Philosophy of String Theory Richard Dawid∗ August 21, 2019 Abstract 1 Introduction The basic idea of string theory goes back to the late 1960s. (For textbooks on string theory, see Polchinski 1999, Zwiebach 2007, Becker, Becker and Schwarz 2007. For a collection of texts on early string theory, see Cap- pelli, Castellani, Colomo, Di Vecchia 2012. A philosophy-minded history of string theory is Rickles 2013.) After its foundations had been laid from 1968 onwards as a candidate theory for describing strong interaction (Veneziano 1968), string theory was proposed as a universal theory of all interactions in 1974 (Scherk and Schwarz 1974) and became popular after the formulation of the action of a quantized superstring (Green and Schwarz 1984). Since then, string theory has played the role of the leading approach to a unified theory of all interactions. String theory's history as a subject of philosophical investigation is much shorter. Apart from Weingard (1989), which introduced string theory to philosophers, not a single philosophical paper on string theory was written in the 20th century. After a second philosophical "suggestion" to look at the theory at turn of the 21st century in Butterfield and Isham (2001), the theory became a subject of more extensive philosophical inquiry about a decade ago. Increasing activity in recent years may indicate the emergence of a fully fledged philosophical field of research. ∗Department of Philosophy, Stockholm University, 10691 Stockholm, Sweden. email: [email protected] 1 2 The Role of String Theory A consistent theory of quantum gravity is a main desideratum of contempo- rary fundamental physics. Observed phenomena in high energy physics at this point can be very well accounted for by the standard model of particle physics. Observed gravitational phenomena are covered in a satisfactory way by general relativity. However, neither of those two theories on its own can provide a satisfactory description of the very early and dense states of the universe. What is needed is a consistent theoretical scheme that accounts for both types of phenomena, nuclear interactions and gravity. There are two and a half ways to search for such a theory. The half- option would be to retain the theories of general relativity and quantum field theory and just try to make them consistent with each other so that they can work in conjunction to describe regimes where both types of interaction are relevant.1 No promising headway has been made in that direction and there are reasons to doubt that this is a viable way to go. The other two options start from one of the existing conceptual frameworks and build a theory from that starting point that can cover the other side as well. Canonical quantum gravity, loop quantum gravity, and related approaches start from gravity and aim at developing a quantized theory of gravity. String theory starts from the perspective of particle physics and aims to generalize it to include gravity. In the eyes of string theorists, two general observations speaks in favor of the latter approach. First, the principles of gauge field theory, on which the standard model of particle physics is based, put strong constraints on theory building. The requirement that the theory of quantum gravity should enforce that its low energy effective theory is a gauge field theory therefore is a powerful guideline for theory building. Second, the approach seems to work in principle, which is by no means a trivial observation. An extension of the gauge principle to supersymmetry leads to a graviton, which suggests that quantum gravity is a natural extension of gauge field theory. String theory started from a perturbative perspective, keeping the for- mat of calculating Feynman diagrams but replacing the pointlike particles of quantum field theory by small one-dimensional objects, the strings. This modification is assumed to generate a finite theory, thereby offering a solution to the problem of the non-renormalizability of quantum field theories of grav- ity. Moreover, the fact that a quantized string necessarily contains a graviton as one of its oscillation modes renders the approach a natural framework for describing quantum gravity. The posit of extended elementary objects also seems consistent with the high energy behaviour one is led to expect from 1for a philosophical perspective on that strategy, see W¨uthrich (2004). 2 a theory of quantum gravity. The generation of black holes in particle col- lisions at the Planck scale enforces an upper limit to testing energy scales that fits well with the intrinsic fundamental length scale of the string. This vague initial argument was later fleshed out based on the minimal length scale imposed by string theory's duality structure (see below). The seemingly innocent step towards extended fundamental objects car- ries huge conceptual implications. A quantized string theory that describes both fermions and bosons must be supersymmetric (that is, show a symmetry under transformations between fermionic and bosonic degrees of freedom). The quantization of this superstring only works in a consistent way in 10 spatiotemporal dimensions. The 6 extra dimensions remain invisible at low energies. They are understood to run back into themselves like cylinder surfaces, thereby generating a topologically complex spactime structure (a Calabi-Yau space). Moving beyond a strictly perturbative perspective reveals that string the- ory contains higher-dimensional objects of various dimensions called branes (Polchinski 1995). Branes play a crucial role in one of the most remarkable features of string theory. In a number of cases, specific realizations of string theory that differ with respect to the kinds of symmetries they have, the radii of their compact dimensions, their spacetime topologies, the dimensionality of their higher dimensional objects and other characteristics are dual to each other: they are empirically fully equivalent and the features of one formula- tion are related to features of its dual by a duality transformation. Duality relations connect all five types of superstring theory.(Witten 1995) Another duality relation connects string theory on AdS space (a space with constant negative curvature that corresponds to the solution of the Einstein equa- tions for empty space with a negative cosmological constant) to a conformal string theory on the boundary (Maldacena 1998), thereby revealing a deep connection between string theory and gauge field theory. String theory in many respects is a very different kind of conceptual scheme than any other physical theory we know. In the following, I will give a brief survey of some of the most important novel characteristics of string theory that deserve serious philosophical attention. A number of them have by now been addressed extensively in a philosophical context. Others still lack the philosophical attention they deserve. 3 3 Specific Physical Characteristics of String Theory 3.1 The central role of the concept of duality As already emphasized in the introduction, dualities play a pivotal role in string theory. They have also been at the center of the theory's philosophical analysis. Dawid (2007, 2013), Matsubara (2013) and Rickles (2011, 2017) identified string dualities as a serious problem for scientific realism. The extent to which dual theories differ from each other with respect to their fundamental ontologies is incompatible with ontological scientific realism (Dawid 2007). For a number of reasons, dual formulations of string theory should be treated as different perspectives on one theory rather than as distinct theories: string theorists clearly treat them as one theory (Matsubara 2013); only the entire web of dual formulations allows an adequate understanding of string physics (Dawid 2013); dual theories can be transformed into each other by duality transformations (Rickles 2017). As pointed out by Castellani (2009), viewing duals as different perspectives on the same theory goes counter to the classical view that links theory individuation to a theory's ontological import.2 Dawid (2007, 2013) and Matsubara (2103) argue that structural realism is in a better position than ontological realism to account for dualities but faces problems of its own. Dawid (2007) suggests that string theory might support a specific form of structural realism (consistent structure realism) that relies on the fact that string theory at a fundamental level is fully deter- mined by consistency arguments. (It has no free parameters and no freedom of model choice.) Rickles (2017) also favors a structuralist approach. He emphasises that duality transformations, in revealing physically irrelevant transformational degrees of freedom, are comparable to gauge transforma- tions (see also de Haro, Teh, Butterfield 2017). This analogy suggests that anything that can be changed under duality transformations is unphysical and no candidate for the theory's real content. Only characteristics invariant under duality transformations, such as the global symmetry group, should thus be acknowledged as real. Rickles argues that this leaves sufficient room for a structural realist take on string theory. An interesting specific context for analysing the anti-realist import of du- alities is provided by S-duality. S-duality transforms a theory into a dual with inverse coupling constant. In string theory, S-duality arises as one of the pivotal duality relations that connect all five types of superstring theo- 2See e.g. Coffey (2014) for a recent exposition of the latter view. 4 ries. The fundamental strings of one theory show up as solitonic solutions (nonperturbative effects characterised by a topological charge) in its S-dual theory (Harvey and Strominger 1995). The fundamental objects of one the- ory thus emerge as complex composite objects of its dual. String physicists Sen (1999) and Susskind (2013) have taken this characteristic of string theory to indicate that the theory does not allow for a reductionist understanding of the world. Objects don't stand in an unequivocal constituent-compound relations to each other. Sen's and Susskind's arguments support the incom- patibility of string theory with ontological scientific realism.