# What are the strings in string theory made of?

This is a follow-up to an intriguing question last year about tension in string theory.

What are the strings in string theory composed of?

I am serious. Strings made of matter are complex objects that require a highly specific form of long-chain inter-atomic bonding (mostly carbon based) that would be difficult to implement if the physics parameters of our universe were tweaked even a tiny bit. That bonding gets even more complicated when you add in elasticity. The vibration modes of a real string are the non-obvious emergent outcome of a complex interplay of mass, angular momentum, various conservation laws, and convenient linearities inherent in of our form of spacetime.

In short, a matter-based vibrating real string is the outcome of the interplay of most of the more important physics rules of our universe. Its composition -- what is is made of -- is particularly complex. Real strings are composed out of a statistically unlikely form of long-chain bonding, which in turn depend on the rather unlikely properties that emerge from highly complex multiparticle entities called atoms.

So how does string theory handle all of this? What are the strings in string theory made of, and what is it about this substance that makes string-theories simple in comparison to the emergent and non-obvious complexities required to produce string-like vibrations in real, matter-based strings?

Addendum 2012-12-28 (all new as of 2012-12-29):

OK, I'm trying to go back to my original question after some apt complaints that my addendum yesterday had morphed it into an entirely new question. But I don't want to trash the great responses that addendum produced, so I'm trying to walk the razor's edge by creating an entirely new addendum that I hope expands on the intent of my question without changing it in any fundamental way. Here goes:

The simplest answer to my question is that strings are pure mathematical abstractions, and so need no further explanation. All of the initial answers were variants of that answer. I truly did not expect that to happen!

While such answers are sincere and certainly well-intended, I suspect that most people reading my original question will find them a bit disappointing and almost certainly not terribly insightful. They will be hoping for more, and here's why.

While most of modern mathematical physics arguably is derived from materials analogies, early wave analogies tended towards placing waves within homogeneous and isotropic "water like" or "air like" media, e.g. the aether of the late 1800s.

Over time and with no small amount of insight, these early analogies were transformed into sets of equations that increasingly removed the need for physical media analogies. The history of Maxwell's equations and then SR is a gorgeous example. That one nicely demonstrates the remarkable progress of the associated physics theories away from using physical media, and towards more universal mathematical constructs. In those cases I understand immediately why the outcomes are considered "fundamental." After all, they started out with clunky material-science analogies, and then managed over time to strip away the encumbering analogies, leaving for us shiny little nuggets of pure math that to this day are gorgeous to behold.

Now in the more recent case of string theory, here's where I think the rub is for most of us who are not immersed in it on a daily basis: The very word "string" invokes the image of a vibrating entity that is a good deal more complicated and specific than some isotropic wave medium. For one thing the word string invokes (perhaps incorrectly) an image of an object localized in space. That is, the vibrations are taking place not within some isotropic field located throughout space, but within some entity located in some very specific region of space. Strings in string theory also seem to possess a rather complicated and certainly non-trivial suite materials-like properties such as length, rigidity, tension, and I'm sure others (e.g. some analog of angular momentum?).

So, again trying to keep to my original question:

Can someone explain what a string in string theory is made of in a way that provides some insight into why such an unusually object-like "medium of vibration" was selected as the basis for building all of the surrounding mathematics of string theory?

From one excellent comment (you know who you are!), I can even give an example of the kind of answer I was hoping for. Paraphrasing, the comment was this:

"Strings vibrate in ways that are immediately reminiscent of the harmonic oscillators that have proven so useful analytically in wave and quantum theory."

Now I like that style of answer a lot! For one thing, anyone who has read Feynman's section on such oscillators in his lectures will immediately get the idea. Based on that, my own understanding of the origins of strings has now shifted to something far more specific and "connectable" to historical physics, which is this:

Making tuning forks smaller and smaller has been been shown repeatedly in the history of physics to provide an exceptionally powerful analytical method for analyzing how various types of vibrations propagate and interact. So, why not take this idea to the logical limit and make space itself into what amounts to a huge field of very small, tuning-fork-like harmonic oscillators?

Now that I can at least understand as an argument for why strings "resonated" well with a lot of physicists as an interesting approach to unifying physics.

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This is a google-searchable question, and I vote to close... The fundamental objects in String theory are strings (more generally, p-branes), so you cannot talk about their composition. – Chris Gerig Dec 11 '12 at 18:09

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WHAT? YOU CHANGED THE QUESTION ENTIRELY. "Why strings" instead of "what are strings made of"... this is inappropriate etiquette, you should make a new question! (To answer this new question, the point is that string theory works, it recovers a ton of stuff we want/need, and that's why strings -- a wave is fundamental.) – Chris Gerig Dec 28 '12 at 8:40

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And this new question is also google-searchable!! And questioning the theory as a philosophy is more appropriate as a meta question, or in the Philosophy StackExchange (if one exists). – Chris Gerig Dec 28 '12 at 8:57

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No need to get crazy about it @Chris ;-) Terry, your addendum does diverge from the original point of the question. Could you reword it to stay more on point, or remove it post a separate question to ask why strings are assumed instead of some other system? – David Zaslavsky♦ Dec 28 '12 at 20:01

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Dear Terry Bollinger. @Chris Gerig shouldn't be shouting but he nevertheless got a point. Why string theory? is a huge question in itself, and it would not be constructive to ask it as a subquestion to another question. Please roll back your question to e.g.: In string theory, what are strings made of? – Qmechanic♦ Dec 29 '12 at 17:00
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## 7 Answers

OP wrote(v4):

[...] Strings in string theory also seem to possess a rather complicated and certainly non-trivial suite materials-like properties such as length, rigidity, tension, and I'm sure others (e.g. some analog of angular momentum?). [...]

Well, the relativistic string should not be confused with the non-relativistic material string, compare e.g. chapter 6 and 4 in Ref. 1, respectively. In contrast, the relativistic string is e.g. required to be world-sheet reparametrization-invariant, i.e. the world-sheet coordinates are no longer physical/material labels of the string, but merely unphysical gauge degree of freedom.

Moreover, in principle, all dimensionless continuous constants in string theory may be calculated from any stabilized string vacuum, see e.g. this Phys.SE answer by Lubos Motl.

OP wrote(v1):

What are strings made of?

One answer is that it is only meaningful to answer this question if the answer has physical consequences. Popularly speaking, string theory is supposed to be the innermost Russian doll of modern physics, and there are no more dolls inside that we can explain it in terms. However, we may be able to find equivalent formulations.

For instance, Thorn has proposed in Ref. 2 that strings are made of point-like objects that he calls string bits. More precisely, he has shown that this string bit formulation is mathematically equivalent to the light-cone formulation of string theory; first in the bosonic string and later in the superstring. The corresponding formulas are indeed quadratic a la harmonic oscillators (cf. a comment by anna v) with the twist that the "Newtonian mass" of the string bit oscillators are given by light-cone $P^+$ momentum. Thorn was inspired by fishnet Feynman diagrams (think triangularized world-sheets), which were discussed in Refs. 3 and 4. However, string bit formulation does not really answer the question What are strings made of?; it merely adds a dual description.

References:

1. B. Zwiebach, A first course in String Theory.

2. C.B. Thorn, Reformulating String Theory with the 1/N Expansion, in Sakharov Memorial Lectures in Physics, Ed. L. V. Keldysh and V. Ya. Fainberg, Nova Science Publishers Inc., Commack, New York, 1992; arXiv:hep-th/9405069.

3. H.B. Nielsen and P. Olesen, Phys. Lett. 32B (1970) 203.

4. B. Sakita and M.A. Virasoro, Phys. Rev. Lett. 24 (1970) 1146.

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This is nice, +1 – Dilaton Dec 30 '12 at 0:21
Qmechanic, wow, thank you!! That was superb and very much the kind of answer I had been hoping for! – Terry Bollinger Dec 30 '12 at 7:12
@TerryBollinger: seriously? This says nothing different than what has been said about strings. I do not understand your problem. – Chris Gerig Dec 30 '12 at 18:05

The question "what is xxx made of" is really asking "what can xxx be decomposed into"?

For example we know matter is made of atoms because it can be decomposed into atoms. We know atoms are made of electrons, protons and neutrons because atoms can be broken down into electrons, protons and neutrons. But electrons can't be decomposed into anything, so it's meaningless to ask what an electron is made of. We can ask what an electron's mass is, or its energy, or its spin, etc etc, but to ask what it's made from is a question that has no answer.

Exactly the same applies to a string. It is an object that has properties, but it's meaningless to ask what it's made from because it can't be broken down into anything.

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It is not that meaningless to ask if strings are made of something else, it depends on the parameters of the theory and the context, see my (complementary) answer. – Dilaton Dec 29 '12 at 12:11

Lenny Susskind explains that the answer to this question depends on the parameters of the theory at 1:10:50 to the end of this video.

He makes use of the fact that the question if strings are fundamental or if they are composed of something else is analogous to the question if in electrodynamics, electrons or magnetic monopols have to be considered fundamental to by able to develope a perturbation theory with Feynman diagrams. It can be shown that magnetic charges q and electric charges e are related by

$$e\, q = 2 \pi$$

This means, that if the charge of the electron (and therefore their mass) is small, the charge of the magnetic monopoles is (and their mass) is huge and vice versa. If the charge and the mass of the electron are small, the electron is considered fundamental and a converging theory (QED) can be developed because the coupling constant $e$ is small. At the same time the magnetic monopoles are heavy complicated things composed of whole bunches of photons and magnetic charges because the coupling constant $q$ is large. This regime corresponds to what we observe with QED being a weakly coupled theory and the magnetic monopoles (if they exist) being to large to be observed. Increasing the electric charge of the electron would lead to a transition to a situation, where the electons become heavy and complicated and in this case it would be more useful to consider a quantized electromagnetic theory with the ligth magnetic monopoles described as fundamental particles.

A similar relationship as described to hold for the pair of electric and magnetic charges exists in string theory between fundamental (f-) strings and D-branes. Depending on the parameters of the theory, either it is more appropriate to consider the D-branes as complicated heavy things composed of fundamental strings, or the D-branes are light and fundamental whereas strings are heavy and complicated things composed of D-branes. The technical term describing this ambiguity is S-duality.

In summary, a uniques and universally valid answer to the question what strings are made of can not be given; it depends on the parameters of the theory and the context if it is more useful to consider strings or D-branes as fundamental.

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In string theory the strings are fundamental objects and cannot be made of anything.

However, the strings of string theory, like more general extended objects --e.g., the membranes in brane theory--, can be considered to be made of more fundamental point-like objects.

An interesting picture is given in Point-Like Structure in Strings

I would finally emphasize that the D0-branes used in Banks' matrix theory or the Thorn's bits are not the more fundamental pointlike objects. For instance, believing that universe is really made of D0-branes would be so misguided as when string theorists believed that universe was really made of strings.

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This is to complete @Dilaton 's answer.

The very basic reason theoretical physicist are entranced by string models and their extensions is because they promise to be the framework of the Theory Of Everything, the holy grail of theoretical physics.

String theories and their extensions provide for the quantization of gravity, the long standing difficulty in formulating a TOE. If there existed a competing theory with composite preons or what not, which included the quantization of gravity in a unified manner, one would estimate the merits of each as a TOE. At the moment string theory has no competition, and strings are the fundamental entities of reality in these theories.

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Yeah, thanks for the nice introduction Anna ;-) – Dilaton Dec 29 '12 at 12:50

In short, string is a dislocation defect of the vacuum crystalline structure.

This by the way explains why apparent full angle around a string seems to be smaller than $2 \pi$.

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(Please note that I am attempting to answer my own question.)

In string theory it has been implicitly hypothesized, but not rigorously proven, that the mathematical constructs used to describe the vibrations of certain of isotropic materials in simple geometric simple shapes (e.g. strings or rings) are examples of mathematical constructs so fundamental that they show up at many different levels and circumstances in physics. If this string hypothesis is true, then the vibrations of ordinary material strings are a distant echo of these far more fundamental mathematical rules.

There is a precedent for this in modern physics. When James Clerk Maxwell first integrated the knowledge of electricity and magnetism of his time into a single unified theory, he did not at first use differential equations. Instead, he intentionally built a purely mechanical rotating-cell model based on generalizations of specific properties encountered in everyday material objects.

It was not until after Maxwell had used his mechanical model to prove that light was electromagnetic radiation that he realized that all the behaviors of his model could instead be expressed using 20 quaternion-based differential equations with 20 variables, which Oliver Heaviside later compressed down to a mere four vector-based equations that are now called (not entirely accurately) "Maxwell's equations".

The situation hypothesized for string theory is roughly comparable. It also starts with a materials-based dynamic analogy, and similarly proposes that the mathematics that describe that dynamic model are expressions of some deeper and more profound mathematical model. However, it is also true that what constitutes a "fundamental" set of mathematical constructs is much less clear in string theory than it was for the far simpler domain of electromagnetism. That is in part because for string theory the analogies from materials science are extended to much higher numbers of dimensions, and because string theory postulates modes of vibration that are not accessible to direct experimentation and refinement.

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-1, you gave literally no explanation, but went off on random tangents in history. My comment above on your question takes care of this. – Chris Gerig Dec 25 '12 at 0:49
Heh! To be accurate, Chris, reading your comment is why I thought I should at least try to put a more positive spin on the answers so far. Declaring something "fundamental" because, well, it just is has to be one of the weakest approaches imaginable for analyzing the structure of a truly complex problem. Are you aware of no data whatsoever to defend why the p-brane approach arguably fits the structure of universe better and with fewer assumptions? If so, what is it? Have analyses or comparisons been done? Does a p-brane approach produce persuasive predictions, or massive simplifications? – Terry Bollinger Dec 26 '12 at 7:49
"Declaring something "fundamental" because, well, it just is has to be one of the weakest approaches imaginable"... This is irrelevant. Your question was "what are strings made of", and the answer is that they are not made of anything. QED. If you want to change the question, make a new post (do not abruptly alter the current one!). – Chris Gerig Dec 28 '12 at 8:39

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Terry, when I first heard of string theory as the TOE, my first reaction was "of course, the ubiquitous harmonic oscillator" . If you have solved enough quantum mechanical problems you would know that the first approximation to the solution of symmetrical potentials is the harmonic oscillator, because it is the first term in the Tailor expansion of any symmetrical potential. It could be that the real functional form of "string theories" has higher order terms, but at the moment it seems that this is a good candidate for a TOE. – anna v Dec 29 '12 at 12:35
anna v, I love your "If you have solved enough quantum mechanical problems" whack (mea culpa, mea culpa)! I also sort of wish you had made that into an answer. Since most folks reading this haven't had that very cool experience base, the transition from intensive use of harmonic oscillators (a much earlier materials-to-fundamental transition) just doesn't leap out as a reason for going to the specific structure (1D with tension) of strings. Even with your great point, I still can't help thinking "but isn't that taking the analogy in the wrong direction -- more towards material objects?" – Terry Bollinger Dec 29 '12 at 16:34

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