Size of strings compared to size of elementary particles

Ulrich Thiel

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Hi!\n\nI\'m a novice so please excuse my question.\nSo far as I\'ve \'understood\' string theory, strings are very small\n(they\'re supposed to be as long as the Planck length) and that certain\nvibrational patterns of a string correspond to certain elementary particles.\nIf this is right I wonder how a small string can be identified as an\nelectron for example which has a tremendous size compared to the size of a\nstring. I don\'t understand this. Is it my classical view of an electron\nas a small \'ball\' that\'s wrong here?\n\nIt would be nice if somebody could help me here.\n\nUli\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hi!

I'm a novice so please excuse my question.
So far as I've 'understood' string theory, strings are very small
(they're supposed to be as long as the Planck length) and that certain
vibrational patterns of a string correspond to certain elementary particles.
If this is right I wonder how a small string can be identified as an
electron for example which has a tremendous size compared to the size of a
string. I don't understand this. Is it my classical view of an electron
as a small 'ball' that's wrong here?

It would be nice if somebody could help me here.

Uli

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>"Ulrich Thiel" <not_avail@gmx.net> schrieb im Newsbeitrag\nnews:426570cd\\$0\\$7518\\$9b4e6d93@newsread2.arcor-online.net...\n\n> I\'m a novice so please excuse my question.\n> So far as I\'ve \'understood\' string theory, strings are very small\n> (they\'re supposed to be as long as the Planck length) and that certain\n> vibrational patterns of a string correspond to certain elementary\n> particles.\n\nThis is often said, but is a little subtle. For superstrings, which are the\nstrings that can have fermions in the spectrum, the "vibrational patterns"\nthat leads to different particles in the massless sector are actually not\ntrue vibrations but fermionic vibrations, if you wish. See the discussion\nhere:\n\nhttp://golem.ph.utexas.edu/string/archives/000334.html .\n\n\n> If this is right I wonder how a small string can be identified as an\n> electron for example which has a tremendous size compared to the size of a\n> string. I don\'t understand this. Is it my classical view of an electron\n> as a small \'ball\' that\'s wrong here?\n\nYes, your classical view is wrong. Electrons appear in all accelerator\nexperiments as pointlike. No substructure or extension is being observed, up\nto the currently available precision. The reasoning that leads to the\n"classical electron radius" is outdated since the conception of quantum\nmechanics and quantum field theory.\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>"Ulrich Thiel" <not_avail@gmx.net> schrieb im Newsbeitrag
news:426570cd$0$7518$9b4e6d93@newsre...-online.net...

> I'm a novice so please excuse my question.
> So far as I've 'understood' string theory, strings are very small
> (they're supposed to be as long as the Planck length) and that certain
> vibrational patterns of a string correspond to certain elementary
> particles.

This is often said, but is a little subtle. For superstrings, which are the
strings that can have fermions in the spectrum, the "vibrational patterns"
that leads to different particles in the massless sector are actually not
true vibrations but fermionic vibrations, if you wish. See the discussion
here:

http://golem.ph.utexas.edu/string/archives/000334.html .

> If this is right I wonder how a small string can be identified as an
> electron for example which has a tremendous size compared to the size of a
> string. I don't understand this. Is it my classical view of an electron
> as a small 'ball' that's wrong here?

Yes, your classical view is wrong. Electrons appear in all accelerator
experiments as pointlike. No substructure or extension is being observed, up
to the currently available precision. The reasoning that leads to the
"classical electron radius" is outdated since the conception of quantum
mechanics and quantum field theory.

Ulrich Thiel

<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 2005-04-20, Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote:\nHi!\n\nThanks for the answer.\n\n> Yes, your classical view is wrong. Electrons appear in all accelerator\n> experiments as pointlike. No substructure or extension is being observed, up\n> to the currently available precision. The reasoning that leads to the\n> "classical electron radius" is outdated since the conception of quantum\n> mechanics and quantum field theory.\n\nThey really appear pointlike? I didn\'t know this although I remember now the\ndeBroglie wave description of electrons (which is also outdated I\nsuppose). Is it right that string theory tells us now that electrons are not\npointlike and they only appear to be pointlike because the size of a string\nis so small that we cannot see it with our technical equipment?\nBut what about protons? Do they also appear to be pointlike?\n\nThanks for the answer again and sorry for the disturbance of the\nscientific atmosphere ;)\n\nUli\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 [itex]2005-04-20,[/itex] Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote:
Hi!

Thanks for the answer.

> Yes, your classical view is wrong. Electrons appear in all accelerator
> experiments as pointlike. No substructure or extension is being observed, up
> to the currently available precision. The reasoning that leads to the
> "classical electron radius" is outdated since the conception of quantum
> mechanics and quantum field theory.

They really appear pointlike? I didn't know this although I remember now the
deBroglie wave description of electrons (which is also outdated I
suppose). Is it right that string theory tells us now that electrons are not
pointlike and they only appear to be pointlike because the size of a string
is so small that we cannot see it with our technical equipment?
But what about protons? Do they also appear to be pointlike?

Thanks for the answer again and sorry for the disturbance of the
scientific atmosphere ;)

Uli

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>\nOn Wed, 20 Apr 2005, Ulrich Thiel wrote:\n\n> They really appear pointlike?\n\n\nYes. You collide them in accelerators with other stuff, like with\npositrons, and you don\'t see any inelastic scattering or anything which\nwould reveal an extension or composition of either electrons or positrons.\n\n\n> I didn\'t know this although I remember now the\n> deBroglie wave description of electrons (which is also outdated I\n> suppose)\n\n\nThis is not outdated in the sense that the idea of a "classical electron\nradius" is. The deBroglie wavelenth as well as the Compton wavelength of\nany particle are, however, not the same as the fundamental extension of\nthis particle. For practical purposes, like for instance in solid state\nphysics, it is often helpful to think of electrons as being smeared over a\nregion of the deBroglie wavelength or something. But the electron itself\nis pointlike.\n\nYou may be familiar with the textbook discussion of the hydrogen atom.\nNote that here both the electron and the nucleus are taken to be\npointlike. The configuration of the system is described by the coordinates\nx_n of the nucleus and those x_e of the electron. Their potential energy\nis proportional to the inverse of the distance between these two\npositions. Clearly all this assumes that both objects are points.\n\nNow, this is an approximation. We know that the nucleus is not really a\npoint. It may consist of several protons and neutrons, or at least one\nproton in the case of the H-atom. These are held togther by lots of\ngluons, too.\n\nSo in most QM textbooks somewhere in the later chapters on perturbation\ntheory you will see the effects discussed that appear once we realize the\nmistake of having treated the nucleus as pointlike.\n\nThe electron, however, is pointlike to such a good approximation at least\nthat so far no deviation from its pointlike-ness could be measured.\n\n\n> Is it right that string theory tells us now that electrons are not\n> pointlike and they only appear to be pointlike because the size of a string\n> is so small that we cannot see it with our technical equipment?\n\n\nYes!\n\n\n> But what about protons? Do they also appear to be pointlike?\n\n\nProtons are composed of quarks. QUurks are elementary particles in the\nstandard model of particle physics, protons and neutrons are not. All\nelementary particles appear pointlike to all our current equipment.\n\nAnd all these apparently pointlike particles of the standard model would\nturn out to be really little wiggly strings on very small scales, if\nperturbative string theory is the right description of nature.\n\n\n> Thanks for the answer again and sorry for the disturbance of the\n> scientific atmosphere ;)\n\n\nNo problem. You should pester everybody around here until they break down\nand give you a good scientific answer to a good layman question. :-)\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, 20 Apr 2005, Ulrich Thiel wrote:

> They really appear pointlike?

Yes. You collide them in accelerators with other stuff, like with
positrons, and you don't see any inelastic scattering or anything which
would reveal an extension or composition of either electrons or positrons.

> I didn't know this although I remember now the
> deBroglie wave description of electrons (which is also outdated I
> suppose)

This is not outdated in the sense that the idea of a "classical electron
radius" is. The deBroglie wavelenth as well as the Compton wavelength of
any particle are, however, not the same as the fundamental extension of
this particle. For practical purposes, like for instance in solid state
physics, it is often helpful to think of electrons as being smeared over a
region of the deBroglie wavelength or something. But the electron itself
is pointlike.

You may be familiar with the textbook discussion of the hydrogen atom.
Note that here both the electron and the nucleus are taken to be
pointlike. The configuration of the system is described by the coordinates
[itex]x_n[/itex] of the nucleus and those [itex]x_e[/itex] of the electron. Their potential energy
is proportional to the inverse of the distance between these two
positions. Clearly all this assumes that both objects are points.

Now, this is an approximation. We know that the nucleus is not really a
point. It may consist of several protons and neutrons, or at least one
proton in the case of the H-atom. These are held togther by lots of
gluons, too.

So in most QM textbooks somewhere in the later chapters on perturbation
theory you will see the effects discussed that appear once we realize the
mistake of having treated the nucleus as pointlike.

The electron, however, is pointlike to such a good approximation at least
that so far no deviation from its pointlike-ness could be measured.

> Is it right that string theory tells us now that electrons are not
> pointlike and they only appear to be pointlike because the size of a string
> is so small that we cannot see it with our technical equipment?

Yes!

> But what about protons? Do they also appear to be pointlike?

Protons are composed of quarks. QUurks are elementary particles in the
standard model of particle physics, protons and neutrons are not. All
elementary particles appear pointlike to all our current equipment.

And all these apparently pointlike particles of the standard model would
turn out to be really little wiggly strings on very small scales, if
perturbative string theory is the right description of nature.

> Thanks for the answer again and sorry for the disturbance of the
> scientific atmosphere ;)

No problem. You should pester everybody around here until they break down
and give you a good scientific answer to a good layman question. :-)

Ulrich Thiel

<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 wrote:\n\n> Protons are composed of quarks. QUurks are elementary particles in the\n> standard model of particle physics, protons and neutrons are not. All\n> elementary particles appear pointlike to all our current equipment.\n\nOkay, thanks for clarification!\n\n> No problem. You should pester everybody around here until they break\n> down and give you a good scientific answer to a good layman question. :-)\n\nGood to know :)\n\n\nUli\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 wrote:

> Protons are composed of quarks. QUurks are elementary particles in the
> standard model of particle physics, protons and neutrons are not. All
> elementary particles appear pointlike to all our current equipment.

Okay, thanks for clarification!

> No problem. You should pester everybody around here until they break
> down and give you a good scientific answer to a good layman question. :-)

Good to know :)

Uli

pirillo

<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>I think ultimately (and even in the intermediate steps)]\nthe size of the string 1) does not matter 2) is Ill defined.\nOne first has to define what one means by string size.\n1) Conceptually\n2) Experimentally\nTo some people string size may just be the value\nof a coupling constant.\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 think ultimately (and even in the intermediate steps)]
the size of the string 1) does not matter 2) is Ill defined.
One first has to define what one means by string size.
1) Conceptually
2) Experimentally
To some people string size may just be the value
of a coupling constant.

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>\n"pirillo" <ultraman2002@hotmail.com> schrieb im Newsbeitrag\nnews:1114877221.057878.148140@g14g2000cwa.googlegroups.com ...\n>I think ultimately (and even in the intermediate steps)]\n> the size of the string 1) does not matter 2) is Ill defined.\n> One first has to define what one means by string size.\n> 1) Conceptually\n\nThis is another FAQ. The last time this came up was here:\n\nhttp://groups.google.de/group/sci.physics.strings/msg/01c88b017e3ccc62?hl=de\nThe following was my reply at that time. (There is of course much room for\nimproving on that reply.)\n\n>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>&gt ;>>>>>>\n\n"mandro" <ultraman2...@hotmail.com> schrieb im Newsbeitrag\nnews:dec722c5.0407131057.2602b41b-100000@posting.google.com...\n\n\n\n> Well, I already said, that I\'d been informed that the average length of a\n> string is infinity.\n\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\n\nhttp://groups.google.de/groups?selm=dec722c5.0303061133.1bf83085%40po...\n\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\n\nThibault Damour, Gabriele Veneziano:\nSelf-gravitating fundamental strings and black-holes\nhep-th/9907030\n\n\nand references given there, where the observable measuring the rms size of a\nstring is given in equations (2.9)-(2.11).\n\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\n\\sum_{n=1}^\\infty \\frac{1}{n^2} (\\alpha_{-n} \\cdot \\alpha_n + \\alpha_n\n\\cdot \\alpha_{-n}).\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\n\nIn particular, the finite part is related to string/black hole\ncorrespondence, which I have tried to review here:\n\n\nhttp://golem.ph.utexas.edu/string/archives/000379.html .\n\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<<<<<<<<<<<<<<< <<<<<<<<<<<<<<<<<&lt ;<<<<<<<<<<<<<<<<<\n \n\n> To some people string size may just be the value\n> of a coupling constant.\n\nThat\'s not quite right. The value of the coupling constant in 10D string\ntheory is related to the dilaton which again is related to the circumference\nof an extra dimension.\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>"pirillo" <ultraman2002@hotmail.com> schrieb im Newsbeitrag
news:1114877221.057878.148140@g14g20...egroups.com...
>I think ultimately (and even in the intermediate steps)]
> the size of the string 1) does not matter 2) is Ill defined.
> One first has to define what one means by string size.
> 1) Conceptually

This is another FAQ. The last time this came up was here:

http://groups.google.de/group/sci.ph...7e3ccc62?hl=de
The following was my reply at that time. (There is of course much room for
improving on that reply.)

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

"mandro" <ultraman2...@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=...f83085%40po...

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.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

> To some people string size may just be the value
> of a coupling constant.

That's not quite right. The value of the coupling constant in 10D string
theory is related to the dilaton which again is related to the circumference
of an extra dimension.

pirillo

<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> > To some people string size may just be the value\n> > of a coupling constant.\n>\n> That\'s not quite right. The value of the coupling constant in 10D\nstring\n> theory is related to the dilaton which again is related to the\ncircumference\n> of an extra dimension.\n\nWhat if there\'s no extra compactified dimension, what then.\nWhat if I visualize a bosonic string living in 4 spacetime dimensions\nSee, the word "string size" is nearly meaningless without adding a lot\nof qualifiers. If it\'s the average size [as you prescibed wrt a given\ncutoff\nprocedure] , wrt a string state then I expect this to wary as the state\n\nvaries, what state are you talking about?\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>To some people string size may just be the value
> > of a coupling constant.
>
> That's not quite right. The value of the coupling constant in 10D
string
> theory is related to the dilaton which again is related to the
circumference
> of an extra dimension.

What if there's no extra compactified dimension, what then.
What if I visualize a bosonic string living in 4 spacetime dimensions
See, the word "string size" is nearly meaningless without adding a lot
of qualifiers. If it's the average size [as you prescibed wrt a given
cutoff
procedure] , wrt a string state then I expect this to wary as the state

varies, what state are you talking about?

pirillo

<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>Do you integrate over the wholeworldsheet (X-X_0 )^2 ,\nor do you integrate over the sigma coordinate only?\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>Do you integrate over the wholeworldsheet [itex](X-X_0 )^2 ,[/itex]
or do you integrate over the [itex]\sigma[/itex] coordinate only?

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>\n\nOn Tue, 10 May 2005, pirillo wrote:\n\n> Do you integrate over the wholeworldsheet (X-X_0 )^2 ,\n> or do you integrate over the sigma coordinate only?\n\n\nYou want to average that over space _and_ time to get the rms size of the\nstring. I seem to recall that this is discussed in the references that I\nprovided.\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 Tue, 10 May 2005, pirillo wrote:

> Do you integrate over the wholeworldsheet [itex](X-X_0 )^2 ,[/itex]
> or do you integrate over the [itex]\sigma[/itex] coordinate only?

You want to average that over space _and_ time to get the rms size of the
string. I seem to recall that this is discussed in the references that I
provided.

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>\n\nOn Tue, 10 May 2005, pirillo wrote:\n\n>\n>> > To some people string size may just be the value\n>> > of a coupling constant.\n>>\n>> That\'s not quite right. The value of the coupling constant in 10D\n> string\n>> theory is related to the dilaton which again is related to the\n> circumference\n>> of an extra dimension.\n>\n> What if there\'s no extra compactified dimension, what then.\n\n\nThen it\'s still not true that the string size is the value of a coupling\nconstant.\n\n\n> What if I visualize a bosonic string living in 4 spacetime dimensions\n\n\nThe you have a noncritical string and are in pretty deep waters.\n\n\n> See, the word "string size" is nearly meaningless without adding a lot\n> of qualifiers.\n\n\nTrue. So go ahead and specify precisely which notion of "string size" you\nare interested in.\n\n\n\n> If it\'s the average size [as you prescibed wrt a given\n> cutoff\n> procedure] , wrt a string state then I expect this to wary as the state\n> varies, what state are you talking about?\n\n\nIndeed. That procedure I mentioned gives you an operator and taking the\nexpectation value of that operator in a given state of the string gives\nthe rms size of the string in that state.\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 Tue, 10 May 2005, pirillo wrote:

>
>> > To some people string size may just be the value
>> > of a coupling constant.
>>
>> That's not quite right. The value of the coupling constant in 10D
> string
>> theory is related to the dilaton which again is related to the
> circumference
>> of an extra dimension.
>
> What if there's no extra compactified dimension, what then.

Then it's still not true that the string size is the value of a coupling
constant.

> What if I visualize a bosonic string living in 4 spacetime dimensions

The you have a noncritical string and are in pretty deep waters.

> See, the word "string size" is nearly meaningless without adding a lot
> of qualifiers.

True. So go ahead and specify precisely which notion of "string size" you
are interested in.

> If it's the average size [as you prescibed wrt a given
> cutoff
> procedure] , wrt a string state then I expect this to wary as the state
> varies, what state are you talking about?

Indeed. That procedure I mentioned gives you an operator and taking the
expectation value of that operator in a given state of the string gives
the rms size of the string in that state.

pirillo

<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>> You want to average that over space _and_ time to get the rms size of\n> the string. I seem to recall that this is discussed in the references\n> that I provided.\n\nOh, so you do sort of a " average size for the whole history"\noperator which say first computes the average distance from cm at each\ntime and then averages this over the whole history.\n\nHmmm?\n\nI thought in curved backgrounds you did this at one instant\nand found that the string became larger as time passed.\nOr, were you saying more like there\'s an external parameter\nwhich labels a family of spacetimes (the string lives in)\nand as you vary this parameter, the quantity you described\nabove varies, although --if one changes the target space,\nthen one changes the states.\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>> You want to average that over space _and_ time to get the rms size of
> the string. I seem to recall that this is discussed in the references
> that I provided.

Oh, so you do sort of a " average size for the whole history"
operator which say first computes the average distance from cm at each
time and then averages this over the whole history.

Hmmm?

I thought in curved backgrounds you did this at one instant
and found that the string became larger as time passed.
Or, were you saying more like there's an external parameter
which labels a family of spacetimes (the string lives in)
and as you vary this parameter, the quantity you described
above varies, although --if one changes the target space,
then one changes the states.

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>"pirillo" <ultraman2002@hotmail.com> schrieb im Newsbeitrag\nnews:1115858009.327557.225680@z14g2000cwz.googlegroups.com ...\n>> You want to average that over space _and_ time to get the rms size of\n>> the string. I seem to recall that this is discussed in the references\n>> that I provided.\n>\n> Oh, so you do sort of a " average size for the whole history"\n> operator which say first computes the average distance from cm at each\n> time and then averages this over the whole history.\n>\n> Hmmm?\n\nI am sorry, but I have a hard time understanding what you are confused\nabout.\n\nThe idea we are talking about is not particular to string theory at\nall but seems to be just a matter of common sense: You have some fluctuating\nsomething and want to get an idea of its rough size. So you average the\ndistance of all its points from its center of mass and, since its\nfluctuating, average these distances over some period of time. If that piece\nof something is systematically growing or shrinking on larger time scales\nyou will want to take the time average over an interval which is large\nenough compared to the fluctuations but small enough to be local in time\nwith respect to the long-term behaviour.\n\nTo be frank, I feel that the discussion of this point is getting a little\noff-topic for sci.physics.strings.\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>"pirillo" <ultraman2002@hotmail.com> schrieb im Newsbeitrag
news:1115858009.327557.225680@z14g20...egroups.com...
>> You want to average that over space _and_ time to get the rms size of
>> the string. I seem to recall that this is discussed in the references
>> that I provided.
>
> Oh, so you do sort of a " average size for the whole history"
> operator which say first computes the average distance from cm at each
> time and then averages this over the whole history.
>
> Hmmm?

I am sorry, but I have a hard time understanding what you are confused
about.

The idea we are talking about is not particular to string theory at
all but seems to be just a matter of common sense: You have some fluctuating
something and want to get an idea of its rough size. So you average the
distance of all its points from its center of mass and, since its
fluctuating, average these distances over some period of time. If that piece
of something is systematically growing or shrinking on larger time scales
you will want to take the time average over an interval which is large
enough compared to the fluctuations but small enough to be local in time
with respect to the long-term behaviour.

To be frank, I feel that the discussion of this point is getting a little
off-topic for sci.physics.strings.

pirillo

<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>> you will want to take the time average over an interval which is\n> large enough compared to the fluctuations but small enough to be local\n> in time with respect to the long-term behaviour.\n\nYeah, but you said integrate over the "whole" world sheet\nnot over a "short time band" on the worldsheet. So you\'re averaging\nover the "whole" infinite history. I\'m just saying what you seemed to\nsay --- not what you meant. Which I now think is to integrate over a small\ntime band.\n\n> To be frank, I feel that the discussion of this point is getting a\n> little off-topic for sci.physics.strings.\n\nAnd questions about Gerbes, Calabi Yau manifolds and all these objects\nwhich are purely mathematical are not! Ha :-)\nI think this "is" very stringy!\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>> you will want to take the time average over an interval which is
> large enough compared to the fluctuations but small enough to be local
> in time with respect to the long-term behaviour.

Yeah, but you said integrate over the "whole" world sheet
not over a "short time band" on the worldsheet. So you're averaging
over the "whole" infinite history. I'm just saying what you seemed to
say --- not what you meant. Which I now think is to integrate over a small
time band.

> To be frank, I feel that the discussion of this point is getting a
> little off-topic for sci.physics.strings.

And questions about Gerbes, Calabi Yau manifolds and all these objects
which are purely mathematical are not! Ha :-)
I think this "is" very stringy!

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