The Music of the Superstrings

String theorist Oswaldo Zapata continues (see here for an earlier posting about this) his remarkable series of essays about string theory and how it came to dominate research in theoretical high energy physics. The latest one, entitled The Music of the Superstrings is about the metaphorical use of classical music to promote superstring theory, and it concludes:

Metaphors are powerful rhetorical tools. But, at the same time, they are much more than that. Indeed, when used astutely, that is, when anchored in deep shared meanings and aspirations, they can create an enthusiastic army of supporters to the discourse displayed. This has been one of the strongest weapons of string theorists in the battle for the control of future research in high energy theoretical physics.

Zapata examines how and why string theorists have chosen to advertise string theory to the public by claiming a deep connection to music, especially to classical music. He recalls the many ways this analogy has been promoted by many different string theorists, from Brian Greene, who has made it a prominent part of his popular explanations of the theory, to Edward Witten, who told an interviewer in 1988:

In the case of a violin string, the different harmonics correspond to different sounds. In the case of superstring, the different harmonics correspond to different elementary particles.

I’ve always found this kind of thing grating, for a reason that Zapata doesn’t address. Statements like Witten’s give people the impression that the known fundamental particles of nature somehow correspond to the harmonics produced by vibration of a string. This is rather misleading, since all known particles correspond to the lowest energy state of the string. The quantum states corresponding to “harmonics” of a string are all supposed to be at unobservably high energy. The way the theory is sold to the public, via the musical metaphor that electrons and muons are different “harmonics” of a string vibrating at different frequencies makes it seem that such particles can be matched to the characteristic behavior of the harmonics of a string-like mechanical system, which is simply not true.

Zapata also now has a Reactions page, where he has posted links to commentary about his essays, as well as some comments from Bert Schroer in a recent preprint.

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22 Responses to The Music of the Superstrings

  1. Matt Leifer says:

    Personally, I’ve always found comparisons to classical music rather pretentious and off-putting. If you want to get me interested in a subject then you would be much better off comparing it to punk rock :)

  2. jpd says:

    paging Mr. Ramone….Mr. Joey Ramone

  3. piscator says:

    >This is rather misleading, since all known particles correspond
    > tothe lowest energy state of the string. The quantum states
    >corresponding to “harmonics” of a string are all supposed to be
    >at unobservably high energy.

    um, in string theory gravitons and gauge bosons are harmonics of the string. the ground state with no oscillators is tachyonic.


  4. woit says:


    Yes, I know. My point is that the way this is advertised to the public is misleading: the different notes coming from the different harmonics of a vibrating string in a stringed instrument do correspond in a quantized theory to different sets of states. But those different states are not the known different particles.

    Put differently, string theorists go on about an analogy with the musical notes in Bach string concertos, failing to mention that, as far as their strings are concerned, there’s only one note.

    You can argue that this is justifiable poetic license, but, as Zapata explains, it is license taken in the cause of creating “one of the strongest weapons of string theorists in the battle for the control of future research in high energy theoretical physics.”

  5. Tom Whicker says:

    Yes, grating is the word for it!

    The vibrating string metaphor really falls apart if you consider the internal forces involved in a real vibrating string. Do quantum strings have an internal structure that gives them a characteristic bulk modulus? If so, then the string is certainly not
    a fundamental particle. And in the quantum world, what provides the needed connections to each end of the string so that it may be tensioned? I seem to recall that Randall spoke of strings being anchored at one end to a brane….but if that is so, then how
    do strings move freely as particles?

    One thing that made Greene’s “Elegant Universe” so hard to watch was the repeated use of bad metaphor. For instance, ants walking on the surface of a long piece of wire says nothing of substance regarding “compactification of dimensions”.

    How about a full issue of the blog dedicated to bad (and good, if they exsit) string metaphors?

  6. Hendrik says:

    In response, some classical composers have taken up strings (in the physics sense), e.g. here. Maybe it has to do with all the hype about beauty.
    NewScientist is back onto strings too.

  7. Bert Schroer says:

    The metaphor to a musical string is actually correct, but in a very queer unintended sense. But the string is not in spacetime, it rather “sits” in the little Hilbert space “above” one point i.e. at the place which normally is reserved for the spin indices. And in some contorted way a small number of string theorists (Martinec,…) know that, but by the time they made this observation the metaphor of “those little wiggling strings” was already so powerful within the community that they called it an “invisible string” of which only one point is visible thus deriding decades of year of foundational research on quantum theory, including the work of Bohr and Heisenberg (who are left to rotate in their graves).
    String theory can of course not be corrected by correcting the terminology and calling those objects what they really represent namely the first illustration of infinite component fields or wave functions (which Fronsdal, Barut, Kleinert, the 60 looked for in vain). One really needs the incorrect metaphor and not the real thing in order to make sense of those Feynman-like tube pictures which leeds into one of these abominable “catch 22″ problems.
    Question: do you think that there ever will be a description of those tube rules in terms of operators in a Hilbert space? This is what every object in QT admits, in the entire quantum theory there has been no exception to this rule.

  8. robert says:

    Witten’s off piste lingusitic abilities are well known; I’ve never heard mention made of his musicianship. Is he an accomplished performer or avid listener, by any chance?

  9. Giotis says:

    Peter, my feeling is that you are exaggerating on this one. They just wanted to convey the basic idea to the public. Such pictorial representations are often used by scientists. I don’t think that their intention was to mislead anyone and I don’t see how an intuitive image intended for the public, could possibly influence the trends in theoretical physics.

  10. Peter Woit says:


    The problem is that it doesn’t actually convey the basic idea to the public very well, but gives them a wrong idea about what is going on. While I think this is misleading, I don’t think that’s the intention.

    As for whether I’m exaggerating: the fact is that I thought about writing something on the topic in my book about the problems with the musical metaphor, decided it wasn’t important enough to write more than a sentence about. Note that this posting is about Zapata’s essay, he’s the one arguing that this kind of misleading metaphor has influenced trends in theoretical physics.

  11. Giotis says:

    I see. I misinterpreted then.

  12. Bert Schroer says:

    Giotis and Peter
    You both came very close to what what is the core of the string problem. It is often said that a pointlike free quantum field is a collection of oscillators. This is a somewhat perilous characterization because no student who knows the QM of the oscillator would be able to reconstruct a free field from this indication. The most important aspect of the quantum field is its causal localization in one spacetime point; if it is a free field one most add the information that it obeys a specific equation of motion. From these (or similar formulated) data one can uniquely construct a free field.
    The vibrating oscillators are then the Fouriercomponents of the pointlike field, but it is physically clearer to make the linear decomposition into creation/annihilation operators a(p), a(p)*. In every state, in particular in the vacuum state, there are fluctuations of these oscillators. Most aspects of these oscillators are unphysical, but certain fluctuations have physical consequences. For example the fact that the sum (integral) of all the vacuum fluctuations diverges is not of direct physical relevance, it is equivalent to the fact that the field A(x) is not an operator but a more singular object namely an “operator-vaued distribution” with excellent mathematical credentials.
    As far as localization in the material sense is concerned, the field A(x) is localized in one point and there is no trace of the wiggling from the oscillators, the Wiggling comes when you look at expectations of products A(x­_1)…A(x_n) in states (the most important state being the vacuum).
    Behind these remarks there are two very different concepts of localization namely the Born localization of QM (in the relativistic setting the Born-Newton-Wigner localization) which comes with wave functions and the causal localization which in the above example is the point x i.e. independent of any state in which the local observable is studied. Nobody in his right mind would say that the oscillator wiggling in states has anything to do with the localization of an observable. The causal localization concept has a completely intrinsic meaning, there is a new mathematical theory which allows to liberate this meaning from the contingency of what field-coordinatization one is using: modular localisation.
    What are Nambu-Goto strings or their supersymmetric counterparts? They turn out to be infinite component pointlike wave functions/fields. String theorists know that they only use a different name they call them (those who looked at the localization aspect) “invisible strings” or “strings of which only one point is visible”. Why? because at the time they realized this the string mataphor was already so strong that they coud not resist the suck which they themselves created. What helped this incorrect metaphor was the fact that the classical Lagrangian is indeed that of a string. But all the work of Bohr Heisenberg … was done to liberate QT from false analogs to classical physics.
    Where did all the oscillator degrees of freedom go which correspond to the classical string? They went into the rich infinite components i.e. they are in the inner space which metaphorically one likes to picture “above” the localization point (see my previous remark). There is nothing, I repeat, there is absolutely nothing which resembles a wiggling string in spacetime.

  13. Joe Dimaggio says:

    “This is rather misleading, since all known particles correspond to the lowest energy state of the string.”

    In other words… the string-music analogy falls flat.

    You have to love my triple entendre :)

  14. Bert Schroer says:

    Peter, Giotis and Joe,
    The analogy to a an acoustic string would be a legitimate metaphor (metaphors are never correspondences but at best analogies) if strings would really be what string theorist claim they are, namely stringlike extended objects (as opposed to the pointlike fields of QFT).
    But they are not, and some string theorists (Martinec, Dimock,…) have seen this by explicit calculations. Since at the time of these calculations they were already committed to strings (the community influence which Zapata describes so vividly) they called it an “invisible string” or “a string of which one sees only the c.m.” They should have used the name “infinite component wave function” or (in second quantization infinite component pointlike fields). These objects were searched for before by Fronsdal, Barut, Kleinert…but without success because they were using group theoretical methods. When you permit quantum mechanics of infinitely many oscillators you can do it but only in d=26 resp. 10
    Now if the result of ST would have been a string in spacetime than the analogy would be tolerable at least in order to reveal some flavour of that theory to the public. But the crucial point is that it isn’t and to use the musical analogy with an infinite component field (with all the higher frequencies having gone into the inner (“little” biut now infinitely large) Hilbert space namely that which goes with the indexing of the components is a very misleading metaphor.
    Or in Peter’s words, if you apply the analogy to the infinite component pointlike fields (called string) than you must also allow it for a few component i.e. standard QFT, but you should not do this in either case.
    I would expect a blogger telling me that names are hollow words, so what string theorists discovered (by a tube analogy to Feynman graphs) is a finite interaction between infinite component wave functions. This is their great discovery, something which one cannot do with a finite component field.
    My answer would be: show me an operator realization. Every prescription in QT permits a formulation in terms of operators in Hilbert space other wise it has nothing to do with QT. Witten looked for such a description over many years and did not find any. Anybody in the blogger community who believes that such a thing exists?
    The relation between the above strings and the way how to implement interactions in terms of pictures is hopeless, a genuine “catch 22″ situation if you know Joseph Heller’s novel.

  15. A.J. says:

    Dr. Schroer,

    It’s not quite true that the strings are always point-like objects in spacetime. They can wrap cycles, and this is essential for mirror symmetry.

  16. Bert Schroer says:

    Ihave to disappoint you, all of them are really infinite component wave functions or fields. Real strings also exist in QFT but they are very very different. You can call the objects of ST “invisible strings” or “strings of which only the c.m. point is visisible” (look up the computations of Martinec or Dimock if you find my computation to sketchy or suspect), but that is just a metaphoric circumscription id infinite conponent pointlike objects.
    I expected your reaction which is typical, because how can a young man (assuming that you did not live through pre 1980 particle physics) look through an extremely plausible metaphor which was solidified over 5 decades not only by its proselytizes of ST as Gross and Witten, but also by the silence of all the others including several Nobel laureates.
    How can a young man believe in what somebody like me, a nothing, says about string localization? You probably will not even find it worthwhile and look up the references by string theoreticians where they showed that the (graded) commutator is that of a pointlike field (which is the definition of pointlike localization) which they then unfortunately expressed in the described way. But physics is a democratic science and I have no doubt that at latest at the great ST and TOE crash which has to happen because there is simply no progress without it, you will remember me.
    I am just trying to back up Zapata’s cutting insider report in how facts are created in a community (the only place where this is possible) by massaging conjectures. I am using my 40 years experience as a research scientist in an era where at the end only the truth counts independent of who said it, but where the formation of gigantic communities (as compared to individual researchers up to the 80s) may delay this for a very long time.
    A.J. do you seriously believe that I would write such things in public if I would not have clarified this issue with all my colleagues who do understand QFT on a profound level? Please do me a favor and look up any reference about localization in ST (take the two above) and come back if you find anything else than invisible strings or strings which come with only one point and let me know. For a twitter session where you just day things without backing them up by a proof or at least an argument, time is too valuable. If you want to know how real strings look like, this can be explained and the result is that they have nothing to do with ST.

  17. A.J. says:

    Dr. Schroer,

    Please explain how a string wrapping the circle once is a localized entity. The notion of center of mass is a bit meaningless when the spacetime lacks an affine structure.

  18. Sulfur Surfer says:

    Prof. Schroer’s technical claims about string theory are so manifestly ridiculous as to provide no motivation to read the tomes that he claims are necessary to understanding QFT (and there are many hundreds, perhaps thousands, of theorists using QFT correctly and productively without the formalisms that Schroer claims are necessary). Indeed, AJ has provided two counterexamples, and the long strings that appear along excited Regge trajectories are another: these behave in every physical respect like string-like objects.

  19. Bert Schroer says:

    Dear A.J.
    The metaphor of the invisible wrapped string (with only one point is visible) is not mine but the phrasing of those string theorist theorist who really computed the spacetime extension of the string and found just a point. I am not using such misleading metaphors because the english language offerers a word for what it really is: an infinite-component pointlike field or better wave function.
    This blog discussion is impeded by the weight of almost 50 years of metaphors because when you hear the word “string” you think automatically in terms of those little wiggling closed or open things, don’t you? What I am asking you is to delete this in your memory and find our for yourself. The only reason I mentioned those computations done by string theorists because you trust them more them me. But the result of the computation is the same, the only difference is that they phrase the result in that (misleading) metaphor whereas I present the result without using metaphors.
    By the way to see the uncorrectable metaphoric Maldacena AdS-CFT conjecture cannot be dealt with in terms of a simple calculation, one needs more demanding structural tools: but since it does not come music (besides that of its string theory parents) one would have to open a separate section.
    Of course all these aberrations would not exist if the sociological conditions for particle physics would be similar to what they were at its best times namely by individual researchers as Pauli, Schwinger, Kallen, Lehmann, Weinberg,..and not by globalized communities with a guru at their leader.

  20. Bert Schroer says:

    When I came back to my office just now and looked at this blog, I realized that my last contribution intersected with sulfur’s. It so happened that in anticipation of my contribution and against his will he gave me a helping hand by confirming that particle physics these days is a matter of guru-directed communities who measure the validity of ideas in terms of community size and/or viewing rates.
    I expect however that possible further contributions of this Asperger Neird will be less useful and it would be a good idea if he can be kept out of this series blog in which every statement should be proven or documented following the example set by Oswaldo Zapata (who showed that string theory and objectivity do not necessarily have to be contradictory).

  21. Giotis says:

    Personally I don’t quite understand where the problem is. The EOM of the string is a wave equation. The solution to the EOM is expressed in terms of Fourier series. Upon quantization the commutation relations of the Fourier modes are those of the harmonic oscillator creation and annihilation operators. We have an infinite number of creation operators and by acting on the ground state (of the string i.e. no oscillations) they create the infinite set of basis states that span the infinite dimensional Hilbert space. Each quantum state of the string is described by a wavefunction (that satisfies the Schrodinger equation) and can be thought as a one particle state. Thus there should be the corresponding quantum field in space-time (the realm of String Field theory).

    But that doesn’t change the fact that the string is *really* the fundamental one dimensional object that sweeps a worldsheet in spacetime or wraps around a circle. Likewise in QFT the fundamental object is the field and its Quantum states can be interpreted as particles. Anyway I’m a little confused by these assertions.

  22. Bert Schroer says:

    Sure Giotis, a string of ST like a pointlike field with infinitely many component i.e. an infinite component field in the sense of the book on QFT by Bogoliubov, Oksak, Todorov,… But those degrees of freedom which reside in the e.g. Nambu-Goto Lagrangian are not the oscillator degrees of freedom which you see if you look at the creation/annihilation operators of a finite component free field. Those oscillator degrees of freedom which are in that classical N-G string rather go into the inner Hilbert space i.e. they create the infinite internal dimension which has nothing to do with the creation/annihilation operators of fields. The reason why those people who tried infinite component fields before string theory did not get anywhere is because they did not use vector-valued quantum mechanical variables to built up this infinite dimensional Hilbert space, but they tried it with noncompact group theory. It is very tragic that the dual model people did not realize that the Veneziano solution for a dual amplitude led precisely to those infinite component pointlike objects (the infinitly many poles whose residua are formed according to Gamma function properties), we would have been much better of.
    I agree with you that words are all hollow, but this ceases if words generate series misunderstandings. This is the case here. The oscillators of quantum fields nobody would call strings, they are pointlike localized and that they contain oscillators you only see through taking their expectation values in states (e.g. vacuum fluctuations), e.i. these fluctuations are their spacetime mark. With other words the oscillation (fluctuations) comes in through states, there is nothing oscillating in the observable pointlike localized field A(x), i.e. the a and a* do not start to fluctuate by themselves.
    The role of the oscillators which are characteristic for string theory is very different since they create an inner Hilbert space (which accounts for all those infinitely many spin components) and to speak about fluctuation is physically completely meaningless, their role is just to catalog the particle tower.
    There are two remarks which one could add here
    1) there are genuine stringlike objects; e.g. the electricall charged fields in their sharpest-localized form. They are very different from ST.
    2) dismissing strings/infinite component field as hollow words has its end when you come to the way in which string theorists introduce interaction via tube recipes for those infinite component string wave functions.
    3) The incorrect picture of ST can be traced back to the idea of source and target space (world sheet). You cannot embed a chiral conformal current with 26 internal vector indices into a 26 dimensiomal spacetime, when you do this the chiral degrees of freedom go into the internal space, i.e. the resulting 26 dimensional object is an infinite component pointlike field in 26 dimensions. This is where the tragic journey into metaphor-land begun.

    But I think I answered your question and I do not want unsolicited enter related subjects.
    Resume: the strings you mean when you make this comparison with oscillators (and vacuum fluctuation) in quantum fields are perfectly compatible with the true nature of what ST call strings and which they should have called infinite component fields, but they are not compatible with those metaphoric pictures of ST as an object which has an intrinsic (state independent) extension in form of a string.