2. The Music of the Superstrings (IV of V)

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So, what is string theory?
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Fifteenth years before the interview he gave to The Elegant Universe, the one I have quoted in the first paragraph of this essay, Edward Witten vindicated publicly on a radio program (BBC radio 3, early 1988) the same correspondence between string vibrations and musical notes: “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.”[source] Manifestly surprised by Witten’s comparison, the interviewer responded: “It is stretching the analogy too far to say that the different fundamental particles of nature in some sense represent musical notes?” To which Witten replied categorically: “That’s a pretty good analogy.”

In one of the first widely circulated popular articles on superstring theory, published in October 1986 by Scientific American, Michael Green wrote: “Since a string has extension, it can vibrate much like an ordinary violin string.”[source] In the rest of the article there is no additional allusion to music: no more violins, no beautiful music, and no symphony. That same year, Michio Kaku published his first book devoted to string theory: “The superstring theory can produce a coherent and all-inclusive picture of nature similar to the way a violin string can be used to ‘unite’ all the musical tones and rules of harmony.”[source] And, he continues saying: “The tones created by the vibrating string, such as C or B flat, are not in themselves any more fundamental than any other tone. What is fundamental, however, is the fact that a single concept, vibrating string, can explain the laws of harmony.”[source] Finally, the reductionist approach to string theory is associated with ancient Greek philosophy: “The answer to the ancient question ‘What is matter?’ is simply that matter consists of particles that are different modes of vibration of the string, such as the notes G or F. The ‘music’ created by the string is matter itself.”[source] Ten years later, in January 1996, during the second superstring revolution, Scientific American came out with another popular review on the theory; this time the title was more pompous: “Explaining Everything.”[source] Around the beginning of the first paragraph, Madhusree Mukerjee, not a professional physicist but a staff science writer for the magazine, said: “The undulations of such strings were posited to yield all the particles and forces in the universe. These loops or segments of string are about 10―33 centimeter long and vibrate in many different modes, just as a violin string can.” In the middle of the article, the author repeated: “In superstring theory, the subatomic particles we see in nature are nothing more than different resonances of the vibrating superstrings, in the same way, that different musical notes emanate from the different modes of vibration of a violin string … .”

These examples come from writings intended for the general public, however, the association of string theory with music, and the violin string in particular, is also found in string theory textbooks. In the first reference book on the subject, written in the eighties by three of the fathers of the theory, Michael Green, John Schwarz, and Edward Witten, it is said: “Thus, the Fourier modes α for ≠0 are harmonic-oscillator coordinates, as we might have anticipated from experience with other free field theories or for that matter from experience with violin strings.”[source] In his 2004 introduction to the theory, more or less at the same level as the Green-Schwarz-Witten book, but now oriented to advanced undergraduates, Barton Zwiebach explains why string theory is a “truly” unified theory: “A musical analogy is very apt. Just as a violin string can vibrate in different modes and each mode corresponds to a different sound, the modes of vibration of a fundamental string can be recognized as the different particles we know.”[source]

Coming back to popular discourses, there are reasons to believe that a full understanding of the contemporary relationship that string theorists have established between the music of the superstrings and the music of spheres cannot be satisfactorily achieved without considering, even just in passing, the book which did the most to popularize the theory: Brian Greene’s The Elegant Universe. It is worth stressing once more the importance of Greene’s book.

In December 2005 the prestigious scientific magazine Nature, oriented to a broad audience of physicists, published a review article on superstrings.[source] The short piece, composed by Witten, the field’s leading researcher, just contains two references (indeed, there is a third but it is not relevant to the purpose of this essay): Greene’s The Elegant Universe and Zwiebach’s A First Course in String Theory. From this we can only draw one conclusion: if you want to know more about the theory, then, go and take a look at these two books. This is the recommendation of the “guru” of the discipline. The previous month, Juan Maldacena had also published a review article on string theory. The article, published in Scientific American,[source] summarized some of the recent advances of the holographic correspondence (see my first essay: “On Facts in Superstring Theory.”) To the interested reader he suggested the one book: The Elegant Universe. For a “popular-level exposition of string theory,” Zwiebach also recommends the book by Green. String theorists on the other side of the Atlantic do just the same. For example, Augusto Sagnotti, an influential Italian string theorist, in a contribution to an encyclopaedia on the history of science suggests the reading of The Elegant Universe.[source] This is done in the first entry of the bibliography and there is no other non-expert book mentioned. In a similar manner, in a recent “Überblick” of the subject, German string theorist Jan Louis refers to two popular accounts: Randall’s Verborgene Universum and Greene’s Das elegante Universum.[source] Of course, this list of references to Greene’s The Elegant Universe by string theory practitioners could go on and on. However, the idea of this sample is just to inform the reader of this essay that The Elegant Universe is not simply a book, as any other, that string experts recommend to the lay-public. Indeed, it is much more than that: it is “the book.” The one that better describes what they do, how they see the world, and what they think about themselves.

In the first pages of The Elegant Universe, Brian Greene makes clear what he believes the “basic idea” of the proposal to be: “Far from being a collection of chaotic experimental facts, particle properties in string theory are the manifestation of one and the same physical feature: the resonant patterns of vibration — the music, so to speak — of fundamental loops of string.” (pp. 15-16)

2. Still from The Elegant Universe; broadcast by PBS on the 28th October 2003.
Violin and string vibrations; in Greene’s book.

And, in the middle of the book he talks about the “cosmic symphony”: “What appear to be different elementary particles are actually different ‘notes’ on a fundamental string. The universe — being composed of an enormous number of these vibrating strings — is akin to a cosmic symphony.” (p. 146)

Only to make explicit what he means by “cosmic symphony,” let us quote at length a passage from his book. It comes from the first paragraph of chapter 6, “Nothing but Music: The Essentials of Superstring Theory”:
Music has long since provided the metaphors of choice for those puzzling over questions of cosmic concern. From the ancient Pythagorean “music of the spheres” to the “harmonies of nature” that have guided inquiry through the ages, we have collectively sought the song of nature in the gentle wanderings of celestial bodies and the riotous fulminations of subatomic particles. With the discovery of superstring theory, musical metaphors take on a startling reality, for the theory suggests that the microscopic landscape is suffused with tiny strings whose vibrational patterns orchestrate the evolution of the cosmos. The winds of change, according to superstring theory, gust through an aeolian universe. (p. 135)

Others have followed Greene’s lead. If you go on Google and search for “superstring,” or “superstrings,” the first entry will correspond to The Official Superstring Theory Web Site. As determined by the way Google’s search engine works, this is the website that most people link to, and, as the statistics show, the one that most people see when they look for superstrings on the Internet. On this website you will read:
Pythagoras could be called the first known string theorist. Pythagoras, an excellent lyre player, figured out the first known string physics – the harmonic relationship. Pythagoras realized that vibrating Lyre strings of equal tensions but different lengths would produce harmonious notes (i.e. middle C and high C) if the ratio of the lengths of the two strings were a whole number.[source] (Boldface in the original.)

To put it another way, according to Pythagoras and modern string theorists, the entire complexity of the universe can be understood as harmonious music.

Before discussing why I think string theorists have made resort to the musical analogy, and, especially, to the metaphor of the violin and the piano strings, there is an important point I would like to mention here. To begin with, it will be useful to compare two interviews given by Witten: the one at the beginning of this section, given in 1988, and that quoted at the opening of this essay, from 2003. In both interviews there is a common idea: the vibrations of the fundamental superstrings are pretty much like the vibrations of the violin string; moreover, they can produce the totality of all the possible “notes” of their respective domains. More than twenty years ago he said: “In the case of the violin string, the different harmonics correspond to different sounds. In the case of a superstring, the different harmonics correspond to different elementary particles. The electron, the graviton, the photon, the neutrino and all the others, are different harmonics of a fundamental string just as the different overtones of a violin string are different harmonics of one string.” (Interview 1988.) And, more recently: “So in the case of one of these strings it can oscillate in many different forms — analogously to the overtones of a piano string. And those different forms of vibration are interpreted as different elementary particles: quarks, electrons, photons. All are different forms of vibration of the same basic string.” However, there is a piece of the argument that is missing in the first interview; the part when he says that “one of the basic things about a string is that it can vibrate in many different shapes or forms, which gives music its beauty,” or “the higher overtones that you get from a piano or violin that give music its richness and beauty.” Indeed, this mystical argument (there is no better word to describe it!) is new. As I will show in the next essay, the idea that superstrings are not simply like the strings of an instrument, but what comes out is also as beautiful as music, originated in the late nineties; and gained wide acceptance only after Greene’s book. Previous to those years, Witten’s declaration quoted at the opening of this essay would have been unimaginable.

Let us return to the main question this essay tries to elucidate: why have string theorists chosen a violin string? If we rely on Kuhn’s suggestion that this is due to the fact that music was once a member of the mathematical science, as taught in the quadrivium, there is no way to explain this association. In European countries music ceased to be part of the mathematical sciences long before the violin became an important instrument (in the Baroque period). Furthermore, when institutionalized theoretical physics was established as we know it today, music was certainly not part of the standard instruction given to those eager to pursue a career in the natural sciences. The correct answer is to be sought elsewhere.

An appealing explanation draws on the idea that the violin is the instrument people usually associate with Einstein. I think of this hypothesis as follows: since string theorists are presented reiteratively as Einstein’s successors, then, it is natural that they want to be seen “playing the same music.”

3. Violin and string vibrations; in a popular explanation of the pre-Big Bang era.

As a revealing example of this common association linking string theory, Einstein and music, notice the punchy title of an article which appeared on the 3 January 2000 special edition of Time magazine: “Einstein’s Unfinished Symphony.” The subtitle in turn reads “Strings may do what Einstein finally failed to do: tie together the two great irreconcilable ideas of 20th century physics.”[source]

Since April 2005, Brian Foster, a particle physicist from Oxford University, has been delivering talks worldwide on Einstein’s love of music. What is more interesting is that the lectures are accompanied by Einstein’s favourite violin pieces; moreover, the title of the lecture is striking: “Superstrings.” The lecture is presented as follows:
Superstrings is a lecture that celebrates Einstein Year by linking Einstein’s favourite instrument, the violin, with many of the concepts of modern physics that he did so much to found. The performance begins with an introduction to Einstein’s life and involvement with music and how his ideas have shaped our concepts of space, time and the evolution of the Universe. These slides are accompanied by selections from J.S. Bach’s Sonatas and Partitas for Solo Violin, some of Einstein’s favourite music, plus other works from the pinnacle of the solo violin repertoire.[source]

In none of these cases is it stated explicitly that string theorists have resorted to this association in order to put forward their own musical analogy, nonetheless, as the mere existence of these examples shows, the thesis is not a wild idea. However, I think that the connection between superstrings and music is stronger than this.

It is commonly believed that early twentieth-century theoretical physics, at least in its main breakthroughs, sometimes dubbed The Golden Age of Physics, took place in Germany. Many of the physicists who formulated the theory of relativity were German: Einstein, Minkowski, Hilbert and Schwarzschild, to name but a few. And in quantum physics there was Planck, Einstein, Heisenberg and Born, who were also German. This association between the two main revolutions of twentieth-century physics and Germany is almost unavoidable. In the context of superstring theory, which is currently presented alongside long accounts on relativity and quantum physics, the connection is practically impossible to miss. Furthermore, most of the time a reference to these German physicists is explicit: Einstein’s theory of relativity, Minkowski’s geometry, Hilbert’s action, Schwarzschild’s radius, Planck’s scale, Heisenberg’s uncertainty principle, Pauli’s exclusion principle, Schrödinger’s equation, and so forth. (Although the last two physicists were Austrian rather than German, for the purposes of my explanation what is important is that their names sound German. The recognition given to the physics done in early twentieth-century Germany in fact usually extends to Austrian physicists as well.) Now, if the discussion on string theory (the theory uniting general relativity and quantum mechanics!), as currently presented in popular literature, also makes use of musical analogies, it is natural for the reader to assume that this music was that which was played by these great physicists, that is, classical music. The writer guides his audience towards this mental association, and then strengthens it using the violin metaphor. In this way, the reader follows the same thought process as the writer did beforehand most probably unconsciously. The idea conveyed by these kinds of discourses is that string theorists are following the path of the founding fathers of theoretical physics; the audience feels that they are in the presence of something truly fundamental: ultimate knowledge of the true beauty and harmony of nature. What is more, it has been shown that “serious” and “spiritual” music is still widely associated with Germany today. In an edited volume on the role of music in German national identity, the editors, Celia Applegate and Pamela Potter, open with a strong declaration:
For music audience today, the words “German” and “music” merge so easily into a single concept that their connection is hardly ever questioned. The catechism of the three B’s – Bach, Beethoven, and Brahms – reinforces the notion of German leadership in musical developments of the past three hundred years. Even a cursory glance at the repertoires of concert halls throughout the world reveals a preponderance of works from the German-Austrian masters of the eighteenth, nineteenth, and twentieth centuries. These works form the largest share of what we call “classical” or “serious” music, and sustain not only much of concert life but also the classical music recording industry and tourism.[source]

Then, the association we have between Germany and classical music is widespread and strong. This has certainly strengthened the string theory musical metaphor.

Finally, we have seen that physics, in particular astronomy, has been frequently associated in popular accounts to the harmony of the universe and its beautiful music, ever since Pythagoras. In a note that follows the previous quotation by Applegate and Potter, it is stated: “German music achieved the ultimate in universality when NASA’s Voyagers 1 and 2 headed out into space in 1977, each carrying an aluminium-encased, gold-plated phonograph record with generous portions of Bach, Mozart, and Beethoven among its musical offerings from earth to listeners unknown.”[source] On the website of Voyager, the first record on the list Music from Earth is the first movement of Bach’s Brandenburg Concerto No. 2 in F.[source] And Applegate and Potter also point to the person “largely responsible” for this undertaking: Carl Sagan. Carl Sagan, author of Cosmos and originator of the popular science boom that gave rise to the worldwide success of Greene’s The Elegant Universe.

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