time and
several people told me stuff I didn't
understad. The main reason for this is that
I was looking at it as wavefunctions on
the space of smooth loops (I think that's)
what most amateurs have in mind when they
thik of a string. However, over time, I have
come to believe that what these guys are
actually doing is that they as looking at
it as a QFT in 2d space time (which I've
known for years)but what I didnt know well
was what the configuration space was for
that theory and "how" to apply it to decide
questions like this for string theory. I now
believe that what these guys do, is to take
the space of field configs on a one-dimenstional
space say [0, [itex]\pi] (2-d[/itex] space time) to be a space
that, at least, contains C[0, [itex]\pi][/itex]. Now, there's
some spiel about most functions in [itex]C[0,\pi][/itex]
having infinite length, where the length is
defined via some suitable limit of smooth functions.
So, evidently the length of most objects in
the string configuration space is infinite. Thus
it's foolish to say that a string state has
finite length (unless you allow [itex]\delta[/itex] functions
in your space of wavefunctions).

Now, the argument for the conataining in a ball
part I don't know, but I'm sure how the experts
view this is to ask the question "Can I have states
where the value of the fields in configuration space
are all contained in a certain ball" e.g., analize
the case of a scalar field and ask this question.

Urs Schreiber

<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>"mandro" <ultraman2002@hotmail.com> schrieb im Newsbeitrag\nnews:dec722c5.0407131057.2602b41b-100000@posting.google.com...\n\n> Well, I already said, that I\'d been\n> informed that the average length of\n> a string is infinity.\n\nYes, but by regularizing (normal ordering) the observable which measures the\nsize of the string, one obtains a finite value which is physically very\ninteresting, since it can be related to black hole entropy considerations.\n\nI recall that you, mandro, have asked these questions before, and I think I\nhad answered most of them, for instance in the thread\n\nhttp://groups.google.de/groups?selm=dec722c5.0303061133.1bf83085%40posting.google.com\n\nBut maybe I wasn\'t pointing you to enough literature. Anybody interested in\nthese questions should have a look at the very nice paper\n\nThibault Damour, Gabriele Veneziano:\nSelf-gravitating fundamental strings and black-holes\nhep-th/9907030\n\nand references given there, where the observable measuring the rms size of a\nstring is given in equations (2.9)-(2.11).\n\nThe idea is quite simple: The mean squared diameter of the string is the\naverage of (X-X_0)^2, taken over the worldsheet, where X_0 is the center of\nmass coordinate. Now expand X in terms of worldsheet Fourier modes as usual\nand then integrate over the worldsheet coordinates in order to average. The\nresult is (2.11), which says that the rms size is proportional to\n\n\\sum_{n=1}^\\infty \\frac{1}{n^2} (\\alpha_{-n} \\cdot \\alpha_n + \\alpha_n\n\\cdot \\alpha_{-n}).\n\nClearly, when you take the expectation value of this guy in any string state\nyou\'ll get an infinite contribution from pulling the annihilators \\alpha_n\nthrough the creators \\alpha_{-n}. This is a common quantum effect and is\nremoved by normal ordering. It has been argued that this infinite\ncontribution to the string\'s length has a proper physical meaning - but the\npoint is that the remaining finite part has, too.\n\nIn particular, the finite part is related to string/black hole\ncorrespondence, which I have tried to review here:\n\nhttp://golem.ph.utexas.edu/string/archives/000379.html .\n\nIn Paris I had a chance to look at Barton Zwiebach\'s new textbook on string\ntheory (my own copy has not arribed yet) and I saw that there, too, a very\nnice summary of the string/black hole correspondence along the lines\nsummarized at the above link is given. So maybe mandro and others will\nbenefit from having a look at that book.\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>"mandro" <ultraman2002@hotmail.com> schrieb im Newsbeitrag
news:dec722c5.0407131057.2602b41b-10....google.com...

> Well, I already said, that I'd been
> informed that the average length of
> a string is infinity.

Yes, but by regularizing (normal ordering) the observable which measures the
size of the string, one obtains a finite value which is physically very
interesting, since it can be related to black hole entropy considerations.

I recall that you, mandro, have asked these questions before, and I think I
had answered most of them, for instance in the thread

http://groups.google.de/groups?selm=...ing.google.com

But maybe I wasn't pointing you to enough literature. Anybody interested in
these questions should have a look at the very nice paper

Thibault Damour, Gabriele Veneziano:
Self-gravitating fundamental strings and black-holes
http://www.arxiv.org/abs/hep-th/9907030

and references given there, where the observable measuring the rms size of a
string is given in equations (2.[itex]9)-(2[/itex].11).

The idea is quite simple: The mean squared diameter of the string is the
average of [itex](X-X_0)^2,[/itex] taken over the worldsheet, where [itex]X_0[/itex] is the center of
mass coordinate. Now expand X in terms of worldsheet Fourier modes as usual
and then integrate over the worldsheet coordinates in order to average. The
result is (2.11), which says that the rms size is proportional to

[itex]\sum_{n=1}^\infty \frac{1}{n^2} (\alpha_{-n} \cdot \alpha_n + \alpha_n\cdot \alpha_{-n})[/itex].

Clearly, when you take the expectation value of this guy in any string state
you'll get an infinite contribution from pulling the annihilators [itex]\alpha_n[/itex]
through the creators [itex]\alpha_{-n}[/itex]. This is a common quantum effect and is
removed by normal ordering[itex]. It[/itex] has been argued that this infinite
contribution to the string's length has a proper physical meaning - but the
point is that the remaining finite part has, too.

In particular, the finite part is related to string/black hole
correspondence, which I have tried to review here:

http://golem.ph.utexas.edu/string/archives/000379.html .

In Paris I had a chance to look at Barton Zwiebach's new textbook on string
theory (my own copy has not arribed yet) and I saw that there, too, a very
nice summary of the string/black hole correspondence along the lines
summarized at the above link is given. So maybe mandro and others will
benefit from having a look at that book.

mandro

<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:<2ln50rFeihpsU1-100000@uni-berlin.de>...\n\n> > Mandro wrote: Well, I already said, that I\'d been\n> > informed that the average length of\n> > a string is infinity.\n>\n> Yes, but by regularizing (normal ordering)\n> the observable which measures the\n> size of the string, one obtains a finite\n> value which is physically very\n> interesting, since it can be related to\n> black hole entropy considerations.\n>\n> I recall that you, mandro, have asked these questions\n> before, and I think I had answered most of them,\n> for instance in the thread\n\nI wouldn\'t go as far as saying you answered them.\nMaybe more like tried to answer them. Firstly I\ndon\'t think you were totally articulate in answering\nthem (probably because people don\'t usually talk\nabout this stuff)--although I must admit you know\nyour stuff and are a fairly good expositor. I guess\nit\'s just that things like this don\'t have just one\nanswer, i.e., it\'s more like a family of answers\nthat depends on 1) What aspects you want to concentrate\non, 2) How you decide to define the "string length"\nobservable , and the string length measuring procedure\netc. Naturally, all these aspects are usually not\nobtained in just one reply, unless the person replying\nis a supersmart alien, who sees all the possible aspects\nof this and gives them in his reply. Thus I don\'t think\nyou can just give one aspect and say "case closed".\n\n> The idea is quite simple: The mean squared diameter\n> of the string is the\n> average of (X-X_0)^2, taken over the worldsheet,\n\n[Moderator\'s note: I guess that Urs agrees that in any low-energy state of\na vibrating string, the squared diameter has a logarithmically divergent\n(infinite) expectation value. As soon as we impose a cutoff, the quantity\nbecomes finite and comparable to l_{string} (squared), and imposing\na finite cutoff is something we can afford for any particular physical\nquestion. The pieces of the string that are "infinitely far" are\nassociated with infinite frequencies that are averaged to zero rapidly,\nand their effect on physics is very small. Nevertheless, it is not\nnecessarily true that the squared diameter or the length of the string\nare necessarily the most interesting physical observables. Interesting\nobservables are those that can be measured in experiments. The length or\nthe diameter of a string cannot be measured so easily - you would need\na point-like probe that is able to resolve substringy distances and\nquickly fly along the string - but string theory does not allow for the\nexistence of very small very fast probes. LM]\n\nWhat do you mean by mean square diameter?\n\n[Moderator\'s note: I thought that Urs immediately defined it for you. Is\nnot it more constructive to learn how to read first? LM]\n\nBy the way, the objects that you describe\nhere, are they operators, or simply expectation\nvalues?\n\n[Moderator\'s note: I am afraid that Urs will have a hard time to answer\nsuch a question. The expectation values in quantum mechanics are always\nexpectation values of some operators, so whenever we talk about "simply"\nexpectation values in quantum mechanics, we also talk about operators.\nOne of your unsolvable problems, mandro, one that I have wasted 200\nkilobytes of e-mails with, is that you are not able to understand that\nX - the position - or X(sigma) - a position of a point along the string\n- are operators, too, and they are totally analogous to P, J, or other\noperators. I discourage Urs from trying to answer these questions of\nyours because it seems as a clear waste of time. You are focusing in the\nposition representation of the states in the Hilbert space, and you do\nnot want to see that various operators are equally good operators,\nregardless whether they commute with position or not. LM]\n\nAs Always Thanks\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:<2ln50rFeihpsU1-100000@uni-berlin.de>...

> > Mandro wrote: Well, I already said, that I'd been
> > informed that the average length of
> > a string is infinity.
>
> Yes, but by regularizing (normal ordering)
> the observable which measures the
> size of the string, one obtains a finite
> value which is physically very
> interesting, since it can be related to
> black hole entropy considerations.
>
> I recall that you, mandro, have asked these questions
> before, and I think I had answered most of them,
> for instance in the thread

I wouldn't go as far as saying you answered them.
Maybe more like tried to answer them. Firstly I
don't think you were totally articulate in answering
them (probably because people don't usually talk
about this stuff)--although I must admit you know
your stuff and are a fairly good expositor. I guess
it's just that things like this don't have just one
answer, i.e., it's more like a family of answers
that depends on 1) What aspects you want to concentrate
on, 2) How you decide to define the "string length"
observable , and the string length measuring procedure
etc. Naturally, all these aspects are usually not
obtained in just one reply, unless the person replying
is a supersmart alien, who sees all the possible aspects
of this and gives them in his reply. Thus I don't think
you can just give one aspect and say "case closed".

> The idea is quite simple: The mean squared diameter
> of the string is the
> average of [itex](X-X_0)^2,[/itex] taken over the worldsheet,

[Moderator's note: I guess that Urs agrees that in any low-energy state of
a vibrating string, the squared diameter has a logarithmically divergent
(infinite) expectation value. As soon as we impose a cutoff, the quantity
becomes finite and comparable to [itex]l_{string}[/itex] (squared), and imposing
a finite cutoff is something we can afford for any particular physical
question. The pieces of the string that are "infinitely far" are
associated with infinite frequencies that are averaged to zero rapidly,
and their effect on physics is very small. Nevertheless, it is not
necessarily true that the squared diameter or the length of the string
are necessarily the most interesting physical observables. Interesting
observables are those that can be measured in experiments. The length or
the diameter of a string cannot be measured so easily - you would need
a point-like probe that is able to resolve substringy distances and
quickly fly along the string - but string theory does not allow for the
existence of very small very fast probes. LM]

What do you mean by mean square diameter?

[Moderator's note: I thought that Urs immediately defined it for you. Is
not it more constructive to learn how to read first? LM]

By the way, the objects that you describe
here, are they operators, or simply expectation
values?

[Moderator's note: I am afraid that Urs will have a hard time to answer
such a question. The expectation values in quantum mechanics are always
expectation values of some operators, so whenever we talk about "simply"
expectation values in quantum mechanics, we also talk about operators.
One of your unsolvable problems, mandro, one that I have wasted 200
kilobytes of e-mails with, is that you are not able to understand that
X - the position - or [itex]X(\sigma) - a[/itex] position of a point along the string
- are operators, too, and they are totally analogous to P, J, or other
operators. I discourage Urs from trying to answer these questions of
yours because it seems as a clear waste of time. You are focusing in the
position representation of the states in the Hilbert space, and you do
not want to see that various operators are equally good operators,
regardless whether they commute with position or not. LM]

As Always Thanks

Alejandro

<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:<2ln50rFeihpsU1-100000@uni-berlin.de>...\n\n> "mandro" <ultraman2002@hotmail.com> schrieb im Newsbeitrag\n> news:dec722c5.0407131057.2602b41b-100000@posting.google.com...\n>\n> > Well, I already said, that I\'d been\n> > informed that the average length of\n> > a string is infinity.\n>\n> Yes, but by regularizing (normal ordering) the observable which measures the\n> size of the string, one obtains a finite value which is physically very\n> interesting, since it can be related to black hole entropy considerations.\n\nWhat about the old hadronic string? It was described, in the 1970\'s, as a\nstraight string having a pair quark/antiquark in the extremes, and rotating\nabout relativistic speeds. To get a constant force -for quark confinement-, it\nwas postulated (or proofed, perhaps?) that string energy is proportional to\nits length. So in that time the length has a valid meaning.\n\nAlejandro\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:<2ln50rFeihpsU1-100000@uni-berlin.de>...

> "mandro" <ultraman2002@hotmail.com> schrieb im Newsbeitrag
> news:dec722c5.0407131057.2602b41b-10....google.com...
>
> > Well, I already said, that I'd been
> > informed that the average length of
> > a string is infinity.
>
> Yes, but by regularizing (normal ordering) the observable which measures the
> size of the string, one obtains a finite value which is physically very
> interesting, since it can be related to black hole entropy considerations.

What about the old hadronic string? It was described, in the 1970's, as a
straight string having a pair quark/antiquark in the extremes, and rotating
about relativistic speeds. To get a constant force [itex]-for[/itex] quark confinement-, it
was postulated (or proofed, perhaps?) that string energy is proportional to
its length. So in that time the length has a valid meaning.

Alejandro

mandro

<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>\nI\'ll let the more erudite brainiacs\nrespond to this, but I will venture\nthe following, I don\'t think the\nold hadronic theory is exactly the\nsame as the standard string theories.\nCome to think of it, even though I\'ve\nheard countless times that string theory\nas it is known today evolved from a\ntheory of looking at hadrons as a\nstring with a quark at each end, I really\ndont understand this, or "how" it relates\nto the modern string. Just to say well, dahh\nthey both mention the word "string" will\nno satisfy me either, that\'s like saying that\nclassical mechanics already hints at\nstring theory because it can describe\nstrings. I.e., strings appear in both cases,\nbut in totally different contexts. And,\nfrom this point of view, they have no\nrelation to each other.\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>I'll let the more erudite brainiacs
respond to this, but I will venture
the following, I don't think the
old hadronic theory is exactly the
same as the standard string theories.
Come to think of it, even though I've
heard countless times that string theory
as it is known today evolved from a
theory of looking at hadrons as a
string with a quark at each end, I really
dont understand this, or "how" it relates
to the modern string. Just to say well, dahh
they both mention the word "string" will
no satisfy me either, that's like saying that
classical mechanics already hints at
string theory because it can describe
strings. I.e., strings appear in both cases,
but in totally different contexts. And,
from this point of view, they have no
relation to each other.

Alejandro

<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>mandro <ultraman2002@hotmail.com> wrote in message news:<dec722c5.0407281601.2ee849f5-100000@posting.google.com>...\n\n> I\'ll let the more erudite brainiacs\n> respond to this, but I will venture\n> the following, I don\'t think the\n> old hadronic theory is exactly the\n> same as the standard string theories.\n\nOn the other side, if we were to consider "string theory" to be only\nthe five theories of strings and the results depending mathematically\nof these theories, most of the string papers should be assigned to\nother branchs of theoretical physics. Some authors recognize this by\nspeaking of "string inspired" results.\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>mandro <ultraman2002@hotmail.com> wrote in message news:<dec722c5.0407281601.2ee849f5-1...google.com>...

> I'll let the more erudite brainiacs
> respond to this, but I will venture
> the following, I don't think the
> old hadronic theory is exactly the
> same as the standard string theories.

On the other side, if we were to consider "string theory" to be only
the five theories of strings and the results depending mathematically
of these theories, most of the string papers should be assigned to
other branchs of theoretical physics. Some authors recognize this by
speaking of "string inspired" results.

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kurious	minimum size of a string MANDRO: First of all, what do you mean by "the size of a string" 1) Do you mean minimum radius sized ball which contains the string? 2)Do you mean the length of the string? what do you mean? ALISTAIR writes: I mean the length of an open string.