1.1 A brief introduction to string theory

The evolution of fundamental physics can be construed as a series of unifications. Its beginnings can be traced back to Newton’s introduction of a universal gravitational force that provided a unified explanation of celestial phenomena and gravitational phenomena on earth. About two centuries later, Maxwell developed a unified description of light, electric and magnetic phenomena. In 1905, Einstein’s special relativity provided a coherent framework for classical mechanics and electrodynamics. A decade later, general relativity expanded this new perspective, making it compatible with the phenomenon of gravity. After quantum mechanics had opened a new world of microphysics ruled by the principles of Heisenberg’s uncertainty and quantum statistics in the 1920s (which itself may count as the exception to our rule since it was motivated by accounting for new phenomenology rather than by a quest for unification), quantum physics was soon made compatible with special relativity by the introduction of quantum field theory. In the 1960s and early 1970s, the standard model of particle physics made another step towards unification: a specific form of internal symmetries, gauge symmetry, provided a basis for a coherent description of all three nuclear forces that had been discovered in nuclear and particle physics.

In the 1970s, there remained one fundamental obstacle to an overall description of all known fundamental physical phenomena: the theories of nuclear interactions, which were based on the principles of quantum physics, stubbornly resisted all attempts to be reconciled with general relativity. It became increasingly clear that the standard framework of quantum fields did not allow for any satisfying solution of this problem. Something completely new was needed. The idea that stepped up to play this role was string theory.¹

String theory was first proposed as a universal theory of microphysics in 1974 (Scherk and Schwarz, Reference Scherk and Schwarz1974).² The approach had to struggle with big conceptual difficulties in the beginning. For a long time, it was not clear whether string theory met the most basic requirements for providing a theory of matter. In 1984, Green and Schwarz (Reference Green and Schwarz1984) finally succeeded in writing down a coherent Lagrangian of a quantized string that included matter fields (the so-called superstring). From that time onwards, string theory has constituted the most prominent and influential attempt to formulate a universal theory of all known interactions. String theory builds on the conceptual foundations that have been established in elementary particle physics in the 1970s. It is a quantum theory that aims at reproducing the interaction and symmetry structure of a gauge field theory. Within this framework, the basic idea of string theory is a fairly simple one: the point-like elementary particles of traditional particle theories are replaced by one-dimensional strings.

In order to understand why this looks like a promising step towards providing a basis for the unification of quantum physics and gravitation, we have to say a few words about the core obstacle to an integration of gravity in the context of quantum field theory: the non-renormalizability of quantum gravity.³ The calculation of a scattering process in quantum field theory is based on a perturbation expansion that sums up all possible patterns of particles being emitted and absorbed in the process. These possible patterns are represented by the so-called Feynman diagrams which can be calculated. In the calculation of Feynman diagrams one encounters infinite terms which, roughly speaking, arise due to the possibility of point particles coming arbitrarily close to each other. Once we have infinite terms in our calculation, however, we risk losing the capacity of making meaningful quantitative predictions. In gauge field theories, this problem is solved based on the technique of renormalization: the infinities can be ejected from all phenomenologically relevant quantitative results by introducing a finite number of counter-terms to the infinite terms that arise in the calculation. In other words, all ratios between observable quantities have well-defined finite values because the infinities which arise in the calculations cancel each other in a controlled way. If one includes gravity in a gauge field theoretical description, however, the renormalization program fails. This failure is related to the fact that the gravitational force grows linearly with increasing energies of the interaction process. As a consequence, the infinities which arise in a perturbative expansion of the gravitational interaction process are particularly “dangerous” and it is no longer possible to cancel all of them by a finite number of counter-terms.

Calculations can still be carried out by introducing an energy cut-off (i.e. integrating energies only up to a certain energy scale). As the result then depends on the cut-off value, however, this approach must be based on the assumption that a new, more fundamental theory that is renormalizable or finite can explain the choice of the cut-off scale. A gauge field theoretical approach to quantum gravity thus can work as an effective theory but cannot serve as a fundamental theory. String theory is understood to offer a solution to the problem of intractable infinities in quantum gravity. The extendedness of the strings “smears out” the contact point between any two objects and thus provides a decisively improved framework that seems to allow finite calculations.⁴

The introduction of extended elementary objects that leads up to string theory thus is chosen for entirely theoretical reasons, in order to provide a coherent unification of the particle physics research program with gravity. So far, no immediate empirical signatures of the extendedness of elementary objects have been observed. We therefore know that, if string theory is a viable theory at all, the string length must be too small to be measurable by current experiments. Since the string length is quite directly related to the gravitational constant, the most natural expectation would be that the string scale lies quite close to the Planck scale, the scale where the gravitational coupling constant (which grows linearly with the interaction energy) becomes of order one. If that was the case, canonical scenarios would imply that the string scale lies about 13 to 14 orders of magnitude beyond the so-called electroweak scale,⁵ that is the energy scale testable by the current LHC experiment at CERN. Under some specific circumstances, however, which will be discussed a little later, the string length might lie much closer to empirical observability.

String theory relies on the core principles of a perturbative expansion of relativistic quantum mechanical interaction processes and offers a conceptual modification that seems capable of solving the coherence problems of that approach in the context of gravitational interaction. In this sense, string theory represents a natural continuation of the high energy physics research program. It turns out, however, that the seemingly innocent step from point-like objects to strings has a wide range of complex structural consequences which lead far beyond the conceptual framework of point-like high energy physics.

A first important implication can be derived directly from the quantization of the string. It turns out that a coherent (i.e. anomaly free) quantization of the string is possible only if the string is moving in a spacetime with a specific number of dimensions. In particular, a string theory that can describe matter particles (and not just photons and other particles of integer spin) can only be consistently formulated in ten spacetime dimensions. This prediction marks the first time in the history of physics that the number of spatial dimensions can be derived in a physical theory. The obvious fact that only four spacetime dimensions are macroscopically visible can be taken into account by the assumption that six dimensions are “compactified”: they have the topological shape of a cylinder surface – or, if more than one dimension is compactified, of a higher-dimensional torus – where, after some translation in a “compactified” direction, one ends up again at the point of departure.⁶ Just like the string length, the compactification radius must be assumed to be so small that the additional dimensions are invisible to the current experiments in high energy physics and gravitational physics. The canonical picture would put the compactification radii more or less at the string length and close to the Planck length. There do exist theoretical scenarios of large or “warped” extra dimensions, however, where Planck scale and string scale merely give the misleading impression of lying many orders of magnitude beyond the electroweak scale as long as one does not account for the propagation of gravity through the large or warped extra dimensions.⁷ In such scenarios, the string scale could be low enough even for becoming observable at the LHC.

In conventional quantum physics, elementary particles carry quantum numbers which determine their behavior. A particle’s characteristics like spin or charge, which are expressed by quantum numbers, constitute intrinsic and irreducible properties. Strings, to the contrary, do not have quantum numbers. They can differ from each other only by their topological shape and their dynamics. Strings can be open, meaning that they have two endpoints, or closed like a rubber band. If they are closed, they can be wrapped around the various compactified dimensions in different ways. Both open and closed strings can assume different oscillation modes. These characteristics determine the macroscopic appearance of the string. To the observer lacking experimental tools of sufficient resolution for perceiving the stringy structure, a string in a specific oscillation mode and topological position looks like a point-like particle with certain quantum numbers. A change of the oscillation mode of the string would be perceived as a transmutation into a different particle. Strings at a fundamental level do not have coupling constants either. The strength of their interaction with each other again can be reduced to some aspect of their dynamics. (The ground state of a certain mode of the string expansion, the dilaton, gives the string coupling constant.) All characteristic numbers of a quantum field theory are thus dissolved into geometry and dynamics of an oscillating string. It turns out that the string necessarily contains an oscillation mode that corresponds to the graviton (a massless spin 2 particle). Therefore, string theory automatically includes gravity. String theories which are able to describe matter fields are more difficult to formulate. They have to be supersymmetric, i.e. they must be invariant under specific transformations between particles of different spin. String theoretical models which have this property are called “superstring” models.

A fundamental problem faced by string physicists may be characterized the following way. String theory has started from a perturbative point of view. As noted above, a perturbative approach to a relativistic quantum theory describes interaction processes by expanding them as a series of Feynman diagrams. These Feynman diagrams can in principle be arbitrarily complex and involve an arbitrarily high number of particle exchanges. In a case like electroweak interaction, we know from experiment that the coupling constant is small so that Feynman diagrams with high numbers of particle exchanges (which are suppressed by a high factor of the coupling constants) can be neglected in approximate calculations.⁸ Perturbation theory has thus proved to be a highly powerful technique in the context of weakly coupled quantum field theory.

In string physics, the situation is more difficult than in quantum field theoretical descriptions of nuclear interactions. Neither the overall theory behind the perturbative expansion nor the size of the expansion parameter are known. In fact, as we have mentioned above, the string coupling, which constitutes the expansion parameter of a perturbative expansion of string theory, is no fundamental free parameter but itself emerges from the dynamics of the fundamental theory. String theorists thus cannot trust perturbative calculations. They have to look for non-perturbative information about the theory in order to acquire an understanding of the theory’s general characteristics. Some limited progress has been made in this direction.

An important feature of string physics which has shed some light on the non-perturbative structure of string theory is the occurrence of string dualities. The string world shows a remarkable tendency to link seemingly different string scenarios by so-called duality relations. Two dual theories or models are exactly equivalent concerning their observational signatures, though they are constructed quite differently and may involve different types of elementary objects and different topological scenarios. An example of a duality relation that conveys the basic idea of duality in a nice way is T-duality. String theory, as has been mentioned above, suggests the existence of compactified dimensions. Closed strings can be wrapped around compactified dimensions like a closed rubber band around a cylinder and they can move along compactified dimensions. Due to the basic principles of quantum mechanics, momenta along closed dimensions can only assume certain discrete quantized eigenvalues. Thus, two basic discrete numbers exist which characterize the state of a closed string in a compactified dimension: the number of times the string is wrapped around this dimension, and the eigenvalue of its momentum state in that very same dimension.⁹ Now, T-duality asserts that a model where a string with characteristic length¹⁰l is wrapped n times around a dimension with radius R and has momentum eigenvalue m is dual to a model where a string is wrapped m times around a dimension with radius l²/R and has momentum eigenvalue n. The two descriptions give identical physics.

T-duality is not the only duality relation encountered in string theory. The existence of dualities turns out to be one of string theory’s most characteristic features. Duality relations are conjectured to connect all different types of superstring theories. Before 1995, physicists knew five different possible types of superstring theory which differed by their symmetry structure and therefore seemed physically different. Then it turned out that these five string theories¹¹ and a sixth by then unknown theory named “M-theory” were interconnected by duality relations (Witten, Reference Witten1995; Horava and Witten, Reference Horava and Witten1996). Two kinds of duality are involved in this context. Some string theories can be transformed into each other through the inversion of a compactification radius, which is the phenomenon just discussed under the name of T-duality. Others can be transformed into each other by inversion of the string coupling constant. This duality is called S-duality. Then there is M-theory, which can be reached from specific types of string theory¹² by transforming the coupling constant into an additional 11th dimension whose size is proportional to the coupling strength of the corresponding string theory. M-theory contains two-dimensional membranes rather than one-dimensional strings.¹³ Despite their different appearances, duality implies that the five types of superstring theories and M-theory only represent different formulations of one single actual theory. This statement constitutes the basis for string theory’s uniqueness claims and shows the pivotal role played by the duality principle.

Another important duality relation is the AdS/CFT correspondence that also goes under the name holographic principle. String theory (that is, a theory that contains gravity) in a space with a specific geometry (so-called anti-de Sitter space, in short AdS) is conjectured to be empirically equivalent to a pure supersymmetric gauge theory (which is a theory that contains no gravity) on the boundary of that space (that is, on a space whose dimension is reduced by one compared to the AdS space). In other words, a duality relation is conjectured to hold between a theory with gravity and another one without gravity. Each gravitational process that takes place in AdS space can be translated into a corresponding non-gravitational process on the boundary space.

The AdS/CFT correspondence has recently led to highly fruitful applications which lie far beyond the limits of string theory proper and do not address the question how to unify all physical interactions (Policastro, Son and Starinets, Reference Policastro, Son and Starinets2001; Kovtun, Son and Starinets, Reference Kovtun, Son and Starinets2004). It has turned out that the AdS/CFT correspondence can be used in contexts of complex QCD-calculations (calculations of scattering processes involving strong interactions) where all conventional methods had failed. In that case, the physical situation can be described by a gauge theory and AdS/CFT correspondence leads from there to a gravitational theory that can be calculated more easily. Though strictly speaking the investigated systems cannot be described by a gauge theory that has a gravitational dual (they are not supersymmetric and involve massive fermions), calculations in the dual picture in many cases turn out to provide significantly better results than more conventional methods. The successes of these calculations have recently led to the spread of string-based methods far beyond the borders of the theory itself. The present book will not be concerned with those investigations any further. They must be mentioned, however, as a striking example of the wide range of string theoretical reasoning in present-day physics.

Coming back to genuine string theory, the analysis of non-perturbative aspects of string physics based on dualities has led to important new insights. It was understood that the spectrum of physical objects in string theory was far wider than initially expected. Beyond the initially posited one-dimensional elementary objects, consistency required the additional introduction of a spectrum of various higher-dimensional objects. These objects are called D-branes, where an added number can denote the number of spatial dimensions. (A D5-brane, to give an example, is an object with five spatial dimensions.)

In recent years it has been better understood how to construct string theory ground states with stable compact dimensions based on combined systems of D-branes and fluxes.¹⁴ It turns out that the freedom for constructing such states is huge. Estimates regarding the number of possible ground states go up to 10⁵⁰⁰ or even higher. Working on the question of how to deal with the variety of ground states – which is often called the string landscape (Susskind, Reference Susskind2003) – is one important task for string theory today. One intensely discussed suggestion is to turn the large number of ground states from a problem into a blessing and use it for explaining the fine-tuning of the cosmological constant.¹⁵

String theory lies at the core of many important developments in high energy physics and cosmology today. Supersymmetry, a highly influential theory that is currently being searched for at the LHC experiments at CERN, is predicted by string theory (though not necessarily at energy scales accessible to the LHC) and constitutes one of the theory’s core characteristics. Supergravity, which for some time was seen as a promising candidate theory for a unification of nuclear interactions and gravity, today is mostly deployed as an effective theory of string theory. Discussions of grand unified theories, another highly influential theory in high energy physics, today are often led within a string theoretical framework. Eternal inflation, the leading theory on the early evolution of the universe, is closely linked to string theory with regard to the theory’s basic layout as well as with regard to more far-reaching considerations based on the anthropic principle.¹⁶ One can speak of an interrelated web of theories in contemporary high energy physics and cosmology that is held together by the conception of string theory.

The current theoretical state of development of string theory may be characterized the following way. Four decades of intense work on the theory carried out by large numbers of theoretical physicists and mathematicians have not resulted in the construction of a complete theory. String theory today constitutes a complex web of reasoning consisting of elements of rigorous mathematical analysis, of general conjectures which are based on reasoning in certain limiting cases, of modeling that is done within specified frameworks and of some approximate quantitative assessments. The resulting understanding provides a vast body of structural information and theoretical interconnections between various parts of the theory but leaves unanswered many crucial questions. No real breakthrough has been achieved that would allow specific quantitative calculations of observables from the fundamental principles of string theory. The tediously slow progress witnessed by string physicists over the last few decades does not raise expectations of finding a completion of string theory in the foreseeable future. It seems more realistic to expect a continuation of the kind of development that has characterized the theory’s evolution so far: a sequence of small steps of theoretical progress, interspersed with some significant conceptual breakthroughs and periods of slowed down theory dynamics.

Empirically, the situation is similarly complicated. String theory has not found empirical confirmation up to now. In order to understand the chances for future empirical tests, it is important to distinguish between the theory’s core characteristics and its implications for physics at lower energy scales. The core property of strings, their extendedness, is expected to show only close to the Planck length. In classical scenarios, that means that the extendedness of the string becomes empirically testable only about 13 orders of magnitude¹⁷ beyond the energy scales that can be reached by the most powerful high energy experiment today, the LHC experiments at CERN. There is no hope to reach those scales within the framework of collider physics. We have mentioned above, however, that some scenarios imply a far lower Planck and string scale and thus move both of them towards regions that might be testable by collider physics. A second core prediction of string physics is the existence of extra dimensions. An empirical discovery of extra dimensions could not be taken as full confirmation of string theory since extra dimensions might also occur in non-stringy scenarios. However, they are not implied by any contemporary theory other than string theory. If a prediction as “esoteric” as extra dimensions turned out to be vindicated by experiment, this discovery would clearly be considered strong corroborative evidence for string theory. The empirical perspectives for the discovery of extra dimensions are similar to those for the discovery of extended elementary objects. The classical scenarios put the size of extra dimensions about 13 orders of magnitude beyond the reach of the LHC. Some scenarios of large or warped extra dimensions would imply, however, that large extra dimensions could be testable by precision measurements of gravity at short distances or by the LHC. To conclude, there is no clear indication that core predictions of string theory can be tested by experiments conceivable today. However, under certain specific conditions, such empirical confirmation might be possible.

String theory may also be supported based on predictions regarding physics at the electroweak scale. If empirically measured parameter values of standard model physics which are not implied by the standard model itself or its GUT or SUSY extensions turned out to be predicted by string theory, this would be taken to constitute strong corroboration of string theory. Depending on the range of such successful predictions, they could assume the status of outright empirical confirmation of string theory even in the absence of direct evidence for extended strings. To consider the most extreme example, let us assume that all standard model parameter values turned out to be precisely predicted by string theory. In that case, it would seem very plausible to believe in string theory’s validity even without having ever observed an extended string. At this point, the chances that any specific predictions of low energy parameter values could be derived from string physics are difficult to assess. While the fundamental structure of string theory is understood to be determined uniquely based on very general pre-assumptions, the current understanding of string physics suggests that a vast number of string theory ground states can be constructed from string physics. The selection of the ground state “we are living in” determines the values of all those parameters which define our observable world. Since this selection constitutes the outcome of a quantum process, its prediction must remain of a statistical nature, just like the outcome of some individual microphysical process. This implies a considerable reduction of string theory’s predictive power. The present incomplete understanding of string theory does not allow a clear assessment as to what extent string theory retains predictive power under the stated conditions. Though speculations that string physics might end up predictively empty seem hardly tenable based on the current physical understanding, the unclear situation naturally adds to the impression that string physics is unsatisfactorily detached from empirical confirmation.

This “statistical” problem is superimposed by the problem of the insufficient understanding of string theory dynamics. As of today, it is not possible to derive any quantitative predictions from basic principles of string physics. Therefore, even to the extent that string theory may predict low energy parameter values, string physicists today are not able to specify and calculate those predictions. The most promising strategy for making some contact with observation may consist in trying to analyze to what extent some general properties of physics at the electroweak scale are implied by or seem likely in the context of string physics. If found, coherence of that kind between string theory and the observed world could provide some degree of corroboration for string physics.

Given its unsatisfactory theoretical state and the lack of empirical confirmation, string theory clearly must be called an unconfirmed speculative hypothesis according to the canonical paradigm of theory assessment. This does not square well, however, with the theory’s actual status in the field of high energy physics. String theory has attained a pivotal role in fundamental physics and has been treated as a well-established and authoritative theory for quite some time by the community of string theorists and by physicists in related fields. As we have described above, large parts of fundamental physics are influenced by string theoretical analysis. The string community is one of the largest communities in all of theoretical physics and for many years has produced the majority of the field’s top-cited papers. Moreover, many string theorists express a remarkably strong trust in their theory’s viability. Though they certainly acknowledge their theory’s theoretical incompleteness and the lack of empirical evidence for it as deplorable obstacles, most of them believe that the theoretical quality of string theory in itself justifies the claim that the theory constitutes an important step towards a deeper understanding of nature. The serious mismatch between the status one would have to attribute to string theory based on the canonical paradigm of theory assessment and the status the theory actually enjoys is being reflected by the intense dispute that has arisen about the status of string physics in recent years. The next section will have a closer look at that discussion.

1.2 The conflicting assessments of the current status of string theory

Before entering into the details of the dispute about the status of string theory, it is important to clarify the role that dispute is going to play in the context of this book. Primarily, the book aims to explain the mechanisms of theory assessment in string theory and related theories. The dispute among physicists that will be discussed in this section is not essential to that analysis. If the dispute had not arisen, the philosophical motivation for developing the arguments presented in this book would have remained unaffected and the core of those arguments would have remained unchanged. However, the dispute may be understood as an additional indicator that something philosophically interesting is happening in physics today that is capable of creating serious divides within the physics community at a deep conceptual level. In other words, the dispute can serve as a marker that theoretical physicists currently face a situation where philosophical considerations on the conceptual foundations of their ways of reasoning can be of interest to them. On that basis, the ensuing analysis of the dispute can serve as a test case for the philosophical perspective suggested in this book. If, as I hope to be able to convey, the suggested perspective is capable of providing a convincing explanation of the dispute, it may be taken to be supported by this explanatory success.

So let us take a closer look at the conflict. Soon after the theoretical breakthrough of string theory in 1984, some degree of skepticism developed among physicists in other fields with respect to the string theorists’ high level of trust in their theory. This skepticism grew with time, as string theory remained empirically unconfirmed and theoretically incomplete whereas its exponents showed no sign of abandoning their strong self confidence. In recent years, criticism of string physics has been presented in an increasing number of articles and books, which made the conflict about the status of string physics clearly visible to a wider public. Let me illustrate the irreconcilably different points of view by citing four remarkably different statements on string physics.

While the four citations may be particularly outspoken, they do represent the two main positions which pertain among physicists with regard to the current status of string physics. On one side of the divide stand most of those physicists who work on string physics and in fields like inflationary cosmology¹⁸ or high energy particle physics model building, which are strongly influenced by string physics. That group represents a slight majority of physicists in theoretical high energy physics today. Based on an internal assessment of string theory and the history of its development, they are convinced that string theory constitutes a crucial step towards a better and more genuine understanding of the world we observe. On the other side stand many theoretical physicists of other fields, most experimental physicists and most philosophers of physics. They consider string theory a vastly overrated speculation.

We witness a confrontation of two sharply diverging positions without much appreciation of the respective opponent’s arguments. It is no big exaggeration to say with Smolin that the string theorists and the critics cited above, though they are all theoretical physicists, live in different worlds. Remarkably, they do so despite the fact that they largely agree on the problems string theory faces. All problems discussed in the previous section with regard to the chances of string theory making contact with empirical data are acknowledged fully by string physicists as well as critics of string theory. The differences between the two sides lie in the conclusions drawn.¹⁹

In the dispute described, the string critics play the role of defenders of the classical empirical paradigm of theory assessment. Therefore, it makes sense to start the characterization of the two diverging positions by looking at their perspective. The string critics’ case shall be presented largely based on Lee Smolin’s book (Smolin, Reference Smolin2006) and Roger Penrose’s remarks on the topic in Penrose (Reference Penrose2005). Similar arguments can be found e.g. in Woit (Reference Woit2006) and Hedrich (2007a, 2007b). By and large, the sketched arguments are representational of the considerations which have led many physicists who do not work in string physics or particle physics model building towards adopting a skeptical assessment of the current status of string physics.

Penrose and Smolin base their assessments on their canonical understanding of the scientific process: scientific theories must face continuous empirical testing in order to avoid going astray. As formulated suggestively in Penrose’s citation above, the steady sequence of theoretical alternatives which open up in the course of the evolution of a research program makes it seem highly implausible that the scientific community could consistently make the right theoretical choices in the absence of empirical guidance. If empirical testing remains absent for a long period of time, the chances seem high that scientists will find themselves – to use Penrose’s picture – lost in a wrong part of town. Therefore, in order to be conducive to scientific progress, scientific theories are expected to fulfil a certain pattern of evolution. A theory is expected to reach a largely complete theoretical state within a reasonable period of time. Only after having reached a fairly complete state does a theory allow for a full assessment of its internal consistency and can it provide quantitative predictions of empirical data. The theory then can be expected to undergo empirical testing within a limited time frame in order to decide whether further work along the lines suggested by the theory makes sense or, in the case the theory was empirically false, would be a waste of time.

Looking at the present condition of string theory about four decades after it was first proposed as a fundamental theory of all interactions, we can see that it has achieved neither of the goals described in the last paragraph. Even in the eyes of most of its critics, this does not imply that the theory should be fully abandoned. It has happened before that theories have taken too long to reach maturity and empirical testability and have been shelved until, after some period of general experimental or theoretical progress, they turned out to have the capacity of contributing to scientific progress after all. The critics’ point is, however, that one cannot know whether or not such late success will occur before a theory has found empirical confirmation. A theory that has not reached theoretical completion and empirical confirmation therefore cannot be called successful by classical scientific standards. Given the large number of physicists who have worked on string theory with high intensity over the last 30 years, the theory may actually be called remarkably unsuccessful by those standards. Thus, its critics take string theory as a scientific speculation that may deserve a certain degree of attention due to its interesting theoretical properties but is unfit to play the role of a pivotal, let alone dominating, conceptual focal point of an entire scientific discipline. Still, this is exactly what string theory has been doing for more than a quarter of a century now.

Smolin and Penrose criticize string theorists for ignoring the canonical rationale for theory assessment that was presented above and for developing an unwarranted degree of trust in their theory’s validity. According to Smolin, string theorists systematically overestimate their theory’s “performance” by creating their own criteria of success which are tailored to be met by string physics. Examples of this strategy would be the straightforward interpretation of mathematical progress as physical progress without empirical backing or the string theorists’ frequent allusions to structural beauty (see e.g. Michael Green’s citation in this section). Smolin argues that such “soft” criteria create arbitrary mirages of genuine scientific success. Their application in his eyes impedes the field’s ability to carry out an objective assessment of its progress and moves the field away from legitimate scientific reasoning with respect to theory appraisal. The resulting overestimation of the theory’s status, according to Smolin, disturbs a healthy scientific process since it binds to string physics too many resources whose allocation to other parts of physics could produce more significant results. It is important to emphasize that the thrust of the string-critical arguments questioning the scientific viability of string physics focuses on the strategies of theory evaluation deployed by string physicists. It does not target the methods applied in the construction of string theory, the scientific quality of which remains largely uncontested.

The question as to how a considerable share of the most eminent physicists can jointly commit the described serious methodological blunder is answered by Smolin at a sociological level by deploying the concept of groupthink. The latter phenomenon allegedly tends to occur in professional groups with high status, strong internal competition and intense internal interaction. Under such circumstances, the members of a group may be forced into the unreflected adoption of the group’s standard positions by a mix of intellectual group pressure, admiration for the group’s leading figures and the understanding that fundamental dissent would harm career perspectives. An all too positive and uncritical self-assessment of the group is the natural consequence.

Let us now turn to the string theorists’ perspective. No string theorist would deny the problems the theory faces. But most of them believe there to be strong theoretical reasons for placing trust in the theory’s viability despite these problems. String theorists adopt an altered understanding of the balance between empirical and theoretical methods of theory appraisal that amounts to a massive strengthening of the status of non-empirical theory assessment in the absence of empirical confirmation.

Before entering the analysis of the conceptual reasons for the described shift, I want to address an interesting general aspect of the view string theorists have of their critics. As described above, critics of string theory take string theorists to violate principles of canonical scientific behavior by having undue trust in an empirically unconfirmed theory. String theorists have a similar kind of complaint about many critics of string theory. They tend to consider the disregard shown by many non-string physicists for their theory-based reasons to believe in string theory a blatant violation of the scientific expert principle. The latter principle establishes an informal code of mutual respect for scientific specialization among scientists in different fields, which is taken to be conducive to an optimized appreciation of the overall body of scientific knowledge by scientists and external observers. According to this principle, non-experts are expected to base their opinion about the content and status of theories in a well-established scientific field largely on the assessments by those who have established themselves as experts in the field. In the case of string physics, this principle often seems to be discarded. Most critics of string theory from other fields base their criticism largely on their own general scientific intuition, bolstered by the statements of a couple of prominent opponents of string theory who do have expertise in the field but are not amongst the field’s foremost figures. Exponents of string theory tend to locate the reasons for this unusual phenomenon in a lack of openness and flexibility with respect to the acceptance of new and unusual physical ideas on the side of the string critics.²⁰

The debate between string physicists and critics of string theory on the legitimate assessment of the theory’s success and viability thus is characterized to a significant extent by allusions to psychological or sociological aspects which are alleged to impede a sober scientific assessment on the side of the respective opponent. While the present book does not aim at offering a psychological or sociological study of modern fundamental physics, it seems appropriate to make a few comments on the plausibility of the involved arguments at that level.

It is probably fair to say that both sides do have a point. The community of string physicists indeed may be characterized by high status, close interaction among its members, and a research dynamics that is largely guided by a few key figures (this may actually be less true in 2012 than in the 1990s). Presumably, few in the community would deny that aspects of groupthink can be identified in the community’s patterns of interaction and behavior. Equally, it is difficult to deny the point stressed by many string theorists that the antagonism between string theorists and physicists who are critical of string physics shows the characteristics of a dispute between the exponents of a new way of thinking and more conservative scientists who are less open to fundamentally new developments and prefer staying closer to known territory.

Still, it appears questionable whether psychological and sociological arguments of the described kind can on their own offer a satisfactory explanation of the dispute about the status of string theory. Regarding the groupthink argument, it may be pointed out that one could very well detect elements of groupthink at several stages of the evolution of theoretical physics throughout the twentieth century. The founding period of quantum physics or the emergence of gauge field theory, to give just two examples, arguably show similar sociological constellations with tightly knit high status groups of physicists who believed in work on a revolutionary new theory, strong leading figures who largely determined the course of events and many followers who just wanted to be part of the game. There are other examples of theories which were supported by leading figures of physics but still were considered mere speculations due to the lack of empirical confirmation. Throughout twentieth century physics, the scientific method has proved strong enough to keep scientific control mechanisms intact despite the presence of elements of groupthink. A convincing groupthink argument thus would have to explain why it is just now that groupthink has succeeded in sustaining an irrationally positive assessment of a theory for more than a quarter of a century.

Moreover, describing the string community solely in terms of groupthink would be grossly one-sided and inadequate. Many of today’s most creative and innovative physicists work in the field. The string community is arguably characterized by a particularly high degree of openness for new ideas and a marked tendency to question old ways of reasoning. This is reflected by the large number of new ideas and ideas coming from other fields of physical research which have been adopted in string physics. The picture of a sheepish group following the directives of a few prophets would be an obvious misrepresentation of the actual situation in the field.

On the other hand, the string theorists’ allusions to their opponents’ backwardness does not provide a fully convincing explanation of the emergence of the string-critical point of view either. A number of strong critics of string physics have contributed important and innovative physical concepts themselves (Roger Penrose and Lee Smolin both are examples). It seems implausible to relate their string criticism to a generally conservative scientific attitude. As an overall phenomenon, the degree to which physicists working in other fields refuse to adopt the string theorists’ assessment of their theory and thereby implicitly distance themselves from the expert principle is as striking as it is atypical in twentieth century physics.²¹ It seems to require an explanation that goes beyond a simple attestation of scientific conservativism.

Irrespective of the actual explanatory power of the involved scientists’ allusions to psychological and sociological arguments, it is significant, however, that such arguments are addressed by physicists at all. Differences of opinion in physics usually tend to be discussed by evaluating the argumentative content of the opposing position. A retreat to criticism at a psychological level may be taken to suggest that the opponents are no longer able to reconstruct the opposing position in a rational way. Such a situation can arise when the two sides enter the discussion with incompatible predispositions which are themselves not sufficiently addressed in the dispute. In the following, it shall be argued that this is exactly what is happening in the dispute on the status of string theory.

Let us reconstruct the argument between string physicists and string critics in a little more detail. String theorists have built up considerable trust in their theory based on the theory’s internal characteristics and the history of its evolution. Critics of string theory protest that the string theorists’ trust in their theory is not tenable on the basis of generally acknowledged scientific criteria of theory assessment. String theorists retort that the convincing quality of string theory, being based on the theory’s specific structural characteristics, only reveals itself to the string theory expert, which implies that most of the critics are just not competent to evaluate the situation. The critics, in turn, do not feel impressed by this argument, since, according to their own understanding, they make a general point about the character of the scientific process, which should remain unaffected by any specific analysis of the theory’s technical details.

The dispute can be construed as a discussion that fails to be productive due to a paradigmatic rift between the two disputants: each side bases its arguments on a different set of fundamental preconceptions. This paradigmatic rift, however, differs from the classical Kuhnian case in two respects.

First, it is placed at a different conceptual level. In Kuhn’s picture, paradigmatic differences can be identified by looking directly at the involved scientific theories. To give an example, Newtonian physics represents the paradigm of deterministic causation while quantum mechanics introduces a new paradigm that allows for irreducible stochastic elements in the dynamics of physical objects. Paradigmatic shifts of this kind may have far-reaching implications at all levels of the understanding of the scientific process. Still, they are rooted in and implied by conceptual differences between the corresponding theories themselves. The paradigmatic rift between proponents and critics of string theory is of a different kind. It cannot be extracted directly from conceptual differences between specific scientific theories but only arises at the meta-level of defining the notion of viable scientific argumentation. In the dispute, the critics of string theory mostly do not contradict claims of string theory itself but question the strategies of theory assessment applied in the context of string physics. One could thus call the rift between string theorists and their critics “meta-paradigmatic” in the sense that it cannot be discussed without focussing on the meta-level question of the choice of viable criteria of scientific theory assessment.

Second, the development of the new paradigm did not happen in a revolutionary step. Rather, the understanding of theory assessment evolved gradually based on the scientific experiences of scientists in the field. Only once that gradual process had lasted for some time and scientists then looked outside the limits of their field, did they discover the paradigmatic rift that had opened up between their understanding and the canonical paradigm of theory assessment prevalent in other parts of physics.

A mutual understanding between string theorists and their critics is prevented by the fact that the meta-paradigmatic character of the rift between the two sides is not addressed as such in the discussion. While string theorists proudly point out the conceptual novelties of their theory, they tend not to emphasize the meta-paradigmatic shift at the level of theory assessment that was induced by the evolution of string theory. A number of reasons may be responsible for this fact. First, being physicists rather than philosophers, string theorists naturally focus on their theory’s direct physical import and consider the functionality of the scientific process a pre-condition that is more or less taken for granted. Second, since the meta-paradigmatic changes evolved gradually for the scientists in the field, they look less dramatic to them than to outside observers. And third, conceding a deviation from canonical scientific praxis would invite a level of criticism that string physicists have no interest to incur.

The critics of string theory, on the other hand, develop their arguments without acknowledging the possibility that a shift of the scientific paradigm might constitute a scientifically legitimate development under some circumstances. Therefore, they discuss string physics strictly based on the canonical scientific paradigm and interpret each mismatch between the two straightforwardly in terms of string theory’s failure to meet scientific standards.

Both sides thus agree in disregarding the meta-paradigmatic aspect of their discussion. In doing so, however, they actually lead the discussion based on incompatible sets of hidden preconceptions and therefore must miss each other’s point. Seen from either perspective, the respective opponent’s position does not have legitimacy based on the preconceptions taken to provide the valid framework for the entire debate. The recourse to mutual imputations of personal insufficiencies follows as a natural consequence. Claims of scientific hubris thus are summoned against claims of insufficient intellectual acuteness.²²

Framing the controversy in terms of a shift of the scientific paradigm allows acknowledgement of the reasonability of both positions on the basis of their respective preconceptions. Largely unintentionally, string physicists have been led towards a novel conception of scientific theory appraisal by their scientific research, which they had carried out in accordance with all standards of scientific reasoning. The scientific process itself thus has led beyond the canonical limits of scientific reasoning. The rise of the new understanding of theory evaluation was clearly accelerated by the fact that the stronger role of purely theoretical argumentation it suggested came in handy in view of the lack of available empirical support for string theory. The lack of empirical support was not the primary source of the former development, though. As will be shown in the next sections, the theory itself and the circumstances of its evolution provide substantial reasons for the altered perspective. Those reasons, however, remain invisible to physicists in other fields who have not experienced the scientific dynamics that instigated the described shift of the scientific paradigm. Therefore, they must understand the described shift as a purely defensive ad hoc measure instigated by the long empirical drought and see no sound scientific reason to follow it. Within the framework of their traditional and well-tested scientific paradigm, they find ample justification for repudiating the string theorists’ assessments of string theory’s status.

Is the string theorists’ move a legitimate one? Can it be legitimate if good arguments support it within the string theorists’ own framework of reasoning? Clearly, a shift of the scientific paradigm that is induced by the dynamical evolution of a research field must be considered a legitimate option in principle. No paradigm of scientific reasoning has been installed as a god-given law before the commencement of scientific research. Rather, such paradigms have emerged based on the successes and the failures of scientific reasoning witnessed by scientists in the past. Novel scientific input thus must be expected to alter the scientific paradigm in the future. The question whether an emerging shift of the scientific paradigm actually constitutes an improvement over the prior situation can be very difficult to answer, however.

In one respect, characterizing the dispute between string physicists and their critics in terms of a paradigmatic rift seems particularly apt. To a greater extent than in most cases of scientific theory change, the debate on string physics is affected by fundamental difficulties to decide between the two positions on an “objective” basis, i.e. without anticipating the outcome by employing the preconceptions related to one or the other position. Since the difference in the understanding of what counts as scientific success is crucial to the difference between the two paradigms, it is obviously impossible to decide straightforwardly between the two paradigms by assessing scientific success. Both paradigms allow for plausible criticism of the respective opponent on their own grounds. Seen from the critic’s perspective, it is quite plausible to argue that a modification of the scientific paradigm in times of crisis is counter-productive, as it carries the risk of overlooking a solution that would satisfy the criteria set up by the old paradigm. Seen from the perspective of the new paradigm, sticking to the old criteria too long inhibits scientific progress by sticking to a misguided chimera of the static nature of scientific principles. All one can do in this case is assess the internal coherence and attractiveness of the old and new positions on their own terms and compare the two internal assessments on a more general – and therefore necessarily more vague – argumentative basis.

I argued in Section 1.1 that the traditional paradigm of theory assessment has run into a substantial crisis in the context of present-day fundamental physics. The next chapters will have a closer look at the question whether and to what extent the newly emerging paradigm of theory assessment in string physics and some other fields can provide a viable basis for overcoming that crisis. Let us begin by looking at the conceptual reasons string theorists rely on for believing in their theory. Later, an attempt will be made to put those reasons into a philosophical perspective.

1.3 Three contextual arguments for the viability of string theory

Why do string physicists invest trust in the viability of their theory? The main problem in this respect is addressed clearly in Penrose’s cited text. Penrose raises one fundamental worry with regard to overly confident assessments of theories that have not been empirically confirmed: those assessments are always threatened by the possibility that other scientific explanations of the available data have been overlooked so far. Kyle Stanford has called this general problem of scientific reasoning the problem of unconceived alternatives (Stanford, Reference Stanford2001, Reference Stanford2006). Any reliable assessment of a theory’s status on theoretical grounds must answer Penrose’s worry by addressing the question of unconceived alternatives in some way. It shall be argued in the following that the current assessments of the status of string physics rely on a number of arguments which indeed amount to addressing that question.

Roughly, string theorists rely on two basic kinds of arguments when developing trust in their theory. Arguments which address structural characteristics of string theory itself shall be discussed in Part III of this book. Part I will focus on the other group of arguments, the contextual arguments which are based on general characteristics of the research process that leads towards string theory. These arguments do not rely on any specific properties of the theory itself and are therefore of wider relevance. Part II will be devoted to demonstrating that they constitute an important part of theory assessment in fundamental physics in general.

Three main contextual reasons for the trust string theorists have in their theory may be distinguished. While all three arguments are “common lore” among string physicists, it is difficult to pinpoint a “locus classicus” for each of them. One can find a combination of all arguments in Chapter 1 of Polchinski (Reference Polchinski1998) and in Polchinski (Reference Polchinski1999). The first and third argument appear in Greene (Reference Greene1999, Chapter 1).

The plain no alternatives argument (NAA): string theorists tend to believe that their theory is the only viable option for constructing a unified theory of elementary particle interactions and gravity. It is important to understand the scope and the limits of that claim. String theory is not the only theory dealing with questions of quantum gravity. Various forms of canonical quantum gravity try to reconcile gravity with the elementary principles of quantum mechanics. They discuss the question of unification at an entirely different level than string theory, however. The latter stands in the tradition of the standard model of particle physics and is based on pivotal concepts such as non-abelian gauge theory, spontaneous symmetry breaking and renormalizability.²³ The goal of string theory is to reconcile gravity with these advanced and successful concepts of contemporary particle physics and therefore to provide a truly unified description of all natural forces. In this endeavor, the traditional investigations of canonical quantum gravity do not constitute alternatives, which leaves string theory as the only available way to go.²⁴ That is not to deny the relevance of the investigations of canonical quantum gravity. String theorists would just argue that, once the viable results of canonical quantum gravity are put into the context of contemporary particle physics, they will blend into the string theory research program.

Why is it so difficult to find a unified description of gravity and nuclear interactions? We have encountered the crucial problem for a unification of point-particle physics and gravity already in Section 1.1: quantum gravity is non-renormalizable within the traditional field-theoretical framework. Non-renormalizable quantum gravity cannot be considered viable at the Planck scale, however, the scale where the gravitational coupling becomes strong. Early attempts to solve this problem applied the traditional methods of gauge field theory and tried to deploy symmetries to cancel the infinities which arise in loop calculations and therefore make the theory finite. For some time, the concept of supergravity, which utilizes supersymmetry, looked like a promising candidate for carrying out this task, but eventually the appeal to symmetry principles was judged insufficient.²⁵ As it turns out, the remaining theoretical options are quite limited. One might venture into giving up some of the most fundamental pillars of present-day physics like causality or unitarity. Ideas in these directions have been considered, but did not lead to any convincing theoretical schemes. If one wants to retain these most fundamental principles, then, according to a wide consensus, there remains only one way to go: drop the idea of point particles, which univocally leads to string theory (see e.g. Polchinski, Reference Polchinski1998, Reference Polchinski1999).

A body of explicit analysis supports the notion that there may be no alternatives to string theory. Those considerations can be exemplified by an argument in Polchinski (Reference Polchinski1999). Polchinski starts with an innocent looking posit of a position–position uncertainty relation instead of the posit of extended elementary objects. He shows that the efforts to make that idea work eventually imply the very string theory he had set out to circumvent. Based on a number of arguments of a similar kind in conjunction with the fact that no alternatives have come up despite intense search, it may be suggested that string theory is the only option for finding a unification of all interactions within the framework of the long standing fundamental principles of physics.²⁶

Naturally, the claim of alternatives does not remain uncontested. On what basis can we be confident that the scientists’ lack of alternative ideas is not just a consequence of their limited creativity? Who can rule out that one of the most fundamental principles of physics indeed has to be jettisoned at this stage to describe nature correctly and that string theory is nothing more than a delusive “easy” way out that just does not accord with nature? Indeed, candidates for alternatives do sometimes appear where no alternatives had been in sight before and thus pose a constant threat to simple arguments of no alternatives.²⁷ It seems necessary to look for additional arguments for the viability of string theory which, rather than focussing on the scientists’ difficulties to think of alternatives, are related to qualities of the theory itself.

Probably the most important argument of that kind is the argument of unexpected explanatory coherence (UEA). It is widely held that a truly convincing confirmation of a scientific theory must be based on those of the theory’s achievements which had not been foreseen at the time of its construction. Normally, this refers to empirical predictions which are later confirmed by experiment. However, there is an alternative. Sometimes, the introduction of a new theoretical principle surprisingly provides a more coherent theoretical picture after the principle’s theoretical implications have been more fully understood. This kind of theoretical corroboration plays an important role in the case of string theory. Once the basic postulate of string physics has been stated, one observes a long sequence of unexpected deeper explanations of seemingly unconnected facts or theoretical concepts. Let us have a brief look at the most important examples.

String theory posits nothing more than the extendedness of elementary particles. The initial motivation for suggesting it as a fundamental theory of all interactions was to cure the renormalizability problems of quantum field theories that include gravity. Remarkably, string theory does not just provide a promising framework for quantum gravity but actually implies the existence of gravity. The gravitational field necessarily emerges as an oscillation mode of the string. String theory also implies that its low energy effective theory must be a Yang–Mills gauge theory, and it provides the basis for possible explanations of the unification of gauge couplings at the GUT-scale. The posit that was introduced as a means of joining two distinct and fairly complex theories, which had themselves been introduced due to specific empirical evidence, thus turns out not just to join them but to imply them.

String theory also puts into a coherent perspective the concept of supersymmetry. Initially, interest in this concept was motivated primarily by the abstract mathematical question whether any generalization of the classical continuous symmetry groups was possible. As it turns out, supersymmetry is the maximal consistent solution in this respect. Soon after the construction of the first supersymmetric toy-model, it became clear that the implementation of supersymmetry as a local gauge symmetry (i.e. supergravity) had the potential to provide a coherent quantum field theoretical perspective on gravity and its interaction particle, the graviton. In the context of string theory, on the other hand, it had been realized early on that a string theory that involves fermions must necessarily be locally supersymmetric.²⁸ The question of the maximal continuous symmetry group, the quest to integrate the graviton naturally into the field theoretical particle structure, and the attempts to formulate a consistent theory of extended elementary objects thus conspicuously blend into one coherent whole.

A problem that arises when general relativity goes quantum is black hole entropy. The necessity to attribute an entropy proportional to the area of its event horizon to the black hole in order to preserve the global viability of the laws of thermodynamics was already understood in the 1970s (Bekenstein, Reference Bekenstein1973). The area law of black hole entropy was merely an ad hoc posit, however, lacking any deeper structural understanding. In the 1990s it turned out that some special cases of supersymmetric black holes allow for a string theoretical description where the black hole entropy can be understood (producing the right numerical factors) in terms of the number of degrees of freedom of the string theoretical system (Strominger and Vafa, Reference Strominger and Vafa1996). Thus, string physics provides a structural understanding of black hole entropy.

All of these explanations represent the extendedness of particles as a feature that seems intricately linked with the phenomenon of gravity and much more adequate than the idea of point particles for a coherent overall understanding of the interface between gravity and microscopic interactions. The subtle coherence of the implications of the extendedness of elementary objects could not have been foreseen at the time when the principle was first suggested. It would look like a miracle if all these instances of delicate coherence arose in the context of a principle that was entirely misguided.

To what extent is it justified to have serious confidence in the viability of string theory’s phenomenological predictions on the basis of the presented “non-empirical no miracles argument”? There do exist cases in the history of science where the inference from a concept’s success to its viability was invalidated by the fact that just one aspect of the concept was responsible for the success while important parts of the concept were misguided. A prominent example would be the ether theories whose success was based on the viability of the wave equation but whose core concept, the ether, had to be dropped eventually. In the case of string theory it is difficult to imagine anything of that kind, since the concept is based on one simple and entirely structural posit which would seem impossible to reduce without taking it back altogether. It must be considered a genuine possibility, however, that a deeper, more fundamental principle than string theory itself could be responsible for unexpected explanatory interconnections without implying string theory itself. Still, as broad a spectrum of unexpected explanatory interconnections as is encountered in the case of string theory, in conjunction with the apparent difficulty to come up with consistent alternatives to the theory, may seem difficult to reconcile with the idea that those explanatory successes do not hinge on the theory itself. One thus may have the impression that the argument of unexpected explanatory interconnections has some strength but may not feel confident enough to rely on it without further analysis. Given that there is no option at this point for carrying out empirical tests of string theory itself, it would thus seem important at least to find a possibility of checking the general validity of the non-empirical arguments for string theory’s viability on an empirical basis. The third argument is based exactly on this kind of empirical test at a meta-level.

The meta-inductive argument from the success of other theories in the research program (MIA): most string theorists, at any rate those of the first generation, are mainly educated in traditional particle physics. Their scientific perspective is based on the tremendous predictive success of the particle physics standard model. The latter was created for solving technical problems related to the structuring of the available empirical data (in particular, the problem of making nuclear interactions renormalizable) and it predicted a whole new world of new particle phenomena without initially having direct empirical confirmation. Just like in the case of string theory, it turned out that none of the alternatives to the standard model that physicists could think of was satisfactory at a theoretical level. In addition, surprising explanatory interconnections emerged. (For example, the distinction between a confining interaction like strong interaction and the non-confining electromagnetic interaction could be explained as a natural consequence of the difference between a non-abelian and an abelian interaction structure.) Given the entirely theoretical motives for its creation, the lack of satisfactory alternatives and the emergence of unexpected explanatory interconnections, the standard model can be called a direct precursor of string theory. Indeed, string theorists view their own endeavor as a natural continuation of the successful particle physics research program. The fact that the standard model theory was at the end impressively confirmed by experiment conveys a specific message to particle physicists: if you knock on all doors you can think of and precisely one of them opens, the chances are good that you are on the right track. Scientists working on unifying gauge field theory and gravity have thought about all currently conceivable options, including those which drop fundamental physical principles. The fact that exactly one approach has gained momentum suggests that the principles of theory selection which have been successfully applied during the development of the standard model are still working.

It is important to emphasize that MIA relies on empirical tests of other theories and thereby in a significant sense resembles the process of theory confirmation by empirical data. The level of reasoning, however, differs from that chosen in the classical case of theory confirmation. In the present context, the empirically testable prediction is placed at the meta-level of the conceptualization of predictive success. We do not test the scientific theory that predicts the collected empirical data but rather a meta-level statement. The following hypothesis is formulated: scientific theories which are developed in the research program of high energy physics in order to solve a substantial conceptual problem, which seem to be without conceptual alternative and which show a significant level of unexpected internal coherence tend to be empirically successful once they can be tested by experiment. This statement is argued for based on past empirical data (in our case, largely data from the standard model of particle physics and from some earlier instances of microphysics) and can be empirically tested by future data whenever any predictions which were extracted from theories in high energy physics along the lines defined above are up to empirical testing.

All data that can be collected within the high energy physics research program thus constitute relevant empirical tests of the viability of MIA and thereby have implications for the status of other theories in the field which are considered likely viable based on that hypothesis. Any experiment that confirms predictions whose viabilities have been considered likely based on purely theoretical reasoning would improve the status of scientific theories of similar status in the research field. On the other hand, the status of non-empirical theory evaluation and therefore also the status of theories believed in on its basis would seriously suffer if predictions that are strongly supported theoretically were empirically refuted. Trust in string physics on that basis is influenced by new empirical data even when that data does not represent a test of string theory itself.

Present-day high energy physics provides two excellent examples for the described mechanism. At the LHC, two theories were and still are tested which, before the start of the experiment, were considered probably viable (to different degrees) based on theoretical reasoning. First, the canonical understanding of high energy physics implied that the LHC was likely to find a Higgs particle.²⁹ The Higgs mechanism constituted the only known method of producing the observed masses of elementary particles in a gauge theoretical framework. Since gauge field theory had proved highly successful in the standard model, where all empirical predictions other than the Higgs particle had already been empirically confirmed, and since the theoretical context of mass creation by spontaneous symmetry breaking³⁰ in gauge field theory was well understood, physicists would have been profoundly surprised if the Higgs particle had not been found at the LHC. (A closer analysis of that case will be carried out in Chapter 4.) The actual discovery of the Higgs particle in summer 2012 clearly constitutes an example of an eventual empirical confirmation of a theory that had been conjectured and taken to be probably viable on theoretical grounds. Thereby, it constitutes a confirmation not just of the Higgs theory but also of the meta-level hypothesis that the involved theoretical strategies of theory assessment are viable. In the given case, the general belief in the existence of the Higgs particle was so strong that its discovery did not alter overall perspectives too much. A failure to find the Higgs, however, would have constituted a serious blow not just to the current understanding of the standard model but to the status of non-empirical theory assessment in general. String physicists in that case would have had to answer the question on what basis they could be confident to get the basic idea of string theory right on entirely theoretical grounds if high energy physics could not even correctly predict the Higgs particle. Since the principle of the viability of non-empirical theory assessment can only be of a statistical nature, it could not be refuted by individual counter instances. Trust in string physics would have seriously suffered, however, if a prediction as well trusted as the one regarding the Higgs particle had failed.

The second theory that may get empirically confirmed at the LHC is low energy supersymmetry. The situation there is a little different than in the case of the Higgs particle. As will be discussed in more detail in Section 4.2, some conceptual arguments do hint towards low energy supersymmetry. The cogency of those arguments, however, is less clear than in the Higgs case or in the case of string theory. Many string physicists would argue that there remain more conceptual options for avoiding low energy supersymmetry than for avoiding string theory. Thus, if low energy supersymmetry was not found at the LHC that would obviously not help the trust in string theory but the damage would be limited. On the other hand, if both the Higgs particle and low energy supersymmetry were found, that would be taken as significant support for the reliability of theory generation based on conceptual reasoning. Trust in non-empirical theory assessment would get considerably strengthened, which in turn would enhance the trust in string theory.³¹

Having discussed the three most important arguments of non-empirical theory assessment, it is now possible to be more specific about what is meant by “non-empirical” in the given context. The term “non-empirical” clearly does not imply that no observation or no empirical data has entered the argument. As we have seen, “non-empirical” theory assessment does rely on observations about the research process, the performance of scientists looking for alternative theories or the success of theories in the research field. What distinguishes empirical from non-empirical evidence in the given sense is the following. Empirical evidence for a theory consists of data of a kind that can be predicted by the theory assessed on its basis. Non-empirical evidence, to the contrary is evidence of a different kind, which cannot be possibly predicted by the theory in question. No scientific theory can predict that scientists will not find other theories which solve the same scientific problem (the observation that enters NAA). Nor can a scientific theory possibly predict that other theories which are developed within the research field independently from the given theory tend to get empirically confirmed (the observation that enters MIA). Non-empirical evidence for a theory thus is evidence that supports a theory even though the theory does not predict the evidence.

In conjunction, the three presented arguments of non-empirical theory assessment lay the foundations for trust in string theory. All three reasons have precursors in earlier scientific theories but arguably appear in string theory in a particularly strong form. The complete lack of empirical evidence in the given case leads to a situation where non-empirical theory assessment is solely responsible for the status attributed to string theory and therefore is of special importance.