Spinning the Superweb: Essays on the History of Superstring Theory

Spinning the Superweb (May - December 2009)

2009-08-31T07:39:00.000-07:00

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Spinning the Superweb: Essays on the History of Superstring Theory has come to its end. Many thanks for reading the essays, sending comments to me, and taking part in the polls. You can continue reading this website for free, there are almost two hundred pages online. However, no more essays will be published. Any updates will be posted on Twitter: http://twitter.com/SpinningSUWEB. If you have any comments, please do not hesitate to contact me: spinningthesuperweb [at] gmail.com. Remember that all essays are copyrighted material. © Copyright 2006-2011 by Oswaldo Zapata M.

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The first blog entirely devoted to the history of physics.

Anecdotes, philosophical issues, great discoveries, and much more from first-hand participants.
A blog for lovers of the history of physics.

Abstract: In essay 1, “On Facts in Superstring Theory,” I described part of the process by which I think the AdS/CFT correspondence became widely thought of as a scientific fact. I devoted special attention to the discourses sustaining that idea and stated that a strict differentiation among participants was needed in order to understand the function of such discourses: experts/non-experts; members/non-members; insiders/outsiders. The strongest claim put forward was that discourses around the conjecture moved freely from the “in” to the “out,” and from the “out” to the “in,” given rise eventually to the fact. In this essay, instead, I focus more on persons rather than on discourses. The idea is to highlight the collective nature of the process leading to a string theory fact. This will be illustrated by considering the participation of some individuals whose contributions to the acceptance of a scientific fact are currently discarded as irrelevant. The final aim, then, is to show that the boundary between the “in” and the “out” so far assumed is quite artificial. It is the huge network of coordinate activities involving social and ideational links between the “in” and the “out” what in the end determines what string theory is. This approach to the history of string theory defines what I have been calling the “Superweb.”

Abstract: In essay 1, “On Facts in Superstring Theory,” I described part of the process by which I think the AdS/CFT correspondence became widely thought of as a scientific fact. I devoted special attention to the discourses sustaining that idea and stated that a strict differentiation among participants was needed in order to understand the function of such discourses: experts/non-experts; members/non-members; insiders/outsiders. The strongest claim put forward was that discourses around the conjecture moved freely from the “in” to the “out,” and from the “out” to the “in,” given rise eventually to the fact. In this essay, instead, I focus more on persons rather than on discourses. The idea is to highlight the collective nature of the process leading to a string theory fact. This will be illustrated by considering the participation of some individuals whose contributions to the acceptance of a scientific fact are currently discarded as irrelevant. The final aim, then, is to show that the boundary between the “in” and the “out” so far assumed is quite artificial. It is the huge network of coordinate activities involving social and ideational links between the “in” and the “out” what in the end determines what string theory is. This approach to the history of string theory defines what I have been calling the “Superweb.”

Abstract: In essay 1, “On Facts in Superstring Theory,” I described part of the process by which I think the AdS/CFT correspondence became widely thought of as a scientific fact. I devoted special attention to the discourses sustaining that idea and stated that a strict differentiation among participants was needed in order to understand the function of such discourses: experts/non-experts; members/non-members; insiders/outsiders. The strongest claim put forward was that discourses around the conjecture moved freely from the “in” to the “out,” and from the “out” to the “in,” given rise eventually to the fact. In this essay, instead, I focus more on persons rather than on discourses. The idea is to highlight the collective nature of the process leading to a string theory fact. This will be illustrated by considering the participation of some individuals whose contributions to the acceptance of a scientific fact are currently discarded as irrelevant. The final aim, then, is to show that the boundary between the “in” and the “out” so far assumed is quite artificial. It is the huge network of coordinate activities involving social and ideational links between the “in” and the “out” what in the end determines what string theory is. This approach to the history of string theory defines what I have been calling the “Superweb.”

Abstract: In essay 1, “On Facts in Superstring Theory,” I described part of the process by which I think the AdS/CFT correspondence became widely thought of as a scientific fact. I devoted special attention to the discourses sustaining that idea and stated that a strict differentiation among participants was needed in order to understand the function of such discourses: experts/non-experts; members/non-members; insiders/outsiders. The strongest claim put forward was that discourses around the conjecture moved freely from the “in” to the “out,” and from the “out” to the “in,” given rise eventually to the fact. In this essay, instead, I focus more on persons rather than on discourses. The idea is to highlight the collective nature of the process leading to a string theory fact. This will be illustrated by considering the participation of some individuals whose contributions to the acceptance of a scientific fact are currently discarded as irrelevant. The final aim, then, is to show that the boundary between the “in” and the “out” so far assumed is quite artificial. It is the huge network of coordinate activities involving social and ideational links between the “in” and the “out” what in the end determines what string theory is. This approach to the history of string theory defines what I have been calling the “Superweb.”

Foreword

2008-12-09T05:50:00.001-08:00

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SELECTED READINGS FOR THE FOREWORD

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String theory was proposed in the late sixties in order to describe the strong interaction taking place in atomic nuclei. After having been discarded by quantum chromodynamics, it reappeared in the early eighties; this time as a quantized theory of gravity and a unified theory of physics. Today, forty years after its initial introduction, superstring theory is one of the most intense areas of research in theoretical high energy physics.

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To illustrate the level of acceptance that the theory enjoys among physicists, consider that in the last fifteen years the third most cited article in high energy physics is a decade old proposal relating superstring theory and particle physics in an intricate way. The proposal of this paper, known as Maldacena’s conjecture or duality, comes just behind the renowned paper of Weinberg and that of Kobayashi and Maskawa, two fundamental components of the standard model of particle physics.[source] Currently this article is not only cited by string theorists but also by many particle physicists and cosmologists. The same can be said about other revolutionary ideas such as the (Antoniadis-) Arkani-Hamed-Dimopoulos-Dvali proposal on large extra dimensions and Randall-Sundrum cosmological models.

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Another sign of its broad approval is the fact that the European Union, in collaboration with other states, from the United States of America to Armenia, is spending several billion euros on a high technology complex (the Large Hadron Collider at the European Centre for Particle Physics, CERN, near Geneva), that is expected, among other things, to reveal two of the fundamental ingredients of superstring theory: supersymmetry and extra dimensions. Everywhere we find evidence that string theory is well thought of among scientists. It is remarkable that David Gross, an influential string theorist and one of the creators of quantum chromodynamics, was awarded the 2004 Nobel Prize for physics, something highly significant if we take into account the influence and authority that a Nobel Prize provides in the world of science.

But the interest in superstring theory goes far beyond the borders of the physics community, involving other actors that in turn inevitably influence its institutional and intellectual evolution. For instance, since the theory involves fundamental research in high energy physics, it allows a large number of physicists to investigate areas with strong military ties such as nuclear physics, without involving them directly in warlike projects. This is one of the reasons why the theory enjoys open political attention and support. In addition to the previous case of the LHC, another example is the string theory group of Teheran. Thanks to generous political and economical support, in a relatively short period of time they have succeeded in creating a solid and respected group. Moreover, researchers in string theory teach courses that directly involve nuclear physics: quantum and statistical mechanics, quantum field theory, particle physics, etc.

Besides the curiosity among non-string theory physicists and political strategists, there is wide evidence that in most Western societies the theory is very popular. Confirmation of this is supplied by the great number of articles appearing regularly in newspapers and popular scientific magazines, as well as best-selling books and TV programmes on the subject. Stephen Hawking, not a string theorist but a strong supporter of a final theory (do not forget that the last chapter of his A Brief History of Time is devoted to string theory), was the first to benefit from the mass media success.

I don’t think anyone, my publishers, my agent, or myself, expected the book to do anything like as well as it did. It was in the London Sunday Times bestseller list for 237 weeks, longer than any other book (apparently, the Bible and Shakespeare aren’t counted). It has been translated into something like forty languages and has sold about one copy for every 750 men, women, and children in the world. As Nathan Myhrvold of Microsoft (a former post-doc of mine) remarked: I have sold more books on physics than Madonna has on sex.[source]

The first true string theorist to become well known for his public explanations of the theory was Michio Kaku:

Kaku, a professor of theoretical physics at the City University of New York, has authored nine books, including Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps and the Tenth Dimension and Visions: How Science Will Revolutionize the 21st Century. He has appeared on countless TV programmes, including Nightline, The Larry King Show and 60 Minutes, as well as in several PBS documentaries. Dr. Kaku has also been featured on networks such as TLC, BBC, TechTV and the SciFi Channel.[source]

More recently, string theorist Brian Greene, author of the best-selling The Elegant Universe, has been acclaimed as ‘‘the most popular science writer alive.’’

The popularity of his books has resulted in many media appearances, including Charlie Rose, The Colbert Report, The NewsHour with Jim Lehrer, The Century with Peter Jennings, CNN, TIME, Nightline in Primetime, Late Night with Conan O'Brien, and The Late Show with David Letterman.[source]

From these quotations it is clear that string theory is in fact very popular. But why is this?

String theorists and in some sense the interested lay public are sure of what Italian physicist Daniele Amati once said: ‘‘String theory is a 21st-century physics that had fallen by chance into the 20th century.’’[source] This sentence subtlety implies that the theory is a sort of otherworldly creation without any connection to the social and historical context in which the theory has developed. My objective is to report partially on the complex web of factors that have contributed to the constitution and actual strength of superstring theory, undoubtedly one of the most exciting and controversial theories of the twentieth century.

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SELECTED READINGS FOR THE FOREWORD

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My exploration into the history of superstring theory will consist of a set of seven essays. In the first essay I try to decipher how superstring theorists have reached what they widely consider to be conclusive results, or facts. Here I argue that this involves complex sociological processes where insiders as well outsiders, experts and non-experts, have a role to play. The second essay is devoted to elucidating the origin of the musical metaphor frequently employed by string theorists: the violin string. My approach relies on the historical relationship that physics has had with music for more than two millennia, as well as on more recent events. Why superstring theorists believe that their construct is beautiful and how this has influenced the discussion on the possible experimental verification of the theory is the subject of the third essay. In order to clarify this, an overview of the concept of beauty as understood in other theories of twentieth-century physics will be examined. In light of the sociological processes seen in the previous essays, the fourth essay reconsiders creativity in science; I believe string theory to be but one illustrative case. The intention is to show that the development of string theory, like any other human creation, has been a collaborative process in which a great number of people have taken part; and not just experts. The next essay deals with string theory as a hybrid subject, where different subcultures have converged. This dynamic approach shows that string theory, even in its most fundamental claims, cannot be defined once and for all. What string theory is is a permanently mutating question. (Essay 5 was not published in this website.) The sixth essay proposes a very subtle connection between string theory and Western visual culture. This essay suggests a possible way in which our modern visual culture has contributed to the propagation and wide acceptance of string theory. Finally, the last essay considers broader political and social factors that in my opinion have fostered the development and acceptance of superstrings. The context is that of the last two decades of the twentieth century. (Essay 7 was not published in this website.)

Oswaldo Zapata Marín.

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SELECTED READINGS FOR THE FOREWORD

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Go to essay 1 →

1. On Facts in Superstring Theory (I of IV)

2008-05-09T18:01:00.000-07:00

Abstract: Despite the lack of experimental confirmation and of unambiguous theoretical proof, superstring theory has long been considered by many the only consistent quantized theory of gravity and the unique viable framework for the unification of all fundamental forces of nature. In the first part of this essay I explore the type of reasoning used to support such statements. In order to illustrate the argument, in the second part I focus on one of the most acclaimed achievements of the theory: the AdS/CFT correspondence. Finally, I conclude by observing that what constitutes a result in superstring theory involves more than purely theoretical arguments. Specifically, the acceptance of facts in superstring theory is inextricably linked to the large group of people that make it possible, whether they are string practitioners or not.

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SELECTED READINGS FOR ESSAY 1 (I)

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The evolving scientific status of string theory results
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Trying to overcome the impasse with what a massless particle with spin two meant for the dual model of strong nuclear interactions, in 1974 Joël Scherk and John Schwarz proposed a reinterpretation of this particle as the quantum carrier of gravitational force: ‘‘The possibility of describing particles other than hadrons (leptons, photons, gauge bosons, gravitons, etc.) by a dual model is explored. The Virasoro-Shapiro model is studied first, interpreting the massless spin-two state of the model as a graviton.’’[source] In their seminal paper Scherk and Schwarz showed that consistency of the dual model entailed a higher dimensional version of the Hilbert action. From this it then followed that the model included gravitational forces as described by Einstein’s equation. These were the primary motives driving the authors to propose that string theory quantized gravity: the spectrum showed a massless spin-2 particle, and, moreover, a ten-dimensional Einstein equation could be derived. In those days many theoretical physicists found these two results too weak to allege that a quantized theory of gravity had been achieved. This explains the cautious reception the theory received in its early years. Unexpectedly, however, this once feeble proposal has become widely established within theoretical physics, even though the mathematical support has remained almost unchanged for more than thirty years. Let us comment further on this.
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In the last chapter of a classic string theory graduate textbook written in 1989, here is how the quantization of gravity is presented:

String theory is claimed to be a unifying framework for the description of all particles and their interactions, including gravity. However, up to now our exposition of the subject was rather formal and it is not at all transparent how it can be relevant for low energy phenomenology. The only hint we got so far was from looking at the spectrum. There especially the occurrence of a spin two tensor particle indicated that gravity might be contained in string theory.[source]

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Note that this observation is relegated to the last part of the book, after some three hundred pages of mathematical details. No doubt this is a queer situation. Why leave the most important argument in favour of the theory, at least in popular accounts and undergraduate level materials, to the final pages of the textbook? The answer to this question is provided by the cautious words of the authors. Even more surprising is that the same argument has been used for decades. The only difference is that nowadays the quantization of gravity is not considered an ‘‘elusive task,’’ as many string theoreticians used to say, but rather an accomplished one. For example, in the midst of what string theorists consider the second major revolution of the field, Edward Witten wrote in Physics Today: ‘‘Moreover, these theories have (or this one theory has) the remarkable property of predicting gravity ― that is, of requiring the existence of a massless spin-2 particle whose coupling at long distances are those of general relativity.’’ [source] (Italics in the original.) And in an up to date textbook, aimed at undergraduate physics students, the author says: ‘‘The striking quantum emergence of gravitation in string theory has the full flavor of a prediction.’’ [source] Understandably, declarations of this kind have given rise to hot discussions among supporters and detractors of the theory. The question is: what happened in those intervening years? Why are string theorists so optimistic now? Did they really find an unquestionable proof, experimental or theoretical, that their theory quantizes gravity?
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In point of fact, to this day nobody has presented an entirely convincing proof of this. For some theoretical physicists, the presence of a massless spin-2 particle in its spectrum is not enough to a quantized theory of gravity. I is also argued that the low energy limit analysis of superstring theory does not imply that that particle is the graviton. The former string theorist Daniel Friedan, one of the early major contributors, is emphatic about this:

In particular, there is no justification for the claim that string theory explains or predicts gravity. String theory gives perturbative scattering amplitudes of gravitons. Gravitons have never been observed. Gravity in the real world is accurately described by general relativity, which is a classical field theory. There is no derivation of general relativity from string theory. … String theory does not produce any mechanical theory of gravity, much less a quantum mechanical theory.[source]

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Why then do practitioners believe that ‘‘string theory is a quantum theory, and, because it includes gravitation, it is a quantum theory of gravity’’? How have string theorists arrived at the conclusion that ‘‘the harmonious union of general relativity and quantum mechanics is a major success’’[source] of superstrings? Moreover, how have they managed to convince other theoreticians of the validity of their explanations? Let us look at another example.

In the abovementioned paper, Scherk and Schwarz also declared that string theory could unify all the fundamental interactions: ‘‘If it is, a scheme of this sort might provide a unified theory of weak, electromagnetic, and gravitational interactions.’’[source] (These known interactions were then complemented with the strong nuclear force, the latter successfully described by quantum chromodynamics.) This was in 1974. Years later, and after intense work, the proposal had still not been proved. The four-dimensional standard model (it exludes gravity), with all its details, could not be deduced from string theory. In a lecture given at the International Centre for Theoretical Physics (ICTP) in 1986, one of the leading string phenomenologists of the time stated: ‘‘Being defined in d=10, some compactification of the six dimensions would be required to make contact with phenomenology. This process is at the moment not understood at all; one has to make crude approximations and then check for consistency a posteriori.’’ [source] The reason why the process of superstring compactification ‘‘was not understood at all’’ is due to the stringent constrains that supersymmetry imposes on the four dimensional model. As expected from the standard model of particle physics, any physical result with supersymmetry must be renormalizable and requires the existence of chiral spinors . However, there are some difficulties with this: firstly, supergravity with one supersymmetry is not renormalizable, and, secondly, models with higher numbers of supersymmetries do not include chiral spinors. Satisfying these two conditions is the difficult mission assigned to string phenomenologists. There are several approaches to the problem: the simplest model considers compactification on a multi-dimensional torus, other string theorists prefer to use constructs known as orbifolds or orientifolds; more recently G2 manifolds were tested. Other Calabi-Yau manifolds are currently under examination. Despite this confusing situation, there is one thing string theorists know they must answer: ‘‘Why do we live on this particular string vacuum or SSC [superstring compactification]?’’[source] This is the most urgent question that needs to be addressed in order to make contact with physical reality. As Michio Kaku writes in the introduction to the 2000 edition of his textbook on elementary string theory: ‘‘The search for the true vacuum of string theory is therefore the central theme of this book.’’[source] So, if we could explain why the universe chose this particular vacuum we would be able to understand how the standard model arises from superstring theory and why the universe expands as it does. It has been argued by critics that this reformulation of the problem does not solve it. On the contrary, it makes it harder and moves it, dangerously, towards the realm of theology.

In this case, as in the previous case of the quantization of gravity, superstring theorists have been unable to offer an accurate and comprehensive explanation of four-dimensional physics. To be sure, string phenomenology, from the old heterotic string to recent brane models, does not provide the correct value for the quantities associated to the elementary particles known so far. In addition to this, critics emphasize, it does not answer crucial questions that intrigue particle physicists: how is the electroweak symmetry broken? what fixes the masses of the Higgs boson, quarks, neutrinos and charged leptons? what are the sources of the cold dark matter? what produced the big bang? why is there matter-antimatter asymmetry? This state of affairs has lead Sheldom Glashow, an eminent particle physicist, to declare that string theory ‘‘has failed in its primary goal, which is to incorporate what we already know into a consistent theory that explains gravity as well. The new theory must incorporate the old theory and say something more. String theory has not succeeded in this fashion.’’[source]

From the previous examples we have learnt some important things about the development of string theory. Firstly, as research progresses in a given topic, an explicit reference to the unsolved problem tends to disappear from the literature. For instance, we saw how the quantization of gravity is considered by string theorists to be an accomplished task that does not deserve further study, or even a mention. Secondly, while research advances, the initial problem changes in such a way that it becomes increasingly difficult to unravel the convoluted relationship connecting the final problem to the original one. This was illustrated by our second example concerning string theory and the unification of the forces. Originally the idea was to extract the standard model from superstring theory, an investigation encouraged during the second half of the eighties by the promising results obtained from the heterotic string. Then, by the mid-nineties, the goal was to determine the unique vacuum of the mother of all the theories, the M-Theory. And, more recently, the focus was on the right ‘‘environment’’ of the anthropic solution. Things have changed, but the fundamental query remains unsolved: how do we get the standard model from string theory? With these examples we have learnt something else: this occurs while an ‘‘outward’’ discourse (from the ‘‘inside’’ to the ‘‘outside’’ of the professional community) proclaims that the theory has solved such problems. Indeed, in this movement disadvantages have been transmuted into virtues.

In spite of these fundamental flaws in the theory, enthusiasts proclaim that ‘‘in string theory all forces are truly unified in a deep and significant way,’’ or, a bit more prudently, ‘‘string theory leads in a remarkably simple way to a reasonable rough draft of particle physics unified with gravity.’’[source] The final outcome of this discourse is the same: the stabilization of string theory as a quantized theory of gravity and unified model. Before concluding this introduction, I would like to add two more quotations. In Zwiebach’s undergraduate textbook he asks:

Why is string theory truly a unified theory? The reason is simple and goes to the heart of the theory. In string theory, each particle is identified as a particular vibrational mode of an elementary microscopic string.[source]

Thus, string theory is a unified theory thanks to its extreme reductionist approach. Brian Greene, in his best-selling book, backs up this statement. Years of hard work have shown that the reductionist approach to string theory is correct.

These works showed conclusively that numerous features of the standard model ― features that had been painstakingly discovered over the course of decades of research ― emerged naturally and simply from the grand structure of string theory.[source]

I think what we have seen in these examples is a characteristic of string theory research and its elaboration of physical reality. At first, a hypothesis is made, explaining openly its significance as well as its difficulties. At this stage no one is sure of the real value of the conjecture, however, it is interesting enough to drive a significant part of the physics community to devote itself to its development. Step by step ‘‘evidence’’ accumulates and after a while the string theory fact emerges. String theorists have created in this way their own nature: a supersymmetric world, a big bang with all the fundamental forces combined, a multi-dimensional universe, and so forth. Although I have provided support to this thesis in the case of the two sanctioned ‘‘achievements’’ of superstring theory, quantization of gravity and unification of the fundamental forces, I will now illustrate in full detail this complex process with another ground-breaking proposal: the AdS/CFT correspondence.

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SELECTED READINGS FOR ESSAY 1 (I)

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Continue reading →

1. On Facts in Superstring Theory (II of IV)

2008-05-09T17:00:00.000-07:00

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SELECTED READINGS FOR ESSAY 1 (II)

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A case study: the AdS/CFT correspondence
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At the end of 1997, Juan Maldacena, at that time a young researcher at Harvard University, proposed what some physicists consider to be one of the main breakthroughs in the history of string theory and even of theoretical physics. Approaching the physics of black holes with the powerful mathematical tools of superstring theory, he conjectured the existence of a deep relationship between pure non-gravitational theories and superstring theories. [source] Even though the proposal was not well understood by everybody, it was welcomed and enjoyed rapid acceptance within the community.

This subject has developed with breathtaking speed: Maldacena’s paper appeared in November 1997, yet by the Strings 98 conference seven months later, more than half the invited speakers chose to speak on this subject.[source]

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Today, Maldacena’s publication is one of the most well-known papers ever written in theoretical high energy physics.
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The first papers submitted to the electronic preprint library citing Maldacena’s conjecture did not delve deeply into the original proposal; they simply mentioned it in a superficial way. In these papers we find the following assertions: ‘‘It would be interesting to understand the relation between our arguments and those of [reference to Maldacena’s paper],’’ and ‘‘Maybe an argument along the lines of [reference to Maldacena’s paper] can be carried out here as well.’’ Things changed dramatically when Edward Witten published a paper formalizing many of the original ideas put forward by Maldacena. He discovered a precise correspondence (here the term “correspondence” is used for the first time) between string states on the ten-dimensional spacetime, dubbed the bulk, and operators of the particle physics-like model. He also computed some scattering processes. To this end Witten identified the boundary of the ten-dimensional bulk with the space where the non-gravitational particles reside and interact. After this essential contribution, more and more people started to work on this correspondence.
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Here is how Witten referred to Maldacena’s proposal (first lines of the abstract):

Recently, it has been proposed by Maldacena that large N limits of certain conformal field theories in d dimensions can be described in terms of supergravity (and string theory) on the product of d + 1-dimensional AdS space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity.[source] (Italics added.)

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Note Witten’s prudence when referring to it: “It has been proposed.” A year and a half later Maldacena’s “conjecture” was still a conjecture, that is, nothing exceptional demanded that its scientific status should be upgraded. This was the state of affairs in 1999 when a group of leading string theorists, including Maldacena himself, published a review article on the subject. This report comprises more than two hundred and fifty pages and is still considered one of the most complete accounts on the subject.

So, we conclude that N=4 U(N) Yang-Mills theory could be the same as ten dimensional superstring theory on AdS5 × S5 [reference to Maldacena’s paper]. Here we have presented a very heuristic argument for this equivalence; later we will be more precise and give more evidence for this correspondence.[source] (Italics added.)

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In the authors’ opinion the correspondence was still in the phase of gathering evidence. It was not yet established as scientific fact. At this point it is worth digressing a moment in order to say a few words about the physics of the correspondence. This will help us to understand its successive evolution towards a higher degree of truthfulness.
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AdS/CFT in its strongest version states that superstring theory in the bulk corresponds to a full quantum non-gravitational theory on the boundary of such volume. But, so far support for it has been provided only in the supergravity approximation: the point-like model where the length of the string is equal to zero (α′ → 0). In addition, since these computations are also very difficult to carry out, the classical limit is necessary. In this last approximation quantum corrections are discarded (only tree diagrams are considered). The theory is said to be weakly coupled. Figure 1 illustrates this process: from strong to weak coupling.

1. String theory perturbative expansion, supergravity limit, and classical limit.

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The consistency of the theory relies on every operation being done on the gravitational theory having a counterpart on the boundary. (Due to this relationship between what happens in the bulk and on its boundary, the correspondence has been called holographic.) Thus, the supergravity and classical limits must have their corresponding procedure in the boundary theory. Experts have found that this relationship is of the type weak ↔ strong. In short, this means that the easier the computations in the gravitational theory, as in the limits above, the harder it is to find the corresponding non-gravitational results on the conformal field theory side. In turn, when the string calculations are difficult, the boundary computations are easier to perform. This explains why the AdS/CFT correspondence is also often called ‘‘AdS/CFT duality.’’
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After these brief observations, we are now ready to evaluate the following extract from MAGOO (as the report by Maldacena and collaborators is sometimes labelled):

One might wonder why the above argument was not a proof rather than a conjecture. It is not a proof because we did not treat the string theory non-perturbatively (not even non-perturbatively in α′). We could also consider different forms of the conjecture. In its weakest form the gravity description would be valid for large gsN [supergravity description with no quantum corrections as explained above], but the full string theory on AdS might not agree with the field theory. A not so weak form would say that the conjecture is valid even for finite gsN, but only in the N → ∞ limit (so that the α′ corrections would agree with the field theory, but the gs corrections may not). The strong form of the conjecture, which is the most interesting one and which we will assume here, is that the two theories are exactly the same for all values of gs and N.[source] (Italics added.)

This passage from MAGOO suggests that in those days many string theorists were not fully convinced of the validity of the correspondence; although something like 1500 papers had already been published on the subject (MAGOO includes 757 references in its bibliography). Despite such wide interest and some important contributions to theoretical physics, the general opinion was that the correspondence was in the process of being proved. In their ‘‘Summary and Discussion’’ the authors concluded saying:

To summarize, the past 18 months have seen much progress in our understanding of string/M theory compactifications on AdS and related spaces, and in our understanding of large N field theories. However, the correspondence is still far from realizing the hopes that it initially raised, and much work still remains to be done.[source] (Italics added.)

So, by May 1999 string theory experts were convinced that the ‘‘simple and powerful observation’’[source] made by Maldacena was in its infancy. At the same time, an optimistic vision was transmitted to young researchers by means of courses and written materials. In a widely used introductory review written by Jens Petersen, which appeared three months earlier than MAGOO, we read:

The Maldacena conjecture [reference to Maldacena’s paper] is a conjecture concerning string theory or M theory on certain backgrounds of the form AdSd × MD-d. … The conjecture asserts that the quantum string- or M-theory on this background is mathematically equivalent — or dual as the word goes — to an ordinary but conformally invariant quantum field theory in a space-time of dimension d-1, which in fact has the interpretation of “the boundary” of AdSd.[source] (Italics in the original.)

Similarly, in the written translation of a couple of lectures delivered during the spring of 1998 at The Abdus Salam International Centre for Theoretical Physics, two leading theoretical physicists wrote: ‘‘Assuming this conjecture, one can derive results for the large ’t Hooft coupling limit of gauge theory, by doing computations in AdS supergravity.’’[source] And concluded, in the last lines, by saying: ‘‘Nevertheless, now that we have a precise and better motivated conjecture for the appropriate string in this case, we can hope that progress along these lines will be made in the near future.’’ Analysis of written publications at that time shows that the veracity of the holographic correspondence was understood by string theoreticians more as a hope rather than as a completed task.

The lines of development for the following three years, from May 1999 to February 2002, were foreseen, and in a certain sense dictated, by Maldacena and collaborators: in chapter 5 they summarized the main results of BTZ black holes and showed how this was related to the boundary theory; in chapter 6, the final one, they focused on QCD-like theories.

Thanks to the great amount of available results on the physics of three-dimensional black holes and a manageable two-dimensional conformal field theory, the AdS3/CFT2 model was for many years the favourite setting for analyzing the correspondence beyond the supergravity limit.

In this paper we study the spectrum of critical bosonic string theory on AdS3 × M with NS-NS backgrounds, where M is a compact space. Understanding string theory on AdS3 is interesting from the point of view of the AdS/CFT correspondence since it enables us to study the correspondence beyond the gravity approximation.[source]

Juan Maldacena and Hirosi Ooguri continued working on this framework for some time, arriving at several remarkable results. Unfortunately, the correspondence was not demonstrated beyond the supergravity approximation as first expected. The other main line of research within AdS/CFT was the construction and description of viable QCD-like theories by means of weak gravitational processes.

A fruitful extension of the basic AdS/CFT correspondence [reference to Maldacena] stems from studying branes at conical singularities [references]. Consider, for instance, a stack of D3-branes placed at the apex of a Ricci-flat 6-d cone Y6 whose base is a 5-d Einstein manifold X5.[source]

Even though the two approaches were different, both were trying to provide evidence for the stronger versions of the correspondence. The AdS3/CFT2 effort wanted to prove the exact correspondence in a special case (classical limit with α′ ≠ 0), and the AdS/QCD attempt tried to find plausible phenomenological results. However, by the end of 2001, after four years of intense work and more than two thousand citations to Maldacena’s original paper, the correspondence was still waiting for a definitive proof.

The Berenstein-Maldacena-Nastase (BMN) conjecture was proposed in February 2002 and it rapidly seized the attention of string theorists working on AdS/CFT. This fervent interest on BMN was reflected by the large number of publications that followed. In the month the paper appeared, a fifth of the publications on AdS/CFT was on BMN or at least mentioned it in the main text. The following month, articles on BMN grabbed half the attention of the research on AdS/CFT. A few months later, up four fifths (June and September 2002) of the citations to Maldacena’s 1997 proposal came from the novel BMN conjecture. This rough count clearly shows that the new conjecture was an essential breakthrough within the field. Moreover, as we will see next, it represented the end of a period and the beginning of a new one. After BMN, the truthfulness of the AdS/CFT correspondence changed: it was nearing a scientific fact.

In this new conjecture Maldacena and collaborators envisaged an alternative setting to verify the correctness of the AdS/CFT correspondence beyond the supergravity limit. The idea was to concentrate on a very special case of the original formulation and see how the standard correspondence between string states and operators matched within this new framework. On the bulk side of the correspondence the spacetime background was changed to parallel plane waves. The new condition, pp-waves, was obtained by taking the Penrose limit of the anti-de Sitter space. In the conformal field theory this corresponded to a truncation of the number of operators. It was believed that this new model could shed light on the full quantum correspondence.

It is interesting to see how Berenstein, Maldacena and Nastase referred to the AdS/CFT correspondence, the basis of their new proposal:

The fact that large N gauge theories have a string theory description was believed for a long time. These strings live in more than four dimensions. One of the surprising aspects of AdS/CFT correspondence is the fact that for N = 4 super Yang Mills these strings move in ten dimensions and are the usual string of type IIB string theory.[source] (Italics added.)

These are the first lines of the paper. Such a presentation suggests that the relationship between gravity and particle physics is a matter of ‘‘fact.’’ They take it for granted. Obviously, there is something paradoxical in all this: what is expected to be proven is at the same time considered true knowledge. But, was this an isolated judgement or rather a belief shared by other string theorists?

Two months after the BMN proposal, Steven Gubser, Igor Klebanov and Alexander Polyakov, collaborating then at Princeton, submitted a paper where it is said:

It was found in [reference to Maldacena, Witten, and a previous article by GKP], developing some earlier findings of [reference to Polyakov], that the desired string theory in this case lives in the space AdS5 × S5 and that there is a unique prescription relating physical quantities in the string and gauge pictures. Many more complicated examples have been analyzed since then, confirming the existence of a dual string picture for various gauge theories.[source] (Italics added.)

Though the authors confess in the next lines that the correspondence has only been ‘‘tested’’ ‘‘mostly in the supergravity limit,’’ as BMN they also presuppose the full validity of the correspondence. Notice the use of the terms ‘‘it was found’’ and ‘‘confirming the existence.’’ The same predisposition is shown in another important paper written by a group of researchers from MIT and Harvard:

More recently the Maldacena conjecture has established a duality between a conformal gauge theory (with a fixed line of couplings) and string theories on an AdS background. However these dualities are well understood only at large values of the gauge coupling [supergravity limit in the bulk].[source] (Italics added.)

A widespread trait among publications following the BMN proposal is that the few lines making explicit reference to the AdS/CFT correspondence are often in the abstract or in the first paragraphs. For instance, the well known article by Joseph Minahan and Konstantin Zarembo begins with a very short discussion on AdS/CFT results and limitations. After the six-line review of AdS/CFT, they move on to the main subject of the paper: BMN.[source] The function of this brief reference to AdS/CFT in the opening to the paper is simply to contextualize the article; a context that everybody must be familiar with, and accept, in order to proceed further. Post-BMN doctoral dissertations show a similar pattern: the correspondence is assumed and chapters once intended to explain it are systematically dropped. A short section or even several citations now replaced the detailed summary. Another confirmation that the correspondence was entering a new state regarding its factuality is that some authors did not even consider relevant the citation of Maldacena’s original paper. From the eight most important papers on AdS/CFT published after BMN, only four of them cited it.

What followed in the next years was a confirmation of the previous analysis. As a sample, let us consider the nine most cited articles on AdS/CFT during that period. Three of the papers deal with phenomenological issues and concentrate on the implications of the AdS/QCD duality; that is, the possibility of using the holographic correspondence to obtain precious information on strongly coupled particle physics processes. As stated in one of these papers: ‘‘Recently, the gravity/gauge, or anti-de Sitter/conformal field theory (AdS/CFT) correspondence [reference to Maldacena] has revived the hope that QCD can be reformulated as a solvable string theory.’’[source] Another three articles focus on a different spacetime background for the correspondence, the Lunin-Maldacena background. This include one written by Oleg Lunin and Juan Maldacena. The other two are by Sergey Frolov and collaborators: ‘‘A relative simplicity of the Lunin-Maldacena supergravity background and the N=1 superconformal theory makes the conjectured duality a new promising arena for studying the AdS/CFT correspondence.’’[source] In contrast to the articles on AdS/QCD, these last three are not phenomenologically motivated; rather they try to prove the correspondence beyond a constraining condition called the BPS limit. It is interesting to notice that Lunin and Maldacena called the new proposal ‘‘conjecture duality,’’ while the original AdS/CFT proposal is simply called ‘‘correspondence.’’ This subtlety differentiation suggests that the latter is in a higher, better consolidated, factual level. Another of the nine papers on AdS/CFT concerns integrable models, a subject seeking a solution to superstring theory on non-trivial backgrounds with RR-fluxes. There are two more papers. One proposes a sort of AdS/CFT correspondence for Sasaki-Einstein backgrounds, and the other is about flux compactifications. Strictly speaking, the last article is not about the correspondence; it simply acknowledges the important contribution of the latter to the renewal of the studies on flux compactifications. And it does it in a single line.

Here concludes our short story of the AdS/CFT correspondence. In it we saw how string theorists treated the conjecture when it was proposed for the first time; how they changed their view in the course of time; and how they communicated it to younger members of the community. We discovered that the AdS/CFT conjecture became a fact at the same time as most of the talks and papers changed the ‘‘recently Maldacena conjectured that …’’ to ‘‘as the AdS/CFT correspondence teaches us …’’ and, finally, to the more impersonal ‘‘as the AdS/CFT establishes.’’ We saw how the sentence ‘‘Maldacena has recently conjectured that …’’ transformed into a single number that pointed to the original paper. Nonetheless this was not imposed, as some interpreters would be incline to declare, by a ‘‘great leader,’’ nor by the ‘‘will of power’’ of an authoritarian group of researchers, nor by mere convention. Instead, it is the end result of several years of long, hard, and exhausting work. I have sustained that the breaking point was the new ‘‘bold’’ conjecture of BMN, a hypothesis that assumed implicitly the correctness of the old AdS/CFT correspondence. After years spent accumulating “evidence,” but without a definitive proof in sight, there was the desire and need within the community to surmount the old correspondence. The research could safely continue only by protecting Maldacena’s conjecture from profanation, namely, elevating it to the factual level of the more authentic mathematical demonstrations. In another context, the historian of science Steven Shapin wrote: ‘‘It was necessary to speak confidently of matters of fact because, as the foundations of proper philosophy, they required protection. And it was proper to speak confidently of matters of fact, because they were not of one’s own making; they were, in the empiricist model, discovered rather than invented.’’[source] To shield the correspondence from attacks was a necessity for the whole community of practitioners. Consequently, more and more discussions on the correspondence were transferred from research papers and PhD theses to graduate and even undergraduate courses. This was the final step towards its final entrance into public lectures and popular science books. Today, the AdS/CFT correspondence pervades the public debate on superstring theory.
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1. On Facts in Superstring Theory (III of IV)

2008-05-09T16:00:00.000-07:00

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Ideas, persons, and reality
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Up to now an utterly convincing proof of the validity of string theory is still missing. What is more, even rigorous proofs of the subsidiary hypotheses are scarce. As we have seen in the previous sections, a fact in string theory is based on a large number of elements supporting it. Concerning the elusive M-theory, that construct which by the turn of the century was thought to be the final theory of physics, Michael Duff wrote in Scientific American: ‘‘New evidence in favor of this theory is appearing daily, representing the most exciting development since strings first swept onto the scene.’’[source] In Zwiebach’s undergraduate textbook which we have already quoted, it is asked: ‘‘Are we sure string theory is a good quantum theory of gravity? There is no complete certainty yet, but the evidence is very good.’’ And in an introductory review article on Maldacena’s conjecture it is stated: ‘‘We describe the initial conjecture, the development of evidence that it is correct, and some further applications.’’[source] For a mathematical model such as string theory, the word “evidence” in these statements seems to have an unusual and peculiar meaning.
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It is a common trait among all theories within the natural sciences not to be fully verifiable; only partial results can be invoked. However, the problem with superstring theory is that it is not an empirically testable model; thus, mathematical demonstrations ought to be extremely scrupulous. Due to these limitations, many members of the physics community offer strong resistance to string theorists’ claims. From both fronts, experimental and theoretical, detractors consider that string theory procedures do not follow standard scientific requirements. Nonetheless, string theorists have succeeded in building a representation of the physical world that can be easily distinguished by everyone: a universe full of vibrating tiny superstrings and unseen extra dimensions. Their world is omnipresent in modern discourses of science, from professional conferences dedicated to the future of experimental high energy physics to its mass media coverage. In a sense, they have convinced us of the scientific nature of their reality. But, how did they construct it? Is there enough “evidence” to support their visions? Where does this evidence come from? The AdS/CFT evolution, from a conjecture to a scientific fact, will provide us with some clues.
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The question we must pose is the following: if nobody has been able to show the full quantum regime of the correspondence (at this level even the most elementary evidence is missing) and only classical supergravity results have been presented, why do then string theorists think it is valid? I think the answer to this question is more sociological than technical. And I am not the only one to think so; others have arrived at similar conclusions. However, our approaches are different. One explanation goes like this: since string theorists form a social group with strict modes of being and behaving, members are simply compelled to accept it. In other words, the AdS/CFT relationship is a matter of fact and that’s all; if you do not accept it then you are out! In contrast to this simplistic point of view, others have elaborated more on their thoughts. Lee Smolin, a vehement anti-string theorist, writes in one of his books: ‘‘I will speak of conjectures that were widely believed to be true, in spite of never having been proved. … I will speak of the pressures that young scientists feel to pursue topics sanctioned by the mainstream in order to have a decent career.’’[source] Further in the book he continues: ‘‘String theory now has such a dominant position in the academy that it is practically career suicide for young theoretical physicists not to join the field.’’ The mathematician Peter Woit, one of the most resolute anti-string theorists in the public arena, declares that ‘‘as long as the leadership of the particle theory community refuses to face up to what has happened and continues to train young theorists to work on a failed project, there is little likelihood of new ideas finding fertile ground in which to grow.’’[source] These considerations are in a sense correct. Unfortunately, in my opinion the whole argument is defective. Smolin and Woit, in different ways, try to explain why younger string theorists presume the correctness of the theory: they simply trust senior experts “in order to have a decent career.” However, they do not say why elder members also believe in the validity of the theory. Our initial question about the AdS/CFT correspondence would then be better posed if formulated as follows: why do string theorists, old and young, think the theory is valid? This reformulation of the question incorporates a temporal dimension that will prove essential to understanding the construction of facts in superstring theory. In effect, if Smolin’s description is incomplete it is because it is based on a static view of the string theory community. The idea is to determine how this “mainstream” was created, or, in other words, how the AdS/CFT became a physical fact. At the root of my discussion is the assumption that the real community of string theorists is very dynamic, with a longstanding flow of ideas and people moving constantly across the ‘‘border’’ between the ‘‘inside’’ and the ‘‘outside.’’ This has ultimately created string theory reality. A glimpse into my general approach will help the reader to follow the argument.
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Everybody is aware that theoretical physics is very difficult, and superstring theory is one of the toughest areas. In fact, string theory is so complex that experts are neither able to understand entirely the main developments nor to follow its rapid growth. In general, practitioners feel confident only in a specific subfield. People working on the AdS/CFT correspondence or twistor theory, for example, do not comprehend the whole area, even though they can be extremely competent when tackling the particular problems of the subfield. Because of this, paradoxically, those that have provided the evidence in support of superstrings do not fully grasp it. Many do not understand the AdS/CFT correspondence completely but they believe in it; it is a matter of fact. A fact in string theory is a shared belief that something is unquestionably true. What I will try to show here is that string theorists often base their beliefs on what they have seen proclaimed everywhere. This ubiquitous discourse includes technical seminars and articles, which I will call the in-in discourse, as well as popular speeches and books, the out-in discourse. Furthermore, I will try to convince the reader that string theorists start to internalize the rules of the game long before they become experts; by means of a discourse that embraces the whole society. I will dub this the out-out discourse when the information comes from non-experts, and the in-out discourse when it comes from professional physicists. Let us begin with this in-out discourse.
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The first contact a teenager has, maybe while studying in high school or even much earlier, with superstrings is crucial. The picture they build in their minds derives from their daily experiences, experiences transmitted mainly by mass media (television, magazines, internet, and newspapers) and taught in institutions (school and museums). Brian Greene’s book provides an illustration of the content of such discourse:

Moreover, in Chapter 13 we will see that string theory has recently solved a central puzzle concerning black holes, associated with the so-called Bekenstein-Hawking entropy, that has stubbornly resisted resolution by more conventional means for more than twenty-five years. This success has convinced many that string theory is in the process of giving us our deepest understanding of how the universe works.[source]

In this best-selling book, Greene affirms that string theory has been able to count the internal degrees of freedom of black holes. This comment is not isolated. Many other authors back up and complement this opinion. Stephen Hawking also talks about the connection between the physics of black holes and superstrings. In The Universe in a Nutshell he included a chapter with a suggestive title: ‘‘Brane New Worlds, Do we live on a brane or are we just holograms?’’ As is usual in most popular books on contemporary theoretical physics, this is simply an eccentric way to talk about the AdS/CFT correspondence. And, eight years after Maldacena first proposed the holographic correspondence, he writes confidently:

Physicist Stephen W. Hawking showed in the 1970s that black holes have a temperature and give off radiation, but physicists since then have been deeply puzzled. Temperature is a property of a collection of particles, but what is the collection that defines a black hole? The holographic theory solves this puzzle by showing that a black hole is equivalent to a swarm of interacting particles on the boundary surface of spacetime.[source]

Considering the host of materials devoted to the topic, and not only written but also visual, we realize immediately that the holographic correspondence is presented as ‘‘scientific truth.’’ The future theoretician builds up their representation of the theory, and its achievements and limitations, from these first accounts. Though we must admit that the idea of superstrings as shown on TV programmes and best-selling books is not the same as the theory later taught in universities and research institutes (extra dimensions are there just to cancel the quantum anomaly of the Virasoro algebra; the graviton is the action of ladder operators on the vacuum of the theory; and supersymmetry on the worldsheet is projected in the spacetime by the Gliozzi-Scherk-Olive artifice), there is a common objective in both discourses: to put forward the exactitude of superstrings. Every single partial result is part of the evidence sustaining the ultimate validity of the theory (here it is important not to forget that, as we saw, the most fundamental claims are constantly displaced by new “non-essential” challenges). In this sense, avowals about the accomplishments of the correspondence, whether in the in-out or the in-in discourses, must be understood as implicit declarations of the success of superstring theory: quantization of gravity and unification of all the forces.

Joseph Polchinski’s classic textbook, the first edition of which came out only a few months after Maldacena’s 1997 paper, briefly introduces the correspondence in a section on ‘‘Black hole quantum mechanics’’:

Very recently, a very powerful new duality proposal has emerged. … Now it appears, at least for theories with enough supersymmetry, that one can calculate amplitudes in the gauge theory by using the dual picture, where at low energy supergravity is essentially classical. If this idea is correct, it is a tremendous advance in the understanding of gauge field theories.[source]

His cautious optimism reflected the general mood of the community of experts at that time. Two years after Polchinski’s book, a new edition of Michio Kaku’s introduction to superstrings was published. For this revised edition he wrote a new chapter on black holes and the ‘‘CFT/AdS correspondence.’’[source] Maldacena’s conjecture was elbowing its way towards the highest degree of factuality, and acceptance. Nowadays the correspondence is an essential topic in any course on string theory. Let us illustrate this with some examples. On the back cover of the recent book written by John Schwarz and collaborators, Nima Arkani-Hamed, a leading string phenomenologist, comments: ‘‘This is the first comprehensive textbook on string theory to also offer an up-to-date picture of the most important theoretical developments of the last decade, including the AdS/CFT correspondence and flux compactifications, which have played a crucial role in modern efforts to made contact with experiment.’’[source] The editors of Clifford Johnson’s textbook on D-branes are of the opinion that “they have lead to many striking discoveries, including the precise microphysics underlying the thermodynamics behaviour of certain black holes, and remarkable holographic dualities between large N-gauge theories and gravity.’’[source] In the chapter ‘‘String thermodynamics and black holes,’’ Zwiebach declares:

It should be emphasized that the correspondence has not yet been proven. Rather, it was originally motivated by some heuristic arguments and has since been tested extensively. There are no grounds to suspect that it fails to hold.[source]

… “there are no grounds to suspect that it fails to hold.”

The discussion above suggests that many string theorists have begun their careers with a biased view of the subject. How they conceive the theory during their formative years depends crucially on previous contact with materials intended for the general public and, later on, on the systematic training given by senior members of the community. We have seen how these two stages in the education of future string theorists coincide at one point: they present new subjects as confirmations of the most fundamental claims of the theory. The theory has succeeded in: quantizing gravity and unifying all the fundamental forces of nature. In addition, it explains the thermodynamics of black holes and has also demonstrated a precise gravity/particle physics correspondence. This is what is taught. Even though young string theorists can feel sometimes uncomfortable with the weakness of some arguments, the challenge usually exceeds their skills. Moreover, in such a competitive field there is no time to digress by asking fundamental questions. When finally the young researcher becomes a full member, with many more resources at hand to tackle fundamental issues, it turns out that they are probably working on a specific topic with its own problems. And, not surprisingly, all these investigations assume the validity of the basic claims of the theory. The once controversial claims are no more questioned; they have been internalized as matters of fact. Eventually, the young researcher becomes an accomplished theoretician; it is now their turn to protect the theory and contribute fervently to the in-out discourse. This final step consolidates further the scientific fact and, very importantly, guarantees the reproduction of well-trained newcomers. This long and tortuous process of internalizing the rules of the game is sociological, but unavoidably also psychological. As I said above, a fact in string theory is a deep and sincere belief, and nobody can dispute certain issues without at the same time denying their own self.

So far I have illustrated two discourses that have fostered the confirmation of string theory. The first resides largely within the physics community; what I have called the in-in discourse. The second embraces the public at large. I dubbed this the in-out discourse. And, by definition, both of them involve the communication of ideas; ideas that define what string theory is and what it means to be a string theorist. We have also seen that when the ideas are broadly diffused, as in the in-out discourse, they can re-enter as matters of fact. Newcomers embody them. This process then accelerates the stabilization of the scientific fact. I will name the combination of these two processes the in-out-•••-in process. The three points are included to signify the embodiment of the discourse. This intermediate step is a mixture of discourse and person, namely, it represents the potentiality that persons from the ‘‘outside’’ who have embodied the ‘‘internal’’ discourse have to modify the scientific explanation. Due to its significance, the in-out-•••-in process is at the heart of my history of superstring theory.

Many years ago the sociologist of science Bruno Latour used a similar construct to understand Pasteur’s studies of anthrax.[source] Both approaches blur the boundary between the inside and the outside. Nevertheless, there are crucial differences between the two. Mainly, the displacements from the inside to the outside and back to the inside as I see them in string theory are continuous and not discrete. String theorists do not go like Pasteur, in Latour’s explanation, to a kind of farm to test the theory and then go back to their laboratories to improve the model for future applications. Latour says that Pasteur brings the laboratory with him to the farm and then in turn, the farm to the laboratory. In string theory we observe a more complicated phenomenon. Firstly, rather than going to a farm, string theorists propagate ideas. Secondly, we do not deal with a single person but with a large community, instead. From the most influential researcher to the most humble undergraduate student, all of them contribute to the in-out discourse. Thirdly, the ideas re-enter the field thanks to a continuous flow of newcomers (in-out-•••-in process). As we will see in the next section, this last point is even more convoluted. The ideas oriented towards public audiences not only re-enter the field thanks to the arrival of new students but by means of immaterial actors such as TV programmes, popular press, and institutional campaigns. To be clear, I am talking about the role of popular science in the constitution and consolidation of scientific explanations. As a consequence of these displacements the boundary between the inside and the outside is not just blurred after a set of discrete steps but at every moment; and not only by a person but by many people and countless ideas.
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What I’ve described in this section is an alternative strategy of validation that string theorists have persistently employed in order to preserve what they consider a worthwhile field of research. The purpose of this is to protect the theory from attacks from defenders of contending models; attacks due in part to theoretical and experimental shortcomings. It is not an exaggeration to say that string theory uses propaganda, more or less as Galileo did in his times: ‘‘He uses psychological tricks in addition to whatever intellectual reasons he has to offer. These tricks are very successful: they lead him to victory.’’[source] String theorists too have expanded the circle of believers to include the lay public. As would have been expected, string theorists have been bitterly criticized for using this stratagem: ‘‘The theory has been spectacularly successful on one front, that of public relations.’’[source] But the same could be said, in different degrees, about any other scientific theory; including Galileo’s physics as well as the theories proposed by anti-string theorists. Finally, it should be said that other proposals advanced thus far to quantize gravity and to unify the fundamental forces are not as developed as superstrings. Indeed, these results are less promising than those obtained by string methods. The reason for the disagreement between the two groups is not only about concrete results, but, at least as they see it, about broader conceptions of science. This explains why the “outside” has been the arena for struggles between string and anti-string theorists.
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1. On Facts in Superstring Theory (IV of IV)

2008-05-09T15:00:00.000-07:00

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The discourse of superstrings
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So far we have seen in some detail how results in superstring theory stabilize. This process of stabilization, that at first appears to be purely theoretical, is actually more complex: it necessarily involves a flow of ideas and people across the diffuse boundary separating the inside from the outside. In this manner, I have argued, string theorists have created their own, yet unproven, reality. However, the picture is not complete. We have yet to consider the contributions from the out-out and the out-in discourses. The former is a discourse constructed by outsiders and aimed, in principle, only at outsiders. This is the traditional view of popular science. The latter expresses the possibility of a certain influence of the external discourse on the internal research. By way of example, consider the next extract from an article which appeared in The New York Times:

And D-branes are an essential part of the choreography of the mathematical dance called the Maldacena ["You start with the brane / and the brane is BPS / Then you go near the brane / and the space is AdS / Who knows what it means / I don’t, I confess / Ehhhh! Maldacena!"], in which string theory and field theory pirouette on the same floor. Dr. Maldacena used D-branes to construct a quantum field theory similar to Q.C.D., in the ordinary four dimensions.
He also used D-branes to build a 10-dimensional string theory (with 5 of the dimensions curled up and hidden away). By their nature string theories include gravity. Thus the excitement when Maldacena showed that the two theories were intimately related. The unification of all four forces may now be a step closer to realization.[source]

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In this article, which I assume was read by tens of thousands of people since it was published in The New York Times, Maldacena’s proposal is presented in its own world: quantum gravity, unification, D-branes, extra dimensions, and so on. In addition, the author affirms that thanks to Maldacena’s correspondence the unification program may be ‘‘closer to realization.’’ This article, and many others of the same sort, reinforce, willingly or not, the social belief that superstring theory is ‘‘on the right track.’’ In this case, the circle of believers is expanded thanks to the participation of non expert actors: science writers and interested readers. This sympathetic environment, which will be illustrated further in the next essays, has been vital for the development of the theory. It must be mentioned that this out-out discourse does not originate independently from professional string theorists. In general, it simply reproduces the in-out discourse of the experts. I do not mean to suggest that string theory popularizers are scientifically illiterate, I just want to highlight that the substance of what they say reflects the opinion and enthusiasm of string theory specialists. In such an abstract area, things could not be any other way. As a consequence of this discourse, a favourable disposition regarding superstrings has permeated into the public domain. The lay public’s attitude functions as a support for the internal discourse. What is more, the layman’s view of superstrings is sometimes internalized by experts on the theory and then works as a reconfirmation of the old belief. To put it differently: the out-out discourse is not only oriented to popular audiences but towards experts as well; the out-out discourse is also an out-in discourse. Consequently, “non-pure” conceptions penetrate and modify the theoretical development of the field. I will call this the in-out-in process. Notice that unlike the in-out-•••-in process explained above, the in-out-in process only concerns the movement of ideas (of course, persons are also involved here, but not in the sociological sense meant before). In this way, with contributions from the in and the out, the creeping belief in the accomplishments of superstring theory is gradually confirmed.
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Examples of what I mean by out-in discourse can be found in books and magazines intended for the general public, and in many newspapers. Dennis Overbye, who works for The New York Times, regularly writes on superstring theory.

Recently it has painted a picture of nature as a kind of hologram. In the holographic images often seen on bank cards, the illusion of three dimensions is created on a two-dimensional surface. Likewise string theory suggests that in nature all the information about what is happening inside some volume of space is somehow encoded on its outer boundary, according to work by several theorists, including Dr. Juan Maldacena of the Institute for Advanced Study and Dr. Raphael Bousso of the University of California, Berkeley.[source]

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Maldacena’s exploit was also reported by Time magazine:

When Maldacena transformed his string-theory black hole into something resembling conventional particle physics, his colleagues reacted first with disbelief, then with delight, dancing and singing (in a spoof of the Macarena), ‘‘A’hhhh, Maldacena!’’[source]

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The effects of these kinds of comments on the theory are two-fold. On one side they create a favourable background for the theory to develop, on the other they send a clear message to string theorists that they are doing right, that nature is really as they think it is. I must confess that this hypothesis is hard to prove. However this is what the next essays try to do. Before moving on to these more detailed discussions, I would like to observe something that a string theorist would be unlike to deny: when a newspaper says that colleagues at Harvard are dancing ‘‘La Maldacena,’’ they feel more confident about their own results. Something similar occurred when David Gross was honoured with the Nobel Prize for physics in 2004. My experience was that the general mood among string theorists was very optimistic. They felt that this award was somehow recognition of their own efforts in string theory. Evidence in support of this claim is varied: from technical seminars to public speeches, and from published articles to forwarded emails.
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I hope I have convincingly shown that string theory is much more than the collection of arcane equations usually stamped in technical papers and textbooks. It is also all the other things that are said and written about it in the non-expert milieu: a classroom or a best-selling book, an advertisement or a photograph. This broad discourse has been an essential ingredient in the development of the theory. I have also mentioned that when string theorists publicize their understanding of the natural world they are not communicating to others how nature really is, as people usually understand scientific objectivity, but only the imaginary world they have created in their minds. As a leading string theorist puts it: ‘‘Clearly, these theories exist only in our imagination at present. However, we look forward to the next generation of high-energy experiments and in particular to the most powerful machine, the LHC.’’[source]
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SELECTED READINGS FOR ESSAY 1 (IV)

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

2008-04-09T21:45:00.000-07:00

Abstract: Watch the following video where Professor Michio Kaku talks about the Music of the Universe and String Theory.

The Music of String Theory

Promotional material for the Strings 04 conference. This image was reproduced, as far as I know, on large posters, on the website of the conference, and on the cover of a compilation of talks intended for a lay public; the latter took place at La Sorbonne on 3rd July 2004. The session for the general public originally included the following speakers: G. Veneziano, J. H. Schwarz (not delivered), R. H. Dijkgraaf, J. M. Maldacena, D. J. Gross, and B. R. Greene.

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Overture
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The interviewer starts by asking “what is string theory?” and “Einstein’s true successor” replies:

String theory is an attempt at a deeper description of nature by thinking of an elementary particle not as a little point but as a little loop of vibrating string. One of the basic things about a string is that it can vibrate in many different shapes or forms, which gives music its beauty. If we listen to a tuning fork, it sounds harsh to the human ear. And that’s because you hear a pure tone rather than the higher overtones that you get from a piano or violin that give music its richness and beauty.

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. Unity of the different forces and particles is achieved because they all come from different kinds of vibrations of the same basic string. In the case of string theory, with our present understanding, there would be nothing more basic than the string.[source] (Italics added.)

That the world around us possesses musical attributes has been a preferred theme of philosophers and mystics since the early days of Western culture. The relationship has also been emphasized by highly regarded scientists, from Johannes Kepler, in the seventeenth century, to Edward Witten ― as the above quotation shows. However, the exact nature of this relationship has been subjected to different interpretations through the centuries. For example, the mystical stance sustained by Pythagoras more than two millennia ago, concerning a musical universe, diverges substantially from that proposed by contemporary string theorists. Thus, even though string theorists claim, as many before them did, that their physical universe has something to do with music, their association is unique. It cannot be reduced to previous conceptions. This new relationship between music and physics is the subject of the present essay. Before embarking upon this study, let us begin by saying a few words about the epistemological posture of string theorists.

As many other theoretical physicists do, string theorists start from the assumption that the complex world we live in is ultimately made up of minuscule elements. Everything we see and experience, from the very small to the bigger structures of the universe, is the result of the interaction of these tiny fundamental constituents ― once called atoms. In the jargon of modern theoretical physics they are known as elementary particles. For popular accounts, instead, “the building blocks of nature” is favoured. The interaction between these particles can be by gravitational or non-gravitational forces; best described by the general theory of relativity and the standard model of particle physics, respectively. This approach to the study of nature has been named “reductionism” by philosophers of science. String theorists, reductionists as they are, of course think that the fundamental ingredients of nature are minute objects. However, for them, these are not punctual objects but rather little strings. “The superstring theory … assumes that the ultimate building blocks of nature consist of tiny vibrating strings.”[source] Moreover, in string theory there is not a “zoo” of fundamental particles like in the standard model ― an unnecessary complication for describing the simplicity of nature according to string theorists. Rather, there is just one type of fundamental string. The rest of the things observed in the universe are simply different modes of vibration of this creative string. Only one string produces the orderly and beautiful universe: the cosmos.

At this point, a question comes to mind: why is this fundamental object called a string and not a particle, or an atom? Just a coincidence ― a happy one as we will see. The point is that the basic equation of the theory (the equations of motion of the fields) is similar to that which describes the oscillations of a string. For many years the formula was known as the “vibrating string equation,” thus, experts in the new field decided to use the same name for the theory and its fundamental object. Pushing the analogy a bit further, proponents of the theory concluded that their string should also produce a sort of sound, as much as the vibrating string produces musical notes. Many string theorists allege that this comparison makes sense since the spectrum of the fundamental superstring includes, in principle, each and every elementary particle of nature. More or less in the same way as the monochord can produce all possible audible notes. Despite these similarities, the association of superstring vibrations with musical notes requires further examination. Because, we can understand the reductionist claim that “there is nothing more basic that the string”; but, why this should give rise to a beautiful composition, as found in music, is not so clear. If we wish to understand this, it is clear that the answer cannot come from within string theory itself. We are forced to take a broader historical and contextual approach.

Some historians of science have tried, as have many aficionados of mystical beliefs, to answer this question. The most serious explanatory accounts deem that the long Western tradition relating music and physics, from Pythagoras to Einstein, is at the base of modern considerations. For instance, some time ago Thomas Kuhn noticed, but, to my knowledge, never tried to fully clarify, the historical reasons behind this relationship:

Other frequently remarked but still little investigated phenomena also hint at a psychological basis for this cleavage. Many mathematicians and theoretical physicists have been passionately interested in and involved with music, some having had great difficulty choosing between a scientific and a musical career. No comparably widespread involvement is visible in the experimental sciences including experimental physics (nor I think, in other disciplines without an apparent relationship to music). But music, or part of it, was once a member of the cluster of mathematical sciences, never of the experimental.[source] (Italics in the original.)

It seems to me that this attempt at an explanation is innacurate. In addition to a long-range perspective, as Kuhn suggests we use, I think that particular historical circumstances must also be considered. But, in spite of its inexactitude, Kuhn’s preoccupation will guide us towards our goal. In this essay I will first identify who those physicists were that “had great difficulty choosing between a scientific and a musical career.” In so doing, we will be ready to embark upon other important questions such as: can we compare Kuhn’s “theoretical physicists” with contemporary string theorists? do these physicists have the same interests and motivations for connecting music and physics? and, are the scientific and cultural contexts the same? These are the sort of questions Kuhn suggested needed investigation. The answers to them will be at the centre of my own discussion concerning the relationship between string theory and music.

I’ve organized the essay as follows. The first part recounts the history of the relationship between music, and philosophical and scientific descriptions of nature. The focus is on Western culture and on doctrines and theories of relevance to understanding “the music of the superstrings.” This introductory part will be useful, as well, for the discussion that follows in the next essays. I then point to those theoretical physicists that Kuhn was, maybe without knowing, talking about. After giving the floor to some string theorists, I put forward my own thesis on string theory and music. I explore why string theory supporters say that the music of their theory is as beautiful as a Bach concerto. It is crucial to know this beforehand. Because, string theorists do not make reference to just any sort of music. Not to the notes of a lyre, the instrument of Apollo, god of order and harmony, nor to the chants performed in the magnificent European Gothic cathedrals of the High and Late Middle Ages; but exclusively to Classical and Romantic concertos.
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SELECTED READINGS FOR ESSAY 2 (I)

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

2008-04-09T21:35:00.000-07:00

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SELECTED READINGS FOR ESSAY 2 (II)

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The cosmic symphony
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Pythagoras’ world was imbued with sound; a sound produced by each and every element within it. On one side there was the divine cosmos, composed of the central fire, also called the “guardpost of Zeus,” the orbiting bodies (including the earth and the counter-earth, the five planets, and the moon) which were inserted in immaterial spheres, and the outermost sphere of the fixed stars. The planets, thought to be gods, in their perpetual revolutions around the sun, “hearth” of the universe, emitted a celestial sound that pervaded the entire cosmos. This sound was the music of the spheres. “The Pythagoreans conceived of the cosmos as a vast lyre, with crystal spheres in the place of strings.”[source] On the other side there was the human being, with its mortal body and eternal soul. Due to its divine nature, only the latter generated its own music.

For Pythagoras, a universe impregnated with harsh sound was inconceivable. Its music had to be harmonious, like the motion of the heavenly bodies in the starry sky. What is more, this observable order of the universe was not pure chance; it was the wonderful design of its creator. Indeed, the demiurge had created the entire world, which included the microcosm, that is, the individual, and the macrocosm, the universe, in harmony. This is an essential point in Pythagoras’ mystical doctrine, for there was no real cosmic harmony without the concord of the human soul. And even if the heavenly music of the spheres was inaudible to human ears, an idea of it could be apprehended by reaching inner harmony. Inner harmony meant to Pythagoras to be in tune with the cosmos, that is, to produce an internal music in harmony with the rest of the surrounding musical universe. There were several religious and ascetical practices with the aim of attaining this state, and it was the duty of the philosopher to restore this harmony wherever it was disturbed.

These are some of the few things that can be said with certainty about the doctrine of Pythagoras; religious man, mystic and philosopher of the sixth century BC. To what extent he also indulged in mathematics, astronomy, and music is still a matter of scholarly debate. Nowadays it is generally thought that the members of the religious community he founded in southern Italy are responsible (in addition to other thinkers of the ancient world who lived much later, the so called Pythagoreans) for many of the ideas originally attributed to him. However, since the evidence has determined without doubt that he was a travelled and wise man, leader of an influential school and venerated as a saint in the antiquity, the possibility that he did indeed inquire into scientific and musical subjects is maintained by many historians of Greek philosophy. For this reason, some scholars have accredited to Pythagoras himself the discovery of an exact numerical relationship between the different notes produced by a plucked string and the corresponding lengths: the octave (2:1), the fifth (3:2), and the fourth (4:3). There is even an ancient tale supporting this position. As the story goes, Pythagoras was passing a smith workshop when he heard the notes the hammers produced when beating the metal. This fortuitous event suggested to him a deep relationship between measurable physical quantities and musical notes. Pythagoras then went back to his school and experimented arduously with several objects in order to determine the precise proportions (see Figure 1).

1. Illustration from Franchinus Gaffurius’ Theorica musicae (1492). Sculpture of Pythagoras on the Portail Royal of Chartres Cathedral.

On the other hand, that Pythagoras was fond of numerical interpretations of the world has been conclusively established. The profane as well as the sacred world were for him susceptible to numerical readings. And deserving scrupulous attention were the integer numbers. For instance, since the number ten was particularly sacred, it was perfect, the Pythagoreans thought that there must be ten planets; this is what gave rise to the unobservable counter-earth introduced in their heliocentric model. This belief in the power of numbers was strengthened by the finding, as above recalled, that the ratios of the first integer numbers could explain musical consonances. The Pythagoreans then consistently applied the mathematical relationship between number and music to the heavens. The pleasant music of the cosmos had to have a precise numerical expression, more or less as the notes of a lyre were numerically related to the lengths of the string. According to this idea, since the earth was located at two-thirds of the distance between the central fire and the sphere of the fixed stars, the pitch of the earth was a perfect fifth. All the other orbiting planets contributed in a similar manner to the symphony of the universe. In this way , connecting cosmos, music, and number, the Pythagoreans had determined the exact mathematical formulas explaining the beautiful music of the spheres.

One century after the dissolution of the school that Pythagoras had founded in Croton, the Pythagorean tradition was to be revived by one of the greatest minds in ancient Greece: Plato. It is known that Plato was familiar with the work of Archytas, the knowledgeable mathematician leading the Pythagorean community in Tarentum at the time. This expertise, in addition to the philosophical influence that the mathematician could have had on his friend, is considered to be one of the main reasons why many of the mathematical ideas of Pythagoras have reached us. In particular, Plato gave new life to the relationship between mathematics, music, and the cosmos.

Like Pythagoras, Plato imagined that the creator, the demiurge, had created the cosmos with mathematical significance and had filled it with harmonious music. In Plato’s Myth of Er, in the last part of The Republic, he recounts how the songs of the Sirens sitting on each of the planetary spheres produced a harmonious composition. Plato, moreover, also used numerical arguments to support his thesis. There is, however, an important difference between the two philosophers. While Pythagoras considered that numbers and music had concrete manifestations in the physical world, Plato thought of them as abstract entities. It is common belief that Pythagoras experimented with several objects in order to support his theory of harmonics. Plato, in contrast, would have considered this a futile action. Numbers were, for Plato, transcendent realities with an existence beyond the material world; they were eternal and changeless. In addition to this, the only way to apprehend them was by pure thought. This discrepancy between mathematical objects ― numbers and geometrical figures ― and the natural world, was explicitly stated by Plato himself when he observed that Archytas was a great mathematician, but, alas, also a bad philosopher. Thus, according to Plato’s thought, perceptible things are subject to change; we can say that something “was” or “will be,” but, on the other hand, a mathematical object always “is.” As stated in an introduction to Plato’s work: “He holds that these objects alone are changeless, and contrasts their invulnerability to alteration with the constant fluctuation that characterizes objects in the world of sensation; because of these radical differences, the Forms are capable of being known, whereas objects of sensation are not.”[source] It is particularly in Plato’s later work Timaeus, “the single most important text for the future of the Pythagorean tradition,” [source] that he extends on this.

Cicero, one of the most illustrious Romans of antiquity, in the first century BC ideated in his political dialogue De Re Publica a musical cosmos that resembles that of Plato. As in Plato’s Myth of Er, in Cicero’s Scipio’s Dream the universe is imbued with the music of the spheres. In this allegory, the Roman consul and hero Scipio Aemilianus hears in a dream vision the grand and pleasant sound of the seven planetary spheres. Cicero’s dialogue, as well as Plato’s Myth of Er and Timaeus, had an influence that spanned through the Middle Ages and the Renaissance. Two centuries after Cicero, the Roman scientist Claudius Ptolemy wrote comprehensively on mathematics, music, and astronomy. And his approach to music, as to the other physical sciences he studied, was highly mathematical. This was made clear in his Harmonics, where he tried to give explicit mathematical expressions to musical notes. He also wrote about the music of the spheres; but this time, of course, with the centre of the universe occupied by the earth. The Neo-Platonist movement of those centuries, with Plotinus as its most notable figure, is deserving of a special analysis. However, even a short survey of Neo-Platonism would be too large to fit into this brief introduction. Suffice to say that in addition to Plotinus, the Neo-Platonists Porphyry and Iamblichus have been the subject of increasing interest as a way of revealing the continuity of the Pythagorean tradition in Western culture. Concerning the music of the spheres, Iamblichus once wrote: “It is better … to assert that the soul, before she gave herself to body, was an auditor of the divine harmony, and that hence, when she proceeded into body, and heard melodies of such a kind as especially preserve the divine vestige of harmony, she embrace these, from them recollected divine harmony, and tends and is allied to it, and as much as possible participates of it.”[source]

By the first decades of the fourth century Chalcidius translated the first part of Plato’s Timaeus into Latin. A translation which remained until the twelfth century one of the most important books on natural philosophy. In the fifth century, the commentaries of the Neo-platonist Macrobius on Scipio’s Dream were another central contribution to the cosmological discussions of the day and constituted a fundamental link between Greek and Medieval culture. Almost at the same time, the philosopher and theologian Saint Augustine was drawing on Plato and the Neo-Platonists, in particular Plotinus, to deepen and expand on his Christian philosophical thoughts. In fact, the religious questions he delved into after his baptism, in 387, were copiously supported, and motivated, by Platonic reasonings. Another early influence on him was Cicero, from which he quoted profusely during his entire lifetime; quotations including most notably Cicero’s De Re Publica and Scipio’s dream. In Augustine’s conception of a fundamental changeless reality, Plato’s influence is clearly recognizable. However, in contrast to his intellectual predecessor, for Augustine, the most influential Father of the early Church, God was the only truth. All other truths were, whatever their nature, abstract or material, fictitious. And the road to this eternal changeless reality was spiritual rather than rational or sensorial. Reason and experience were useless without belief. For the theologian, truth was an unreachable without faith. Augustine believed reason to be a method enabling on to reach mathematical reality. However, mathematical reality was not equivalent to truthfulness in the Christian sense. Augustine also diverged from Plato in his assessment of the sensorial experience, and in particular music, which Augustine considered to be number made perceptible. His opinions on music were formulated in his De Musica, where he sustained that music was as beautiful and true as mathematics. Another contribution of major was his classification of mathematics into four different branches: arithmetic, geometry, music and astronomy. He wrote abundantly on these topics, including his outstanding De Musica. His classification of the seven liberal arts, the four above mentioned plus grammar, logic and rhetoric, constituted the standard advanced faculty curriculum during the Middle Ages.

In the sixth century Augustine’s classification was then taken up by Boethius, who grouped the seven subjects into what he dubbed the quadrivium and the trivium. Due to his philosophical eclecticism, merging together Plato and Aristotle with the Christian faith, Boethius is usually considered a Christian Neo-Platonist. In fact, one of the main contributions Boethius made to Western culture is that he recaptured the Pythagorean-Platonist tradition and incorporated it into the Catholic doctrine. In the inexorably fading Roman Empire, today he symbolizes the transition between classical culture and Scholasticism. His massive interpretive work on Greek philosophers, including several translations into Latin and many original evaluations, made him into one of the dominant figures of the Middle Ages. According to the medievalist Jacques Le Goff, everything that was known during the Middle Ages about Aristotle came from Boethius: “The middle ages owed all that it was to know of Aristotle before the mid-twelfth century to Boethius.”[source] Of special interest to our discussion is the fact that the exceptional role played by music during those centuries is due to him. In particular, he emphasized the pre-eminence of music as science of the number and science of the cosmos. As he wrote: “Thus we can begin to understand the apt doctrine of Plato which holds the soul of the universe is united by a musical concord.”[source] It is also thanks to Boethius’ solid works that the trivium and the quadrivium were at the core of education for every Middle Ages student. At that time there was the conviction that following the basic subjects of the trivium, the abstraction of the new subjects covered by the quadrivium could provide the student with the tools needed to immerse themselves into more metaphysical themes such as theology and philosophy. That is, the quadrivium was not intended to teach the occurrence of mundane phenomena, but rather to prepare the mind for more theoretical transcendent issues. Boethius’ books Musica and Arithmetica had an enduring influence on medieval thinking and beyond. These were standard textbooks during the Renaissance, and were still is use in modern Europe.

In the High and Late Middle Ages Plato and Aristotle were still centre stage. But they were read differently. New translations, critical examinations, controversial interpretations, and hot discussions marked the intellectual scene. In the aftermath of this radical period, a novel world-view arose: modern science, with Johannes Kepler one of its most salient figures. The harmony between music and the universe was admitted by Kepler, who thought that the celestial spheres could produce a beautiful, though inaudible, music. His ideas were deeply influenced by Pythagoras, Plato and Augustine. In particular, in his Mysterium Cosmographicum “he was possessed and enchanted by the idea of harmony; he erected an astrological system for himself on the basis of his psychology; he held the thought that a World Soul embraces and professes Plato’s idealistic theory of knowledge.”[source] Kepler thought that the heavenly motions were nothing but a continual music of several voices.

This is in broad terms the historical relationship connecting music and physics, or theoretical physics as Kuhn would say, in the Western world. This is where we should look if we want to discover the origins of the passionate interest that mathematicians and theoretical physicists have for music. But, what about the last part of Kuhn’s extract quoted above: “Some having had great difficulty choosing between a scientific and a musical career”? The process of deciding on a career is something more concrete than the millenarian relationship we have related. And it is this that will provide us with the clues needed to examine string theorist arguments. But, first, who were those theoretical physicists who had to decide between a career in music or in physics.
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SELECTED READINGS FOR ESSAY 2 (II)

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

2008-04-09T21:25:00.000-07:00

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SELECTED READINGS FOR ESSAY 2 (III)

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Twentieth-century theoretical physics and music
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In Charles Kahn’s overview of the Pythagorean tradition I have cited above, he asserts that there has been a strong resurgence of Pythagoreanism in modern Western culture. In spite of this revival, he notes with regret that the phenomenon has not yet received adequate consideration from professional historians of ancient Pythagoreanism. This is in itself a very striking fact; however, what I find particularly interesting is the concluding paragraph of his book. There Kahn explicitly mentions what he means by a revival of the Pythagorean thought:

If, as Whitehead and others supposed, Pythagoras and his followers had dimly divined “the possible importance of mathematics in the formation of science,” then it is obvious that a modern scientist like Einstein is “following the pure Pythagorean tradition.”[source]

From this last paragraph it can be understood that Einstein’s philosophical thought is a consequence of this revival. To show that he is also a cause of the reinforcement of the Pythagorean tradition during the twentieth century is part of the aim of this section. The other implication of the passage, that Pythagoreanism has penetrated modern physics, is something that hardly anyone would deny. From string theorists to historians of science and philosophers, there is wide consensus that modern physics is somehow Pythagorean. Sometimes not only “is” but “must be” is alleged. What is more, this resumption of Pythagoreanism in modern science is stronger in theoretical physics than it is in any other field of research. Let us then retrace the story of the relationship between physics and music with some salient figures of early modern theoretical physics. This will provide us with a satisfactory answer to Kuhn’s query and, finally, an understanding of string theory’s association with music.

That Einstein was a passionate musician is well-known. Every single written biography, museum exhibition, television program, magazine or newspaper article, repeats it over and over again. In one famous biography we read: “A Einstein le apacionaba la música de Mozart porque en ella encontraba lo que había buscado siempre en la ciencia: belleza, claridad, sencillez.”[source] This observation comes accompanied with the famous photograph where Einstein appears playing the violin. Another biographer makes a similar assertion: “Il a cherché l’harmonie de l’univers dans la musique aussi bien que dans la physique mathématique et ces deux domaines l’ont retenu tout au long de son existence.”[source] Einstein himself once said: “If I were not a physicist, I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music.” Of course, similar comments can be found in many other languages. Pages and pages could be filled with such testimonies. Since, as I have previously said, this is one of Einstein’s best known facets, let us move to another early theoretical physicist.

“The dean and definition of theoretical physics in Germany” at the turn of the nineteenth century. This is how John Heilbron introduces Max Planck.[source] Like Einstein, Planck loved music. In their comprehensive history of the beginnings of German theoretical physics, Jungnickel and McCormmach affirm that Planck “early considered making a career in music, but he decided that he lacked talent for composition; he considered the humanities, too, and he later supposed he might have made a passable philologist or historian.”[source] It is not worthless saying a few words about Planck. He was born in 1858 to Wilhelm Johan Julius Planck, who came from a long line of theologians and lawyers, and Emma Patzig, born into a family of pastors. The Plancks were a typical upper-class educated family of nineteenth-century Germany. That is, they were members of that social class which several years later would constitute the strongest social support for the German monarchy. Under these circumstances, the young Max grew up in an intellectual milieu, made up mainly of professors, lawyers, clerics and high government officials. When the family moved to Munich, Max Planck attended, as was expected from a young man in his position, the gymnasium. In effect, the gymnasium was a precondition for anybody wanting to pursue an academic career. During those years Max Planck acted the young patrician; interested in literary meetings and high society cultural conversations. Many years later Planck would remember this as the period of his life when began his greatest passion: “To investigate the harmony that reigns between the strictness of mathematics and the multitude of natural laws.”[source] In the gymnasium, he attended elementary mathematics and physics courses, subjects to which he devoted special attention and encouraged him to opt for physics at university. But, at the same time he was very engaged in musical affairs. Among other activities he composed songs which were executed in student and music halls, he was a talented player of various instruments, he performed at public presentations, he studied music theory assiduously, and he conducted an orchestra. Physics and music were two of his most adored subjects during his studies at the University of Munich, but he finally resolved himself to the study of natural sciences. Heilbron points to a possible explanation as to why Planck chose physics instead of music: “It [thermodynamics] claimed a universal dominion to which all the laws of physics had to conform, and it dealt with the permanent and the unchanging, which physicists since Aristotle had identified with the true and the good. Such lofty considerations, Planck wrote at the end of his long life, had brought him to physics instead of to mathematics or history or music.”[source] Nevertheless, why Planck thought that physics “dealt with the permanent and the unchanging” more than mathematics, or music, is not clear from this explanation. The point is that he decided on physics on the basis of a sort of Pythagorean argument. This difficult decision, however, did not mean he drifted away from music. In later years he attained a genuine professional level on the piano. He played several times in the company of his friend and prominent violinist Joseph Joachim. On several occasions Einstein joined them. Heilbron also notes that Planck had achieved such a musical sensitivity that he could scarcely enjoy the concerts he attended. According to the biographer, Planck’s preference for composers such as Brahms, Schumann, Schubert, and Bach (some parts of his Saint Matthew Passion) were part of his inherent romanticism, which “was a piece with his quest for a super- or transhumant world picture and with his sense of tradition and country.”[source] Planck’s example alone seems to be a strong case in favour of those declaring a transcendent connection between music and theoretical physics. But, there is still more.

Music was also an important aspect of Werner Heisenberg’s life. His fervour for music was, at least, as intense as that felt by Einstein and Planck. Coming from an upper middle class family, Werner entered, as expected, the gymnasium. He went in 1911 to the discerning and elite Maximilian gymnasium in Munich; forty years after Max Planck. For Heisenberg, as it had been for his predecessor, it was a hard decision to choose physics over music. He had loved music since he was a child. And, unlike many other music enthusiasts, this powerful emotion was not mere contemplation ― for him, music was a real obsession. He used to spend hours and hours in front of the piano trying to master the instrument, repeating incessantly the most challenging pieces or performing the assignments given to him by his private teacher. The latter was a celebrated pianist in Munich. Barbara Blum, one of Heisenberg’s daughters, said of him: “His teacher, Hans Beltz, was not unknown: he gave concerts in various places in Germany and seems to have had critical acclaim. Beltz taught him a basic routine for practicing his technique and above all the theoretical foundation for a methodical access to music: cadenzas, bass line, counter point, sonata form, thematic development, analysis of a fugue, etc.”[source] The ability gained by Heisenberg with his assiduous practice was subsequently exhibited in many public presentations. It is clear then that it was not easy for him to choose between physics and music. As David Cassidy relates: “In Physics and Beyond [Heisenberg’s autobiography], Heisenberg recalls a long discussion with Rolf Walter, and Walter’s mother about his decision, soon after entering the university, to make a career of atomic physics rather than classical music.”[source] However, his devotion to music remained over the years. Evoking her childhood, Barbara Blum remembered: “When we were little, we were lulled to sleep by my father’s nightly practice of scales and finger exercises.” This systematic training had for Heisenberg a special significance: “This analytical work, in particular, aroused his greatest interest, since he now could detect in music mathematically structured principles not unlike those in science.”[source] Thus, if Heisenberg “loved music as a source of beauty and harmony,” as he says in his autobiography, it is not due only to the kind of spiritual serenity that many find in music, but because the intricacy of a musical composition revealed somehow the “meaningfully ordered world.”

Max Born, another prominent contributor to early quantum mechanics, was a devoted musician, too. As his mother had died when he was still a child, his father, a medical scientist, was responsible for his early education. After the death of his father, when he was an adolescent, he then began to frequent more often his mother’s family. It happened that in contrast to his father’s scientific vocation, his mother’s side was more culturally oriented; a fact that the young Born found fascinating. The house of the Kauffmanns was regularly visited by many musicians, including celebrated pianists who took pleasure in playing the two grand pianos in the designated music room. Like Planck and Heisenberg, Born studied music theory diligently and practiced as much as he could. Years later, when he moved to Göttingen, he found in Heisenberg the perfect partner with whom to share his passion. For Heisenberg’s twenty-first birthday, Born, who at that time was thirty-nine, played Mozart and Beethoven pieces. Heisenberg remembers that agreeable occasion with joy: “We played a Mozart and a Beethoven Piano Concerto on two pianos, that is, one piano took on the orchestra part. Especially the Beethoven Concerto – which was new to me – was incredibly beautiful.”[source] Born loved music throughout his entire lifetime. Even during the hard wartime years of the forties he found solace in music. In a letter sent to his son during the Second World War he alternated war news with musical interests. Especially in the music of Bach, Schubert, and Brahms, could Born feel “the noble form of romanticism … the key to all that is bitter ad sweet, great and gentle in human life.”[source]

After all these examples, the conjecture stating that there is a deep connection between music and physics, as the ancient believed, seems very plausible. However, not every physicist of the early twentieth century had this penchant for music. Erwin Schrödinger, Niels Bohr, and Paul Dirac, for example, were not interested in music at all. According to a biographer, Schrödinger himself gave details concerning his aversion to music: “Almost uniquely among theoretical physicists, Erwin not only did not play any instrument himself, but even displayed an active dislike for most kinds of music, except the occasional love song. He once ascribed this antipathy to the fact that his mother died from a cancer of the breast, which he thought was caused by mechanical trauma from her violin.” Forthwith, the biographer provides his own explanation: “More likely he learned this distaste for music as a child, echoing his father’s lack of response to this mother’s art.”[source] Abraham Pais, biographer of both Einstein and Bohr, was categorical about the role of music in Bohr’s life and work: “Music was a profound necessity in Einstein’s life, not in Bohr’s.”[source] Bohr was interested in other artistic expressions, such as visual art, but “music played no role to speak of in Bohr’s life.”[source] The historian of physics Helge Kragh appropriately describes the cultural environment surrounding the young Dirac: “Unlike other great physicists – Bohr, Heisenberg, and Schrödinger, for example – Paul Dirac did not grow up under conditions that were culturally or socially stimulating. Art, poetry, and music were unknown elements during his early years, and discussions were not welcomed in the house of Monk Road.”[source] About Dirac’s taste for music, Kragh recounts an illustrative story. Once Heisenberg played several piano pieces and then asked him what he thought about them. Being an accomplished pianist, for sure Heisenberg was waiting for a suitable comment; however, Dirac plainly replied, “the one in which you crossed your hand.”[source] And this was a lifetime attitude, “as to art, music, and literature, Dirac was ignorant and mostly indifferent.”[source]
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To show in detail why Schrödinger, Bohr, and Dirac, did not feel particularly attracted to music, or even disliked it as in the first case, is out of the scope of this essay. What should be retained from these instances, though, is that the relationship a physicist has with music depends decisively on the specific social circumstances in which they were brought up and educated. There is no supernatural or psychological connection between physics and music beyond these concrete realities. In her biography of Max Born, Greenspan asserts that: “A gift for music is not uncommon among theoretical physicists and mathematicians. Like mathematics – in representing extraordinary creations with its symbolic language – music seems to produce a sense of the familiar in the physicist’s mind. Einstein a violinist, thought that his music and work were both ‘born of the same source and complement each other through the satisfaction they bestow.’”[source] Well, there is no real evidence for such a “gift.” From my point of view, this is simply a myth. What determined Einstein’s, Planck’s, Heisenberg’s, and Born’s fascination with music was a set of definite conditions: educational, cultural, socio-economic, religious, psychological, and so on. Of course, they too were not raised in identical milieus and consequently did not think of the relationship in the same way: Einstein was a Jew, Planck came from a conservative patrician family, Heisenberg’s family aspired to social reforms that could improve their status, and Born was educated without a maternal figure. However, in spite of these differences there are some shared general characteristics that allow us to group them. What follows is my explanation; a sociological one rather than mystical.

In the late eighteenth and early nineteenth century, German educational programs were the subject of intense reforms as they adjusted them to the new demands of society. The educational reforms aimed at elevating the cultural level of all strata of German society, and very particularly that of the upper classes. In addition to the economic benefits that it was hoped these reforms would bring, cultural pride and national ambition were too at stake. The cultural heritage sustaining these aspirations was very rich: philosophy, with the early German idealism; visual arts and literature, with Romanticism; and music, with late Baroque and Classical composers such as Bach, Beethoven, Mozart, and Schubert (strictly speaking the last two composers were Austrian, however, remember that the Austrian Empire maintained strong links, and not just linguistic, with German lands; the Austrian Empire and the Kingdom of Prussia were the two main states constituting the German Confederation founded in 1815). It is no coincidence that the reorganization of the school curriculum occurred at the same time as a liberal and nationalistic bourgeoisie was gaining relevance. This happened during and after the Napoleonic wars, when many young intellectuals started to proclaim a new type of society. Industrialists, professionals, lawyers, bankers, and traders, constituted the new active class. In contrast to nobility, which received status through inheritance, the ascending bourgeoisie stimulated cultural achievements as its distinctive social feature. High culture, including classical languages, philosophy, music and literature, would have to be an integral part of the German identity. It was also intended that educational reforms would develop the potential of the individual – a characteristic trait of the new mode of production. One thing that the reform stipulated was obligatory schooling for every child in the Germanic lands. Music, in particular, was valued as “an art that developed ‘the disposition for regularity, accuracy, order, and harmony’” so desired and needed by the ascending bourgeoisie. In this sense, the idea of a new generation of citizens educated in the spirit of the great German culture, including of course its musical legacy, was at the base of the model society the ascending bourgeoisie expected to rule in the future. “Elementary music education thus occupied a crucial role in a vision of music as a part of a larger project of cultivation.”[source] This general attitude towards music was reinforced throughout the century and became even more significant following the German Empire foundation in 1871. The parents of the young Germans tried to inculcate them the high values of their national identity through musical culture. For future professionals, most of them coming from the middle and upper classes, music instruction was also mandatory. All the German physicists discussed above had their first contact with music at a tender age, and cultivated it through the years. They were members of the academic bourgeoisie, the Bildungsbürgertum, which struggled persistently to ascend in nineteenth-century German society. The Heisenbergs were a typical family. As Cassidy notes, “public deportment and professional demeanor were expected to reflect their superior social station” and “allegiance to nationalist trappings.” This included being infused with the bourgeoisie musical culture and taking part in it. In later years, Heisenberg used his musical knowledge and talent to make his way into the elite crowd. The biographer also notes: “Musical pleasures were indeed more serious than mere relaxation and escape: music also provided Heisenberg a direct entrée into the elite social circles of Leipzig.”[source] With certain variations, some of them sketched above, this situation applies to Einstein’s, Planck’s, and Born’s experience with music. However, in contrast to this tradition prevalent in Germany, it was different in other countries. For instance, Dirac’s education was not oriented to humanistic studies – and this was certainly the case for many other English theoretical physicists: “Like most schools in England at the time, this school [Dirac’s] did not emphasize classics or the arts but concentrated instead on science, practical subjects, and modern languages.”[source]

This short account should explain why so many early twentieth-century German physicists had a special feeling for music, or, more specifically, for classical music. But, this was not all. The predisposition gained in their early school years was then reinforced when they began their more advanced academic studies. Consider for example the case of Woldemar Voigt. Nowadays few physicists have heard of him, nonetheless, he was an authority in crystallography at the turn of the century. Like other German physicists in this story, it was not easy for him to decide between physics and music: “Although he was drawn to music as well as to physics, he doubted that he had the talent to make a career in music and decided for physics instead.”[source] The symmetry of crystal physics was admired by Voigt, who explicitly made this clear in his classic textbook Lehrbuch der Kristallphysik. As Jungnickel and McCormmach recall:

Voigt called on an image drawn from his other great intellectual love, music: if every player in an orchestra played the same piece, but not in unison, the result would have no esthetic appeal; molecules in gases, liquids, and amorphous solids produced “music” of just that sort. But if the players played in harmony, the result would be like the “music” of crystals. That was why certain phenomena occurring with “wonderful manifoldness and elegance” in crystals occurred only in “sad monotone average values” in other bodies. “According to my feeling,” Voigt said, “the music of physical regularities is intoned in no other field in such and rich chords as in crystal physics.”[source]

This is an association that Voigt also emphasized in 1905, on the occasion of the opening of the new physics department building at Göttingen University. I will not extend on Voigt’s observations, I shall comment, instead, on the place where Voigt gave the speech: Göttingen University. Firstly, with outstanding figures such as David Hilbert, Felix Klein, Hermann Minkowski, and Hermann Weyl, Göttingen University was the early twentieth century mecca for mathematical physics. Secondly, it was precisely in this institution where mathematics and physics fused in an unprecedented manner, giving rise to what we now call theoretical physics. Thirdly, in Göttingen, Max Born, Pascual Jordan, and Werner Heisenberg wrote the papers that revolutionized our understanding of the microscopic physical world. They worked in close collaboration with the mathematicians. The three of them formed what was known as the Göttingen School. Fourthly, in Göttingen a kind of Pythagorean mysticism was associated with mathematics: “Weyl’s goal was to reveal,” quotes the historian of science Lewis Pyenson, “a few of the fundamental chords from that harmony of the spheres of which Pythagoras and Kepler once dreamed.”[source] Fifthly, under the auspices of Felix Klein, Göttingen University promoted school reforms that changed the way mathematics was taught at all levels in Germany. Many of these recommendations where then implemented in many countries around the world. In Göttingen it was defined for decades to come, and still holds today, what is and what is not theoretical physics. Perhaps there were some theoretical physicists before Göttingen, but not theoretical physics and as an institutionalized practice.

Before concluding this first part of this essay, I would like to say a few words about Arnold Sommerfeld. As a young physicist he worked first in Göttingen as Felix Klein’s assistant and then became his collaborator. He then moved to the University of Munich were he taught and advised innumerable students. In 1919 he published the lectures on atomic theory which he had taught there during the academic year 1916–1917. The influence of Sommerfeld and in particular of his Atombau und Spektrallinien was immense. Helge Kragh tells us about the real impact of the book: “During subsequent years, it ran through several new editions and became the ‘bible’ of atomic theory to the postwar generation of physicists. In 1923 the third German edition was translated into English as Atomic Structure and Spectral Lines.”[source] This book encloses something especially pertinent to our analysis. In the “bible” of atomic spectra Sommerfeld makes explicit reference to the music of the spheres of the Pythagorean tradition. I guess that the impact this observation must have had in all those students learning quantum physics with Sommerfeld’s book was huge. However its effect propagated well beyond the physics community. For instance, the Jungian psychologist Marie-Louise von Franz quoted the abovementioned passage in one of her books.

What we hear today in the language of the spectra is a real music of the spheres of the atom, a concord of whole numbers, numerical relations, a progressive order and harmony of all diversities. … In the final analysis all whole-number laws of the spectral lines and the atom are derived from quantum theory. It is the mysterious organ on which Nature plays the music of the spectra according to those rhythms it controls the structure of the atom and its nucleus.[source]

In which way Sommerfeld influenced the future of physics is hard to quantify. In particular if we think that he was the PhD advisor of several great physicists, including Werner Heisenberg and Wolfgang Pauli. Once, Pauli characterised Sommerfeld’s understanding of the Zeeman Effect in the following terms: “Sommerfeld tried to overcome the difficulties … by following, as Kepler once did in his investigations of the planetary system, an inner feeling of harmony.”[source]

We have seen that German physicists, such as Einstein, Planck, Heisenberg, and Born, were those that “had great difficulty choosing between a scientific and a musical career,” as Kuhn said. Victor Weisskopf, the great Austrian theoretical physicist and fervent musician, is our final example: “Among his passions was music. In his youth, Viki became an accomplished pianist and even considered a career as a professional musician.”[source] The social role of serious music in the constitution of German society cannot be understated since musical knowledge represented a valuable cultural capital for those who possessed it. This has affected the way we associate music with theoretical physics today.

After the Second World War, physics in Germany changed irrevocably. Many German physicists left the country, predominantly for the United States of America. This period, the cold war, was dominated by applied science. The historian of science David Kaiser says of physics at that time: “Thus the pattern seems clear. Where enrolment pressures loomed largest, physicists on both sides of the Iron curtain drilled their students to ‘turn the crank’ and work through more and more quantitative problems, rather than spend their times philosophizing.”[source] This rejection of philosophical debate in science was enduring and extended to almost every area of physics. Einstein’s and Bohr’s concerns were a matter for philosophers. If any physicist did still timidly dare to treat philosophical issues, it was in quantum mechanics: Bell’s inequalities, Aspect’s experiments, the many worlds interpretation, and other related things. All other philosophical topics were banned from any “serious” physical discussion. This was, of course, applied to mystical beliefs such as a possible relationship between music and physics. Such discussions abounded in philosophical and mystical texts but not in physics. In his extensive experience writing on the connection music has with physics, Jamie James remembers that: “But even the purest of the pure scientists would smile at the naïveté of such questions, and tell us that they are imponderables, incommensurables matters better left to the philosophers and theologians.”[source] It was only through popular physics that the subject would re-emerge.

The astonishing observable order of the universe has been a favourite subject for science writers ever since popular science first gained an established readership. In the early decades of the twentieth century, books such Eddington’s Space, Time and Gravitation and The Nature of the Physical World, as well as Jean’s The Mysterius Universe, achieved real success. Both of them later wrote, during the war, on philosophical issues related to science: Eddington published The Philosophy of Physical Science, and Jean his Physics and Philosophy. According to the literary critic Elizabeth Leane, the rhetorical style employed by Jean, “with its sublime metaphors,” “can be heard throughout the physics popularizations of the late twentieth-century boom.”[source] After the war, as noted above, physicists rejected philosophical discussion and were more interested in practical issues that could bring tangible social, or political, benefits; something that was reflected in the areas of physics which were popularized. With the space race between the two superpowers the cosmos and its exploration became again one of the favoured subjects of popular physics. “One of the exceptions to the slump in popular physics publishing, according to [Paul] Davies, was popular astronomy; this perhaps reflects the excitement of the space race, as well as the dissociation of this field from weapons and other immediate human concerns.”[source] With books such as Steven Weinberg’s The First Three Minutes (1977), the public became familiar with the origin and destiny of our universe. However, it is worth saying that these books did not ponder mystical issues such as the music of the cosmos, but rather concentrated on showing “objectively” to the reader the marvel of the physics of the universe. This trend became more popular when Cosmos: A personal Voyage, by Carl Sagan, was broadcast in 1980. Cosmos was an immediate success; it was watched by millions and millions of people around the globe. “Cosmos was the first science TV blockbuster, and Carl Sagan was its (human) star. By the time of Sagan’s death in 1996, the series had been seen by half a billion people; Sagan was perhaps the best-known scientist on the planet.”[source] In addition to the television series, there was also a book which accompanied it. Another success! As can be read on the front cover of a recent edition (in big capital letters): “THE #1 BESTSELLER. MORE THAN FIVE MILLION COPIES IN PRINT.” Presented as historical overviews of the evolution of astronomical and cosmological discoveries, the reality is that the book and the TV program were far from historically accurate. This was in great part due to the mystic-philosophical commentaries made by Sagan (most notably, his manifest intention to present the history of science as a journey towards a final answer to the significance of humankind in the universe). For example, Sagan introduced his “voyage” as follows: “We’re going to explore the cosmos in a ship of the imagination, unfettered by ordinary limits on speed and size, drawn by the music of cosmic harmonies. It can take us anywhere in space and time. Perfect as a snowflake, organic as a dandelion seed, it will carry us to worlds of dreams and worlds of facts. Come with me.”[source] (Italics added.) Kepler is introduced in the episode “The Harmony of the Worlds” [source] as “the man who sought harmony in the cosmos” and discovered it: “His three laws of planetary motion represent, as we now know, a real harmony of the worlds.” This cosmic harmony, or “music of the spheres” as Kepler explicitly called it, meant “that we can find a resonance, a harmony between the way we think and the way the world works.” Simply another way to say that the human soul participates in the divine harmony of the cosmos, as Iamblichus put it in the third century AD (see above).
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2. The Music of the Superstrings (IV of V)

2008-04-09T21:15:00.000-07:00

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

2008-04-09T07:11:00.000-07:00

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Conclusion
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In this essay we have seen why the string theorists’ metaphor of the violin string has been so successful. This analogy has helped them to be firmly identified, by both scientific colleagues and the lay public, with the very best of twentieth-century physics — and physicists! In addition, thanks to the metaphor their fundamental research is currently associated with the modern mystical belief, which assigns to the harmony of the universe the most sublime music, that is, classical music. The first association can be summarized as follows. Many physicists know that the contributions of German scientists to twentieth-century physics were of fundamental importance. Planck, Einstein and Heisenberg are well-known physicists even for the first semester physics student. Most of them are also familiar with the fact that these great physicists were also passionate musicians. This link between twentieth-century physics and classical music is present in many professional and amateur histories of modern physics. Let us consider, for example, William Cropper’s history of physics: Great Physicists. This history, and many others written by non-professional contemporary historians of science, is developed through its main breakthroughs and contributors.[source] In Cropper’s book we discover that the Austrian physicist Ludwig Boltzmann, the founding father of statistical mechanics, was a talented musician: “an accomplished pianist.” (p. 181) Another physicist-musician was Max Planck, the German aristocrat who triggered the quantum revolution: “an excellent pianist; he had even considered a musical career.” (p. 240) Quantum mechanics had its musicians too: “At first, he [Heisenberg] considered a career as a pianist, but Einstein’s creation seemed nearer and more exciting than those of Mozart.” (p. 264) The profound affection felt by the creator of the theory of relativity for music is well known. In previous sections I observed that most of these precursors of modern theoretical physics were Austrians or Germans, and, moreover, were members of the upper middle-class. Due to their social stratum, sensitivity for music was part of their standard education. I then argued that in the context of popular accounts of string theory, where string theorists are likened to modern Plancks and Einsteins, the metaphor of the violin string brings us naturally to the music played by these prominent physicists.
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The second connection between string theory and classical music, though related to the former, is of mystical origin.

From Jeans’s The Mysterious Universe (1930) to Sagan’s Cosmos (1980), and from Hawking’s A Brief history of Time (1988) to Greene’s The Elegant Universe (1999), the orderly cosmos has been a preferred topic of popular science writers. The great success of these titles shows that throughout the twentieth century the subject enjoyed a large and enthusiastic readership. In this essay I have argued that even though the idea of a musical universe has been around for centuries, and was employed by Sagan with some success, only Brian Green’s best-selling book fully exploited it with utmost effectiveness. This was a cogent idea: the beautiful symphony of the universe produced by the harmonious concord of tiny vibrating superstrings. I must mention that in order to be effective, this reference to music required the mystic-religious feeling typical of Western societies. In the context of the end of the millennium, a period dominated by uncertainty and growing mysticism, this is a non-negligible fact (see essay 7).

The reader will have certainly noticed that the role of popular science in all this has not been slight. In effect, recently, popular science has been converted into a battle field where contenders fight for the monopoly of future scientific research. Dorothy Nelkin acutely remarked on this tendency: “As research founds decline in the 1990s, scientists are increasingly using rhetorical strategies to attract attention. We read of chaos and quarks, big bangs and black holes, bucky balls and superstrings, master molecules and medical crystal balls. The assumption is that media interest will influence those who control the purse.”[source] (Italics added.) Those controlling the budget will eventually decide on the physicists to be hired, the young researchers to be supported financially, and the conferences to be organized. It is better to have them on ones own side if one wants to pursue a field of research. Moreover, popular science and media coverage works as a magnet to attract fresh minds to the domain. In this sense, the simple but powerful metaphor of the violin string has had a direct effect on contemporary theoretical physics. It should come as no surprise that thanks to strategies of this sort, string theorists have annihilated any possible contender claiming an alternative quantized theory of gravity or the unification of the fundamental forces of nature. “The only game in town,” as some involved in the dispute used to say.
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Before concluding, I would like to pose a question that until now has not been answered: why have string theorists chosen the violin rather than a more popular instrument such as the guitar? If the role of a metaphor is simply to elucidate a difficult subject, as some claim, why is the guitar string analogy scarcely used by string theorists? At this point the answer should be obvious to the reader. The secrets of the universe cannot be revealed nor understood by the uneducated person. And this extends to their musical tastes. To make this point clear, imagine the following scenario: substitute the graceful girl playing the cello in the above-mentioned episode of The Elegant Universe with a contemporary guitarist playing a rock song. How could we then rewrite the following observation made by the narrator?

Just as the strings of a cello [guitar] can give rise to a rich variety of musical notes, the tiny strings in string theory vibrate in a multitude of different ways making up all the constituents of nature. In other words, the universe is like a grand cosmic symphony [rock song] resonating with all the various notes these tiny vibrating strands of energy can play.[source]

With this substitution the meaning of the commentary is completely lost, because we associate with the music of the universe a “symphony,” not rock music. The music of the universe is a Bach Concerto, not Hendrix’s “Purple Haze.” This is why classical music is also sometimes called “serious music”; to distinguish it from the music listened to by the uneducated crowd. German musicologist Carl Dahlhaus dubbed “absolute music” what we currently know as classical music. [source] With this terminology he tried to convey the idea that German classical music is generally considered the purest and most sublime music. Listening to absolute music is a quasi-religious experience. And, like the secrets of the universe, it is not apt for everyone. Hence, returning to our question, if you change the violin to the guitar, superstring theorists would be horrified; they would ask, as Erasmus did some five hundred years ago: “What would Plato have said to the noisiness of modern music.”[source] André Malraux once said about this elitist view of classical music that there was a music oriented to the masses, but understandably not a Bach or Beethoven oriented to them.
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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.

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3. The Most Beautiful of All Existing Theories? (I of V)

2008-02-09T23:52:00.000-08:00

Abstract: Research in superstring theory rests upon the theoretical physics tradition that seeks mathematical simplicity and beauty in the fundamental laws of nature. In this article I show how string theorists have interpreted and adapted to their own needs the consensually declared beauty of some exemplary theories of twentieth century physics: electromagnetism, quantum mechanics, particle physics, and general relativity. I also explore the specific circumstances under which superstring theory began to be considered a beautiful theory. The problems raised by these reinterpretations are then discussed.

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Introduction
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Many physicists are aware of the fact that at the very beginning of modern science, Galileo Galilei, the founding father of the discipline, was convinced that God had written the great book of nature in geometrical and mathematical characters. They are acquainted with what Galileo wrote in 1623 in Il Saggiatore: “This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is humanly impossible to comprehend a single word of it, and without which one wanders in vain through a dark labyrinth.”[source] Four hundred years after Galileo, contemporary physicists embrace his philosophical stance. Eugene Wigner, considered to be one of the first theoretical physicists to consistently make recourse to symmetry arguments, was a key figure in this regard. He once asserted that ‘‘the statement that the laws of nature are written in the language of mathematics was properly made three hundred years ago [in a note he also notices that this original idea ‘‘is attributed to Galileo’’]; it is now more true than ever before.’’[source] Wigner wrote this in an article that has become ever since a reference to all those interested in the role of mathematical thinking in theoretical physics. Wigner’s creed on this point is similar to Einstein’s; as in that famous quote where Einstein declares that “the most incomprehensible thing about the world is that it is comprehensible.” Of course, “comprehensible” here means mathematically comprehensible.
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Nowadays, references to Galileo and the book of nature are very common. At the 1980 Nobel Conference, Chen Ning Yang, one of the most influential theoretical particle physicists of the last century, said to his attentive audience: “It was Galileo who taught the world of science the lesson that you must make a selection, and if you judiciously select the things that you observe, you will find that the purified, idealized experiments of nature result in physical laws which can be described in precise mathematical terms. That is the truly great lesson of Galileo, and that, of course also introduced the beginning of the quantitative science of physics. Galileo’s was a profound and beautiful idea.”[source]
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According to this belief, widely held among theoretical physicists, the natural world coexists with, and reflects, a hidden changeless reality where mathematical symbols, and their relations, live. What we experience by means of our senses is then the chaotic projection of an ordered transcendent world. This is a brief outline of the Platonist view of the correspondence between the physical world and mathematics. To this ontological stand, modern physicists have added a methodological one. The latter can be summarized as follows: since mathematics is an exact and logical system, the laws of nature can be ‘‘grasped by pure thought.’’ Or, in other words, the fundamental laws of nature can, in principle, be discovered by mathematical reasoning, and without any resort to experiments or observations. Maybe this is not precisely what Galileo thought, but, as we shall see, it is the posture taken by many contemporary physicists, especially string theorists. This prevalent historical interpretation of physics research, highly valued during the twentieth century, has marked in a profound manner the way these theoreticians envisage their work.
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For some, including several prominent theoretical physicists, mathematical skills do not suffice to read the book of nature; a fine aesthetic sense is also required. Fifty years ago the prominent art historian Erwin Panofsky, following in the footsteps of the philosopher and historian of science Alexandre Koyré, declared:

Galileo’s aesthetic judgement [italics added] – whether of music, painting or poetry – thus appear to be dictated by a consistent principle or, if you will, by an insurmountable prejudice: a classicistic prejudice in favor of simplicity, order, and separation des genres [italics in the original], and against complexity, imbalance, and all kinds of conflation.[source]

Thus, modern science, some have argued, has always required a “sense of beauty” from the scientist; more or less in the same way as the fine arts does.

Many theoretical physicists today sustain that the main goal of research carried out within the domain should be the discovery of these imperishable beautiful mathematical truths. As particle physicist Steven Weinberg, Nobel laureate and enthusiastic supporter of the theory of superstrings, puts it: ‘‘There is a ‘hard’ part of modern physical theories (‘hard’ meaning not difficult, but durable, like bones in paleontology or potsherds in archeology) that usually consists of the equations themselves, together with some understandings about what the symbols mean operationally and about the sort of phenomena to which they apply.’’[source] And he states firmly that: ‘‘What drives us onward in the work of science is precisely the sense that there are truths out there to be discovered, truths that once discovered will form a permanent part of human knowledge.’’[source] Additionally, as we pointed out, these ‘‘truths out there to be discovered’’ are thought to be as beautiful as artworks: “But the great equations of modern physics are permanent part of scientific knowledge, which may outlast even the beautiful cathedrals of earlier ages.”[source] (This is the sentence with which Weinberg chose to close an edited volume on the relationship between aesthetics and science. Authors include historians of science and professional scientists. Among these, several are theoretical physicists: two of them were honored with a Nobel Prize, Weinberg and Frank Wilczek, and the other is a well-known public figure, Roger Penrose.) In addition to the above aesthetico-ontological position, in the same text Weinberg also sustains the epistemological thesis putting forward that a fine aesthetic sense can lead us to the most fundamental laws of nature. Theoretical physicists from other fields share this belief. Stephen Hawking, a gravitational physicist and a public supporter of superstring theory, claims that ‘‘to a large extent, we shall have to rely on mathematical beauty and consistency to find the ultimate theory of everything.’’[source]

Before concluding this introduction, it must be said that this metaphysical discourse about the book of nature and its supposed beauty is not exclusively oriented to senior and young physicists (as for example in Yang’s talk and Weinberg’s book). By diverse means, such as magazines and science books, it is also addressed to the more general public. For instance, in one of the first popular books dealing with string theory, science writer Paul Davies wrote:

Perhaps the greatest scientific discovery of all times is that nature is written in mathematical code. We do not know the reason for this, but it is the single most important fact that enables us to understand, control, and predict the outcome of physical processes. Once we have cracked the code for some particular physical system, we can read nature like a book.[source]

Other popular books, such as those written by Penrose and Hawking, are abound with comments of the same sort. In The Large, the Small and the Human Mind, Penrose states: “The more we understand about the physical world, and the deeper we probe into the laws of nature, the more it seems as though the physical world almost evaporates and we are left only with mathematics.”[source] At the beginning of the second chapter he also mentions the “famous lecture” Eugene Wigner delivered in 1960 and which above we have referred to.
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In this paper, I try to seize the meanings of the terms ‘‘simplicity,’’ ‘‘elegance,’’ and ‘‘beauty,’’ in modern theoretical physics and especially in superstring theory. Firstly, I revise the different interpretations that the above terms received in four fundamental theories of twentieth-century physics: electromagnetism, quantum mechanics, particle physics, and general relativity. At the same time, I examine how superstring theorists have interpreted them. Finally, I conclude with a section on the relationship between string theory, its beauty, and the experimental tradition in physics. My intention is to provide a context for understanding declarations made by string theorists such as the following by Andrew Strominger: ‘‘There is disappointment that despite all our efforts, experimental verification or disproof still seems far away. On the other hand, the depth and beauty of the subject, and the way it has reached out, influenced and connected other areas of physics and mathematics, is beyond the wildest imaginations of 20 years ago.’’[source] Comments of these kinds are repeated time and time again. For instance, Dennis Overbye, science writer and deputy science editor of The New York Times, a couple of years ago declared that: “As of now, however, there is scant evidence other than the beauty of their equations that the string theorists are right.”[source] But, what do they mean by beauty? Can we consider superstrings to be a beautiful theory? And, what are the implications of this? I’ll try to answer.

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3. The Most Beautiful of All Existing Theories? (II of V)

2008-02-09T22:54:00.000-08:00

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Beauty in twentieth-century theories
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In this section, the essence of the discussion concerning beauty and physics during the last century is exemplified by four cases: Maxwell’s equations, quantum mechanics, particle physics, and the general theory of relativity. I also assess how string theorists have incorporated interpretations of these theories into their own and in turn how this process has affected the way in which standard physics is now viewed and taught.

A. Maxwell’s equations:

When Maxwell began his studies on electric and magnetic phenomena, in the 1850’s, four laws were known to be of proven validity: Coulomb’s law, accounting for the interaction between static electric charges; Ampère’s law, describing the orientation in space of the magnetic field created by an electric current; Faraday’s law, quantifying the electromotive force produced by a varying magnetic flow; and, finally, the equation imposing the absence of magnetic monopoles. As the historical evidence shows, the problem confronted by Maxwell was the incompatibility of Ampère’s law with the local conservation of electric charge; the latter expressed in the continuity equation of charge and current. Maxwell’s solution, the introduction of the displacement current, has been the subject of much concern among historians of physics, especially due to its significance in contemporary teaching of electromagnetism. This has been particularly emphasized by the historian of electromagnetism Daniel Siegel. In his thorough study of Maxwell’s theory he warns: “Each year many thousands of students in physics courses through the world learn that Maxwell, on the basis of the theoretical considerations, modified Ampère’s law, through the introduction of a new term called the displacement current, and thereby perfected the enduring foundation for modern electromagnetic theory. The centrality of this episode in the history of physics, its paradigmatic status as an example of theoretically motivated innovation, and its prominence in the pedagogy of physics have all contributed to making it a topic of prime concern for historians of physics.”[source] That is, instead of going through an historical account of the early reception and adaptation by others of Maxwell’s findings (which would divert our attention away from our main aim: contemporary interpretations by string theorists), I will obviate physical considerations of the time and concentrate more on the nature of the inconsistency of the set of equations Maxwell was confronted with and its subsequent reinterpretations. The “paradigmatic status” of Maxwell’s equations and its symbolic function in string theory is the subject of this subsection.

That Maxwell’s investigation was conducted by a ‘‘physical way of thinking,’’ with mathematics as a useful tool, is a fact according to historians of science. However, under the strain of subsequent theoretical and experimental achievements, we observe the temptation by many active physicists and contemporary science writers to overestimate the role of mathematical consistency in the elaboration of the electromagnetic theory. In the same book mentioned above, Paul Davies also writes: ‘‘Maxwell found initially that the equations looked unbalanced; the electric and magnetic parts did not come in quite symmetrically. He therefore added an extra term to make the equation look more pleasing and symmetric. […] Nature obviously agreed with Maxwell's aesthetic sense!’’[source] This temptation to reify Maxwell’s equations and to play with them looking for consistency is very normal in theoretical treatises on electromagnetism.

Take, for example, Jackson’s Classical Electrodynamics.[source] This textbook has been acclaimed since its first edition in 1962 as the definitive reference on the subject; taught for decades to advanced undergraduate and graduate students across the globe. As the author emphasizes in the Preface, the theoretical approach is favoured: “My choice of topics is governed by what I feel is important and useful for students interested in theoretical physics, experimental nuclear and high-energy physics, and that as yet ill-defined field of plasma physics.”[source] Even though he is here talking about the last part of the book, containing new topics, the advanced mathematical level of the whole material presupposes a theoretical inclination from the reader; a feeling for mathematical consistency, so to say. In the section “Maxwell’s Displacement Current, Maxwell’s Equations,” after a thorough presentation of electrostatics and magnetostatics, Jackson starts by writing down “Maxwell’s equations” without the displacement current (equations 6.22 in the text); then, he writes:

In fact, the equations in set (6.22) are inconsistent as they stand.
It required the genius of J. C. Maxwell, spurred on by Faraday’s observations, to see the inconsistency in equations (6.22) and to modify them into a consistent set which implied new physical phenomena, at that time unknown but subsequently verified in all details by experiment. For this brilliant stroke in 1865, the modified set of equations is justly known as Maxwell’s equations.[source]

At first, it is not clear what he means by “inconsistent as they stand,” because, in fact, nothing, from the mathematical point of view, prevents them from being correct. But turning the page we get the answer: they are inconsistent because they do not agree with the continuity equation for charge and current. Afterwards, in two simple steps Jackson is able to tell the student how to reproduce the right equations; written at the bottom of the page. Now they are “mathematically consistent with the continuity equations.” In this simple form ― of course, also motivated by pedagogical reasons ― Maxwell’s contribution is reduced to physical ingenuity and “mathematical consistency.”

Jackson’s presentation is an example of what the historian of physics Daniel Siegel has pointed out to be the paradigmatic status of the displacement current episode. Just one case, though an important one, among the many prevalent theory-laden readings of the history of physics. As we shall see, for string theorists Maxwell’s case is an exemplary one. For them, this is one of the best examples of what mathematical consistency can lead to, as Jackson says, “new physical phenomena, at that time unknown but subsequently verified in all details by experiment.”

Let us illustrate this well-established interpretation of Maxwell’s equations with another widely used textbook: The Feynman Lectures on Physics.[source] This set of lectures, delivered by one of the most creative and influential theoretical physicists of the twentieth century, has been the most important contribution to physics undergraduate education in fifty years. Thousands of physicists were, and some still are, trained according to the idea that ‘‘if we take away the scaffolding [the mechanistic ether model] he used to build it, we find that Maxwell’s beautiful edifice stands on its own. He brought together all of the laws of electricity and magnetism and made one complete and beautiful theory.’’[source] (Italics added.) In his lectures, Feynman approached Maxwell’s equations in the same way as Jackson does in his book; that is, prioritizing mathematical consistency. However, there is an ingredient in Feynman’s passage that I would like to stress here. I mean, the completeness of the unification of electricity and magnetism ― something that seems to be absent in Jackson’s presentation. Mathematical consistency, according to this interpretation, does not only provide us with new discoveries, it can also give us a unified and complete description of apparently diverse phenomena. In crude terms, the discussion so far can be summarized as follows: if you take a set of equations and play with them intelligently, that is, fit them in a consistent way, you will obtain a beautiful theoretical edifice. Future experiments will prove that the procedure was correct.

Mathematical consistency and unification are two aesthetic attributes that string theorists, following the paradigmatic interpretation of Maxwell’s equations, ascribe to their model. In order to see how string theorists have exploited in their favour this widespread interpretation of Maxwell’s legacy, let us consider once again Barton Zwiebach’s textbook for novices. Since string theory is a theory of unification, we shall first examine what he says about this attribute and how it is related to Maxwell’s theory of electromagnetism. At the very beginning, in the first paragraph of the Introduction, he narrates why he thinks string theory “fits into the historical development of physics”: “Over the course of time, the development of physics has been marked by unifications: events when different phenomena were recognized to be related and theories were adjusted to reflect such recognition. One of the most significant of these unifications occurred in the nineteenth century.”[source] Of course, he means Maxwell’s equations. And, after a brief summary of the main discoveries of the nineteenth century in the realm of electricity and magnetism, he concludes saying: “These equations [Maxwell’s] unify electricity and magnetism into a consistent whole. This elegant and aesthetically pleasing unification was not optional. Separate theories of electricity and magnetism would be inconsistent.”[source] As we shall see in the rest of this essay, the unification program is one of the strongest motivations for pursuing research in string theory. And, in this sense, Maxwell’s exemplary case is a source of inspiration.

But Zwiebach also refers to the other aesthetic attribute currently associated with Maxwell’s equations: experimental consequences from mathematical consistency. In between the two previous quotes, Zwiebach notes that before Maxwell’s discovery there were several laws describing all the electric and magnetic experiments of the time (he is certainly thinking about the set of equations written down in 6.22 in Jackson’s book). However, Zwiebach notes that “they were, in fact, inconsistent. It was James Clerk Maxwell (1865) who constructed a consistent set of equations by adding a new term to one of the equations. Not only did this term remove inconsistencies, but it also resulted in the prediction of electromagnetic waves.”[source]

It is worth pausing for a moment in order to repeat Zwiebach’s arguments once more; for they sum up very well the assessment that string theorists usually make of the introduction of the displacement current in particular, and Maxwell’s theory in general. Firstly, Zwiebach, interpreting the historical event, accentuates the role of Maxwell’s work in unifying electric and magnetic phenomena. Whatever the historical accuracy of his account, as I have argued, he relies on the mainstream interpretation of the episode. In this sense, we must recognize that he is very lucid with respect to the message he wants to pass on to his audience: string theorists, following Maxwell’s example, look for unity, for a ‘‘consistent whole.’’ Moreover, string theory tries to solve, as Maxwell’s theory did, the oldest and most crucial problem of physics: unification. Secondly, string theory is, or should be, as Maxwell’s equations are, an ‘‘elegant and aesthetically pleasing unification.’’ However, it must be remembered that beauty in its own equations is “not optional,” it is mandatory. Thus, this implies that the final unification can be reached by pure aesthetic judgements.

Let us illustrate how string experts have incorporated Maxwell’s discoveries into their theory. Electromagnetism tells us that electricity and magnetism are of similar nature: varying magnetic fields produce electrical phenomena and vice versa. Some have suggested, and not only string theorists, that this co-dependent relationship is confirmed by the fact that under the switch E → B and B → − E, Maxwell’s equations in vacuum remain unchanged. Edward Witten, in an article intended for physicists working in various areas, affirms that this duality ‘‘has been known for nearly as long as the Maxwell equations themselves.’’[source] Saying this Witten intends to persuade the reader that string theorists’ use of the duality E ↔ B does not rely on an elaborate and desperate reasoning, but an analogous procedure has always been at the root of Maxwell’s theory itself.

The limitation of the duality E ↔ B to the vacuum condition has been superseded by contemporary theoretical physicists who have constructed models where the electric/magnetic duality is accomplished even in the presence of both electric charges and magnetic monopoles. A construct of this sort was built in 1978 by Georgi and Glashow; soon after, monopole solutions were found by ’t Hooft and Polyakov. Interesting extensions to supersymmetric models, such as N = 2 and N = 4, were subsequently devised and monopole and dyon solutions obtained.

Theoretical physicists have also generalized these results to dimensions higher than four. In technical terms, an electric gauge field Ae(p+1) in D dimensions ¬is identified with a (p+1)-form whose dual is the (D – 3 – p)-form associated with the magnetic dual field Am(D-3-p). Notice that with p = 0 and D = 4, Maxwell’s duality is recovered: Ae1 = Am1. That is, in four dimensions magnetic and electric fields are interchangeable. The physical interpretation of these mathematical properties is as follows: as well as a point particle generates a 1-form electric field, and a (p+1)-form is attached to a p-dimensional object, the corresponding dual fields are produced by dimensionless magnetic monopoles and (D – 4 – p) dimensional objects. Multidimensional objects of this sort have dramatically changed the way string theorists conceive their theory: ‘‘Researchers have gradually realized that string theory is not a theory that contains only strings. A crucial observation, central to the second superstring revolution initiated by Witten and others in 1995, is that string theory actually includes ingredients with a variety of different dimensions: two-dimensional Frisbee-like constituents, three-dimensional blob-like constituents, and even more exotic possibilities to boot.’’[source] These ‘‘p-branes,’’ known to be solutions of the supergravity equations, are essential objects for connecting and assembling the “final theory of physics”: the M-Theory.

The previous discussion suggests that string theorists have taken the latest developments of Maxwell’s theory and incorporated them successfully into their own theory. In addition to these concrete achievements, the historical interpretations of string theorists, and string theory enthusiasts, on the implications that Maxwell’s equations have had on the construction of modern unified models, are diffusing into many different areas of physics. Consequently, this influence is modifying the mode classical electrodynamics is currently being conceived of and taught. In the introduction of an intermediate textbook on electrodynamics, a textbook published a decade ago, the impact contemporary research in unified models has had on the teaching of Maxwell’s equation is made explicit.

Einstein dreamed of a further unification, which would combine gravity and electrodynamics, in much the same way as electricity and magnetism had been combined a century earlier. His unified field theory was not particularly successful, but in recent years the same impulse has spawned a hierarchy of increasingly ambitious (and speculative) unification schemes, beginning in the 1960s with the electroweak theory of Glashow, Weinberg, and Salam (which joins the weak and electromagnetic forces), and culminating in the 1980s with the superstring theory (which, according to its proponents, incorporates all four forces in a single ‘‘theory of everything’’). At each step in this hierarchy the mathematical difficulties mount, and the gap between inspired conjecture and experimental test widens; nevertheless, it is clear that the unification of forces initiated by electrodynamics has become a major theme in the progress of physics.[source] (Italics added.)

The introductory section is titled “Advertisement: What is electrodynamics, and how does it fit into the general scheme of physics?” It is remarkable that Zwiebach also opens his introduction with an historical assessment of its subject: “We see how it [string theory] fits into the historical development of physics, and how it aims to provide a unified description of all fundamental interactions.” The author of the textbook on electrodynamics concludes by confirming what we have been saying until now: ‘‘So electrodynamics, a beautifully complete and successful theory, has become a kind of paradigm for physicists: an ideal model that other theories strive to emulate.’’[source] From the point of view of string theory, we cannot but agree with this statement.

B. Quantum mechanics:

Quantum mechanics was conceived alongside experimental results and grew strong on the solid soil of a massive amount of physical data. This well-known experimental backdrop of quantum mechanics has compelled string theorists to associate with it an aesthetic discourse that differs substantially from that constructed around electromagnetism. To examine how string theorists evaluate the aesthetic attributes of quantum mechanics is the goal of this subsection.

Spurred on by Einstein’s philosophy and under the influence of the authoritative mathematical teaching at the University of Göttingen, the chief creators of quantum mechanics had a high regard for “beauty” in the physical sciences. On his early contribution to quantum mechanics, de Broglie recalled that his 1923 revolutionary proposal affirming that measurable particles also behave like waves was based entirely on its intellectual beauty.[source] Dirac also underlined the unusual beauty of Schrödinger’s equation: “I found myself getting into agreement with Schrödinger more readily than with anyone else. I believe the reason for this is that Schrödinger and I both had very strong appreciation of mathematical beauty, and this appreciation of mathematical beauty dominated all our work. It was a sort of faith with us that any equations which describe fundamental laws of nature must have great mathematical beauty in them. It was like a religion with us.”[source] It must be said, however, that despite their yearning for order and beauty in the realm of microphysics, the founders of quantum mechanics never attained it satisfactorily. It was never clear what they meant by beauty. The historian of science Arthur I. Miller has for years insisted on the importance of the role of aesthetic considerations in the early development of quantum mechanics. Miller has devoted special attention to the dispute between Schrödinger, with his wave mechanics, and Heisenberg, with his preference for, according to Schrödinger, complicated mathematics and-non-visual representations of atomic processes. Nevertheless, his evaluation is not often brought up in present discussions among theoretical physicists interested in the aesthetics of science. Indeed, and contrary to Miller’s historical interpretation, quantum mechanics is generally not considered to be a beautiful theory.[source] Only particle physicists (to be discussed in the next subsection) satisfied their longing with the extensive exploitation of the concept of symmetry first introduced in the microphysical world by Eugene Wigner.

Dirac’s equation, the first to combine quantum mechanics and relativity, deserves a special mention. Let us give some examples as how Dirac’s equation and personal conception and attitude on beauty and science has influenced contemporary appraisements of the subject. Two historians of science are emphatic on Dirac’s momentous contribution to the discussion: “Inspired by the views of Albert Einstein and Hermann Weyl, Dirac, more than any modern physicist, became preoccupied with the concept of ‘mathematical beauty’ as an intrinsic feature of nature and as a methodological guide for its scientific investigation.”[source] (Italics added.) Steven Weinberg opens his chapter “Beautiful Theories,” contained in his popular book Dreams of a Final Theory, with a significant story: “In 1974 Paul Dirac came to Harvard to speak about his historic work as one of the founders of modern quantum electrodynamics. Toward the end of his talk he addressed himself to our graduate students and advised them to be concerned only with the beauty of their equations, not with what the equations mean. It was not good advice for students, but the search for beauty in physics was a theme that ran through Dirac’s work and indeed through much of the history of physics.”[source] (Italics added.) Something similar was sustained by Chen Ning Yang: “To many physicists today what Dirac said contains a great truth. It is astonishing that sometimes if you follow the guidance toward beauty that your instincts provide, you arrive at the profound truth, even though contradictory to experiments. Dirac himself was led in this way to the theory of anti-matter.” As a final example, consider what John Barrow, a professional cosmologist and science writer, says about Dirac. According to him, most theoretical physicists, like Dirac, “make aesthetic quality a guide or even a prerequisite for the formulation of correct mathematical theories of nature.”[source] Concerning Dirac’s equation, Frank Wilczek claims that “of all the equations of physics, perhaps the most ‘magical’ is the Dirac equation. It is the most freely invented, the least conditioned by experiment, the one with the strangest and most startling consequences.”[source]

Hence, it should come as no surprise if we found out that many physicists are familiar with the following anecdote: “When someone asked him (as many must have done before) ‘How did you find the Dirac equation?’ he is said to have replied: ‘I found it beautiful.’’’[source] Or with the following passage by Dirac, published in a popular scientific magazine thirty five years after his revolutionary paper:

It is more important to have beauty in one’s equations than to have them fit the experiment … . It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one’s work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further development of the theory.

Echoing Dirac’s innumerable declarations like these where he affirmed that beauty was a requisite and a guide to theoretical progress, modern theoreticians have assumed that beauty can show them the road to truth. Like Maxwell’s equations, the aesthetic criterion that supposedly led to Dirac’s equation has become an exemplary case.

The originality of Dirac’s philosophy cannot be fully understood without referring to his interpretations of electromagnetism and general relativity (remember that, in addition to his great devotion to general relativity, he did pioneering work on magnetic monopoles). According to him and his followers, what he did was to seize, bring up to date, and apply ‘‘Maxwell’s legacy’’: take two physical theories, combine them in a consistent manner, and get something unexpected. This interpretation of Dirac’s contribution has been determinant in the constitution of quantum field theory, as stated firmly by Weinberg: ‘‘The point of view of this book is that quantum field theory is the way it is because (with certain qualifications) this is the only way to reconcile quantum mechanics with special relativity.’’[source]

The distinguished theoretician Joseph Polchinski, author of a classic textbook on superstrings, in a commemorative conference honouring Dirac said:

Dirac comes across in many ways as the first modern theoretical physicist. Many of his statements illustrate this, but the following strikes me as particularly apt:

One must be prepared to follow up the consequences of theory, and feel
that one just has to accept the consequences no matter where they lead.

Dirac is often quoted on the importance of mathematical beauty in one’s equations; I did not choose one of these quotations because beauty is so difficult to define. He also made various statements that one should not being distracted by experiment; I did not choose one of these because they are inflammatory.

The reason that I find the chosen quotation so striking is that it is not supposed to be possible to follow theory alone. Without experimental guidance, it is said, one will quickly become lost. But of course today in high energy theory we are to a large extent following theory where it leads us, and we are rather confident that this is a correct and fruitful path. Why this approach can work is illustrated by Dirac’s great discovery:

quantum mechanics + special relativity → antiparticles .

This was not a direct deduction (though in the framework of quantum field theory, one can show that antiparticles are necessary for causality.). Rather, when Dirac tried to find a consistent framework that combined quantum theory and special relativity, he found it very difficult — so much so that when he did find one he had great confidence in its inevitability, and was prepared to take its other consequences seriously.[source]

The reasoning of string theorists, here uttered by Polchinski, is very simple: if quantum mechanics + special relativity → quantum field theory, then, quantum mechanics + general relativity → M-theory. As for electromagnetism, we note the tendency to stress the beauty of the unification rather than the beauty of mathematical consistency: ‘‘The existence of a single structure that unifies such a broad range of physical and mathematical ideas, and many others as well, is unexpected and remarkable. Earlier I declined to define beauty, but one can recognize it when one sees it, and here it is. This is one illustration of why the scientific path that Dirac laid out has been such a fruitful one in recent times.’’[source] (Italics added.)

C. Particle physics:

In his Nobel Lecture, given on 11 December 1957, Chen Ning Yang underlined the ontological base which drove the investigation of the majority of the particle physicists at that time: ‘‘One learns to hope that Nature possesses an order that one may aspire to comprehend [mathematically].’’[source] This belief (a learnt stance as Yang correctly says), was reinforced a few years later with the confirmation of Murray Gell-Mann’s ‘‘Eightfold Way.’’ Gell-Mann, dubbed by some the ‘‘Mendeleev of elementary particle physics,’’ arranged in simple geometrical structures all the baryons and mesons that were known. The conclusive experimental evidence for his predicted Ω− arrived in early 1964 (see Figure 1). After this astonishing success, in addition to new experimental discoveries and the theoretical introduction of quarks, including the b (b for beauty, or bottom) and the t (t for truth, or top), particle physicists started to ideate more fascinating geometries in order to understand the most fundamental structure of matter. For particle physicists, these geometrical structures have become ever since an indubitable sign that the microphysical world is beautifully organized. Needless to say this disposition reflects the strong Platonic preconception in which most theoretical physicists are being educated.

1. The baryon decuplet showing the ‘‘missing’’ Ω- and a supermultiplet for baryons of spin ½.

Nowadays, almost half a century after Murray Gell-Mann introduced his revolutionary ideas, some of these proposed independently by Yuval Ne’eman, nobody doubts that it is a ‘‘fact that Lie groups have become as essential to modern theoretical physics as complex analysis and partial differential equations.’’ This assessment was made by Sheldon Glashow, another influential particle physicist, in his Introduction to Howard Georgi’s widely taught textbook on Lie Algebras.[source] In the same Introduction, Glashow brilliantly summarized the basic function assigned to symmetry principles in the study of particle physics. His interest concerning what he thought were the most pressing questions of particle physics, adopted the form of a recommendation:

We cannot yet answer these questions, but it is clear that a command of the simple and beautiful theory of Lie groups will be needed. For the future, we can only repeat the remarks of an earlier Harvard colleague, P.W. Bridgman, who wrote in 1927 that ‘‘whatever may be one’s opinion as to the simplicity of either the laws or the material structure of nature, there can be no question that the possessors of some such conviction have a real advantage in the race for physical discovery. Doubtless there are many simple connections still to be discovered, and he who has a strong conviction of the existence of these connections is much more likely to find them than he who is not at all sure they are there.’’
Amen.[source]

Therefore, for Glashow, a truly modern theoretical physicist who tries to understand the fundamental structure of nature, ‘‘the simple connections,’’ must be guided by the ‘‘simple and beautiful theory of Lie groups.’’ That is, by the belief that fundamental matter is geometrically organized and its dynamics respect such simple symmetries. Only by following this attested procedure can one organize matter and, consequently, foresee new elementary particles to discover in the laboratory. From this perspective, theoretical particle physicists read Gell-Mann’s episode as follows: they assume that Gell-Mann did not introduce any ad hoc assumption into his geometrical structures in order to predict new particles, but it was only the simplicity of the mathematics used which prompted particle physicists to realize the predictive power of the model. And, if someone did not recognize at first this power, it was due to ignorance or lack of self-confidence. Today, no theoretical particle physicist, according to this accepted viewpoint, can commit this mistake.

In his address delivered before the Nobel Foundation in December 2004, David Gross expressed his gratitude in the following terms: ‘‘As I end I would like to thank not only the Nobel Foundation, but nature itself, who has given us the opportunity to explore her secrets and the fortune to have revealed one of her most mysterious and beautiful aspects – the strong force.’’[source] (Italics added.) This declaration is very significant, and not only because Gross is one of the most influential theoretical physicists of our time, both within and without the community of experts, but also because he has been one of the leading theorists to have built the ‘‘beautiful edifice’’ of superstrings.

So far I have argued that the beauty physicists find most appealing in particle physics is its simple geometries allowing them to organize the fundamental building blocks of nature. This contrasts somehow with the two previous paradigmatic cases discussed above. In all three cases, Maxwell’s equations, quantum mechanics, and particle physics, mathematical consistency is considered crucial; however, it must be noted that the visual symmetrical forms of group representations give it extra credit.

Like other theoretical particle physicists, string theorists assume that symmetry principles play a crucial role in microphysics and must be considered the supreme guide in the search for reality. Moreover, they have drawn on previous results in order to support their theory. As is the case for the grand unification models:

The second motivation for supersymmetry in the TeV range comes from the idea of gauge unification. Recent experiments have yielded precise determinations of the strengths of the SU(3) × SU(2) × U(1) gauge interactions – the analogs of the fine structure constant for these interactions. They are usually denoted by α3, α2 and α1 for the three factors in SU(3) × SU(2) × U(1). In quantum field theory these values depend on the energy at which they are measured in a way that depends on the particle content of the theory. Using the measured values of the coupling constants and the particle content of the standard model, one can extrapolate to higher energies and determine the coupling constants there. The result is that the three coupling constants do not meet at the same point. However, repeating this extrapolation with the particles belonging to the minimal supersymmetric extension of the standard model, the three gauge coupling constants meet at a point, MGUT, as sketched in Fig. 2 [see Figure 1]. At that point the strengths of the various gauge interactions become equal and the interactions can be unified into a grand unified theory. Possible grand unified theories embed the known SU(3) × SU(2) × U(1) gauge group into SU(5) or SO(10).[source]

2. ‘‘Coupling constant unification in supersymmetric theories.’’[source]

More precisely: including the particles of the Minimal Supersymmetric Standard Model (MSSM), the gauge couplings unify at MGUT ≈ 2 × 10^16 GeV, taking the approximate value 5/3 α1 = α2 = α3 ≈ 1/25. The grand unification group SO(10) contains the standard model symmetries according to the decomposition SO(10) → SU(5) × U(1)’ → SU(3) × SU(2) × U(1) × U(1)’. It is worth noting that these conclusions are currently upheld independently of superstring theory arguments. There are several ways in which string theorists integrate these results into their explanatory framework.

A standard ‘‘top-bottom’’ approach is that of the heterotic string E8 × E8 formulated by Gross and collaborators more than twenty years ago. Since the gauge group of this heterotic string decomposes as E8 × E8’ → SU(3) × E6 × E8’ → SU(3) × SU(3) × SU(3)L × SU(3)R × E8’, where the last two SU(3)s contain the SU(2) and the hypercharge U(1) of the electroweak force, the system guarantees, at least in principle, that all the implications of the standard model are deducible from it. (Of course, things are much more complicated than this rough analysis suggests. A string phenomenologist advises us: ‘‘But what for this theoreticians is a nice classification, for the phenomenologist is a horrible nightmare. He has a incredible mess, a jungle, in his hands.’’[source])

This argument seems too simple for some people, however, I consider it very powerful: if symmetries are, as particle physicists have taught us, the supreme guide in the search for the most fundamental truths of nature, then string theory has satisfied one of the most stringent conditions required to any theoretical model. For string theorists, the beauty of nature, characterized by the application of symmetry principles to the microphysical world, has been realized in the unification of all the forces. Once again, as in the case of electromagnetism and Dirac’s equation, we observe that string theorists have brought the discussion on beauty and simplicity to their own ground: the unity of the physical laws.

More than thirty years after the introduction of the Eightfold Way, in The Quark and the Jaguar, Murray Gell-Mann explained his reasons for thinking that the standard model could not be the ultimate theory of elementary particles. There, he advanced that ‘‘Il se peut que ce rêve ait été realisé. Une théorie d’un nouveau genre, nommée théorie des ‘‘supercordes’’, semble posséder les bonnes propriétés pour accomplir l’unification.’’[source] This type of support from authoritative theoretical particle physicists has strongly contributed to the acceptance of superstrings as the simplest, most beautiful, organization and description of matter.

This general discourse has already penetrated some standard texts on particle physics and quantum field theory. On page 4 of a new edition of their classic book, Aitchinson and Hey write: ‘‘Despite remarkable recent developments of strings (Green et al 1987, Polchinski 1998), it is fair to say that the vision of the unification of all the forces, which possessed Einstein, is still some way from realization.’’ At the end of chapter 2 they comment again on superstring theory and Planck-scale physics.[source] Weinberg’s affection for string theory is well known; for example, in the first of his volumes on QFT he says: ‘‘We have learned in recent years to think of our successful quantum field theories, including quantum electrodynamics, as ‘effective field theories,’ low-energy approximations to a deeper theory that may not even be a field theory, but something different like a string theory,’’ and, in another place, ‘‘the underlying theory might not be a theory of fields or particles, but perhaps of something quite different, like strings.’’[source] In the final section of Peskin and Schroeder’s textbook on QFT, ‘‘Toward an Ultimate Theory of Nature,’’ there is an extensive discussion on superstring theory’s potentials. The character of the conclusion is not very surprising if we consider that Michael Peskin, the main author of this new classic, has lectured many courses on superstring theory.[source] Of course, Michio Kaku’s textbook on quantum field theory also discusses at length, it dedicates a full chapter, the basics of superstring theory.[source]

D. The general theory of relativity:

Einstein himself publicly declared on many occasions what he considered to be the beauty of general relativity. In his popular account Relativity: The Special and General Theory, first published in late 1916, he said: ‘‘The theory of gravitation derived in this way from the general postulate of relativity excels not only in its beauty … .’’[source] The beauty of the theory resided, according to Einstein’s explanation, in its ability to correctly interpret and predict the whole variety of gravitational phenomena from a single principle: the principle of equivalence. Until his death, which occurred four decades later, Einstein maintained this opinion. Actually, it is fair to say that this belief became stronger as he got older, turning into a sort of religious dogma.

The simplicity of the theory, what gave it its beauty, was not quickly acknowledged by Einstein’s colleagues. In fact, for most physicists at the time the theory was a conceptually difficult and convoluted mathematical construct. It was only during the years that followed the theory’s first experimental verification, in 1919, that Einstein’s point of view started to gain wide acceptance. But the experimental confirmation was not the only factor that played a role in the growing positive reception of Einstein’s idea. This was also due to the efforts made by scientists and science amateurs to popularize the basics of the theory. For instance, the work of Arthur Eddington was a significant contribution to English popular literature on the subject. There, Einstein’s theory of the universe was presented as a great achievement of mathematical physics and its search for simpler explanations. Eddington also published an advanced book on general relativity; a book that received a favourable response from the specialist reader and which was highly praised by Einstein. Around the same time the beauty of the theory was conveyed to a larger number of professional physicists by one of the first widely used textbooks on the subject: Relativity, Thermodynamics, and Cosmology, by Richard Tolman. Here, the spirit of Einstein’s legacy was guaranteed:

In addition to these observational verifications, which justify the introduction of the principle of equivalence, we must also assign a high importance to our intuitive appreciation of the rationality of assuming the abolition of gravitational effects for a freely falling observer, and to our intellectual appreciation of the simplicity, clarity, and effectiveness of the postulate that we thus obtain. These qualities of intuitive rationality and of intellectual simplicity, clarity, and effectiveness, which bespeak so unmistakably the insight and genius of Einstein, furnish of themselves of course no evidence of correspondence with experimental and observational fact. They are, nevertheless, necessary qualities for those principles which the human mind is willing to use as the fundamental postulates for science, and their presence must hence be regarded as also furnishing important justification for the acceptance of the principle of equivalence.[source]

In other words: independently of its experimental verification, simplicity of nature and its mental representations must be a basic prerequisite when doing physics. The scientific enquiry, the ‘‘human mind’’ in Tolman’s words, must be guided by the fact that nature is ruled by a few simple fundamental principles. The human mind can bypass the intricate phenomenal world and reach by pure thought these essential principles; once there, the physical world can be reconstructed: this is what Einstein did from 1905 to 1915. To reconstruct the physical world from a few principles, maybe even a single one, should be the ultimate task for every real theoretical physicist: these constituting principles are beautiful by definition.

For many decades, and thanks to Einstein’s influence and the personal effort he put into the propagation of his metaphysical thoughts, this common conception was normally associated with his theory. After the Second World War and the ensuing recession of the atomic projects on both sides of the Iron Curtain, there was a revival of fundamental research in gravitational physics.

In 1973 the voluminous Gravitation, by Charles Misner, Kip Thorne and John Wheeler was published; a textbook extensively employed in general relativity courses and the inspiration for a new approach to the field: the “bible” of general relativity as some still call it. In the Preface the authors talk about their motivations for writing a new book on the topic: ‘‘We have not seen any way to meet our responsibilities to our students at our three institutions except by a new exposition, aimed at establishing a solid competence in the subject, contemporary in its mathematics, oriented to the physical and astrophysical applications of greatest present-day interest, and animated by belief in the beauty and simplicity of nature.’’[source] For them, the use of modern mathematics, such as differential geometry and topology, and the analysis of new gravitational phenomena, such as relativistic stars and gravitational collapse, had left unaltered the essence of the theory: the beauty of the laws governing gravitational phenomena and its incorporation into the theory by a few general principles.

In a lesser known textbook, written by Norbert Straumann, based on personal notes of his course taught at Zurich in 1979, he recalled what Pauli once said on the occasion of the unveiling of a bust of Einstein: ‘‘The general theory of relativity then completed and – in contrast to the special theory – worked out by Einstein alone without simultaneous contributions by other researchers, will forever remain the classical example of a theory of perfect beauty in its mathematical structure.’’[source] It must be remembered that Wolfgang Pauli was not only an extraordinarily talented nuclear physicist; he was also a great admirer of Einstein’s theory. When he was still very young he wrote a short, but very influential, monograph compiling the most important results of the novel theory. His high regard for Einstein’s relativity lasted his entire lifetime.

Another devotee of general relativity was the eminent Indian-American astrophysicist Subrahmanyan Chandrasekhar. He has a lecture entitled ‘‘The General Theory of Relativity: Why ‘‘It is Probable the Most Beautiful of All Existing Theories’’?’’ (A title inspired, according to Chandrasekhar himself, by a comment he found in the weighty Classical Fields of Landau and Lifschitz.) After considering the major achievements of the theory at both theoretical and experimental level, he declares:

The foregoing examples provide evidence that a theory developed by a scientist with an exceptionally well-developed aesthetic sensibility can turn out to be true even if at the time of its formulation, it did not appear relevant to the physical world.
It is, indeed, an incredible fact that what the human mind, at its deepest and most profound, perceives as beautiful finds its realization in external nature.
What is intelligible is also beautiful.[source]

Chandrasekhar wrote this in the mid-eighties. Ten years later, Kip Thorne echoes this tenet in his bestseller Black Holes and Time Warps. He asks himself rhetorically: ‘‘What is the single most important thing that you want your reader to learn?’’ to which he replies, ‘‘My answer: the amazing power of the human mind – by fits and starts, blind eyes, and leaps of insight – to unravel the complexities of our Universe, and reveal the ultimate simplicity, the elegance, and the glorious beauty of the fundamental laws that govern it.’’[source]

The reader must have noted that the previous quotations by Tolman, Chandrasekhar and Thorne, have a common trait: they talk about the ‘‘human mind.’’ The person unacquainted with these sorts of interpretations would think it incongruent to combine physics and philosophy in this way. Yet, discourses of this type are indeed very frequent and constitute the sanctioned metaphysical foundation of the general theory of relativity. For admirers of this theory, nature is not only ontologically beauty but the ‘‘human mind’’ is actually capable of deciphering such beauty. Many things have changed since Einstein originally formulated the general theory of relativity — we now have a different and more powerful mathematics which allows us to understand an ever growing number of physical phenomena — however, the philosophical foundation remains intact: fundamental principles are beautiful and as human beings, we are able to grasp them. What must be retained from this discussion is that beauty, according to the established interpretation of general relativity, means basically reduction to fundamental physical principles. (The relationship between the human and the natural world will be discussed more extensively in the next essay.)

Before bringing this section to a close, let us conclude by referring to a frequent evaluation of the work of two of the most prominent theoretical physicists of the last decades: Roger Penrose and Stephen Hawking. These two physicists have played a leading role in the contemporary infusion of Platonism in general relativity, exalting even more the role of mathematical beauty in theoretical physics. By a way of example, in his influential book The Emperor’s New Mind Penrose, a declared Platonist, asserts that ‘‘Plato’s world consists not of tangible objects, but of ‘mathematical things.’ This world is accessible to us not in the ordinary physical way but, instead, via the intellect. One’s mind makes contact with Plato’s world whenever it contemplates a mathematical truth, perceiving it by the exercise of mathematical reasoning and insight.’’[source] (Italics in the original)

Have string theorists been preoccupied with this issue? If yes, what are the different attempts they have made in order to include in their theory a principle comparable to the equivalence principle of general relativity? Though they have tried, this has been the most elusive task of all. Indeed, so far string theorists have failed to propose a unique principle embracing all the properties of the theory, and, consequently, of the physical world.

As early as 1987, Green, Schwarz, and Witten, wrote: ‘‘In fact, historically, in the case of general relativity, it was the concepts that came first; Einstein first identified the concepts on which a relativistic theory of gravity should be based, and then found the theory. String theory has been the other way around. … At best we have perhaps just begun to scratch the surface of this question.’’[source] Around the same time Michael Green was asking a younger audience: ‘‘How can the logic of superstring theory be discovered? The principles of general relativity must be a special case of the more general principles of superstring theory, and so in a sense general relativity can serve as a guide.’’[source]

The first comprehensive proposal came many years later. This occurred in the mid-nineties. At that time, a fresh, numerous, and robust generation of string theorists were at work. Leonard Susskind proposed to them that this ‘‘simple organizing principle that can be expressed in a phrase or two’’ could be the Holographic Principle: ‘‘My own view is that the lasting idea will be the holographic principle …, the assertion that the number of possible states of a region of space is the same as that of a system of binary degrees of freedom distributed on the boundary of the region.’’[source] The AdS/CFT correspondence has provided some evidence in support of this idea, however, as we saw in the first essay, much remains to be done. Witten’s query: ‘‘What is the core idea [of string theory] analogous to the principle of equivalence in the case of general relativity?’’[source] still awaits an answer.

In this section I have exemplified by means of four theories, electromagnetism, quantum mechanics, particle physics, and general relativity, how the assessment of beauty in twenty-century physics changed over time. I depicted the evolution of these four cases, showing that they are not reducible to a single common pattern of change. I have also described how string theorists have taken advantage of these consensual interpretations of beauty in order to advance their own theory as a beautiful construct. These interpretations, already existing and widely accepted, have provided the basis for string theorists’ rhetoric. In turn, string theorists’ main criterion of beauty, unification, has begun to influence the way these more standard subjects are conceived.

It must be noted that the aesthetic appreciation of a particular physical theory is not indifferent to the way beauty is seen in neighbouring theories. For this reason, the previous demarcation between electromagnetism, quantum mechanics, particle physics, and general relativity, must be considered a schematic one. In fact, physicists from diverse areas share a set of ideas and attitudes, including sometimes aesthetic criteria, and the different subdomains are in constant interaction. An expert in one subfield can inoculate his colleagues in other subfields with the aesthetic criteria he generally uses to assess his theory. The constant reinterpretation and adaptation of aesthetic criteria from other subfields is what I had in mind when I observed that Pauli and Dirac were deep admirers of Einstein’s theory. The same applies when Steven Weinberg, a particle physicist, refers to Hermann Weyl, a mathematical physicist, in his textbook on general relativity: ‘‘Symmetry, as a wide or as a narrow as you may define it, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection.’’[source] Many physicists also quote Weyl saying: ‘‘My work always tried to unite the true with the beautiful, but when I had to choose one or the other, I usually chose the beautiful.’’ In conclusion, a systematic analysis of the role of aesthetics in physics must consider that the idea of beauty changes over time and travels across subfields.

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3. The Most Beautiful of All Existing Theories? (III of V)

2008-02-09T21:55:00.000-08:00

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The beauty of superstrings
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High energy theoretical physicists, including, of course, string theorists, would hardly disagree with what Godfrey Harold Hardy, one of the finest twentieth-century mathematicians, once said: ‘‘The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.’’[source] (Italics in the original.) Like many mathematicians, theoretical physicists have also tried to convince the outsider that this is exactly what they do in their everyday work: they search for beauty. This idea, as we have seen in this essay, is well disseminated. Popular science writers and historians of science have given into this temptation and assure us that mathematical beauty is the most suitable guide to unveiling the laws of nature. For example, the French historian of science René Taton was convinced by his compatriots Henry Poincaré and Jacques Hadamard that the best guide for making progress in mathematics was that sense of beauty which in diverse degrees every practitioner of the activity possesses.[source] Under the influence of this deeply rooted belief and due in part to the absence of concrete historical analyses of the term, string theorists have been led to employ the word ‘‘beauty’’ in a vague sense; many times with religious connotations. This has given rise to inappropriate metaphysical pronouncements such as the following: ‘‘It’s the kind of beauty that might be hard to explain to a person from a different walk of life who doesn’t deal with science or math professionally.’’[source] According to this belief, mathematical beauty cannot be understood or explained, like a faith it must be felt. Since this ‘‘beauty of superstring theory’’ is a cliché which appears in every single account on the subject, and I could easily resort to hundreds of citations in order to illustrate this, I will instead try to decipher when, and in which circumstances, did string theorists start to talk publicly about it. The idea of this section is then to go through some of the most important articles that string theorists have published since the very beginning of the theory and try to grasp the meaning of the concept of beauty in every specific case. At the same time, I will try to uncover a possible pattern of change in their conception of beauty. The discussion of the previous section will help in this aim.

John Schwarz, considered to be the father of superstrings, has persistently insisted that the strongest motivation for pursuing his research in the early days of the theory was the internal beauty it showed. At a remembrance ceremony for his collaborator Joël Scherk, he said: ‘‘I think we were kind of struck by the mathematical beauty; we found the thing a very compelling structure. I don’t know that we said it explicitly, but we must have both felt that it had to be good for something, since it was just such a beautiful, tight structure.’’[source] And in another place he reiterates: ‘‘We felt that the theory has such a compelling mathematical structure that it ought to be good enough for something.’’[source]

In order to track the origin of this alleged ‘‘beautiful mathematical structure,’’ I have consulted several of the most important early review articles on dual models and string theory. There, I looked for explicit mention of the following words: simplicity, elegance, and beauty. Here it is what I found. (I did not take into consideration references of the kind, ‘‘introducing this parameterization the equation x looks more elegant,’’ or, ‘‘the previous notation allows a simplification of the expression x.” As in the following example: ‘‘Lovelace [25] has introduced a notation in which the results of the above papers can be expressed fairly simply and elegantly.’’[source] In all the cases I detected, the meaning of these uses is simply a desire for a simpler mathematical formulation, more manageable and less troublesome. Here this has little to do with an aesthetical criterion or an ontological conception; the main concern of this essay.)

The first mention of simplicity and elegance appears in Gabriele Veneziano’s review of 1973. This occurred five years after the publishing of his well-known paper on dual models, generally considered the starting point of string theory. In this later review he says:

What makes this approach interesting is that, in spite of looking a priori a desperate problem, construction of dual models has been achieved and the solutions are simple, elegant, and seem to have quite a few properties in common with nature. The problem is not completely solved though, for reasons to be discussed at the end of this review. On the other hand, the number of requirements a dual model has to obey is so large, that it comes as no surprise to find extremely small freedom to manoeuvre. This is of course what makes the dual program most fascinating.[source]

In addition to the standard S-matrix postulates, which Geoffrey Chew introduced in the mid twentieth century, dual models are defined according to an extra set of conditions. The general method is a standard procedure in theoretical physics: all the conditions to be imposed on the model are defined and then the necessary consequences are reached. From the application of the postulates it follows that the symmetries of these quantum relativistic models produce a spectrum that is free of ghosts, negative norm states, and includes low energy masses in accordance with experimental observations (states fitting the linear Regge trajectory). What was then needed was to check if the theoretical model would adjust to a broader range of experimental data yet to be carried out. This conundrum was recognized by Veneziano at the end of the article:

I am now faced with the most embarrassing question of where this duality game is going to take us in the future. Are we really close to a breakthrough explanation of the hadronic spectrum of particles and their interactions, or are we just being carried away from physical reality by some perverse though beautiful mathematical apparatus?[source]

These passages contain two of the three references to elegance and beauty made by Veneziano in his review paper. A third reference can be found in a paragraph going from page 209 to 210: ‘‘On the other hand, when unitarity is enforced on these Regge models, the resulting constraints seem to spoil their original beauty and simplicity.’’ (Italics added.) What he actually means by ‘‘the beauty and simplicity of Regge models’’ does not concern us directly since a few paragraphs above he had noted: ‘‘Hence we shall not need to enter into details of Regge theory.’’ But, what did he mean when he said that ‘‘construction of dual models has been achieved and the solutions are simple, elegant, and seem to have quite a few properties in common with nature’’? He meant that the stringent duality constraint imposed on the model, as expressed in equation (5.20) of the paper, was satisfied by a group of transformations that on the one hand were not very complicated and on the other were rich enough to generate the expected low mass states. This synthesis of an unsophisticated mathematical formulation and successful physical predictions was what Veneziano dubbed ‘‘simple and elegant solutions.’’ There is nothing new about this; it is simply the way physics has been done for centuries. And, what was he suggesting when he talked about the possibility of ‘‘being carried away from physical reality by some perverse though beautiful mathematical apparatus’’? Note that he said ‘‘beautiful mathematical apparatus,’’ implying that mathematics ought to be regarded, for dual model theorists, as a practical tool and nothing more. In this sense, the importance of mathematics for dual models was fairly similar to the role of complex numbers in electrical engineering: complex numbers can be very interesting, beautiful if you wish, however, engineers must restrict their attention to the resolution of real, sometimes highly complicated, physical circuits.

In his 1973 report John Schwarz wrote: ‘‘Since the Veneziano model is especially elegant for a particular ‘critical’ space-time dimensionality, it is natural to ask whether the model can be modified so as to change the critical dimension.’’[source] In fact, during 1971 and 1972 it was proved that the Veneziano model (which Veneziano had named the generalized beta-function model and which we now call the bosonic string) was free of ghosts for spacetime dimensions equal or lesser than twenty-six. The critical dimension Dc = 26 was especially attractive because the cancellation of the quantum anomaly in the algebra of projective transformations was accompanied by the existence of null states, giving rise, among other interesting results, to a complete basis for the construction of physical states. These unexpected properties of the solutions in the D = 26 of the Veneziano model is what Schwarz meant by ‘‘especially elegant.’’

Joël Scherk once used the term elegant in his review paper, though not referring to his own theory but to supersymmetry: ‘‘Section V covers the spinning string (Neveu-Schwarz-Ramond model) beginning with the elegant equations of Wess and Zumino (1973), then solving them and quantizing them. Fermions and mesons are obtained from two opposite boundary conditions of the classical equations.’’[source] It is interesting to note that even though this paper was published in January 1975 – only eight months after Scherk’s and Schwarz’s claim that dual models described ‘‘particles other than hadrons,’’ namely, gravitons − there is no mention of the ‘‘beautiful tight structure’’ of the theory, which Schwarz today tries to persuade us of.

These are the only allusions to simplicity, beauty and elegance I could find in these early articles on dual models and strings. There is again an explicit mention of beauty and elegance in the 1982 Schwarz paper on superstring theory, the new name assigned to dual models. In this new review there is no notable difference in his use of the term “elegant” to his previous paper published ten years earlier:

As already discussed in section 1, any attempt to define the superstring theories for D [less than] 10 is likely to lead to serious problems. Even if this were possible, I would still argue that the D = 10 choice is so much more elegant and beautiful that it may be more fruitful to try to interpret the extra dimensions physically rather than to reject them summarily in favor of less attractive alternatives. This approach — first proposed in the superstring context in ref. (138) and developed further in ref. (139) — requires that six of the spatial dimensions form a compact space small enough to have avoided experimental detection.[source]

During the late eighties and early nineties, and motivated by the relative success of the heterotic superstrings, string theorists were submerged in intricate and endless computations trying to recover the standard model using a ‘‘top-bottom’’ approach. At that time no one was talking publicly about a beautiful construct. In fact, the theory was in an ugly impasse and mathematical consistency was the only remote trace of beauty.

In contrast to string theory, the beauty of supersymmetry, and its local version, supergravity, was recognized very early on. In 1981, talking about supersymmetry, Peter van Nieuwenhuizen wrote metaphorically that: ‘‘It is the most beautiful gauge theory known, so beautiful, in fact, that Nature should be aware of it!’’[source] In a similar vein, Martin Sohnius wrote in a well-known review: ‘‘Supersymmetric theories (the subject of this report) are highly symmetric and very beautiful. They are remarkable in that they unify fermions (matter) with bosons (the carriers of force), either in flat space (supersymmetry) or in curved space-time (supergravity). Supergravity naturally unifies the gravitational with other interactions.’’[source] In fact, for a long time (from the late seventies to the early nineties) the idea of a beautiful unification of all the forces in a single theoretical framework was headed by supergravity theorists. At that time supergravity was the stronger candidate for a unified theory. In Sohnius’ review, the Introduction begin by stating that: ‘‘The aim of theoretical physics is to describe as many phenomena as possible by a simple and natural theory. In elementary particle physics, the hope is that we will eventually achieve a unified scheme which combines all particles and all their interactions into one consistent theory. We wish to make further progress on the path which started with Maxwell's unification of magnetism and electrostatics, and which has more recently led to unified gauge theories of the weak and of the electromagnetic, and perhaps also of the strong interaction.’’[source] At the end of the paper we find a short reference to superstring theory. In popular accounts too supergravity used to receive more attention than it does today. Only in the early nineties, motivated by the finding of mathematical dualities connecting the five different superstring theories and the proposal of the M-theory, did the discourse of a unified theory begin to be led by string theorists. Nowadays, indeed, it is very hard to find an article or a book proclaiming that supergravity is a consistent unified theory. In this respect, supergravity and superstrings have swapped positions. Why superstring theory superseded supergravity is another story.

Let us turn back to string theory. During the same period, late eighties-early nineties, something quite significant was happening. There was a growing public interest in science and in theoretical physics particularly. This move resulted in a considerable amount of popular science books being published and sold. We have already pointed out the books by Paul Davies, Roger Penrose, Kip Thorne, and Murray Gell-Mann. Other best-sellers were written by Stephen Hawking, Dennis Overbye, Steven Weinberg, and, the only string theorist, Michio Kaku. It is not hard to verify that all of them set out to exalt the beauty of the universe and the human quest for these ultimate mathematical truths. It was generally asserted in these accounts that physicists were reaching a theory capable of explaining the birth of our universe as well as its future death, in addition to everything it contained; the so called ‘‘theory of everything.’’ An old dream was reaching an end. As Kaku put it in 1987: ‘‘Over the last two thousand years, we gradually have realized that there are four fundamental forces: gravity, electromagnetism (light), and two types of nuclear forces, the weak and the strong. One of the great scientific puzzles of our universe, however, has been why these four forces seemed so different. For the past fifty years, physicists have grappled with the problem of uniting them into a coherent picture.’’[source]

Although we observe in these popular accounts a clear association between a mystical beauty of the universe and an ontological unity, ‘‘the unity of nature is beautiful,’’ we do not find in most of the string theory literature of the time a straightforward identification of the term beauty with the theory itself. In 1996, one year after the emergence of M-theory, an article entitled ‘‘Explaining Everything’’ appeared in the most popular scientific magazine worldwide. It begins by stating:

The Theory of Everything, or TOE, theorists believe, is hovering right around the corner. When finally grasped — the fantasy goes — the TOE will be simple enough to write down as a single equation and to solve. The solution will describe a universe that is unmistakably ours: with three spatial dimensions and one time dimension; with quarks, electrons and the other particles that make up chairs, magpies and stars; with gravity, nuclear forces and electromagnetism to hold it all together; with even the big bang from which everything began.[source]

In this extract, and throughout the entire article, ‘‘The TOE’’ is deemed to be the mathematical description of the beautiful unity of nature, however, there is still no reference to the beauty of the theory itself. Two years later, again in Scientific American, an article appeared making explicit mention of the M-theory: ‘‘Until recently, the best hope for a theory that would unite gravity with quantum mechanics and describe all physical phenomena was based on strings: one-dimensional objects whose modes of vibration represent the elementary particles. In 1995, however, strings were subsumed by M-theory.’’[source] Once more, there is no comment on the ‘‘beautiful mathematical structure of the theory.’’

In 1999 The Elegant Universe was published. Here, for the first time, string theorists publicly declared that they had found the ‘‘beautiful unified theory’’ grasping the ‘‘beautiful unity of nature.’’ In the first paragraphs of the Preface Brian Greene writes:

Instead, he [Einstein] was driven by a passionate belief that the deepest understanding of the universe would reveal its truest wonder: the simplicity and power of the principles on which it is based. Einstein wanted to illuminate the workings of the universe with a clarity never before achieved, allowing us all to stand in awe of its sheer beauty and elegance. … And now, long after Einstein articulated his quest for a unified theory but came up empty-handed, physicists believe they have finally found a framework for stitching these insights together into a seamless whole—a single theory that, in principle, is capable of describing all phenomena. The theory, superstring theory, is the subject of this book.[source]

Resorting to Einstein’s natural philosophy and “aesthetic criterion,” in addition to, of course, Einstein’s symbolic power, Greene sought to introduce superstring theory to the public at large as the most beautiful theory ever conceived. That this constituted the general opinion within the community, rather than a personal judgement, is confirmed by the fact that The Elegant Universe has been considered since its publication, by string theorists themselves, the essential reference book for every public discussion on the theory (see essay 1). The popularity of the theory during recent years has shown that to some extent they succeeded.

I think that popular science literature and all that it involves (an appropriate social and cultural context, science writers, an interested and stable audience, publishers, an established network of commercialization, among other factors) explains in great part the confidence, first veiled then declared, that many string theorists have had in proclaiming the beauty and simplicity of their theory. For them, as we have seen, it is crucial to know that their theory is a beautiful theory according to the established criteria imposed by other theories. However, the most important criterion is unity. In order to enforce their own criteria string theorists have intelligently interpreted the significance of the other theories and modified their alternative, useless, ‘‘aesthetic criteria.’’ A propitious context favoured them, and the logic for capitalizing on it is straightforward:

1. The general theory of relativity is a beautiful theory The standard model is a beautiful theory
2. If, general relativity + standard model = superstring theory
3. Then, superstring theory is a beautiful theory

A last word on string theorists’ motivations. What brought them to reinterpret the aesthetic criteria of previous theories according to their own needs and to take advantage of the broader context cannot be seen as a wicked practice meriting banishment from science. Firstly, reinterpretations are a common practice in science. Secondly, the degree of acceptance of competing theories by the “scientific” as well as by the “extra-scientific” milieu allow supporters of each camp to gain valuable positions in the field of struggles confronting their intellectual creations. As it is well known, this is one of the major purposes of modern scientific magazines and science books. No doubt, string theorists have been very clever on this sociological issue; much more than its contenders. The ground prepared, the next generations of string theorists are ready to admit and repeat the message: ‘‘String theory dovetails beautifully with the previous ideas for explaining the patterns in the Standard Model, and does so with a structure more elegant and unified than in quantum field theory.’’[source]

In this section we have seen that, in contrast to what is currently claimed, string theory was not always considered to be a beautiful theory. The public recognition of the beauty of the theory is recent, dating from around 1999, and it was due mainly to the convergence of two factors: a favourable context, “internal” and “external,” and an acute sense of opportunism. *******You can read

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3. The Most Beautiful of All Existing Theories? (IV of V)

2008-02-09T20:57:00.000-08:00

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String theory and its experimental foundation
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In spite of the significant effort that string theorists have made to gain credibility and respect from other physicists there is still no global consensus regarding the way they conceive science. Criticisms concerning the lack of a concrete link between mathematical formulae and the empirical physical world are abound, especially from physicists with a more experimental orientation. In the previous section I have shown how diverse interpretations of the past, made by groups with different traditions, are often exploited in order to promote a certain way of doing science. This is the case with the connection between the concept of beauty as seen by string theorists and the experimental tradition of science.

One group of detractors, educated in the experimental tradition, argue that it is absurd to talk about the mathematical beauty of a physical theory before any experimental verification. As they see it, there might be many beautiful theories but there can only be one that accurately describes reality. It is the goal of the experiment to determine the right one. If Maxwell’s theory is correct it is because it predicted the electromagnetic waves then discovered by Hertz; Dirac’s equation is exact for the simple reason that positrons were discovered in the early thirties by Carl Anderson; the standard model is correct since its prediction of the existence and precise properties of the intermediate bosons W and Z was confirmed at CERN in 1983 (in addition to this, the last quark, the top or truth, was discovered in 1995 at Fermilab); and Einstein’s general theory of relativity is truthful only because the bending of light was conclusively confirmed in 1919 by Arthur Eddington. To them, string theorists reply that they are proceeding in the same exemplary way as Einstein and Dirac did: ‘‘In a certain sense, therefore, I hold it true that pure [mathematical] thought can grasp [the unique] reality, as the ancients dreamed.’’ In this famous sentence Einstein implicitly assumed that there is a one to one relationship between the natural and the mathematical world. To ‘‘grasp’’ the mathematical world means to understand nature. Then, there cannot be many beautiful theories for a unique natural world, as some string theory critics maintain; rather, there is one unique beautiful and simple theory for a unique physical reality. And, string theorists sustain, in the same way as general relativity is the unique theory precisely describing gravitational phenomena, superstring theory is the unique consistent theory describing the whole physical world. This belief is shared by many contemporary theoretical gravitational physicists: ‘‘Within theoretical physics, the search for logical self-consistency has been always more important for progress than experimental results.’’[source] This confidence is their motivation for pushing onward with the theory.

As it was proved a posteriori that Einstein had been right to remain optimistic regarding his general theory of relativity, string theorists believe that the ‘‘beautiful structure’’ of their theory will be someday verified in the laboratories. Every physicist knows that when Einstein was asked about the possibility that Eddington’s observations could have disproved his gravitational theory he replied: ‘‘I would have felt sorry of the dear Lord, because the theory is correct.’’ Similarly, David Gross says: ‘‘Never, never, never, never give up!’’ For string theorists, the validity of the theory cannot solely rely on the results of future ‘‘crucial experiments.’’ If a theory is beautiful, that is, correct, experiments cannot change that. When John Schwarz was asked about the risk of superstring theory being invalidated by experiments, he emphatically replied:

I believe that we have found the unique mathematical structure that consistently combines quantum mechanics and general relativity. So it must almost certainly be correct. For this reason, even though I do expect supersymmetry to be found, I would not abandon this theory if supersymmetry turns out to be absent.[source]

The above argument can be summarized in one single phrase: string theorists, by means of mathematical beauty and simplicity, discover rather than invent.

Another common criticism, also coming from the experimental tradition, asserts that the development of the theory has ignored the most recent experimental data. Philip Anderson, a distinguished condensed matter physicist, is one of these critics and is convinced that string theory is taking us back to the pre-scientific era:

My belief is based on the fact that string theory is the first science in hundreds of years to be pursued in pre-Baconian fashion, without any adequate experimental guidance. It proposes that Nature is the way we would like it to be rather than the way we see it to be; and it is improbable that Nature thinks the same way we do.[source]

To these attacks, string theorists are prompt to respond that Newton did not require any observational data to discover his gravitational law (he was isolated from everything else due to the plague hitting Europe) neither did Einstein need any to discover the theory of relativity (in fact, during his ‘‘annus mirabilis’’ he was confined in a gloomy patent office). It is thus currently claimed that if physicists are sufficiently smart, ‘‘pure thought’’ is more than enough to unravel the ‘‘ultimate truths of the universe.’’

Even though theoretical physicists differ on certain points with colleagues who have a more experimentalist disposition, there is fundamental agreement on one point: the existence of an ordered world governed by simple laws which are there to be ‘‘dis-covered.’’ Both groups are convinced that nature is ruled by simple mathematical laws. The main difference between them is that one thinks that these laws can be discovered only by means of experience, and the other group believes that they can bypass natural experience and reach reality through pure thought. However, they concur with each other that nature and its mathematical description is beautiful. Modern physics would be inconceivable without this premise.

Recently, Leonard Susskind has proposed the possibility, within string theory, that the laws of physics may not be as elegant as it has been proclaimed:

Physicists, particularly theoretical physicists, have a very strong sense of beauty, elegance, and uniqueness. They have always believed that the laws of nature are the unique inevitable consequence of some elegant mathematical principle. The belief is so deeply ingrained that most of my colleagues would feel an immense sense of loss and disappointment if this uniqueness and elegance turned out to be absent-if the Laws of Physics are “ugly” … . Despite the protestations of physicists that the laws of elementary particles are elegant, the empirical evidence points much more convincingly to the opposite conclusion.[source]

It is impossible to know the transcendence that Susskind’s words will have in the near future in the realm of theoretical physics and superstring theory. Maybe none. Nevertheless, one thing is certain: Western science will look completely different the day it stops believing in and searching for beautiful physical laws.

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3. The Most Beautiful of All Existing Theories? (V of V)

2008-02-09T19:58:00.000-08:00

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Conclusions
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The first thing I have tried to show in this essay is that it is impossible to universally define what a beautiful theory is. In fact, twentieth-century physics illustrates that the idea of what is beautiful within physics and in a particular theory is subject to change. Some models have being raised in order to explain such changes. The philosopher of science James McAllister, refuting Thomas Kuhn, has proposed that ‘‘aesthetic criteria’’ of empirically successful theories tend to be appreciated as the norm of beauty. This process, dubbed ‘‘aesthetic induction’’ by McAllister, establishes the ‘‘aesthetic canon’’ employed for evaluating other empirically unverified theories.[source] In my opinion, instead, the beauty of a physical theory is not determined by the experimental success of such canonical theories. Let us take, for instance, electromagnetism. It is a theory that has been empirically confirmed an infinite number of times since its formulation, nevertheless, string theorists assess its beauty in a very precise sense: the unity of electricity and magnetism. (The same holds true for general relativity, quantum mechanics and particle physics.) But this interpretation, favoured by string theorists and other supporters of the unification program, is not always shared by physicists from other subdisciplines. In my view, what a group of physicists tend to see as beautiful in a specific theory and at a given time depends on certain manifest properties of the theory and on its position in the space of competing theories. Relying on this, practitioners will try to take advantage of present interpretations of well established theories as well as force new reinterpretations. The idea of this strategy is to maximise the chances of imposing their own explanatory model. In general, the evaluation is carried out on the basis of historical, theoretical, and sociological grounds.
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From this perspective, if string theorists consider a particular theory to be beautiful it is because it is prevalently interpreted as containing the idea of unity (for example, the electroweak model). On the other hand, if current interpretations of a theory do not explicitly highlight its unifying aspect, string theorists will try to interpret it as such. For supporters of the unification program, the entire history of physics, or at least its main achievements, ought to be understood as a long march towards the beautiful unification of all the forces in a final theory. As Steven Weinberg puts it:

One of the primary goals of physics is to understand the wonderful variety of nature in a unified way. The greatest advances of the past have been steps toward this goal: the unification of terrestrial and celestial mechanics by Isaac Newton in the 17th century; of optics with the theories of electricity and magnetism by James Clerk Maxwell in the 19th century; of space-time geometry and the theory of gravitation by Albert Einstein in the years 1905 to 1916; and of chemistry and atomic physics through the advent of quantum mechanics in the 1920s.[source]

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In short: in order to promote their own creation, string theorists have interpreted past theories in such a way as to stress the importance of unity.
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But, superstring theory has not been always thought to be a beautiful theory. In the third section I suggested that until the early nineties a crucial ingredient was missing: a propagandist Neo-Platonic discourse praising the mystical connection between the material world and our mathematical constructs. It was claimed that we were on the right track to the ultimate explanation of everything, ready to discover the fundamental equations in which God had written the elegant book of nature. Just to quote one final example, consider what John Barrow wrote in one of the most popular books on the theory of everything:

Our attraction to that quality which we have come to call “beauty,” and which we associate with the detection of innate unity and harmony in the face of superficial diversity, has led us to expect that the unity of the Universe should be expressed in certain particular ways.[source]

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Under the pressure of this motivating ‘‘external’’ discourse, string theory became around the turn of the century a popular beautiful theory. This appreciation reached its apex of popularity during the first years of the twenty-first century; since then it has considerably waned.
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If the beauty of superstring theory can be understood as having concrete historical and sociological roots, why then do so many people talk about the “sense of beauty” in physics as something indescribable or too complicated to be conveyed to the non-expert? First of all, I must observe that the metaphysical discourse concerning physics and beauty is monopolized by the leaders, those who have been authorised by the community to write popular books and give public talks on the subject. These are the persons who are always interviewed by journalists working for scientific magazines and famous newspapers. In addition, this attitude has been promoted by an elitist approach to the history of physics. Poincaré, Einstein, Schrödinger, Dirac, Weinberg, Witten, and so on, these are the “Greats” who have grasped the beauty of nature and expressed it in beautiful equations. Even Thomas Kuhn once wrote: ‘‘Something must make at least a few scientists feel that the new proposal is on the right track, and sometimes it is only personal and inarticulate aesthetic considerations that can do that.’’[source] (Italics added.) This prejudice is reiterated again and again. But, after some experience within the field, I can assert that the anonymous string theorist, he or she who silently builds the beautiful edifice but never appears in the newspapers, does not know what is meant by mathematical beauty. The large majority of the members of the community (including junior and senior professors, postdocs, and graduate students), have never felt this unexplainable sensation that connects the ‘‘human mind’’ with the ‘‘glorious beauty’’ of nature. When they look for mathematical solutions to a particular problem, they are not guided by beauty, and, when they explain their results to other colleagues, beauty is never proposed as an argument. Hence, I think that if they publicly repeat this belief, it is simply because they have been educated within this hegemonic discourse and because the authority of the theory depends on it. The discourse on beauty has been important in two aspects: to attract new members to the field and to shield the theory from attacks coming from, but not limited to, the experimental tradition.
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If I refuse the common idea that theoretical physicists may be effectively guided in their work by a ‘‘sense of beauty,’’ does it mean that I reject the significance of the assumption that the laws of nature are beautifully simple? Absolutely not! Contemporary physicists, including experimentalists, are persuaded that they are the inheritors of an old tradition begun in ancient times by Plato, or at least by Galileo almost four hundred years ago: “Sometimes in discussions among physicists, when it turns out that mathematical beautiful ideas are actually relevant to the real world, we get the feeling that there is something behind the blackboard, some deeper truth foreshadowing a final theory that makes our ideas turn out so well.”[source] That is, they believe that the fundamental laws of nature are written in mathematical characters and that their task is to discover them. Of course, this conviction is imprecise and from the historical point of view it is incorrect. Many theoretical physicists would be astonished to discover that the mathematization of natural phenomena was still a controversial issue during the nineteenth century and is only recently that it has become a common practice. However, the assumption has been very successful and modern physics stands on it. In conclusion, to Gabriele Veneziano’s question: “And what would happen if the simplicity of nature were a myth?” (“E se poi la semplicità della natura fosse un mito?”) I reply: of course it is a myth, but if you removed it the whole beautiful edifice of modern science would collapse.[source]
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SELECTED READINGS FOR ESSAY 3 (V)

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4. The Superstring World (I of IV)

2008-02-09T19:50:00.000-08:00

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Introduction
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Even today, five hundred years after the scientific revolution and in the midst of an era where scientific collaboration has reached global scale, many physicists still think that the scientific fact is the sudden discovery of an inspired individual. The flash of insight – the “aha” moment, currently pictured as a light bulb appearing over the head of somebody having an unexpected brilliant idea – is a personal experience, and the social and cultural context has nothing to do with it. It is said that the real genius works isolated from the external world; the influence of the latter could only lead him astray from the road to truth. Once the revolutionary hypotheses of this unknown man are finally made public, the myth continues, they are aggressively repelled by those supporting the established system of beliefs. But, since natural truths are universal, at the end of the day the new ideas become adopted and the discoverer receives public recognition. The penchant for the biographical genre of many accounts on the history of physics is a clear sign of the broad acceptance of this myth of the lone genius. Examples of these extraordinary individuals are Isaac Newton, Albert Einstein, Marie Curie, and Stephen Hawking. The young Newton secluded himself in Cambridge with the intention of sheltering from the plague; there, he discovered the laws governing the fall and motion of earthy and heavenly bodies. Einstein was destined, due to incomprehension from his incompetent peers, to squander his most creative years on a tedious job at a patent office; there, he transformed forever our understanding of space and time. Curie worked all her life in a gloomy laboratory like an old alchemist; there, she discovered radioactivity. And Hawking, though reduced for decades to living in a wheelchair, has achieved what Einstein could not do: the unification of gravitation and quantum mechanics!

The tendency to conceive the scientific discovery as purely individual is explicit in the following quote:

Consider the mad but brilliant scientist, long deprived of food, sleep, soap, and water, pacing the hallways until the “aha” insight hits at 4 a.m. Say he has just solved a fundamental problem in modern physics concerning the behaviour of subatomic particles. If he can demonstrate through a mathematical proof his logic ... his tenure worries are probably behind him. True, he must be able to convince one journal to publish his idea. However, even if his idea is not well received by his immediate colleagues, as long as it is recognized by eminent members of the scientific community, his future is relatively secure.[source]

According to these two psychologists of creativity, the fundamental step is done by the lone particle physicist; the task of the other physicists is simply to approve, or reject, the proposal. We can summarize the previous individualist approach by saying that the essence of the process underlying creativity occurs in the individual’s mind.

The unprecedented scale and complexity of contemporary science – a phenomenon normally attributed to the events of the Second World War – has awakened the interest of psychologists, sociologists, and historians, in the cooperative character of works of science. Historians of physics, in particular, have realized this aspect of modern science and nowadays physical facts or theories are most of the time rightly described as collective undertakings. Whether the subject is the discovery of X-rays, the theory of relativity, the spectral lines of atoms, or the quarks, these studies explicitly take into account the collective side of the endeavour. In this way, and contrary to most pre-war accounts that emphasized the role of the isolated scientist producing unique breakthroughs, the involvement of a large number of participants is preferred in present discussions.

Like other modern histories of science, my description of the evolution of string theory is not that of a genius discovering the truths of nature. I believe that there is no such book of nature that an elite few are able to read by pure inspiration. (See the discussion of essay 3, “Superstrings, The Most Beautiful of All Existing Theories?”) I too consider the scientific work to be a joint effort where many professionals take active part. Even so, my contextualist approach is still broader than that suggested by previous models.

As a way of clarifying the difference between these two approaches, which I consider complementary, let me refer to a personal anecdote. Just before finishing my PhD, which I did on the AdS/CFT correspondence, I contacted several professional historians of science by email; I hoped they could furnish me with some guidance on my ongoing project on the history of string theory. One of these persons was a historian of physics, director of a distinguished science history department in the USA. As expected, he replied to me. In the email, the scholar told me that he too was very enthusiastic about the history of string theory and that this interest had spurred him to spend two years at the Institute for Advanced Study in Princeton. Since he did not supply me with extra information concerning his results, and since I did not know about any published material following his stay, I assumed that the research was a sort of ethnographic investigation such as those carried out by traditional laboratory studies: two years trying to decipher what string theory was; what Edward Witten and company had in mind; and, consequently, how progress was made. If my assumption was correct, then, the idea was to grasp string theory by means of a detailed survey of one of the most creative groups in the field. My prior scepticism about this classical approach in science studies grew when the historian of science told me that – during the whole time he spent at the AIS – he could not witness any of the features I sketched in my note. My immediate reaction, which of course I kept for myself, was: but, how can you aspire to understand string theory confining your observations to such a reduced group of theorists? There is no doubt that string theorists at the IAS are leading experts; however, there is much more happening out there. And, I am not just talking about the hundreds of other string theorists currently contributing to the articulation of the theory; I am thinking more broadly. What about all the people that have talked and written about string theory on radio and TV shows, high school classrooms, newspapers, magazines, and the internet? And, what about the audience? What about the millions of people that have read or seen Brian Greene’s The Elegant Universe? Are they simply spectators of the plot performed by professional string theorists? If not, what is their role in this huge enterprise called string theory? That, of course, could not be answered within the walls of the IAS.

As stated earlier, it is impossible to properly value the influence of the environmental milieu to scientific creativity within the Romantic perspective of the lone genius; however, from my point of view, a similar misunderstanding results when the collaborative work is reduced to the sole contribution of the specialists in the domain. This is what occurs when people try to understand string theory centring on the thoughts and feelings of Witten and other famous experts. It is my belief that science, like any other human activity, is the product of the cooperation of numerous individuals, both from the “in” and the “out,” and each of them performing an essential task to bring to a conclusion the work of science. This complex web of interactions is what has given rise to string theory as we know it today. (The reference to a “web of interactions” provided the title to this set of essays: “Spinning the Superweb.”)

Accordingly, I sustain that string theory, or a fact within it, is the collaborative product of a huge number of individuals, including – of course – those not trained professionally within the field. We can think of the superstring world, to use the term of the American sociologist Howard Becker[source], as the network of cooperative links among participants; where “participants” means all those, from the inside and the outside, having something to do with the theory. Therefore, a fact in superstring theory, such as the AdS/CFT correspondence, must be seen as the product of the superstring world and not the creation of a single individual (Juan Maldacena) or group of talented theorists (Edward Witten, Igor Klebanov, Alexander Polyakov, etc.).

Like all my previous essays, this one also takes a contextualist stand, i.e., it focuses on the influence of the social and cultural context of string theory. It examines the links of the web of interconnections between the in and the out constituting the superstring world. Consequently, if, as I have argued in essay 1, textbooks and popular science materials have had an impact on the progress of string theory, it is natural to enquire about the function of their authors in the superstring world. This is precisely the subject of the main section of this essay.

The essay is laid out as follows. In the first section, I will revise two ordinary myths about creativity in theoretical physics: the gifted child and the creative dream. Well-known anecdotes will be briefly recounted in order to prepare the ground for the more advanced discussion that follows. The subject of the next section will be the collective nature of string theory. This is the main section of the essay and it is divided into two parts. In the first part, I will describe the network of string theorists who have formulated the AdS/CFT correspondence. In the second part, I will concentrate on those contributors who are usually ignored, such as popular science writers and string theory fanatics. Finally, I will summarize the main results and discuss ways to elaborate on the hypotheses here proposed.

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4. The Superstring World (II of IV)

2008-02-09T19:45:00.000-08:00

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SELECTED READINGS FOR ESSAY 4 (II)

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Creativity and theoretical physics
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For more than fifty years, from the first psychometric experiments to contemporary contextualist approaches, creativity in science has been a growing topic of research interest. The outstanding achievements and lives of Charles Darwin, Sigmund Freud and Albert Einstein have been the theme of innumerable psychological investigations. At the base of this interest in scientific creativity is the conviction that it entails mental processes that are common to other creative manifestations. As an introduction to the understanding of creativity as a collective endeavour, in this section I will review two common theories of the individualist perspective: the gifted child and the creative dream.

Albert Einstein is well-known for having been one of the greatest physicists of all time. His accomplishments, including his crucial contribution to the birth of quantum theory and his formulation of the theory of relativity, are highly celebrated by both the professional physicist and the non-expert. In the innumerable psychological descriptions that have been made of him, he is invariably presented as the archetype of the creative person. In the following paragraphs I will use Einstein’s renowned figure to reconsider the theories of the gifted child and the creative dream; afterwards, I will suggest a possible relationship, though subtle, between each of these widespread ideas and current beliefs concerning the production of string theory.

In the comprehensive Encyclopedia of Creativity edited by the psychologists Mark Runco and Steven Pritzker[source], there is, as expected, an entry to Albert Einstein. The article was written by Arthur I. Miller, a known biographer of Einstein. There, he writes: “For the most part, during his childhood Albert was a solitary child, preferring private games that required patience and perseverance ... .” (p. 643.) And, in the next page he quotes Einstein: “teachers in the elementary school seemed to me like sergeant and the teachers in the [Luitpold] Gymnasium the lieutenants.” (Note and italics in the original.) In the first passage, the youngster Einstein is depicted as an aloof and intelligent kid who abstained from participating in the dull games of other children of his age, favouring, instead, activities where he could use his intellect. His early rejection of social norms then extended, as stated in the second extract, to the school, which, it is implied, he saw as a disciplinary institution where he could not fully develop his talent. That is why he decided to teach himself physics, and mathematics: “... he knew integral and differential calculus, self-taught at about age 13.” (p. 644.) Years later, and despite his innumerable moves to escape from it, he had to pass a final sociability check: “Einstein’s independence of thought was not appreciated by the professors at the ETH [Eidgenoessische Technische Hochschule] ... .” (Note added.) According to this picture of Einstein’s early life – common to many of his biographies – he was an unsociable person inclined to meditate on fundamental questions since his early childhood. The idea to be communicated is that there was something special about Einstein the kid, as though he was already thinking about how to transform our old conceptions of space and time.

There is no indication that Einstein was an exceptional child. Indeed, his academic achievements and his teachers’ reports could point to exactly the contrary. But, while he was not what experts call a “prodigy,” it is currently believed that he was a “gifted child,” which is to say, he showed an unusual natural talent. The most famous story about Einstein’s giftedness is that of the pocket compass: “A wonder of such nature I experienced as a child of 4 or 5, when my father showed me a compass.”[source] The anecdote asseverates that since nothing visible moved the iron needle, the little boy concluded by pure intellect that there was a quality of the empty space that forced the needle to point in one specific direction. The child was impressed in such a profound manner that since then he could not stop reflecting on the physical attributes of the space ... and time. It is said that this infantile faculty of being constantly amazed by such simple phenomena was something that Einstein never lost. Even more, some claim that – following Einstein’s own avowals – he was a creative physicist precisely because he used to ask himself questions that were normally posed in childhood. In our case, he was just five when he first cogitated about the physical properties of the space-time; two decades later he found a solution to his childish inquiries. As the historian of physics Peter Galison writes referring to Einstein’s early mental picture where he sees himself travelling at the speed of light: “… Einstein asking a question that (as Einstein put it) was normally posed ‘only in early childhood,’ a matter that he, peculiarly, was still asking when he was ‘already grown up.’”[source]

That children are more creative than mature people is a regular idea about creativity. The assumption has been applied to many creative people, from Leonardo da Vinci to Albert Einstein. About Leonardo, Freud famously wrote: “Indeed, the great Leonardo remained like a child for the whole of his life in more than one way; it is said that all great men are bound to retain some infantile part. Even as an adult he continued to play, and this was another reason why he often appeared uncanny and incomprehensible to his contemporaries.”[source] This is not very different from Einstein’s judgment concerning physical research. According to him, the search for truth and beauty gives us consent to behave like little children our entire lives. Nevertheless, psychological research has established that there is no solid evidence to the claim that children are more creative than adults nor that childish attitudes trigger off creative processes. In fact, many contemporary psychologists are convinced that this is merely a myth. The myth initiated in the Romantic age, when it was widely thought that human beings were closer to nature at birth; the state of corruption being a condition of the social being. I suspect that most of Einstein’s biographers have been persuaded by this modern myth.

The previous discussion will allow us to fully grasp the meaning of the following assertions put forward by string theory’s supporters. My first example is by Steven Weinberg: “That series of why, why, why questions, like an unpleasant child, will come to an end in a final theory and then we will know. We will know the book of rules that govern everything.” David Gross made a similar statement in an interview to Nova’s The Elegant Universe:

Nova: So why should anybody care about string theory?
Gross: Well, for one thing, because it’s attempting to answer the “why” questions that children ask.[source]

In the same program, the allegory of the persistent child looking for fundamental truths was repeated by another string theorist: “We’re like excited little two-years-olds that are never satisfied to be told, ‘That’s just because I say it is.’ We want to know why.”[source]

But: where are these children that ask why the spacetime is the way it is or why there are four independent forces instead of one? Sincerely speaking, I know none of them, and I am sure nobody has ever met one. Compare what these physicists say with Saint Paul’s declaration in his first letter to the Corynthians: “When I was a child, I used to speak like a child; I used to think like a child; I used to reason like a child. When I became a man, I put an end to childish things.” This was the prevalent viewpoint on children’s creativity until very recently, that is to say, they were considered not to be especially creative. But in the Romantic period the idea that children had an unusual talent to see things where others could not was in vogue. Rousseau’s “état de nature” had a great impact in the conception of children as closer to nature than socialized adults. With Freud’s studies this myth rooted still further and the adult’s unconscious, a reservoir of the individual’s babyish experiences, began to be considered as possessing an exceptional ability to inquire and discover fundamental truths. Some still feel that a naive thinking can be adduced in support of a final theory of physics, i.e., string theory.

Let us now look at our second myth regarding creativity: the creative dream. As everyone knows, after Freud’s work the human mind and the dream are related. When the unconscious was discovered it was thought that the dream could give us the hint to another, maybe more pleasant and faithful, perception of reality. The Romantic composer Max Bruch once said: “My most beautiful melodies have come to me in dreams.”[source] Stories about creative dreams are many; for instance, Paul McCartney’s “Yesterday” was composed entirely while he was sleeping; in science, the story of Kekulé’s discovery of the benzene structure is famous.

Einstein has also been the subject of this creativity myth. One of these works of mythification was written by the physicist Banesh Hoffmann: “But the real key to the theory of relativity came to him unexpectedly, after years of bafflement, as he awoke one morning and sat up in bed. Suddenly the pieces of a majestic jigsaw puzzle fell into place with an ease and naturalness that gave him immediate confidence.”[source] Several pages later he continues: “What flashed on Einstein as he sat up in bed that momentous morning was that he would have to give up one of our most cherished notions about time.”[source] That is, Einstein’s flash of insight came to him in a dream – or more accurately after waking up. But, there is no evidence that this really happened, so I presume that Hoffmann was simply echoing a common idea of the early twentieth century: Freud’s psychoanalysis.

Since it first became popular, the theory of relativity has been associated with the state of dreaming. “One was the suggestion that the theory itself was just the product of a dream. This suggestion was made by Professor Poor in his first critical in the New York Times of 16 November 1919, and the same suggestion was made with a less critical tone in Current Opinion in June 1921. … When interest began to turn to Einstein himself, in 1920 and 1921, it was noted that as a youth Einstein had just been considered a dreamer [Current Opinion May 1920, 651-53], and his wife said that when he was inspired, he just dreamed and played the violin. [New York Times, 3 April 1921, 1.]”[source] (Both notes in the original.) This interpretation was possible thanks to the discovery of psychoanalysis. Subsequently, the social and cultural context has favoured this durable relationship between relativity and dream.

I was shocked once when I heard on Discovery Channel that Stephen Hawking – Einstein’s heir – had discovered “string theory” (!) in a dream. Now, I have a better understanding of why they said that.

The discussion of the next section is in frank opposition to the two preceding Romantic interpretations of scientific creativity. I do believe that an accurate study of the individual can shed light on creative thinking; however, in order to capture global factors a contextualist approach is required. We will discover that the social group intervening in the creative process is far broader than currently thought.

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SELECTED READINGS FOR ESSAY 4 (II)

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