Effective Field Theory and the Pragmatics of Explanation
Abstract
I discuss how there has been a recent trend in the philosophy of scientific explanation towards a pluralistic view that acknowledges the importance of both of the major accounts of explanation of the last thirty years- the unificationist account, as proposed in (Kitcher, 1989), and the causal account, primarily as described in (Cartwright, 1983), but with aspects from (Salmon, 1998)- and admits the possibility of other, as yet undiscovered, accounts. Although I believe that a pluralist position is essentially correct, I argue that no satisfactory description has been given of how one determines which explanatory contexts call for which kind of explanation. Limiting my analysis to the contemporary particle physics techniques associated with Effective Field Theories, which I believe offer a particularly good case study for distinguishing between contexts, I argue that the determination of explanatory type from context is a pragmatic issue. To address this issue, I turn to a third account of explanation,the pragmatic account, as described in (van Fraassen, 1980). Although I argue the pragmatic account fails as a full account of explanation, it succeeds, in modified form, in describing the pragmatics of explanation,specifically of the pluralist account. In the end, I argue that explanatory context in particle physics is determined by the relationship between the experimental context in which the person demanding the explanation is interested, and the characteristic energy scale of the phenomenon to be explained. When the experimental context in question overlaps with the characteristic scale of the phenomenon, a causal explanation is called for; if the experimental context is higher than the characteristic scale, then explanatory unification is called for.
Chapter I
Introduction and Overview
1.1 Introduction
The philosophy of scientific explanation originated with the work of the logical positivists, formalized by Carl Hempel and Paul Oppenheim in the 1960s (see their essays in (Colodny, 1962), for example). In excising metaphysics from philosophy and replacing it with logic and scientific observation, they found that many aspects of science needed specification and formalization. Their efforts to define quotidian concepts of science like theory choice, inductive support, and explanation succeeded in simultaneously laying a groundwork for future questions on these topics (many of which had not been previously considered by philosophers) and revealing fundamental inconsistencies in their own program. Virtually all work on scientific explanation of the last fifty years has been targeted at responding to and resolving the shortcomings of the two models of explanation expounded by the logical positivists: the deductonomological (DN) model, and the inducto-statistical (IS) model, collectively known as covering law models.
Much has been written about both these models, (See (Salmon, 1989b) and (Kitcher, 1989) for particularly good expositions), so I will not dwell on them here any more than required for a brief outline of each. The rough idea of the DN model is that an explanation consists of a deduction (hence deducto) taking as premises (a) one or more laws of nature (hence nomological) and (b) the specifics of a situation. A statement S (the explanandum) is said to be explained if it can be deduced by formal logic from (a) and (b). Another, more intuitive way of thinking about this model is
that S is explained if one can show that S should be expected, given known laws and the circumstances surrounding the content of S. The IS model, on the other hand, begins with a statistical law from which one induces the explanandum.
These pictures of explanation face a number of insurmountable problems (for instance- no one has been able to point to a single law of the sort that Hempel requires for the DN model). Two major responses have arisen in their stead. The first, a distant relation of the DN and IS models that avoids many of their problems and which I will call the “unificationist account”, was first posited by Michael Friedman in his (1974) and has been expanded on famously by Philip Kitcher (there are several papers, but (Kitcher, 1989) is the most encompassing). The idea is that to explain S, one should try to fit it into a framework of other statements, all of which one believes to be true and which are dependent on and consistent with each other. More precisely, one tries to find a pattern of argument that can be used to relate many disparate phenomena back to a relatively small number of first principles. Although different from Hempel’s account, again the intuition is that to explain something is to show that it is expected, in this case by showing how it relates (presumably in a more complex way than either the DN or IS account allows, although each could be construed as a special case of the unificationist account) to other true statements.
The second response, which I will call the “causal account”, has two major instantiations, respectively supported by Wesley Salmon (see (Salmon, 1985),(Salmon, 1997), and (Salmon, 1998)) and Nancy Cartwright (see especially (Cartwright, 1983)).
There are some important differences between Cartwright and Salmon. In general, however, I will tend to focus on Cartwright more than Salmon because her position is stronger, more radical, and, in the end, more interesting. For now, suffice it to say that the common ground between the two accounts is that explanations should be thought of as causal stories, focusing on the relevant causal properties of the system under consideration. So on the causal account, S is explained by a series of statements the contents of which are causally dependent on each other (this series would look like “we have situation X, in which S0 causes S1 to occur, which causes S2 to occur, ..., which causes Sn to occur, which causes S to occur”). These accounts bring with them the various problems associated with theories of causation, originally pointed out by Hume (although Salmon has made some progress here). But at the same time, they have a great deal of intuitive attractiveness: causal stories feel like ordinary explanations from outside of science.
Recently, there has been a growing consensus among philosophers that both the unficationist account and the causal account(s) are correct, in appropriate situations in science (see especially (Salmon, 1989a) and (Godfrey-Smith, 2003)). This is probably the right step forward. One of the strongest arguments against the DN and IS models was essentially phenomenalistic- no examples could be produced from actual science that had the forms Hempel described. Both the unificationist and the causal accounts, on the other hand, have innumerable examples of explanations in their support. In fact, one of the largest problems for each account is the great success of its opponent in describing some (although neither can lay claim to all) explanations.
Short of labeling a large section of science “bad”, there is little option but for the polemicists to concede to a plurality of accounts: sometimes, a proper explanation is a specific causal story, at other times, a proper explanation involves fitting the explanandum into a larger structure. Some philosophers (see (Salmon, 1989a), (Hartmann, 2001)) have distinguished between the kinds of understanding achieved in each case, arguing that the unificationist account produces global understanding, whereas the causal account produces local understanding. Other philosophers (see
(Godfrey-Smith, 2003)) have avoided the complicating step of fragmenting explanation by proposing a kind of contextualism for scientific explanation, in which different areas of science have different explanatory systems.
Pluralism seems correct, but leaves open the, essentially pragmatic, question of distinguishing between explanatory contexts. To begin to answer this question, I turn to a third major account of explanation, originally proposed by van Fraassen in his (1977) and expanded in his (1980), which I will call the “pragmatic account”. The pragmatic account has generally been considered unorthodox because it sidesteps the debate between the causal and unificationist accounts entirely. At the same time, and most interestingly, properly construed, neither the unificationist account nor the causal account is inconsistent with the pragmatic account.1 Moreover, the pragmatic account is intended to resolve exactly the same issue of determining what kind of explanation is appropriate in a given context that faces the pluralist account.
The inspiration behind the pragmatic account is to consider what an explanation is supposed to do: answer a why question. A proper understanding of explanation, then, lies in an understanding of the logic of why questions and their answers2. Van Fraassen suggests the following structure for a why question. A question can be thought of as an ordered triplet consisting of the topic T, the contrast class X, and a relevance relation R which the answer is expected to bear to T. R and X are usually implicit in the context in which the question is asked, but to be clear, the question “Why T?” is elliptical for “Why T as opposed to X, where the answer should bear R to T”. Van Fraassen does not specify constraints on R, a point on which he has been heav-1 By properly construed, I mean that once one recognizes that X account is only part of the story of explanation rather than the whole, then X account is consistent with the pragmatic account. When van Fraassen first presented the idea, it was anathema to both camps to suggest a plurality of accounts. Since such a plurality has become fashionable recently, it seems reasonable to construe contemporary conceptions of the causal and unificationist accounts as consistent with such a plurality.
Many calls for explanation are why questions, but it has been suggested that other questions (how questions, what questions, etc.) can also be important. However, there has been some suggestion that all what and how questions can be rephrased as why questions. I do not suppose to prove this.
Instead, I will keep with the philosophical tradition and consider only why questions, which are generally recognized to be important (besides van Fraassen, see (Kitcher, 1981), (Salmon, 1989b)).
If other question-types turn out to be important as well, they may need independent consideration. Wily criticized (see (Kitcher, 1989), (Kitcher and Salmon, 1987)). It seems, however, in light of the move towards plurality, that by leaving R unspecified, van Fraassen has proven something of a visionary, paving the way for the kind of contextualism that Godfrey-Smith suggests3. Indeed, R could be a causal story, a fitting into a unified framework, or something else entirely. Because the structure of the pragmatic account already incorporates a pluralistic description of understanding in a natural way that makes the relationship between the different elements of the pluralism clear, I think it is valuable to adopt that structure as a way of speaking about explanation, bracketing for a moment the acceptability of the account from which the structure originates.
There are two closely related questions that I would like to address in this paper. The first is with respect to the compromise between the unificationist and causal accounts. If we accept a pluralistic account, then we must accept that there are times when a causal explanation is the best form to give, and similarly, there are times when a unificationist explanation is best, because otherwise one kind or the other would always be best, in which case we would be committed to a single account. But if sometimes the causal form is better and sometimes the unificationist form is better, the question immediately arises: when? There seems to be the danger of a free-for-all, in which the decision to employ one form of explanation or the other is random. So it seems important to understand the situations in which each form of explanation is not only appropriate, but best. And distinguishing between explanatory contexts 3 do not mean to suggest here that van Fraassen and Godfrey-Smith are arguing the same point.
In fact, as Godfrey-Smith makes clear in his (2003), the two views are quite different in ways that Iwill come back to when I evaluate arguments against van Fraassen. Both views, however (and this
Gofrey-Smith concedes) are similar in that they derive the correct form of an explanation from the context in which the explanation is demanded. By this, I mean I will talk about the causal and unificationist accounts as relevance relations of why questions. In the end, I will argue that I am justified in doing this by adopting a modified version of the pragmatic account that remains context dependent without facing trivialization in the way that it has been argued (Kitcher and Salmon, 1987) the original version does.
In general, the views I am considering are parts of larger (inconsistent) metaphysical frameworks. I am intentionally divorcing the explanatory accounts from their metaphysical backgrounds seems to be a pragmatic issue.
Attempting to understand the contextual relationships between the causal and unificationist account leads to the second question: can the pragmatic account be modified to resolve the pragmatic issues raised by a pluralist view of explanation, and if so, how? Van Fraassen’s decision to leave the class of possible relevance relations unspecified presents two major issues. The first is that, without any constraints on R, the pragmatic account is open to trivialization (Kitcher and Salmon, 1987), since one could present a relevance relation Rtrivial such that any true statement Strue (or, even worse, a false statement) bears Rtrivial to the topic in question. The natural response to this concern is that Rtrivial, although conceptually acceptable, would never arise in a real context, or at least, it would never arise in a scientific context. Which leads to the second issue with van Fraassen’s account (and subsumes the first): there are many contexts in which why questions can be asked. Only some of these contexts are scientific (see the introduction to (Salmon, 1989b) for examples), in which case one would expect the relevance relations to have a certain set of possible forms. So now it is important to ask what relevant relations are scientific and which explanatory contexts call for which elements of this, now limited, set of relevance relations. Note here that there is a temptation to be prescriptive about which relevance relations are scientific. I believe it is a mistake to succumb to this temptation. Instead, I want to be careful to ask what relevance relations do arise in mainstream science, and in what contexts, as opposed to asking which should arise, since this second path comes dangerously close to undermining the pluralistic view.
Now I can state the question that this paper is intended to begin to answer: When do why questions asked in scientific contexts have unificationist relevance relations, when do they have causal relevance relations, and how should the relationship between the two sets of contexts be understood? Before I continue, there are two notes. First, I am going to immediately limit the question by replacing “scientific contexts” with “the contexts of particle physics”. Secondly, I have specified two kinds of explanation.
There may be others; I would be contradicting myself if I said there were not. However, it is well established that at least sometimes causal relevance relations are important and sometimes unificationist ones are. Even if this is not an exhaustive list, it is a useful first step to understand the relationship between these two already acceptable explanatory accounts. The discovery of additional relevance relations in science would not reduce the value of this work, it would only suggest new avenues towards completing it. I will come back to both of these limitations in the concluding remarks of the paper, in an effort to understand how my results generalize.
In order to address this question, I will consider a special class of theories that have gained prominence in high energy and condensed matter physics over the course of the last 30 years. The motivation for choosing these theories, called Effective Field Theories (EFTs), is that they provide an excellent case study for two things: a) they allow one to relate distinct energy scales (or length scales)6 in a well-defined way, which, I will argue, is crucial to understanding the contexts in which the unificationist and causal accounts are each most successful, and b) they offer an extra-philosophical way of distinguishing between which causal features of a system are the “relevant” ones, a problem that has plagued the causal account from its beginning, and which I will come back to often.
Based originally on work on coupling constant renormalization by Kenneth Wilson as early as 1965, EFTs appeared in their first instantiations when, in 1979, Steven Weinberg adapted Wilson’s renormalization techniques to relativistic systems and combined them with Appelquist and Carazzone’s decoupling theorem. Wilson’s renormalization technique originated with straightforward “cut-off” renormalization, where one would resolve infinite results in Quantum Field Theory (QFT) by chang-By high or low energy, I mean that energy of the particles being scattered (or, energy of scattered particles required to achieve proper resolution) to probe in an experiment. The higher the energy of the incident particles, the shorter the distances that can be probed. In section 2.4, I give a more precise definition of the energy scale of a theory.
Redefining the bounds of integrals from infinity to some finite value _ and then redefining parameters in the theory to eliminate references to _ before letting it go to infinity again. Unfortunately, there were cases when one could not consistently take the limit of _ ! 1 (called nonrenormalizable theories), so this method sometimes resulted in theories that were dependent on the value of _. Initially, these results seemed unphysical, since predictions of nonrenormalizable theories were dependent on the choice of an arbitrary constant.
Wilson’s contribution was to develop a way of understanding how those predictions varied with the choice of a cut-off. Specifically, he developed a way, called the renormalization group (RG), of describing how coupling constants would have to change as one changed the cut-off so that the predictions made by nonrenormalizable theories would remain the same for different choices of the cut-off. The idea was that one could then measure a coupling constant under known circumstances, fix its value for some cut-off, and then vary the cut-off to obtain other predictions.
Joined with the decoupling theorem, Weinberg showed that the RG produced some very powerful results: since phenomena at different energy scales could be shown to be dissociated from each other, varying the cut-off to below the energy required to produce some particles in a theory dynamically (essentially limiting the ontology of the theory) produced new, phenomenological theories that, although only applicable at relatively low energies, were much easier to use than their more complicated high energy counterparts.
The way in which EFTs have been conceived has changed fairly drastically since Weinberg’s first paper. First, nonrenormalizable theories became physically acceptable, as low energy approximations to (potentially unknown) high energy theories. This drastically increased the size of the possible theory space, since renormalizability had been a constraint since early work on quantum electrodynamics. Secondly, and more interestingly, many physicists have come to think of successful high-energy theories (including the Standard Model, which is currently the closest thing to a “final theory” in physics), even when renormalizable, as EFTs for even higher energy theories. Some philosophers and many physicists have begun to wonder, in light of the EFT program, whether the idea of a final theory is sensible, or at least, if research into such theory is worthwhile, since it may never be clear if the most “fundamental” theory known is actually final, or just an approximation valid only at appropriate energy scales. In fact, the EFT techniques have been used to argue that fundamentality is an arbitrary attribute. If one cannot be certain about whether the highest energy theory known at any given time describes the smallest distance interactions possible (as the EFT program may suggest, although this interpretation remains contentious), and if high energy theories only offer partial information about low energy phenomena (as emergence suggests), the primacy of higher energy theories required to define fundamentality properly is undermined.
The relevant feature of EFTs with respect to scientific explanation, however, is that they allow one to link theories at different energy scales to each other in a very well-defined way, via RG calculations. It has been suggested (see (Hartmann, 2001)) that the different explanatory accounts I have singled out lend themselves to different kinds of descriptions of nature. Hartmann argues that the causal account (at least Cartwright’s version) tends to rely on models, which focus on the relevant causal properties of a system, bundling extraneous material into conceptual shortcuts7.
Unificationist accounts, on the other hand, rely on complete theories, since the robustness of an explanation is directly tied to the number of disparate phenomena that can be shown to fit together. Hartmann only cites a tendency here, and although there is evidence to support his pattern, it seems reductive. However, his approach does highlight a crucial difference between the two relevance relations: causal explain. To see what I mean here, consider the bag model of quark confinement, which captures shortdistance quark interactions in a physically realistic manner, but parameterizes the thornier idea of asymptotic freedom by introducing an elastic “bag”, which, although explicitly fictional, offers a shortcut of description. Nations do focus only on the parts of a system directly relevant to the phenomena being explained, since the kinds of “stories” prescribed by the causal account only involve direct causal relationships, and unificationist explanations do gain robustness if the structure on which they rely is as encompassing as it can be.
In the context of particle physics, the RG offers a way of relating these cases, by allowing one to rigorously isolate the relevant particle interactions for any given energy level. By appeal to the EFT program, the causal and unificationist accounts can be seen as appropriate for different ends of a spectrum of related scenarios. And since energy levels translate directly to experimentation- the cut-off of a theory has to be larger than the energy of the particles used in experiments if the theory’s predictions are to be accurate- explanatory context can be reduced to experimental context. Low energy explanations, with irrelevant interactions (causal powers) removed lend themselves to causal explanations, whereas high energy theories unify many interactions into a single framework, lending themselves to unificationist explanations. In order to explain a phenomenon, then, one needs to specify the energy scale at which she is interested in the explanation. I will argue that all phenomena have characteristic energy scales- essentially the range between when they emerge from underlying structures as individual particles with distinct causal properties, and when the become subsumed into still larger structures- at which they are important, and at which causal explanations are best. For energy scales higher than a phenomenon’s characteristic scale, unificationist accounts are better. By understanding the relationship between these energy levels, a why question can be made to be specific enough to define explanatory contexts rigorously and to determine which explanatory account is appropriate.
1.2 Overview
My goal is to make this paper accessible to a mixed audience of physicists and philosophers, which is not necessarily simple. To accommodate varied backgrounds and interests, I will structure this paper in the following way. I will focus on arguments that are immediately relevant to my thesis, giving enough background in the body of the paper to give a relatively inexperienced reader a heuristic sense of the structures of the theories I am discussing. In addition, for readers unfamiliar with the physics (or readers familiar enough to question some of my generalizations) and interested in more mathematical detail, I include several appendices containing some of the calculations and derivations I gloss over in the body of the paper.
That said, the structure of the remainder of this paper will be as follows. In chapter 2, I will give a full description of the physics behind the EFT approach, starting from a basic knowledge of quantum mechanics. This chapter is admittedly a detour from the philosophical arguments in the paper, but I have found that most philosophers with whom I have discussed this work are unfamiliar with EFTs. I will try to make it both brief and complete, to keep from going too far afield, but so that a reader with no familiarity with QFT will have an informed perspective from which to evaluate the arguments I make in the rest of the paper. Chapter 3 is a review of the literature on the philosophy of EFTs. Chapter 2 is purely on the techniques used by physicists, with as little interpretation as possible. But to understand the salient philosophical features of the techniques, it is important to discuss how they have been interpreted in the past. The idea is to complement and inform my discussion of the pure physics with the philosophical interpretations, again with a mind towards grounding the arguments of the subsequent chapters.
In chapter 4, I describe the unificationist and causal accounts of explanation. I offer an example of how each can used in physics, and then I cite the main conceptual concerns associated with each. In doing so, I argue that the domains in which the two accounts seem most successful complement each other. I also try to show that the language of EFTs can be used to limit the domains of each account in a way that avoids their main difficulties. In section 4.3, I build on the observation that the domains of the causal and unificationist accounts seem to be complementary, and discuss the pluralist account that this suggests in greater detail. Here I argue that the domains of the accounts can be separated in high energy physics, again by appeal to the language of EFTs. Finally, in chapter 5, I discuss the pragmatic account, proposing several modifications intended to a) resolve the major problems that have been associated with it, and b) adapt it to describe the pragmatic aspects of a coherent pluralist account. All of what I argue in this paper is specific to particle physics, in which the distinctions that I think are important for understanding the pluralist account are particularly clear. In section 5.3, I explore how these ideas may generalize to areas of science in which distinctions between explanatory contexts may be less explicit.
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