2.1 Vices of the standard account

Here I describe three serious problems with Standardly interpreting quantum field theory. I will be brief, for two reasons. First, because much of this ground has been covered at length in (Wallace [2006], [2011]), with whom I am almost entirely in agreement. Second, because Section 3 consists of a positive argument that interpreting EFTs grounds ontological commitments that are more reliable than those any standard interpretation of quantum field theory can provide, and I hope this argument will be more persuasive than any purely critical discussion.

The central vice of standard interpretation, illustrated by the quote from (Halvorson and Müger [2007]) cited earlier, is that it declares essentially all empirically applicable quantum field theories to be unfit for interpretation. This is because no mathematically rigorous version of the standard model—indeed, of any interacting QFT in four spacetime dimensions—has ever been constructed, and a rigorous mathematical model of a physical theory is a precondition for providing a standard interpretation.¹¹ Quantum field theories that satisfy the preconditions for standard interpretation are known to exist only in two or three spacetime dimensions, and lack many of the crucial structural features that characterize the quantum field theories that describe our world, such as invariance under local gauge symmetries. This means that in quantum field theory, the question the standard interpreter aims to answer is actually worse than the counterfactual starting point I attributed to standard interpretation at the outset of the article. In quantum field theory, the standard interpreter sets out to answer the following nested counterfactual: ‘If we lived in a world with two (or three) spacetime dimensions, and if that world could be described by a theory that we know is structurally incapable of describing our world, and if that theory provided a complete and exhaustive description of that two (or three) dimensional world in all respects, what would that world be like?’. The answer to this question is then purported to offer insight into the ontology of the world in which we do, in fact, reside.

A second vice stems from this inability to Standardly Interpret empirically applicable quantum field theories. The manner in which a physical theory is employed in real-world applications offers valuable guidance about which elements of that theory’s mathematical framework play a genuinely representational role and which are likely just mathematical artefacts. The absence of applications for the quantum field theories preferred by standard interpreters thus makes their proposed interpretations even less reliable. Again, this is not just in the general sense that one may reasonably have more confidence in the approximate truth of empirically successful theories, but also in the more specific sense that their preferred toy theories lack an important tool for providing a fine-grained separation of ontological wheat from mathematical chaff. Explaining how this works in EFTs is addressed in detail in Section 3.

The rectitude of standard interpretation is not always just assumed. There have been arguments presented in its favour—in particular, arguments for ignoring EFTs in favour of attempting to extract ontological information by answering the nested counterfactual given above (for example, Fraser [2009], [2011]; Kuhlmann [2010]; Baker [2013]). However, these arguments reveal a third vice of adhering to standard interpretive methodology: it can generate conclusions we have good reason to believe (at best) non-sequiturs, and (at worst) false. As one example, consider the argument in (Fraser [2009]) that the lack of a rigorous mathematical model of quantum field theory in four spacetime dimensions renders it unsuitable for interpretation. Fraser’s argument takes the form of a reductio ad absurdum: she considers an EFT whose breakdown at some short distance L is captured by representing space as a lattice with lattice spacing L. Adherence to standard interpretational methodology (that the description of the world offered by the theory be treated as true and exhaustive, for instance) leads her to conclude that the theory assigns a lattice structure to physical space. Thus, she continues, since no one believes that quantum field theory entails that physical space has a lattice structure, EFTs are unfit for interpretation.¹² Of course, the upshot of any reductio is just that some set of assumptions is inconsistent; one then identifies the assumption(s) to be discarded based on whatever considerations are most appropriate within the context of the investigation. An alternative response to discovering that one’s approach to theory interpretation generates a conclusion that no one believes is to conclude that it may be the approach to interpretation that is unfit for interpretive work, not the theory.

The three objections to standard interpretations of quantum field theories that I’ve offered are: (i) it requires replacing questions about the actual world (answerable by investigating empirically successful EFTs) with questions about remote counterfactual worlds, to be answered by interpreting toy quantum field theories; (ii) the lack of empirical applications of the quantum field theories preferred by standard interpreters weakens even further the realism such investigations can support; and (iii) it is prone to generating absurd ontological conclusions due to artificial restrictions on what information one is allowed to take into account when interpreting a physical theory.

One may worry that allowing the way a theory is applied in practice to inform its interpretation in the fashion I am encouraging makes the endeavour troublingly pragmatic, and so threatens to undercut any strongly realist interpretation of quantum field theory. I think that it strengthens our realist commitments, and it is to that issue that I turn now.

3.1 Approximate truth

The notion of ‘approximate truth’ employed in most traditional formulations of scientific realism is both (i) of central importance, since we know our current scientific theories aren’t exactly true, and (ii) sufficiently opaque as to function as little more than an acknowledgment of this fact. The divide and conquer strategy aims to improve this by identifying elements of a theory that are crucial to its empirical success (as opposed to the ‘idle posits’ of the theory that are not), and by identifying robust entities and structures that are likely to survive episodes of theory change; ideally these two sets will have considerable overlap. In this section I highlight several ways in which EFTs represent a significant improvement on this situation.¹⁹

First, they provide explicit guidance about the domains in which one is warranted in believing claims made by the theory. Consider the most general case: the expected breakdown of the entire theoretical framework of quantum field theory itself. It is well known that quantum field theory has not provided and probably cannot provide a consistent theory of quantum gravitation, and it is generally believed that the entire theoretical framework of quantum field theory itself becomes inapplicable at the length scales where quantum effects of gravity become significant (generally thought to be near the Planck scale).²⁰ A very general appeal of EFTs is that they explicitly incorporate this inevitable breakdown of their theoretical framework. EFTs thus provide formal signposts delineating the physical domains in which one should and should not trust the theory to provide reliable ontological guidance. By making explicit that the theory becomes inapplicable beyond a given length scale, EFTs provide some measure of refinement and clarification of the sense in which quantum field theory is ‘approximately true’; by studying a given EFT in an entirely ‘internal’ fashion, one can learn that its claims about the properties of and interactions between its degrees of freedom in one domain—their symmetries, dynamics, allowed final states in scattering experiments, and so on—are not a reliable guide to the world once one pushes the theory beyond a specified length scale. As physicist Tony Zee ([2010], p. 172) puts it in a discussion of EFTs, ‘I find it sobering and extremely appealing that theories in physics have the ability to announce their own eventual failure and hence their domains of validity’. This is one unique way in which EFTs offer a more precise handle on the sense in which quantum field theories are ‘approximately true’.

A second way EFTs can refine the notion of ‘approximate truth’ is that one can examine the roles different elements of the theoretical framework play in empirical applications in order to evaluate their physical significance. This is apiece with the divide and conquer approach to scientific realism sketched at the outset of this section, and the RG plays an important role in this endeavour. I will focus on one especially salient example of the role that EFTs can play in distinguishing physical significance from mathematical artefact. This takes place in the context of lattice quantum field theory: the short-distance physical breakdown of the theory around some length scale, which I will denote here by a, is incorporated by placing a quantum field theory on a four-dimensional spatiotemporal lattice with lattice spacing a (instead of a continuum spacetime). Most commonly it is EFTs that are invariant under a non-abelian gauge symmetry that one formulates this way—especially quantum chromodynamics (QCD), the theory of the strong interactions—and for concreteness I will focus on that case. My goal is to illustrate how combining the RG with applications of lattice QCD allows one to distinguish theoretical structures with genuine representational content from mere mathematical artefacts. Again for concreteness, I will restrict attention to two particular examples: (i) the way one can use the RG to establish that so-called mirror fermions that arise when one formulates an EFT on a spacetime lattice are mere mathematical artefacts and (ii) how the RG demonstrates the general physical irrelevance of the specific method chosen for formally incorporating the breakdown of an EFT.²¹

Mirror fermions arise whenever one attempts to represent the breakdown of a quantum field theory containing fermions, like electrons or quarks, with a spacetime lattice.²² A well-known theorem, the Nielsen–Ninomiya theorem, proves that any attempt to place a quantum field theory that (i) satisfies a set of physically reasonable conditions and (ii) contains fermion fields on a d-dimensional spacetime lattice runs into trouble: the ‘latticized’ EFT necessarily contains 2^d more fermionic degrees of freedom than the theory intended to describe.²³ for discussion. For instance, if one sets out to give a quantum field theoretic description of a single, non-interacting fermion field propagating on a four-dimensional spacetime and attempts to ‘latticize’ the theory, the result is an EFT on the lattice that now describes sixteen fermions! One could reasonably ask how an EFT containing fifteen more fermionic degrees of freedom than the theory intended to describe could possibly be a source of reliable ontological information. And indeed, a standard interpretation of such an EFT seems to result unavoidably in the conclusion that the theory’s ontology includes sixteen species of fermion—a clear indication, it would seem, that such a theory is unfit for interpretation.²⁴

I think this attitude is mistaken, and that one can extract reliable ontological information as follows. Start by adopting one of several less naïve approaches to putting fermions on a lattice, which isolate the undesired ‘mirror’ fermions from the physical fermion(s) one wanted to describe in the first place.²⁵ After employing a more sophisticated method for ‘latticization’, the action $\mathcal{S}$ (which contains all the theory’s dynamical information) has the following form:

where ${\mathcal{S}}_{mirror}$ is proportional to some positive power p of the lattice spacing a.²⁶ The unwanted mirror fermions are sequestered into a term proportional to the lattice spacing a, while the physical fermion(s) are contained in ${\mathcal{S}}_{continuum}$, which is independent of a and dynamically decoupled from the mirror fermions.²⁷ By the lights of the divide and conquer strategy, there is excellent reason to withhold ontological commitment from them (and other lattice artefacts of similar ilk), even within the EFT framework. The justification for this goes as follows: The standard interpreter’s claim in this case is that since mirror fermions appear in the formalism being interpreted, one is committed to including them in the theory’s ontology. As mentioned above, the mirror fermions are sensitive to the specific choice of the lattice spacing a, while the physical fermions contained in ${\mathcal{S}}_{continuum}$ are not. This means that while they do appear in the formalism, they do so as part of the short distance, cut-off-scale physics that one discards in an EFT on principled grounds, since the theory is not trustworthy in that physical domain.

One can cash this out in more detail using the notion of robustness, our criterion for ontological commitment, as follows: One lesson of the RG is that choosing a specific value for the cut-off length a is somewhat arbitrary—one can choose any number of different lattice spacings $a\prime <a$ without affecting the empirical predictions of the theory. Furthermore, there are several different and independent methods for ‘latticizing’ quantum field theories that contain fermions. Each of these methods produces mirror fermions that manifest differently in the lattice dynamics $\mathcal{S}$, but in all cases they are dynamically decoupled from ${\mathcal{S}}_{continuum}$ and proportional to the lattice spacing. The mirror fermions thus depend on an arbitrary choice of modelling scheme in a way that genuinely representational quantities in physical theories do not. On the other hand, in each of these ‘latticization’ schemes the physical dynamics ${\mathcal{S}}_{continuum}$ are insensitive to the specific physical details of the chosen modelling scheme—in particular, the cut-off length and latticization method—and so remain invariant across a broad variety of independent methods. Of course, in the terminology used above, this is just to say that they are robust.

Recalling the two prongs of the divide and conquer strategy, one can say that while mirror fermions may remain present in the mathematical formalism of lattice QCD (or any EFT describing fermions on a lattice), they are neither (i) stable and robust elements of the theory, since they are sensitive to arbitrary choices of the length a of the lattice spacing and the chosen method of ‘latticization’ in a way that the genuinely physical fermion(s) are not, and (ii) they do not play an essential role in the empirical success of the theory. As such, there is little reason to believe that they are candidates for representing anything ontologically interesting.

A related (but distinct) way in which the RG can identify ‘robust’ physical quantities in an EFT is by demonstrating the differential sensitivity of structures in the theoretical framework to the specific way one chooses to model the physics at the scale of the short-distance breakdown scale.²⁸ This was integral for denying ontological significance to lattice artefacts like mirror fermions, but this function of the RG is entirely general. In fact, it is one of the essential virtues of the RG that it provides a tool for determining how changes in the structure of the theory at the scale of the short-distance breakdown affect physics at longer distances where the theory is empirically reliable. What the RG shows is that the ‘fundamental’ short-distance structure with which standard interpreters are so concerned is largely irrelevant to the physical content of an EFT in the domain where we have any reason to consider it empirically reliable. This includes changes in the way we model physics at the scale of the short-distance breakdown—which includes modelling schemes as diverse as carrying out calculations in a non-integer number of spacetime dimensions or introducing fictional ‘particles’ at the scale of the breakdown—but is not limited to this.²⁹ The RG also demonstrates that the long-distance structure of the theory is stable across variations of many physical conditions: one can add (say) (i) a variety of additional (hypothetical) particles at short distances, including novel interactions between those particles and the particles included in the EFT; or (ii) vary the strengths of the physical couplings in the theory; or (iii) incorporate symmetries present at the ‘fundamental’ scale that differ from those present in the theory at longer length scales, all while leaving unperturbed the structure of the theory in the physical domains in which it can be subjected to experimental tests, and has been shown empirically reliable. An EFT at long distances is ‘robust’ in a way that the short distance ‘fundamental’ theory is demonstrably not: its entities and structures at that scale are ‘accessible (detectable, measurable, derivable, definable, producible, or the like) in a variety of independent ways’, and so are candidates for being included in the ontology of that EFT.

In what follows I provide a single, less frequently discussed example that might be surprising for those inclined to equate a theory’s fundamental ontological structure with its structure at all scales: the recovery of an EFT whose dynamical equations are Lorentz invariant even though the dynamics of that same EFT at short distances (that is, the ‘fundamental’ level) strongly violate those symmetries.

For concreteness, consider a simple EFT describing a single scalar field $\Phi$ that has been placed on a four-dimensional lattice spacetime, with lattice spacing a.³⁰ The structure of the lattice violates Lorentz invariance in multiple ways—for instance, special relativistic spacetimes are symmetric under arbitrary spatial rotations, but on a spacetime lattice one can only carry out spatial rotations in integer multiples of 90 degrees. The action for this theory is:

 Only a subset of the interactions in the action violate the symmetries of special relativity: those multiplied by positive powers of a, all of which are sequestered into the summation on the right-hand side. Starting with this action, one can use the RG to examine how the structure of the theory changes at length scales L that are long compared to the lattice spacing a, that is, in the domain where the theory is empirically adequate. One finds that the interactions in the summation die off at a rate proportional to ${(a/L)}^p$ for some positive integer p. For illustration, let a be the Planck length ${10}^{-35}$ metres and L be the scale at which quarks and gluons become confined into hadrons, $L\sim {10}^{-15}$ metres. The symmetry-violating interactions then decay at a rate of ${({10}^{-20})}^p\approx 0$; in practice, one often allows $L\to \infty$ since this proves a perfectly reasonable approximation for $L\gg a$. The result is that in the physical domain $L\gg a$ where the EFT actually provides reliable ontological guidance, the only interactions that remain in its dynamics are those invariant under Lorentz transformations. Thus, beginning with an EFT that contained interactions at the ‘fundamental’ level that violate the symmetries of special relativity, one obtains a fully Lorentz invariant theory in the long-distance domain where one expects the theory to be physically trustworthy.³¹

Recall that the primary purpose of this particular example was to illustrate that the RG can refine and clarify the notion of ‘approximate truth’ by identifying which theoretical entities and structures in a quantum field theory are ‘robust’ and which are likely mere mathematical artefacts. It also suggests two further conclusions. First, it functions as a response to those such as Fraser ([2009], [2011]) who want to assign physical significance to the fact that (some) methods of representing the short-distance failure of EFTs violate the symmetries of special relativity. Fraser argues that one cannot confine the ontological significance of such violations to physical domains in which the theory is empirically inadequate anyway—they affect the physical content of the (Fraser [2009], p. 560), ‘Cutting off the theory at some short-distance scale has the effect of changing the content of the theory as a whole, including its description of long-distance scales’. I take the examples presented here to go some way toward demonstrating this is mistaken: as long as one is not in the grip of standard interpretation, they are justified in denying that mathematical artefacts at the scale of an EFT’s breakdown carry any ontological significance.

The second conclusion these examples suggest is that we can be misled about the reliable ontological information provided by a quantum field theory by interpreting only its empirically unreliable ‘fundamental’ structure and conflating that with its structure at all scales. It is a mistake to think that one can simply read a quantum field theory’s ontology off its ‘fundamental’ mathematical structure. The next section develops in more detail the implications this has for our interpretational practice and for the ontological commitments of EFTs.

3.2 Scales and ontology

In Section 3.1, I argued that by interpreting EFTs one has resources to make fine-grained distinctions between mathematical artifice and physical significance, which supports a ‘divide and conquer’ approach to ontological commitment. I contrasted this with an excessively egalitarian approach to ontological commitment: standard interpreters treat all of the entities and structures of a theory’s mathematical framework (at least those at the ‘fundamental’ level) as on more or less equal ontological footing. This is one symptom of the ‘fetishism of mathematics’ diagnosed earlier by Stachel.

In this section, I argue that attending to EFTs also makes clear that for many quantum field theories, any interpretation that enables those theories to ‘discharge their scientific duties’ must include higher-level entities in its ontology.³² This is particularly true of their explanatory duties, and it is on these that I will focus here.³³ The contrast again is with standard interpretation: while its insufficiently discriminating approach to a theory’s mathematical structure leaves it open to too much ontological commitment, its focus on only the ‘fundamental’ structure of quantum field theories leaves it prone to committing simultaneously to too little.

As an example, consider (Fraser [2008], p. 856) in which a theory’s ontology is straightforwardly equated with its fundamental ontology: ‘The point at issue is whether entities with certain properties—particlelike properties—exist. More precisely, does QFT support the inclusion of particlelike entities as fundamental entities in our ontology?’.³⁴ After answering ‘no’, Fraser entertains the response that ‘quanta are not part of the ontology of fundamental entities described by QFT, but […] that nevertheless quanta do exist according to QFT’. Her response epitomizes the ‘fundamentalism’ I have attributed to standard interpreters: ‘For this to be a viable response, the cogency of the distinction between fundamental and less fundamental entities must be defended and a case must be made for admitting additional, non-fundamental entities into our ontology […] the important question—which remains outstanding—is not the status of quanta, but what fundamental entities are allowed into our ontology by QFT’ (Fraser [2008], pp. 857–8; my emphasis).

As I stated above, focusing exclusively on fundamental ontology in this fashion leaves one with an interpretation unequipped to support the theory in the performance of its explanatory duties. By paying attention the applications of EFTs and the RG, it becomes clear that many explanatory affirmations made in the theory simply cannot be made true by including in one’s ontology only those entities at the fundamental scale. I emphasize that as long as one grants that scientific explanations aim at providing an at least minimally illuminating and manageable account of their explananda, there is good reason to believe that the ‘cannot’ in the previous sentence will not be eliminated by some ‘future complete physics’ or ‘in principle’ explanations in terms of the fundamental ontology. This belief can be in part motivated by considerations of the sort discussed in Section 3.1, where we saw that the fundamental structure of a quantum field theory can be in many respects irrelevant for answering why-questions about its behaviour at longer distances. I will focus on a specific example in quantum field theory, that of ‘confinement’, that I think makes the motivation for this belief especially salient. This story is itself rather general—the phenomenon of confinement is present in any quantum field theory that is invariant under a non-abelian gauge symmetry—but for concreteness I will focus on an example of considerable physical import: the confinement of quarks and gluons into hadronic bound states in QCD at long distances.³⁵

At the shortest distances at which it is empirically valid, QCD describes the interactions of quark and gluon fields via the strong force.³⁶ Consider a schematic version of the QCD dynamics:

The physical degrees of freedom appearing in the dynamics of QCD at short distances are quarks and gluons, with the final term representing their interactions. When interactions between these fields are relatively weak, as they are in QCD at short distances, a description in terms of quark and gluon particles is available and explanatorily powerful. Calculations performed in the theory at this distance scale have played an enormous role in cementing QCD as the appropriate theory of the strong interaction, and it is these physical degrees of freedom that appear in the fundamental dynamics of the standard model of particle physics.³⁷ It may therefore seem natural to conclude that an interpretation of QCD requires the admission of quark and gluon fields to one’s ontology, but nothing more. This would almost surely constitute the standard interpretation of the ontology of QCD, at least.³⁸

Such an interpretation of QCD would leave it unable to discharge its explanatory duties, and thus fails qua interpretation by the standard of Ruetsche ([2011]) that I have adopted here. Studying the behaviour of QCD at long distances, using the RG and techniques of lattice QCD, reveals that QCD has a rich, scale-dependent structure that is hidden from the perspective of the fundamental level. It also reveals that many physical processes involving these long-distance structures in QCD are not explicable purely using the dynamics and degrees of freedom present at the fundamental level. The feature of QCD responsible for this is that the strength of the interaction between quark and gluon fields increases as one considers the structure of the theory at longer distances. This gives rise to ‘confinement’, the phenomenon I think most clearly illustrates the scale-dependence of the ontology of QCD. Roughly, a quantum field theory is ‘confining’ if, beyond a certain length scale, the strength of the interactions between its short-distance degrees of freedom become so strong as to make explanations of phenomena in terms of particulate states of those fundamental fields intractable and (even if one could provide such a description) entirely unenlightening. In QCD, the fundamental quarks and gluons become confined into hadrons (particles like the proton and neutron, which are bound states of quarks and gluons), preventing particulate states at length scales longer than about ${10}^{-15}$ metres.

This is unlike other familiar bound states, such as a hydrogen atom, in the following sense. In those cases, bound states form under certain energetic conditions, but under other common conditions one can also scatter sufficiently energetic electrons off of a proton and let the two become separated by very long distances without a bound state being formed. The situation is different in the case of quarks and gluons. In that case, it is nomologically impossible to separate a pair of particulate states of quark or gluon fields by a distance of more than about ${10}^{-15}$ metres. Imagine a tiny experimentalist living inside of a hadron, attempting to pull quarks apart. She would discover, presumably after much exertion, that it is impossible to separate them to distances greater than the confinement scale.

This prevents these degrees of freedom from being dynamically active on length scales longer than the confinement scale, which means that they play neither an observational nor explanatory role in physical processes taking place above that scale.³⁹ Rather than quarks and gluons, the degrees of freedom appearing there are bound states: hadrons (like pions, protons, and neutrons) that have different properties (they lack the ‘colour charge’ that quarks and gluons possess, for example), interact via dynamics with a different structure than the fundamental QCD dynamics, and are invariant under different symmetries than is QCD at short distances.

It is true that starting from the fundamental QCD dynamics, one can derive that the fundamental degrees of freedom are confined into hadrons at around ${10}^{-15}$ metres.⁴⁰ However, if one wants to explain physical processes characterized by length scales longer than this—the binding of atoms into molecules, for example—it is a matter of physical law that one cannot ‘zoom out’ to those length scales without a description in terms of particulate states of quark and gluon fields becoming wildly intractable and devoid of explanatory power, and one is required to replace such a description by one in terms of hadrons. Furthermore, the hadronic degrees of freedom play an integral role in a tremendous number of empirical applications and explanations of physical phenomena, such as those currently taking place at the Large Hadron Collider (LHC).

On this last point: Due to the confinement of the quarks and gluons, the strongly interacting particles that experimenters actually prepare, manipulate, and observe in particle physics experiments are hadrons, not quarks and gluons. Furthermore, experimenters and theorists also employ hadrons to explain the results of those experiments: almost every high energy scattering event at the LHC produces so-called jets of hardons that are then observed in particle detectors, and the details of their production are integral for explaining the scattering event (see, for example, Schwartz [2014], Chapter 36). As Montvay and Munster ([1997], p. 231) put it, ‘the transformation of the perturbative predictions at the parton (i.e. quark and gluon) level to the hadronic incoming and outgoing states cannot be done without some knowledge of […] confinement phenomena’ (my emphasis).⁴¹ So in this very flat-footed sense, an interpretation of QCD that does not admit higher-level entities like hadrons into its ontology fails almost immediately its task of enabling the theory to discharge its scientific duties. In fact, this is a special case of a rather general principle about the explanation of experimental results: in the words of Wimsatt ([2007], p. 210):

In the case of QCD, Wimsatt’s principle is a corollary of the fact that any description of any strong-interaction process at distances longer than the confinement scale in terms of particulate states of the quark and gluon fields will be entirely devoid of explanatory power. So our guiding interpretive principle—that an interpretation enables a theory to discharge its scientific duties—entails that any interpretation of QCD had better include, at minimum, higher-level entities like hadronic bound states along with quarks and gluons in its ontology.

QCD thus provides a case in which even though one knows that some higher-level entities are composite states of more fundamental entities, one cannot explain the behaviour of those higher-level entities solely in terms of the behaviour of the fundamental level. Recall that this story about confinement of fundamental degrees of freedom at long distances has some generality: it will occur in any quantum field theory that is invariant under non-abelian gauge symmetries—precisely the sort of theories that make up the standard model of particle physics.⁴³ This is yet another way in which EFTs and the RG provide us with improved realist commitments: they reveal absolutely physical information that is obscured from the perspective of the standard interpreter.

I began by asking what sort of scientific realism could be grounded by EFTs, and I will close with a few remarks on that theme. It demands that we distinguish reliable ontological information from theoretical artefacts, and requires attending in detail to the way theories are applied in practice to do so, in line with my earlier advocacy for the divide and conquer strategy. The result is a more discerning sort of realism, and one that gives the lie to the idea that we can simply read a physical theory’s ontological commitments off of its fundamental mathematical framework. I take this to be a feature, not a bug: the idea that one could responsibly do otherwise seems to me to always have been a mistake.

For this sort of realism it is important that a theory have a broad range of empirical applications.⁴⁴ However, this is not to say that the ontological commitments of an EFT are restricted to its ‘observable’ content. It just emphasizes something that has come to be overlooked by philosophers of physics: examining in detail how a theory makes contact with the world offers important guidance in determining which features of the theory have a genuine representational function and which are excess structure. I should note that I don’t believe that attending to empirical applications is the only method of sorting ontological wheat from theoretical chaff—I have emphasized the importance of the RG in the context of EFTs, and different theoretical contexts are likely to have similar ‘locally’ useful tools. I think it is in general, however, the most important method. Finally, I noted at the outset that one of the original motivations for the divide and conquer strategy was that the ontological commitments it entails are entities and structures that are likely to survive episodes of theory change. In the case of quantum field theory, such an episode is inevitable—the need for a theory of quantum gravity is almost certain to produce a theory describing physics at short distances that differs dramatically from quantum field theory. In light of this virtual guarantee that theory change is on the horizon, I think the ability of EFTs and the RG to identify entities and structures that are robust and insulated against such short-distances changes should be appealing to would-be realists.