3.1. The Plain Argument of No Choice

String theorists tend to believe that their theory is the only viable option for constructing a unified theory of elementary particle interactions and gravity. The various forms of canonical quantum gravity,Footnote ¹³ which do not refer to string theory, try to reconcile gravitation with the elementary principles of quantum mechanics and therefore discuss the question of unification at an entirely different level than string theory. The latter stands in the tradition of the standard model of particle physics that was developed in the 1960s and 1970s as a theory of all microscopic interactions and is based on pivotal concepts such as nonabelian gauge theory, spontaneous symmetry breaking, and renormalizability. String theory's goal 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.Footnote ¹⁴ 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.

The crucial problem for a unification of point-particle physics and gravity is the nonrenormalizability of quantum gravity within the traditional field-theoretical framework. As long as this obstacle remains, quantum gravity cannot be considered viable at the Planck scale, 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 dangerous infinities. For some time the concept of supergravity that utilizes supersymmetry looked like a promising candidate to carry out this task, but eventually the appeal to symmetry principles was understood to be insufficient. As it turns out, the remaining theoretical options are quite limited. One might venture into giving up some of the most fundamental pillars of today's physics such as locality, causality, unitarity, or continuity. 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: to drop the idea of point particles, which univocally leads to string theory (see, e.g., Polchinski Reference Polchinski1998, Reference Polchinski1999). It may thus be said 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.

Naturally, this claim of ‘no choice’ will not remain uncontested: 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? An immediate ‘soft’ answer to this question is provided by an argument that plays an important background role for the string theorists’ self-confidence.Footnote ¹⁵

3.2. The Example of the Particle Physics Standard Model

Most string theorists, at least those of the first generation, are mainly educated within traditional particle physics, and their scientific perspective is based on the tremendous success of the standard model. The latter was created based on entirely theoretical arguments in order to solve a technical problem (how to make nuclear interactions renormalizable), and it predicted a whole new world of new particle phenomena without any initial direct empirical confirmation. In this respect the standard model is a direct precursor of string theory, and string theorists view their endeavor as a natural continuation of the successful particle physics research program. The fact that purely theoretical initial arguments led to the highly ambitious standard model theory that eventually was so 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 quantum 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 that have been successfully applied during the development of the standard model are still working.

Now, in further analogy with the standard model case, it is important to note that the theoretical success of string theory by no means implies the eternal survival of today's most basic physical postulates. The standard model's success did not exclude (and its creators did not intend to exclude) that more fundamental modifications of physical theory might also be able to cure the problem of the renormalizability of nuclear interactions. For example, instead of relying on gauge symmetries, one could have ventured already in the 1960s to make the step toward extended elementary particles, a step that was later successfully realized by string theory. To believe in the standard model in the early 1970s merely meant assuming that any more far-reaching change of physical postulates, inasmuch as it would be successful, would itself imply the standard model predictions. This assumption has been vindicated by the subsequent development of physics. Extended elementary particles have emerged as a (potential) next scientific step, but it turned out that their introduction, if consistently done, implies gauge theory as well.Footnote ¹⁶

In the same vein, the string theorist expects that more fundamental changes of physical principles, if they are required, would be consistent only in a string theoretical context. A body of explicit analysis supports this expectation and may 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, and he shows that the efforts to make that idea work eventually imply the very string theory he had set out to circumvent.

While the example of the highly successful standard model can strengthen confidence in the validity of string theory, it can hardly exclude string theory's failure. The next argument will indicate that such failure would at any rate leave a lot to be explained.

3.3. Internal Coherence

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 phenomenological predictions that 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 has been stated, one observes a long sequence of unexpected deeper explanations of seemingly unconnected facts or theoretical concepts.

String theory posits nothing more than the extendedness of elementary particles. Its initial motivation was to cure the infinity problems of quantum field theories that include gravity.Footnote ¹⁷ Remarkably, string theory does not just provide a promising framework for quantum gravity but actually implies the existence of gravitation. 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 grand unified scale. The posit that was introduced as a means of joining two distinct and fairly complex theories, which had themselves been introduced because of 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, a symmetry between particles of different spin based on an intertwining of the inner symmetries so crucial in gauge theories and the Lorentz symmetries. Initially, interest in this concept was motivated primarily by the abstract mathematical question of whether any generalization of the classical 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 a formulation of supersymmetry as a gauge symmetry (meaning local supersymmetry or supergravity) had the potential to provide a fuller understanding of the particle character of gravity. (The particle corresponding to the gravitational force in a field-theoretical formulation of gravitation, the so-called graviton, turned out to be the superpartner of the gauge particle of supersymmetry.) In the context of string theory, by contrast, it had been realized early on that a string theory that involves fermions must necessarily be locally supersymmetric.Footnote ¹⁸ The question of the maximal 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 miraculously 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. 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 in which the black hole entropy can be understood 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.Footnote ¹⁹

It is difficult to assess at this stage to what extent it is justified to base serious confidence in the viability of string theory's phenomenological predictions on the presented type of no miracles argument. The problem is that one cannot rely on past experience. Though exemplifications of a theory's unexpected power to provide theoretical coherence do exist in earlier scientific research, arguably they have never been so strong while experimental confirmation remained entirely absent. A thorough comparison of the argument of internal coherence in string theory with similar lines of arguments in other fields would be helpful for getting a better grasp of the situation but lies beyond the scope of this article.

Each one of the three presented reasons for string theorists’ self-confidence can be interpreted in terms of a devaluation of the scientific underdetermination principle. The argument of ‘no choice’ suggests that the existence of alternative scientifically satisfactory theories is a less natural assumption in the case of string theory than in prior physical contexts. It therefore works directly against the viability of the scientific underdetermination principle. The other two arguments do not directly affect the principle's viability but question its importance for theory evaluation. The success of the particle physics research program shows that consistency arguments in particle physics can lead reliably toward correct empirical predictions despite the underdetermination argument. String theory's tendency to create unexpected internal coherence provides a specific argument for the theory's viability that circumvents considerations about scientific underdetermination.

While the arguments discussed so far have been based on characteristics of the research process that lead toward string theory, the following section will show that arguments based on specific properties of string theory work in a very similar way against the principle of scientific underdetermination. These arguments naturally rely on the precondition that string theory is a valid theory and thus are circular if used in an isolated way. Taken in conjunction with the previous considerations, however, which strengthen the status of purely theoretical arguments for string theory's viability, they can make the overall case stronger and more coherent.

4.1. Structural Uniqueness

String theory's basic postulates uniquely determine the theory's structure. All prior physical theories have free parameters that can be tuned in order to fit the quantitative specifics of the empirical evidence. Special relativity does not specify the velocity of light, neither Newtonian mechanics nor general relativity specifies the size of the gravitational constant, and Maxwell's electromagnetism and quantum electrodynamics do not fix the size of the elementary charge and the fine structure constant, respectively.Footnote ²⁰ The standard model of particle physics, the current joint description of all nuclear interactions, involves more than 20 free parameters such as mass terms, coupling constants, and mixing angles, which have to be determined experimentally. String theory is the first physical theory that does not contain or allow any free parameters (see, e.g., Polchinski Reference Polchinski1998, Chapter 1). According to string theory, all quantitative characteristics of the world stem from purely structural characteristics of the string and are a result of string theory's complex dynamics.

A similar statement can be made concerning the spectrum of possible models of the theory, which are defined by various discrete characteristics such as symmetry structure, the number of particle generations, the number of space-time dimensions, and so forth.Footnote ²¹ Under very basic conditions such as the existence of fermions and more than one spatial dimension, string theory seems to allow only one model. Until the early 1990s, it was believed that five different consistent superstring models existed, which differed by symmetry structure.Footnote ²² The discovery of the important role of string dualities, however, led to the well-founded conjecture that these five models merely constituted different formulations of the same theoretical structure (Witten Reference Witten1995; Horava and Witten Reference Horava and Witten1996).Footnote ²³ Today it is generally assumed that there is exactly one way to build a superstring theory. This situation once again distinguishes string theory from most traditional theories, which allow a considerable amount of structural choice within their fundamental theoretical framework. Let us take the example of a theory that, like string theory, provides the basis for the description of a large number of different phenomena. Gauge field theory is highly flexible in accommodating all those microscopic phenomena that happen to show up in an experiment. Theoretical arguments do not predetermine the gauge symmetry structure and the number of particle generations and therefore allow a nearly unlimited number of models with different interaction structures and particle contents.

I will refer to the fact that string theory knows neither free parameters, nor a variety of models, with the term ‘structural uniqueness’. The structural uniqueness of the fundamental theory has to be clearly distinguished from the question of the string theory ground state. Consistency arguments imply that superstring theory must live in 10 space-time dimensions. All dimensions except the four visible ones are thought to be ‘compactified’; that is, each of them runs back into itself after a minimal distance like a tiny cylinder surface. The compactification of the six extra dimensions is a matter of the theory's dynamics, and its outcome constitutes the ground state of the theory. If the physical equations allowed several or many energetically equivalent ground states, the choice of the actual ground state would be a matter of the statistical quantum dynamics of the early string universe and could not be theoretically predicted. Since there are enormous numbers of mathematically imaginable compactification patterns for the six extra dimensions, string theory would require some physical vacuum selection mechanism that reduces the number of physically possible ground states to a relatively small number, or one, in order to retain the theory's low-energy predictive power.

It has always been a natural goal of string theoretical research to establish the theory's predictive power at low energies. However, the dynamics of string theory are far too little understood today to allow any reliable judgment whether a vacuum selection mechanism exists in the theory and, if so, what it would look like. Current assessments of the situation range from (i) the traditional stance that one can expect enough so far unexplored structure to be confident that a vacuum selection mechanism will show up through (ii) attempts to deal with the status quo statistically without anticipating any final answer to the question (Douglas Reference Douglas2003) to (iii) suggestions to drop the idea of a vacuum selection mechanism altogether (Susskind Reference Susskind2003). The following analysis will address the philosophical implications of string theory's more favorable prospective scenario (i).

Let us imagine that a highly predictive structurally unique theory is phenomenologically viable at some stage.Footnote ²⁴ How would structural uniqueness affect the status of the scientific underdetermination principle? The principle of scientific underdetermination acquires its plausibility based on a specific understanding of the scientific process. According to this understanding, the scientist builds theoretical structures, which reflect the regularities observed in nature up to some precision, and tunes the structures’ free parameters to fit the quantitative details of observation. The successful construction of a suitable theory for a significant and repeatedly observable regularity that characterizes the world is assumed to be just a matter of the scientist's creativity and diligence. If it is always possible to find one suitable scientific theory, however, it seems natural to assume that there can be others as well. There may always exist different choices of theoretical structure that have coinciding empirical implications up to some precision in the observed regime if their respective free parameters are fixed accordingly. The principle of underdetermination follows from this.

If one considers only the class of highly predictive, structurally unique theories, the situation is entirely different. Compared to the general case of all possible scientific theories, the chances of being able to describe a specific empirical data set with a highly predictive structurally unique theory are strongly reduced for two reasons. First, a highly predictive theory that does not leave any freedom of choosing parameter values or modifying its qualitative characteristics is compatible with far fewer sets of empirical data than is a conventional theory. Second, as discussed in Section 3, even on the basis of a very general set of physical principles, it is difficult to formulate any coherent, structurally unique theories at all. Actually, the only structurally unique theory known in science today is string theory.

Considering both the generality of the principles that define a theory like string theory and the vast range of possible phenomenological regularities and parameter values, it seems natural to assume that highly predictive structurally unique theories, if found at all, can be found only for a very small subset of points within the huge space of all possible regularities. There is no reason to expect that those structurally unique theories that do exist, each of them based on a different set of fundamental physical principles, have a tendency to give similar empirical predictions. The notion that several highly predictive structurally unique theories have empirical implications that are nearly, but not precisely, equal in this light must be considered highly improbable. The principle of scientific underdetermination, which looks convincing if applied to the set of all scientific theories, therefore lacks plausibility if applied to the set of highly predictive structurally unique theories.

An empirically confirmed highly predictive structurally unique theory that lacks structurally unique and highly predictive alternatives could still have alternatives that contain free parameters or lack predictive power. Such alternatives may be of two different kinds. First, an alternative theory could introduce free parameters that are relevant only for phenomena unknown to the initial structurally unique theory while it remains structurally unique with respect to the description of all phenomena that had been accounted for by the latter. Since such new free parameters would not enhance their theory's chances of being coherent with the empirical data that were accounted for by the structurally unique theory, however, the occurrence of an empirically viable theory of that kind cannot be considered more likely than the occurrence of an alternative highly predictive structurally unique theory. The scenario therefore leads back to the assessment of the likelihood of scientific underdetermination among structurally unique theories.

Second, alternative theories could lack structural uniqueness or high predictiveness with respect to phenomena correctly accounted for by the highly predictive structurally unique theory. The likelihood of the existence of such alternative theories is not constrained by the previous considerations. However, a different kind of argument can be raised against the assumption that those alternatives could turn out to be scientifically successful. If a structurally unique highly predictive theory was able to reproduce the available empirical data at some stage, its later replacement by a theory that is not either structurally unique or highly predictive in the same regime would turn its prior success into a miracle: why should a highly predictive theory be able to reproduce the empirical data without any tuning of parameters at some stage if it eventually has to give way to a theory that either requires the tuning of parameters or lacks comparable predictive force for other reasons? The principle that scientific theories should be able to explain their predecessor's success therefore suggests that theories with free parameters should not be expected to be viable successors of a highly predictive structurally unique theory.Footnote ²⁵ The question of the existence of alternative theories that are not structurally unique or lack predictive power in this light loses its crucial importance for the understanding of theory succession.

Let us sum up the previous arguments: a highly predictive structurally unique theory that fits the empirical data at some stage can be expected to be replaced neither by another structurally unique theory nor by a theory that does not belong to that class. This suggests the termination of the progressing sequence of scientific theories. It must be expected that a highly predictive structurally unique theory that fits the present experimental data should describe all future experiments correctly as well. The pessimistic metainduction thus fails, and one must feel compelled to call any empirically successful structurally unique theory a serious candidate for a final theory.Footnote ²⁶

This conclusion has an interesting further implication. If a highly predictive structurally unique theory was able to reproduce the empirical data at any energy scale, this could be taken as a strong confirmation of that theory's characteristic predictions, even if those predictions had not been tested themselves and the available data could also be reproduced by other theories. In the case of conventional theories, the inference from a theory's empirical adequacy at one scale to its viability at another scale was prevented by the scientific underdetermination principle. But in the context of highly predictive structural uniqueness, that principle loses its pivotal role and the inference becomes viable as a statement about the most reasonable expectation. String theory might some day show the significance of this consideration: if it turned out that string theory delivered specific low-energy predictions that fit all presently known phenomenological data in particle physics within the given experimental limits of accuracy (just as the particle physics standard model does today), this would obviously not constitute experimental confirmation of strings at their own characteristic scale. Nevertheless, even the staunchest supporter of the predominance of experimental confirmation would be obliged to attribute a very high probability to the validity of string theory's high-energy predictions.

4.2. The Final Theory Claim

The property of structural uniqueness suggests that string theory, if valid and predictive at low energies, should be taken as a ‘final theory’ that will not be superseded by a more accurate or more far-reaching physical theory later on. Interestingly, similar ‘final theory claims’ occur in two other contexts in string theory without having to rely on the theory's low-energy predictive power. To begin with, there is a simple historical point. String theory is the first physical theory that seriously claims to provide a fully unified description of all known elementary physical phenomena.Footnote ²⁷ Therefore it is the first theory that allows a final theory claim if full unification of all fundamental phenomena is taken to be a goal of science.Footnote ²⁸ In this light, it looks natural that a structurally unique theory arises precisely at the stage when the entire range of observed phenomena is being covered by one theory.

A more powerful final theory claim is related to an interesting implication of string dualities. The string world shows a remarkable tendency to link seemingly different string scenarios by so-called duality relations. Two dual theories (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. The kind of duality relation relevant in our present context 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. Because of the basic principles of quantum mechanics, momenta along closed dimensions can assume only certain discrete quantized eigenvalues. Thus, two basic discrete numbers exist that characterize the state of a closed string in a compactified dimension: the number of times that the string is wrapped around this dimension and the eigenvalue of its momentum state in that very same dimension.Footnote ²⁹ Now, T-duality asserts that a model in which a string with characteristic length l is wrapped n times around a dimension with radius R and has momentum eigenvalue m is dual to a model in which a string is wrapped m times around a dimension with radius $l^{2}/ R$ and has momentum eigenvalue n.Footnote ³⁰ The two descriptions give identical physics.

This fact can be generalized and eventually implies that all tests of distances smaller than the string length can be understood as tests of correspondingly larger distances as well. Duality thus translates all information below the string length into information above the string length, rendering the former fully redundant. An absolute limit is set on attaining new physical information below a certain scale and so formally puts an end to the continuous physical search for new phenomena at ever smaller distance scales (see, e.g., Witten Reference Witten, Callender and Huggett1996). String theory implies that one cannot go beyond it by looking closer at nature. The internal structure of the theory thus contains a final theory claim.

The string-theoretical posit of a minimum length must be clearly distinguished from weaker finality assertions that appear in earlier physical theories without justifying a final theory claim. Thus the posit of elementary particles in microphysics generally does not exclude independent new phenomena that require additional theory building, and the absolute speed limit introduced by special relativity does not translate into a finite kinetic energy per particle—any experiment carried out at a finite energy scale therefore leaves room for new physics beyond that scale. String theory is the first theory in which a universal limit in microphysics is established and in which physics up to that limit could in principle be tested by experiment.

In a traditional scientific context, a final theory claim that is based on a specific scientific theory must remain questionable because of the scientific underdetermination principle. The devaluation of scientific underdetermination described in previous sections therefore constitutes a necessary precondition for a truly powerful final theory claim, which, in turn, further weakens underdetermination. Thus the termination of the process of theory succession and the limit to new empirical evidence form a coherent whole.

4.3. A New Conception of Scientific Progress

Claims of a final theory smack suspiciously of a declaration of the end of science. The current condition of string theory, however, suggests a quite different conclusion. The standard conception of scientific progress takes for granted a significant disparity between experimental search and theoretical fit with respect to their respective time horizon. While the ongoing discovery of new physical phenomena is elevated to an eternally valid principle of scientific research that puts a final empirical inventory (and consequently a final physical theory) forever beyond the grasp of human inquiry, the completion of the specific scientific theories that fit a certain set of phenomenological data is considered a finite and predictable enterprise. The scientists who take on the challenge to create a theory about some phenomena based on some set of principles and assumptions are expected to be able to complete that theory as a coherent and calculable structure (modulo some minor unsolved aspects, perhaps) within a reasonable amount of time. The distinction between the infinite duration of the quest for new physics and the limited creational period of single theories clearly mirrors the reality of traditional scientific research. In the case of string theory, it blocks the appreciation of the genuine novelty of the situation.

As described above, string theory provides a concrete notion of a final theory. Thus, if valid, it reduces the time until we reach a final description of nature to the time we need to complete string theory itself. This step, however, goes along with a vastly extended time horizon for the completion of this one theoretical scheme. It may be helpful at this point to remember the situation 4 centuries ago, when philosophers like Francis Bacon and René Descartes laid the foundations of the scientific worldview. Bacon as well as Descartes considered the creation of the scientific method itself to be the main achievement on the way toward a correct understanding of the world. The scientific details in their understanding could then be filled in within a lifetime. History has confirmed the immense fertility of the scientific method, but it has also disappointed the early expectations of imminent full enlightenment. The scientific method turned out to be a starting point for many generations of ever deepening research, which, despite its success, did not reach the elusive end point of a full description of nature.

The situation in string theory today might bear some resemblance to the old history of science. String theory, by establishing the notion of a final theory, might well prove to be of great significance for our understanding of nature but might nevertheless disappoint hopes for providing a specific time frame for the fulfilment of its ultimate promise. We are in no position today to assess whether—and, if so, when—a full formulation of string theory will be found, and we have no reason to assume that it will happen anytime soon. The arguments by analogy derived from the examples of earlier theoretical schemes fail because of the significantly different level of complexity of string theory and its nature as a final theory. One might well compare the seemingly never-ending sequence of theoretical problems arising on the way toward a complete understanding of string theory with the sequence of new physical phenomena that characterizes traditional physical research. In the same way as the perspective has emerged in the traditional scientific setting that science will always face new phenomena and, therefore, will never reach a final theory, one could now be led to suspect that string theory will always face new theoretical problems and will therefore never become fully mature. String theory thus should not be taken to announce an end of science but, rather, to represent a new phase of scientific progress. In this new phase, progress in fundamental physics is no longer carried by a sequence of limited, internally fully developed theories but, rather, by the discovery of new aspects of one overall theoretical scheme whose general characteristics identify it as a candidate for a final theory, yet whose enormous complexity bars hope of a full understanding in the foreseeable future.