Novice: Indivisibility of string

Rudy Gildehaus

<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>\nThis is from a non-scientist, as you will soon deduce. I hope however\nfor some reply for my question, to me at least, is very basic and\nsimple. It is this:\n\nIf a string is the smallest possible particle, if that is the correct\nterm, and indivisible then how can it vibrate. How can anything\nindivisible vibrate?\n\nI realize that to you this may seem an inconsequential question and\nperhaps not answerable in a language I could understand but I certainly\nwould appreciate some answer. I have tried other sources but with a\nnotable lack of success.\n\nRudy Gildehaus\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>This is from a non-scientist, as you will soon deduce. I hope however
for some reply for my question, to me at least, is very basic and
simple. It is this:

If a string is the smallest possible particle, if that is the correct
term, and indivisible then how can it vibrate. How can anything
indivisible vibrate?

I realize that to you this may seem an inconsequential question and
perhaps not answerable in a language I could understand but I certainly
would appreciate some answer. I have tried other sources but with a
notable lack of success.

Rudy Gildehaus

richard miller

<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"John" <john@spam.is.evil.com> wrote in message\nnews:116qbkarhcd01aa@corp.supernews.com...\n\n> I\'m having a very hard time picturing what\'s vibrating. Vibration\n> seems to require parts of the string moving wrt other parts.\n> But doesn\'t that require there to be different parts, meaning\n> strings should be further divisible? Your example\n> of the rubber band doesn\'t help me, because it seems to me\n> that after enough divisions you\'re down to a string of 1 angstrom\n> diameter, and after that you\'ve lost the rubber band...\n>\n> Is this another one of those areas (like particle-wave duality\n> or 4 dimensional space-time) that just can\'t be pictured in terms\n> of our everyday models, or am I just having a hard time seeing\n> what should be an obvious point?\n\n\nSounds a nice question, we (one) have ascribed continuous laws over a length\nof the Planck scale. do we have the justifiication for this continuity or\nare all the action integrals etc. not validate nowadays (things have moved\non since the 80s?), at least as continuous functions? I don\'t know either.\nLook forward to the answer.\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>"John" <john@spam.is.evil.com> wrote in message
news:116qbkarhcd01aa@corp.supernews.com...

> I'm having a very hard time picturing what's vibrating. Vibration
> seems to require parts of the string moving wrt other parts.
> But doesn't that require there to be different parts, meaning
> strings should be further divisible? Your example
> of the rubber band doesn't help me, because it seems to me
> that after enough divisions you're down to a string of 1 angstrom
> diameter, and after that you've lost the rubber band...
>
> Is this another one of those areas (like particle-wave duality
> or 4 dimensional space-time) that just can't be pictured in terms
> of our everyday models, or am I just having a hard time seeing
> what should be an obvious point?

Sounds a nice question, we (one) have ascribed continuous laws over a length
of the Planck scale. do we have the justifiication for this continuity or
are all the action integrals etc. not validate nowadays (things have moved
on since the 80s?), at least as continuous functions? I don't know either.
Look forward to the answer.

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 Mon, 25 Apr 2005, John wrote:\n\n>\n> "Urs Schreiber" <Urs.Schreiber@uni-essen.de> wrote in message\n> news:Pine.LNX.4.62.0504050518510.21168@feynman.harvard.edu...\n>> \n>\n>>> How can anything indivisible vibrate?\n>>\n>>\n>> A rubber band of diameter d can vibrate. One of diameter d/2 can vibrate,\n>> and so on.\n\n> I\'m having a very hard time picturing what\'s vibrating. Vibration\n> seems to require parts of the string moving wrt other parts.\n\n\nWell, if the string is a line, there are points on that line and the\ndistance between them may vary.\n\nIn essence this is not different from any continuum description of, say, a\nviolin string, which you may found in classical mechanics textbooks.\nFor the prupose of getting a good description of its vibrational dynamics\nwe can forget about the fact that the violin string consists of atoms and\nmodel it as a 1-dimensional continuum.\n\nOn the other hand, there is a small subtlety with comparing the violin\nstring to the relativistic string. For the relativistic string the\ncoordinates on the worldsheet do not have an intrinsic physical meaning.\nThis can however be dealt with by what is called gauge fixing. The most\npopular form of this is called "lightcone gauge". After this is done the\nresulting oscillations of the string in what are called its "transversal"\ndirections are really just those of a vilon string.\n\n\n> But doesn\'t that require there to be different parts, meaning\n> strings should be further divisible?\n\nThey are, in a sense. A string can split into two strings, just as\ntwo strings can merge to become a single one. This "cubic vertex" (cube =\nthree strings in one interaction) is the unique interaction among strings\nfrom which all other interactions of the particles that it represents due\nto its excitations follow from.\n\nBut it turns out in fact that at least in some situations it makes sense\nto think of the string as consisting of certain undivisible "atoms of\nstring" in a certain sense. These are known as "string bits" and have\na while ago become famous again as it was found that certain products of a\nfinite number of N field operators in some field theory correspond in the\n_dual_ string theory picture to strings consisting of N string bits.\nRoughly.\n\nThen there is the "Matrix String" description, which is the approximation\nof strings in the Matrix Theory description of string theory for finite\ndimension N of these matrices. Here, too, the strings appear discretized\nin a certain sense.\n\n\n> Is this another one of those areas (like particle-wave duality\n> or 4 dimensional space-time) that just can\'t be pictured in terms\n> of our everyday models, or am I just having a hard time seeing\n> what should be an obvious point?\n\n\nIn as far as you are worried about the continuum description of a violin\nstring you could try to have another look at the discussion of this point\nin some textbook on classical mechanics.\n\nIn as far as you are concerned with more subtle issues regarding the\nrelativistic fundamental string I have tried to give some hints above.\nPlease ask again if you have further questions on that. (It can become a\nlong story...)\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, 25 Apr 2005, John wrote:

>
> "Urs Schreiber" <Urs.Schreiber@uni-essen.de> wrote in message
> news:Pine.LNX.4.62.0504050518510.211...harvard.edu...
>>
>
>>> How can anything indivisible vibrate?
>>
>>
>> A rubber band of diameter d can vibrate. One of diameter d/2 can vibrate,
>> and so on.

> I'm having a very hard time picturing what's vibrating. Vibration
> seems to require parts of the string moving wrt other parts.

Well, if the string is a line, there are points on that line and the
distance between them may vary.

In essence this is not different from any continuum description of, say, a
violin string, which you may found in classical mechanics textbooks.
For the prupose of getting a good description of its vibrational dynamics
we can forget about the fact that the violin string consists of atoms and
model it as a 1-dimensional continuum.

On the other hand, there is a small subtlety with comparing the violin
string to the relativistic string. For the relativistic string the
coordinates on the worldsheet do not have an intrinsic physical meaning.
This can however be dealt with by what is called gauge fixing. The most
popular form of this is called "lightcone gauge". After this is done the
resulting oscillations of the string in what are called its "transversal"
directions are really just those of a vilon string.

> But doesn't that require there to be different parts, meaning
> strings should be further divisible?

They are, in a sense. A string can split into two strings, just as
two strings can merge to become a single one. This "cubic vertex" (cube =
three strings in one interaction) is the unique interaction among strings
from which all other interactions of the particles that it represents due
to its excitations follow from.

But it turns out in fact that at least in some situations it makes sense
to think of the string as consisting of certain undivisible "atoms of
string" in a certain sense. These are known as "string bits" and have
a while ago become famous again as it was found that certain products of a
finite number of N field operators in some field theory correspond in the
_dual_ string theory picture to strings consisting of N string bits.
Roughly.

Then there is the "Matrix String" description, which is the approximation
of strings in the Matrix Theory description of string theory for finite
dimension N of these matrices. Here, too, the strings appear discretized
in a certain sense.

> Is this another one of those areas (like particle-wave duality
> or 4 dimensional space-time) that just can't be pictured in terms
> of our everyday models, or am I just having a hard time seeing
> what should be an obvious point?

In as far as you are worried about the continuum description of a violin
string you could try to have another look at the discussion of this point
in some textbook on classical mechanics.

In as far as you are concerned with more subtle issues regarding the
relativistic fundamental string I have tried to give some hints above.
Please ask again if you have further questions on that. (It can become a
long story...)

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, 26 Apr 2005, richard miller wrote:\n\n> Sounds a nice question, we (one) have ascribed continuous laws over a length\n> of the Planck scale. do we have the justifiication for this continuity or\n> are all the action integrals etc. not validate nowadays (things have moved\n> on since the 80s?), at least as continuous functions? I don\'t know either.\n> Look forward to the answer.\n\n\nThis is actually a deep question, I believe. It has been asked a couple of\ntimes before on this group, if I recall correctly, in one way or another.\nI am nor sure if Eric Zaslow is still collecting FAQs, maybe this should\nbe included in our list (Is anyone compiling attempts at giving answers\nto the FAQs?):\n\n\nFAQ: "How can it be that the string is a mathematical line?"\n\n\nI believe one should say at least three things as comments on that\nquestion:\n\n1) Elementary particles are mathemtaical points. Is that less mysterious\nthan being a mathematical line?\n\nOf course one may suspect that elementary particles are not fundamentally elementary\nprecisley because they are mathematical points. This leads me to point 2)\nand 3).\n\n\n\n1) Spacetime is emergent. What we really have in perturbative string\ntheory is just any superconformal field theory of central charge c=15 on abstract\n2-dimensional Riemannian surfaces.\n\nIn _some_ cases this superconformal field theory can be interpreted as\ndescribing the dynamics of "embedding fields" which describe how this\nRiemannian surface sits inside a manifold which we interpret as spacetime\n(the "background spacetime").\n(And, BTW, it need not be an embeeding at all, there are in general lots\nof self-intersection).\n\nIn other cases it may not be possible to have such a geometric\ninterpretation of your CFT. CFTs without such a geometric interpretation\ndescribe "spacetimes" which are not manifolds in the classical sense.\nSometimes these are referred to as being a "non-geometric phase" of\nspacetime, or something like that.\n\nSo in general it is not even true that a string is a line and that it\nsweeps ot a worldsheet in spacetime!\n\nIn "most" cases however, it is.\n\n(Hm, do we know how much is "most"?)\n\n\n3) Perturbative string theory is not the last word, so much is for sure.\nM-theory is the last word, by definition. (Imagine an appropriate simley\nhere...) Do strings still look like mathematical lines in M-theory?\n\nOf course they become membranes, but that doesn\'t help us with our\nquestion. There is the Matrix Theory description of everything, where all\nthings become kind of fuzzy.\n\nA good discussion of this point requires more time than I can currently\nafford, I am afraid. Lubos has to say much more about this. Maybe if you\nkindly ask him he\'ll write a more complete FAQ entry to the above FAQ. :-)\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 Tue, 26 Apr 2005, richard miller wrote:

> Sounds a nice question, we (one) have ascribed continuous laws over a length
> of the Planck scale. do we have the justifiication for this continuity or
> are all the action integrals etc. not validate nowadays (things have moved
> on since the 80s?), at least as continuous functions? I don't know either.
> Look forward to the answer.

This is actually a deep question, I believe. It has been asked a couple of
times before on this group, if I recall correctly, in one way or another.
I am nor sure if Eric Zaslow is still collecting FAQs, maybe this should
be included in our list (Is anyone compiling attempts at giving answers
to the FAQs?):

FAQ: "How can it be that the string is a mathematical line?"

I believe one should say at least three things as comments on that
question:

1) Elementary particles are mathemtaical points. Is that less mysterious
than being a mathematical line?

Of course one may suspect that elementary particles are not fundamentally elementary
precisley because they are mathematical points. This leads me to point 2)
and 3).

1) Spacetime is emergent. What we really have in perturbative string
theory is just any superconformal field theory of central charge [itex]c=15[/itex] on abstract
2-dimensional Riemannian surfaces.

In _some_ cases this superconformal field theory can be interpreted as
describing the dynamics of "embedding fields" which describe how this
Riemannian surface sits inside a manifold which we interpret as spacetime
(the "background spacetime").
(And, BTW, it need not be an embeeding at all, there are in general lots
of self-intersection).

In other cases it may not be possible to have such a geometric
interpretation of your CFT. CFTs without such a geometric interpretation
describe "spacetimes" which are not manifolds in the classical sense.
Sometimes these are referred to as being a "non-geometric phase" of
spacetime, or something like that.

So in general it is not even true that a string is a line and that it
sweeps ot a worldsheet in spacetime!

In "most" cases however, it is.

(Hm, do we know how much is "most"?)

3) Perturbative string theory is not the last word, so much is for sure.
M-theory is the last word, by definition. (Imagine an appropriate simley
here...) Do strings still look like mathematical lines in M-theory?

Of course they become membranes, but that doesn't help us with our
question. There is the Matrix Theory description of everything, where all
things become kind of fuzzy.

A good discussion of this point requires more time than I can currently
afford, I am afraid. Lubos has to say much more about this. Maybe if you
kindly ask him he'll write a more complete FAQ entry to the above FAQ. :-)

JS2

<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\nnews:Pine.LNX.4.62.0504270925220.17446@feynman.harvard.edu...\ n\n> ...Well, if the string is a line, there are points on that line and the\n> distance between them may vary.\n>\n> In essence this is not different from any continuum description of, say, a\n> violin string, which you may found in classical mechanics textbooks.\n> For the prupose of getting a good description of its vibrational dynamics\n> we can forget about the fact that the violin string consists of atoms and\n> model it as a 1-dimensional continuum.\n\nSo I guess the question comes down to the string being a one dimensional\nstring look like, and like your next post says, its really no stranger\nthan a mathematical point as an elementary particle. Okay, I can\nlive with that, seeing as how the only reason a point is easier to\ntake is that I\'m used to the idea ... thanks for your help. Its a pretty\nstrange theory ... I suppose that\'s how all the people felt about relativity\nand quantum mechanics at the start of the 20th century.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Urs Schreiber" <Urs.Schreiber@uni-essen.de> wrote in message
news:Pine.LNX.4.62.0504270925220.174...harvard.edu...

> ...Well, if the string is a line, there are points on that line and the
> distance between them may vary.
>
> In essence this is not different from any continuum description of, say, a
> violin string, which you may found in classical mechanics textbooks.
> For the prupose of getting a good description of its vibrational dynamics
> we can forget about the fact that the violin string consists of atoms and
> model it as a 1-dimensional continuum.

So I guess the question comes down to the string being a one dimensional
string look like, and like your next post says, its really no stranger
than a mathematical point as an elementary particle. Okay, I can
live with that, seeing as how the only reason a point is easier to
take is that I'm used to the idea ... thanks for your help. Its a pretty
strange theory ... I suppose that's how all the people felt about relativity
and quantum mechanics at the start of the 20th century.

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