## Size of strings compared to size of elementary particles

<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">&nbsp;&nbsp;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
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"Ulrich Thiel" 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.



On $2005-04-20,$ Urs Schreiber 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

## Size of strings compared to size of elementary particles

<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&gt; 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&gt; I didn\'t know this although I remember now the\n&gt; deBroglie wave description of electrons (which is also outdated I\n&gt; 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&gt; Is it right that string theory tells us now that electrons are not\n&gt; pointlike and they only appear to be pointlike because the size of a string\n&gt; is so small that we cannot see it with our technical equipment?\n\n\nYes!\n\n\n&gt; 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&gt; Thanks for the answer again and sorry for the disturbance of the\n&gt; 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">&nbsp;&nbsp;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
$x_n$ of the nucleus and those $x_e$ 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. :-)


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



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.



"pirillo" 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" 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.$9)-(2$.11). The idea is quite simple: The mean squared diameter of the string is the average of $(X-X_0)^2,$ taken over the worldsheet, where $X_0$ 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 $\sum_{n=1}^\infty \frac{1}{n^2} (\alpha_{-n} \cdot \alpha_n + \alpha_n\cdot \alpha_{-n})$. Clearly, when you take the expectation value of this guy in any string state you'll get an infinite contribution from pulling the annihilators $\alpha_n$ through the creators $\alpha_{-n}$. This is a common quantum effect and is removed by normal ordering$. It$ 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.



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?



Do you integrate over the wholeworldsheet $(X-X_0 )^2 ,$ or do you integrate over the $\sigma$ coordinate only?



On Tue, 10 May 2005, pirillo wrote: > Do you integrate over the wholeworldsheet $(X-X_0 )^2 ,$ > or do you integrate over the $\sigma$ 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.



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.



> 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.



"pirillo" 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.



> 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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