## Novice: Indivisibility of string

<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">&nbsp;&nbsp;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



"John" 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.



On Mon, 25 Apr 2005, John wrote: > > "Urs Schreiber" 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...)

## Novice: Indivisibility of string

> 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 $c=15$ 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