what is string theory? [Archive]

alistair

May13-04, 06:58 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>In non-string physics particles trace out a world line.In string\ntheory a world surface replaces a world line.Can the world surface be\nviewed as a set of world lines? In other words,is the original particle\nnow a delocalised set of smaller particles?\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>In non-string physics particles trace out a world line.In string
theory a world surface replaces a world line.Can the world surface be
viewed as a set of world lines? In other words,is the original particle
now a delocalised set of smaller particles?

Lubos Motl

May13-04, 07:37 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Thu, 13 May 2004, alistair wrote:\n\n> In non-string physics particles trace out a world line.In string\n> theory a world surface replaces a world line.Can the world surface be\n> viewed as a set of world lines? In other words,is the original particle\n> now a delocalised set of smaller particles?\n\nIt is against the philosophy of string theory to imagine that the\nworldsheet is "made of" individual worldlines. This would mean that on the\ntwo-dimensional worldsheet, there is a preferred direction of time at each\npoint - this direction would describe the direction of the worldline of\nthe point-like particle.\n\nOn the worldsheet of a string, all directions are treated democratically.\nIn fact, the two-dimensional theory that describes the internal dynamics\nof the worldsheet has a much bigger group of symmetries: the general\ndiffeomorphism symmetry: this theory is a two-dimensional counterpart of\ngeneral relativity and implies that all "reference frames" are equally\ngood in formulating the physical laws. Any extra structure of lines (or\nchoice of coordinates) that you imagine on the worldsheet is unphysical.\n\nIf we look at a particular point P of the string at time t_2, it is not\npossible to say where this point of the string was at time t_1. In fact,\nthis feature helps string theory to regulate short-distance divergences\nbecause it is also impossible to say exactly at which point of the stringy\nworldsheet (imagine the pants diagram) the interaction occured.\n\nThe string worldsheet has another symmetry - the Weyl symmetry that allows\none to multiply the worldsheet metric by an arbitrary scalar function of\nthe worldsheet coordinates. This symmetry, together with the\ndiffeomorphism symmetry, forms "conformal symmetry" - and therefore the\ntwo-dimensional theory describing the worldsheet is a "conformal field\ntheory", a theory whose local dynamics only depends on the angles, not the\ndistances. The Weyl symmetry guarantees that the string carries no\ninformation about its "density" of particles - it only matters which curve\n(or worldsheet) it spans in spacetime, but it does not matter how you\nparameterize the string or the worldsheet.\n\nAll these things mean that you should be very careful when you try to\nimagine the string as a family of point-like particles. Despite all these\nfacts, we can often encounter situations in string theory that allow us to\ndescribe the string as a composite of point-like particles called the\n"string bits". String bits can be identified in Matrix string theory or\nthe PP-wave limit of AdS/CFT correspondence.\n\nThere are other extended objects in string theory - such as D-branes - and\nthe discussion would have to be changed a bit for them. For example, they\nare not invariant under conformal symmetry, and on the other hand, a\nD-brane of dimension "p" can be usefully imagined as a bound state of\nD-branes of smaller dimensionalities p-2k.\n\nAll the best\nLubos\n_____________________________________ _________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Thu, 13 May 2004, alistair wrote:

> In non-string physics particles trace out a world line.In string
> theory a world surface replaces a world line.Can the world surface be
> viewed as a set of world lines? In other words,is the original particle
> now a delocalised set of smaller particles?

It is against the philosophy of string theory to imagine that the
worldsheet is "made of" individual worldlines. This would mean that on the
two-dimensional worldsheet, there is a preferred direction of time at each
point - this direction would describe the direction of the worldline of
the point-like particle.

On the worldsheet of a string, all directions are treated democratically.
In fact, the two-dimensional theory that describes the internal dynamics
of the worldsheet has a much bigger group of symmetries: the general
diffeomorphism symmetry: this theory is a two-dimensional counterpart of
general relativity and implies that all "reference frames" are equally
good in formulating the physical laws. Any extra structure of lines (or
choice of coordinates) that you imagine on the worldsheet is unphysical.

If we look at a particular point P of the string at time t_2, it is not
possible to say where this point of the string was at time t_1. In fact,
this feature helps string theory to regulate short-distance divergences
because it is also impossible to say exactly at which point of the stringy
worldsheet (imagine the pants diagram) the interaction occured.

The string worldsheet has another symmetry - the Weyl symmetry that allows
one to multiply the worldsheet metric by an arbitrary scalar function of
the worldsheet coordinates. This symmetry, together with the
diffeomorphism symmetry, forms "conformal symmetry" - and therefore the
two-dimensional theory describing the worldsheet is a "conformal field
theory", a theory whose local dynamics only depends on the angles, not the
distances. The Weyl symmetry guarantees that the string carries no
information about its "density" of particles - it only matters which curve
(or worldsheet) it spans in spacetime, but it does not matter how you
parameterize the string or the worldsheet.

All these things mean that you should be very careful when you try to
imagine the string as a family of point-like particles. Despite all these
facts, we can often encounter situations in string theory that allow us to
describe the string as a composite of point-like particles called the
"string bits". String bits can be identified in Matrix string theory or
the PP-wave limit of AdS/CFT correspondence.

There are other extended objects in string theory - such as D-branes - and
the discussion would have to be changed a bit for them. For example, they
are not invariant under conformal symmetry, and on the other hand, a
D-brane of dimension "p" can be usefully imagined as a bound state of
D-branes of smaller dimensionalities p-2k.

All the best
Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

alistair

May14-04, 06:12 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0405130719410.7060-100000@feynman.harvard.edu>...\n\n> The Weyl symmetry guarantees that the string carries no\n> information about its "density" of particles\n\nIs this the same as saying all density configurations are equally possible?\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>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0405130719410.7060-100000@feynman.harvard.edu>...

> The Weyl symmetry guarantees that the string carries no
> information about its "density" of particles

Is this the same as saying all density configurations are equally possible?

Urs Schreiber

May14-04, 06:27 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Fri, 14 May 2004, alistair wrote:\n\n> Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0405130719410.7060-100000@feynman.harvard.edu>...\n>\n> > The Weyl symmetry guarantees that the string carries no\n> > information about its "density" of particles\n>\n> Is this the same as saying all density configurations are equally possible?\n\nI would rather say that it says that there is nothing like a density\nconfiguration of the string. The dynamics of fields in a theory\nwith Weyl symmetry only depends on angles, not on volumes.\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 Fri, 14 May 2004, alistair wrote:

> Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0405130719410.7060-100000@feynman.harvard.edu>...
>
> > The Weyl symmetry guarantees that the string carries no
> > information about its "density" of particles
>
> Is this the same as saying all density configurations are equally possible?

I would rather say that it says that there is nothing like a density
configuration of the string. The dynamics of fields in a theory
with Weyl symmetry only depends on angles, not on volumes.

alistair

May15-04, 08:22 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>If strings had variable mass density along their length this would be very\ninteresting indeed because it would mean that particles such as electrons\nwould not necessarily be identical to each other and would lead to\nquestions about the entropy of strings, for example.And it would reflect\nthe macroscopic world in which no two large masses are ever\nidentical.However, I am aware that this is all rather speculative.\n\n===\n[Moderator\'s note: This extra information about "density" is essentially\nwhat we find in non-critical strings - i.e. strings in non-critical spacetime\ndimension where the Weyl symmetry (scaling of the worldsheet metric) is\nbroken by quantum effects. In such theories, there is indeed an extra\nscalar function phi of sigma,tau - of the coordinates on the worldsheet.\nIt is your "density", but we usually call it the conformal factor, or\nthe Liouville direction - and if you study physics of such a string\ntheory with the "density" properly, you will find out that the "density"\nactually behaves as a new direction of space in which the string can\noscillate. The dilaton (or the string coupling constant) is however an\nincreasing function of this new dimension phi, and therefore this\nnew dimension behaves a bit differently than the other dimensions\nof spacetime. LM]\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>If strings had variable mass density along their length this would be very
interesting indeed because it would mean that particles such as electrons
would not necessarily be identical to each other and would lead to
questions about the entropy of strings, for example.And it would reflect
the macroscopic world in which no two large masses are ever
identical.However, I am aware that this is all rather speculative.

===
[Moderator's note: This extra information about "density" is essentially
what we find in non-critical strings - i.e. strings in non-critical spacetime
dimension where the Weyl symmetry (scaling of the worldsheet metric) is
broken by quantum effects. In such theories, there is indeed an extra
scalar function \phi of \sigma,\tau - of the coordinates on the worldsheet.
It is your "density", but we usually call it the conformal factor, or
the Liouville direction - and if you study physics of such a string
theory with the "density" properly, you will find out that the "density"
actually behaves as a new direction of space in which the string can
oscillate. The dilaton (or the string coupling constant) is however an
increasing function of this new dimension \phi, and therefore this
new dimension behaves a bit differently than the other dimensions
of spacetime. LM]

Charlie Stromeyer Jr.

May16-04, 12:28 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>alistair <alistair@goforit64.fsnet.co.uk> wrote in message news:\n\n> In non-string physics particles trace out a world line.In string\n> theory a world surface replaces a world line.Can the world surface be\n> viewed as a set of world lines? In other words,is the original particle\n> now a delocalised set of smaller particles?\n\nI agree with what both Lubos and Urs have written within this thread\n(at least, I agree with their answers in terms of the classical string\ntheory context). Furthermore, if the answer to your question was yes\nthen string theory might have already been invalidated by actual\nexperiments - see e.g. my post "On acausality in string theory".\n\nPerhaps you might try to better intuitively understand what the\ndistinction between the worldsheet and worldlines should be like by\nconsidering ways in which the classical Einstein-Hilbert action would\nbe inadequate.\n\nI don\'t know the history of how this way of thinking developed, but\nperhaps it was B. deWitt you first made a significant result in this\ndirection, and perhaps it was G. Veneziano who first started to\nrealize how the string theory version of the EH action should be\ndifferent.\n\nYou may be able to first gain some insight about this before even\nhaving to think about what kind of geometry should be needed to\ndescribe physical phenomena with axion and dilaton fields or how it is\nthat quanta of these fields might yield classical particles.\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>alistair <alistair@goforit64.fsnet.co.uk> wrote in message news:

> In non-string physics particles trace out a world line.In string
> theory a world surface replaces a world line.Can the world surface be
> viewed as a set of world lines? In other words,is the original particle
> now a delocalised set of smaller particles?

I agree with what both Lubos and Urs have written within this thread
(at least, I agree with their answers in terms of the classical string
theory context). Furthermore, if the answer to your question was yes
then string theory might have already been invalidated by actual
experiments - see e.g. my post "On acausality in string theory".

Perhaps you might try to better intuitively understand what the
distinction between the worldsheet and worldlines should be like by
considering ways in which the classical Einstein-Hilbert action would
be inadequate.

I don't know the history of how this way of thinking developed, but
perhaps it was B. deWitt you first made a significant result in this
direction, and perhaps it was G. Veneziano who first started to
realize how the string theory version of the EH action should be
different.

You may be able to first gain some insight about this before even
having to think about what kind of geometry should be needed to
describe physical phenomena with axion and dilaton fields or how it is
that quanta of these fields might yield classical particles.

Squark

May16-04, 04:04 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>> [Moderator\'s note: This extra information about "density" is essentially\n> what we find in non-critical strings - i.e. strings in non-critical\n> spacetime dimension where the Weyl symmetry (scaling of the worldsheet\n> metric) is broken by quantum effects. In such theories, there is indeed an\n> extra scalar function phi of sigma,tau - of the coordinates on the\n> worldsheet. It is your "density", but we usually call it the conformal\n> factor, or the Liouville direction - and if you study physics of such a\n> string theory with the "density" properly, you will find out that\n> the "density" actually behaves as a new direction of space in which the\n> string can oscillate. The dilaton (or the string coupling constant) is\n> however an increasing function of this new dimension phi, and therefore this\n> new dimension behaves a bit differently than the other dimensions\n> of spacetime. LM]\n\nI\'d like to understand this better. Isn\'t string theory in non-critical\ndimension inconsistent, for instance it is incompatible with Lorentz\nsymmetry? Is it the usual string theory action we acre considering here?\nIs the scalaer function related to the metric on the worldsheet or is it\na new field we have to insert to restore consistency (by changing the\ncentral charge of the theory)?\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>> [Moderator's note: This extra information about "density" is essentially
> what we find in non-critical strings - i.e. strings in non-critical
> spacetime dimension where the Weyl symmetry (scaling of the worldsheet
> metric) is broken by quantum effects. In such theories, there is indeed an
> extra scalar function \phi of \sigma,\tau - of the coordinates on the
> worldsheet. It is your "density", but we usually call it the conformal
> factor, or the Liouville direction - and if you study physics of such a
> string theory with the "density" properly, you will find out that
> the "density" actually behaves as a new direction of space in which the
> string can oscillate. The dilaton (or the string coupling constant) is
> however an increasing function of this new dimension \phi, and therefore this
> new dimension behaves a bit differently than the other dimensions
> of spacetime. LM]

I'd like to understand this better. Isn't string theory in non-critical
dimension inconsistent, for instance it is incompatible with Lorentz
symmetry? Is it the usual string theory action we acre considering here?
Is the scalaer function related to the metric on the worldsheet or is it
a new field we have to insert to restore consistency (by changing the
central charge of the theory)?

Best regards,
Squark.

Urs Schreiber

May18-04, 12:54 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Sun, 16 May 2004, Squark wrote:\n\n> I\'d like to understand this better. Isn\'t string theory in non-critical\n> dimension inconsistent,\n\nI don\'t know the full answer, but I note that on\n\nhttp://www.physics.ucsb.edu/~giddings/Mquest.html\n\nwhere Stefe Giddings lists the "Big questions in M-theory" one question\nby E. Silverstein reads:\n\n"What is the role of noncritical string theory backgrounds: are such\nbackgrounds generically connected to critical string theory backgrounds\nvia tachyon condensation?"\n\n\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>On Sun, 16 May 2004, Squark wrote:

> I'd like to understand this better. Isn't string theory in non-critical
> dimension inconsistent,

I don't know the full answer, but I note that on

http://www.physics.ucsb.edu/~giddings/Mquest.html

where Stefe Giddings lists the "Big questions in M-theory" one question
by E. Silverstein reads:

"What is the role of noncritical string theory backgrounds: are such
backgrounds generically connected to critical string theory backgrounds
via tachyon condensation?"

alistair

May28-04, 02:01 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>LUBOS MOTL said ( summarised!)\n\n"Knowing where a point on a string is at time t2 we can\'t know where\nthat point\nwas at an earlier time t1."\n\nThis assumes that the string leaves no record of its previous position\nin the vacuum where it might have disturbed vacuum particles and could\nhave left a unique imprint, if only briefly.Is string theory complete\nif it isn\'t formulated with vacuum energy in mind?I suppose the same\ncould be said of\ngeneral relativity too.\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 said ( summarised!)

"Knowing where a point on a string is at time t2 we can't know where
that point
was at an earlier time t1."

This assumes that the string leaves no record of its previous position
in the vacuum where it might have disturbed vacuum particles and could
have left a unique imprint, if only briefly.Is string theory complete
if it isn't formulated with vacuum energy in mind?I suppose the same
could be said of
general relativity too.

alistair

May28-04, 01:34 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>Does the accuracy of what we can conclude about how the co-ordinates\nof each point on a string have changed, depend on the number of\ninteractions that string has had with other strings? In other words,\nif we knew the co-ordinates of all the points on a large number of\nother strings, after an interaction,could we deduce exactly what the\nco-ordinates of each point on the single string were at,or before, the\ntime of interaction?\nIf we couldn\'t deduce exact co-ordinates, would the uncertainty in the\nco-ordinates deduced for the single string be smaller, for a larger\nnumber of interactions?\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>Does the accuracy of what we can conclude about how the co-ordinates
of each point on a string have changed, depend on the number of
interactions that string has had with other strings? In other words,
if we knew the co-ordinates of all the points on a large number of
other strings, after an interaction,could we deduce exactly what the
co-ordinates of each point on the single string were at,or before, the
time of interaction?
If we couldn't deduce exact co-ordinates, would the uncertainty in the
co-ordinates deduced for the single string be smaller, for a larger
number of interactions?

Urs Schreiber

May28-04, 01:37 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 Fri, 28 May 2004, alistair wrote:\n\n> Does the accuracy of what we can conclude about how the co-ordinates\n> of each point on a string have changed, depend on the number of\n> interactions that string has had with other strings? In other words,\n\nDear alistair, please note that coordinates on the worldsheet have\nprecisely no physical meaning whatsoever, just as coordinates in spacetime\nare just a tool we use to talk about events, not a physical phenomenon.\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 Fri, 28 May 2004, alistair wrote:

> Does the accuracy of what we can conclude about how the co-ordinates
> of each point on a string have changed, depend on the number of
> interactions that string has had with other strings? In other words,

Dear alistair, please note that coordinates on the worldsheet have
precisely no physical meaning whatsoever, just as coordinates in spacetime
are just a tool we use to talk about events, not a physical phenomenon.