I have a question, that perhaps someone with a much better understanding of physics can help me answer.

Please correct me if I'm wrong. From what I understand, a string in string theory is basically a strand of energy that vibrates. The string can vibrate in a variety of different ways. It is thought that things such as quarks consist of a string vibrating in a very specific way.

The question is, if two of these vibrating strings collide, would not there vibration patterns change?

Is it possible for a string vibrating with one pattern to collide with a string vibrating in the exact opposite pattern in such a way that the two strings are essentially cancelled out?

  • $\begingroup$ As I understand it they can form one larger resulting string (which corresponds to a different particle) with a specific state of excitation ("vibration pattern") depending on the details of the initial state. The final string can then decay again to smaller pieces, etc ... The probabiltity for these processes depends on the string coupling constant. I think two excited strings can form a single one that is in the ground state (not excited) but the two strings themselves can not disappear by "negative interference". $\endgroup$ – Dilaton Feb 11 '12 at 23:38
  • $\begingroup$ Prof Susskind talks a bit about string interactions at the end of this lecture: youtube.com/watch?v=gCyImLu0HSI&feature=relmfu The whole course is quite accessible, easy to understand, and gives a (only slightly technical) good introduction. $\endgroup$ – Dilaton Feb 11 '12 at 23:50
  • $\begingroup$ I'm honestly wondering whether these sort of string-theory questions are even approachable? Isn't a large mathematical background required with which most of us are not familiar? Assuming most of us are not familiar with string theory $\endgroup$ – Timtam Feb 12 '12 at 4:47
  • $\begingroup$ In his course Prof. Susskind always explains the mathematical concepts needed in a simplified version along the way such that no large mathematical background is needed to understand his course :-) $\endgroup$ – Dilaton Feb 12 '12 at 7:01

Strings are not described very accurately in popular science, because much of the physics of strings was only understood long after the mathematical theory was somewhat advanced, and an accurate classical analog for the string wasn't available until relatively recently. The classical analog people often use is a vibrating band of energy, but this is mostly wrong, because strings don't interact by bumping into each other, like rubber bands do. They can only interact in a strange way determined by the consistency of having infinitely many different particles, all conspiring to make a consistent theory. This conspiracy makes it that when strings merge, they do a complicated thing, and the only correct classical analog to this complicated thing is a black hole merger. This wasn't understood very well until at least the late 1990s, so pop-sci has not caught up.

Ordinary astrophysical black holes are big, and complicated, and black, and gooey. They are electrically resistive, their oscillations decay quickly, they are very irreversible in the statistical sense. The string describes the case that the black hole is extended and charged so much that it is in the non-viscous extremal limit, so that strings are not gooey and lossy like ordinary black holes, but shiny and reversible. The one dimensional shiny black holes are the strings, in the limit that these black holes are weakly interacting, so that the lightest ones are light, and consequently weakly charged (because extremality relates charge and mass).

When black holes collide, the oscillations do not combine in a simple way, they combine the way black holes combine, in a strange acausal way that only makes sense teleologically. So you can't say "this pattern made this pattern", at least not in a causal way precisely, you need to describe the whole thing at once. The ripples running along the string doesn't add to the ripple running along another string when they combine, but if the two combine at high energies to make a long string with many ripples running in a statistical way, so that it has a classical interpretation, they combine to an object which is gooey because it has a lot of junk running around on it, and this is no different than a viscous liquid. When the strings cool down again by shooting out other cold strings, the oscillations die down. The laws of combination are not like superposing waves on a pond, but they are described over the entire space-time world-sheet.

Strings are more elementary than black holes, they are small and simple. You shouldn't be intimidated by the above to thinking that the laws of string collisions require you to understand the classical collisions of black holes! This is no more true than saying that describing a collision in the Born approximation in quantum mechanics requires you to solve the much more difficult classical problem of particles scattering around in that potential. The quantum behavior is simpler than the classical behavior in many cases.

The laws of string collisions, for those strings which are lightest at the lowest energies, that is for those distance scales which reproduce our experience, are extremely simple: they just reproduce the laws of Feynman diagrams, so that the particles combine into other particles the same way they do in the standard model. On the string world sheet, these laws of particle combination are the laws of algebraic products of operators, they describe how to expand a product of two operators in an infinite series of a third operator. This process takes a limit where the points of merger of the incoming particles are smooshed close together by a conformal transformation, so that each of their oscillations is no longer distinct, but merged into a combined oscillation a long long time ago (the collision limit is not really a short-distance limit, but a long-time limit). The combined oscillation just looks like an infinite series of particles in the theory, an infinite series of operators on the world sheet which create the oscillation corresponding to sending in one of these particles from infinity.

This is just like a Taylor expansion, except for fluctuating quantities, and the operator product laws are the laws of string merger and vibration-adding. You can't make nothing, because you always have a world sheet, and the addition law is strange, not by the laws of superposition (like water waves, or oscillations on rubber bands) but by the rules of operator product expansion.

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  • $\begingroup$ I like this enlightening and interesting answer +1 $\endgroup$ – Dilaton Feb 12 '12 at 12:18
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    $\begingroup$ Also +1, but can you provide a cite for your statement: "...the only correct classical analog to this complicated thing is a black hole merger. This wasn't understood very well until at least the late 1990s..." No one believes me when I try to tell them about this because the most popular examples like ads/cft describe dualities with spacetimes that are not like ours. $\endgroup$ – user1247 Feb 13 '12 at 12:24
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    $\begingroup$ @user1247: There is no point in trying to convince people--- horse water but horse thirsty. It is amazing enough that you can convince yourself. I am sorry I cannot provide a good reference, but I can give a simple argument--- the D-string in type IIB string theory is S-dual to the F-string of the perturbation theory, and T-dual to a 2-brane in IIA string theory, which is S-dual to the M2 brane in SUGRA which is both known to be a classical black hole when you stack N of them, and has an AdS-CFT description. You make any brane classical black hole by stacking, and brane is T/S dual to strings. $\endgroup$ – Ron Maimon Feb 13 '12 at 14:00

Here is a lecture to CERN summer students on "what is string theory" so physicists should be able to get a gist of the idea. There are more lectures in the "summer student lecture program" if somebody is really interested. I used "strings" to search.

String scattering is a "simple" extension from Feynman diagrams, for those who know Feynman diagrams, as far as drawings go.

When two particles scatter more particles come out if the energy is high. In Feynman diagrams there are specific rules about vertices etc which allow for calculating the crossection of a specific output.

The same is true when the two particles are represented as excitations on two strings. When they collide they may just change the energy level and so represent a different particle following the conservation rules, as with Feynman diagrams, or more complicated generation of strings can be mapped, when one is looking at a two to many particles scattering.

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