… there is something in this more than natural, if philosophy could find it out. Shakespeare , Hamlet, Act 2 Scene 2 Introduction The philosophical importance of semiclassical appeals to classical structures in explaining quantum phenomena was first recognized by Robert Batterman (1993; 1995; 2002). More generally, Batterman has argued that when it comes to explaining phenomena in the asymptotic domain between two theories, the fundamental theory describing that domain is often explanatorily deficient, and an adequate explanation must make essential reference to the less fundamental theory. For example, in discussing the relation between classical and quantum mechanics, Batterman writes, “There are many aspects of the semiclassical limit of quantum mechanics that cannot be explained purely in quantum mechanical terms, though they are in some sense quantum mechanical … [T]hese quantum mechanical features require reference to classical properties for their full explanation” (Batterman 2002, pp. 109–10). He has extended these arguments to other theory pairs with singular limits as well, arguing that in optics, for example, one finds explanations of wave-theoretic phenomena that make an essential and ineliminable appeal to ray-theoretic structures such as caustics. More recently, Batterman's arguments have been the subject of considerable criticism from figures such as Clifford Hooker (2004), Michael Redhead (2004), and Gordon Belot (2005). These criticisms have tended to cluster around the following two assumptions: First, in saying that a classical structure (such as a trajectory or caustic) explains , one is thereby committed to the claim that the structure exists .
… there is something in this more than natural, if philosophy could find it out. Shakespeare , Hamlet, Act 2 Scene 2 Introduction The philosophical importance of semiclassical appeals to classical structures in explaining quantum phenomena was first recognized by Robert Batterman (1993; 1995; 2002). More generally, Batterman has argued that when it comes to explaining phenomena in the asymptotic domain between two theories, the fundamental theory describing that domain is often explanatorily deficient, and an adequate explanation must make essential reference to the less fundamental theory. For example, in discussing the relation between classical and quantum mechanics, Batterman writes, “There are many aspects of the semiclassical limit of quantum mechanics that cannot be explained purely in quantum mechanical terms, though they are in some sense quantum mechanical … [T]hese quantum mechanical features require reference to classical properties for their full explanation” (Batterman 2002, pp. 109–10). He has extended these arguments to other theory pairs with singular limits as well, arguing that in optics, for example, one finds explanations of wave-theoretic phenomena that make an essential and ineliminable appeal to ray-theoretic structures such as caustics. More recently, Batterman's arguments have been the subject of considerable criticism from figures such as Clifford Hooker (2004), Michael Redhead (2004), and Gordon Belot (2005). These criticisms have tended to cluster around the following two assumptions: First, in saying that a classical structure (such as a trajectory or caustic) explains , one is thereby committed to the claim that the structure exists .
In semiclassical mechanics one finds explanations of quantum phenomena that appeal to classical structures. These explanations are prima facie problematic insofar as the classical structures they appeal to do not exist. Here I defend the view that fictional structures can be genuinely explanatory by introducing a model-based account of scientific explanation. Applying this framework to the semiclassical phenomenon of wavefunction scarring, I argue that not only can the fictional classical trajectories explain certain aspects of this quantum phenomenon, but also that an explanation that does not make reference to these classical structures is, in a certain sense, deficient. 1. Introduction2. The Case of Wavefunction Scarring3. Model Explanations, or How Fictional Structures Can Explain4. Putting Understanding Back into Explanation
There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy. Shakespeare , Hamlet, Act 1 Scene 5 The challenge of semiclassical mechanics: Reassessing the views Semiclassical mechanics significantly broadens our understanding of the relationship between classical and quantum mechanics. It reveals that there is much more to the relation between these theories than simply showing that classical behavior can be recovered from quantum systems in the limit of large actions ( ħ → 0) or large quantum numbers ( n → ∞). Although these limits are an important piece of the puzzle, the usual reductionist account of the quantum–classical relation in terms of these limits alone does not tell the whole story. More specifically, research in semiclassical mechanics has uncovered a number of surprising theoretical and experimental correspondences . Indeed the program of semiclassical research can be broadly understood as the theoretical and experimental task of uncovering these correspondences and extending them in new ways. On the theoretical side, semiclassical methods such as EBK quantization, Gutzwiller's trace formula, and closed orbit theory show how classical structures can be used to construct quantum quantities. These semiclassical methods have proven to be not just useful calculational tools, but also important investigative tools, in that they are often able to provide physical insight into the structure of the quantum dynamics, and hence lead to new discoveries.
Though this be madness, yet there is method in't. Shakespeare , Hamlet, Act 2 Scene 2 Introduction Semiclassical mechanics can be broadly understood as the theoretical and experimental study of the interconnections between classical and quantum mechanics. More narrowly, it is a field that uses classical quantities to investigate, calculate, and even explain quantum phenomena. Its methods involve an unorthodox blending of quantum and classical ideas, such as a classical trajectory with an associated quantum phase. For these reasons, semiclassical mechanics is often referred to as “putting quantum flesh on classical bones,” where classical mechanics provides the skeletal framework on which quantum quantities are constructed. There are three primary motivations for semiclassical mechanics: First, in many systems of physical interest, a full quantum calculation is cumbersome or even unfeasible. Second, even when a full quantum calculation is within reach, semiclassical methods can often provide intuitive physical insight into a problem, when the quantum solutions are opaque. And, third, semiclassical investigations can lead to the discovery of new physical phenomena that have been overlooked by fully quantum-mechanical approaches. Semiclassical methods are ideally suited for studying physics in the so-called mesoscopic regime, which can roughly be understood as the domain between the classically described macro-world and the quantum mechanically described micro-world. An area in which semiclassical studies have proven to be particularly fruitful is in the subfield of quantum chaos.
Quantum mechanics is among the most successful physical theories, yet its formulation and empirical testing rely on classical structures. Following Lev Landau and Niels Bohr, this reliance is not merely pragmatic: quantum observables acquire empirical meaning only relative to classical reference frames, and, in practice, quantization starts from classical models. At the same time, the two domains display forms of mutual irreducibility: intrinsically quantum features (that is, spin and exchange statistics) have no counterpart in the phase-space ontology of classical point-particle mechanics, while classical trajectory chaos does not arise straightforwardly from unitary quantum evolution in closed systems. A hierarchy is commonly established between classical and quantum theories, namely, a claim of ontological and explanatory priority according to which quantum mechanics is fundamental and classical mechanics is only a limiting case. This claim is less secure than is often assumed; therefore, the traditional hierarchy deserves to be examined. In this paper, we argue that a quantum–classical framework provides an effective and structurally faithful representation of empirically accessible physical systems in regimes where quantum and classical degrees of freedom coexist within a single, consistent effective dynamical description. To give this point of view a firm theoretical basis, we discuss the quasi-Lie formal structure underlying quantum–classical hybrid dynamics, with applications ranging from gravity and condensed matter to open, driven systems in biology and complex media.
There are many important questions that do not fall neatly into any one discipline; rather, their full investigation requires the integration of two or more distinct fields. This book is about just such a question – one that arises at the intersection of physics, philosophy, and history. The question can be simply stated as “What is the relation between classical and quantum mechanics?” The simplicity of the question, however, belies the complexity of the answer. Classical mechanics and quantum mechanics are two of the most successful scientific theories ever developed, and yet how these two very different theories can successfully describe one and the same world – the world we live in – is far from clear. One theory is deterministic, the other indeterministic; one theory describes a world in which chaotic behavior is pervasive, and the other a world in which it is almost entirely absent. Did quantum mechanics simply replace classical mechanics as the new universal theory? Do they each describe their own distinct domains of phenomena? Or is one theory really just a continuation of the other? In the philosophy literature, this sort of issue is known as the problem of intertheoretic relations. Currently, there are two accepted philosophical frameworks for thinking about intertheoric relations: the first is reductionism, and the second, pluralism. As we shall see, these labels each actually describe a family of related views.
My aim in this dissertation is to defend a realist interpretation of quantum mechanics.Firstly, I present considerations based on certain general features of theories in the natural sciences which indicate that realism affords a better account of those theories than instrumentalism.In particular, I consider certain issues surrounding the cognitive status of theories, including the role of models, the status of scientific explanation, and the referential character of theoretical terms.Secondly, I develop a detailed realist theory of measurement based on the notion of quantity terms as designators of objective properties of, and relations among, existing entities.I contrast this with the leading instrumentalist theories of measurement, and I argue that the realist theory is the better account of both the logic and practice of scientific measurement.Finally, I consider a number of objections to realism that arise because of certain theoretical features peculiar to quantum mechanics.In the course of this discussion, I consider crucial experimental evidence for the "dual" nature of microentities, various criteria of reality proposed by philosophers of science, the peculiar features of quantum mechanical measurement, and the status of causality in quantum mechanics.I argue that while certain realist viii ix interpretations of the quantum theory, namely the wave and wavicle interpretations, are unsatisfactory, an interpreta tion which construes micro-entities as existing particles is a tenable account.CHAPTER I ignored the considerations which arise at those more general levels of inquiry, but one can not adequately assess the status of quantum mechanics with respect to both realism and instrumentalism apart from those considerations.In the second two chapters of the dissertation, I shall argue that realist interpretations of quantitative theories in the natural sciences are preferable to instrumentalist interpretations.Then in the remainder of the dissertation, I shall go on to argue that realism is tenable at the quantum mechanical level despite the features peculiar to that theory.CHAPTER II THE COGNITIVE STATUS OF THEORIES transitions from one set of experiential statements to another.This view is in marked contrast to that of the realist who regards such terms as referential.This divergence in opinion between realists and instrumentalists about the referential character of theoretical terms leads to a related dispute over the role of models in the inter pretation of scientific theories.Before contrasting the various philosophical positions on this issue, it will be necessary to sort out different senses of the term "model."Upon inspecting the literature surrounding this dispute, it seems that much of the controversy about the role of models stems from a failure to make such distinctions.I will begin this task by distinguishing between 13 model-structures and model-objects.A model-structure is a definitely specifiable schema of mathematical-logical relationships which is exhibited by and can be abstracted from a set of objects.Any set of objects which exhibits a model-structure constitutes a set of model-objects.With respect to any particular scientific theory, there may be a variety of model-objects that scientists employ for various purposes.For example, in the kinetic theory of gases, one can distinguish the following.Firstly, there is the set of molecules themselves, the theoretical entities which we shall 13.For further detail in this regard, see Henry C. Byerly, "Model-Structures and Model-Objects," British Journal for the Philosophy of Science.Vol. 20, 1969, pp.135-144.i In fact, if one were to make that claim, I do not see how it could be supported without again falling prey to Maxwell's criticism cited above.And if one is simply troubled by the "ontological risk" involved in asserting the existence of theoretical entities because of the tentativeness of the corresponding theories, it should be noted that the risk of being wrong is a small price to pay for the potentially deeper understanding of nature that scientific theories afford us in the light of realist commitments.