Presents a guide to the basics of quantum mechanics and measurement.

Robert Batterman examines a form of scientific reasoning called asymptotic reasoning, arguing that it has important consequences for our understanding of the scientific process as a whole. He maintains that asymptotic reasoning is essential for explaining what physicists call universal behavior. With clarity and rigor, he simplifies complex questions about universal behavior, demonstrating a profound understanding of the underlying structures that ground them. This book introduces a valuable new method that is certain to fill explanatory gaps across disciplines.

Quantum gravity poses the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the (...) subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time. (shrink)

Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions.

Using everyday language, spatial concepts, visualizations and his renowned "Feynman diagrams," the author clearly and humorously communicates the substance and spirit of QED (quantum electodynamics).

Quantum mechanics is a subject that has captured the imagination of a surprisingly broad range of thinkers, including many philosophers of science. Quantum field theory, however, is a subject that has been discussed mostly by physicists. This is the first book to present quantum field theory in a manner that makes it accessible to philosophers. Because it presents a lucid view of the theory and debates that surround the theory, An Interpretive Introduction to Quantum Field Theory will interest students of (...) physics as well as students of philosophy. -/- Paul Teller presents the basic ideas of quantum field theory in a way that is understandable to readers who are familiar with non-relativistic quantum mechanics. He provides information about the physics of the theory without calculational detail, and he enlightens readers on how to think about the theory physically. Along the way, he dismantles some popular myths and clarifies the novel ways in which quantum field theory is both a theory about fields and about particles. His goal is to raise questions about the philosophical implications of the theory and to offer some tentative interpretive views of his own. This provocative and thoughtful book challenges philosophers to extend their thinking beyond the realm of quantum mechanics and it challenges physicists to consider the philosophical issues that their explorations have encouraged. (shrink)

Reductionism is often understood to include two theses: (1) every singular occurrence that the special sciences can explain also can be explained by physics; (2) every law in a higher-level science can be explained by physics. These claims are widely supposed to have been refuted by the multiple realizability argument, formulated by Putnam (1967, 1975) and Fodor (1968, 1975). The present paper criticizes the argument and identifies a reductionistic thesis that follows from one of the argument's premises.

An innocent form of emergence—what I call "weak emergence"—is now a commonplace in a thriving interdisciplinary nexus of scientific activity—sometimes called the "sciences of complexity"—that include connectionist modelling, non-linear dynamics (popularly known as "chaos" theory), and artificial life.1 After defining it, illustrating it in two contexts, and reviewing the available evidence, I conclude that the scientific and philosophical prospects for weak emergence are bright.

Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. -/- This expanded edition features several additional chapters, as well as (...) an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading. (shrink)

This paper concerns what Jerry Fodor calls a 'metaphysical mystery': How can there by macroregularities that are realized by wildly heterogeneous lower level mechanisms? But the answer to this question is not as mysterious as many, including Jaegwon Kim, Ned Block, and Jerry Fodor might think. The multiple realizability of the properties of the special sciences such as psychology is best understood as a kind of universality, where 'universality' is used in the technical sense one finds in the physics literature. (...) It is argued that the same explanatory strategy used by physicists to provide understanding of universal behavior in physics can be used to explain how special science properties can be heterogeneously multiply realized. (shrink)

Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effective field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, flexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the specific mechanisms at work at a given energy scale. So will (...) all of physics eventually converge on effective field theories? This paper argues that good scientific research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and effective field theories. All of them have their appropriate functions in the research process, and all of them are indispensable. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientific theorising is inherently pluralistic, and has implications for the debates about reductionism and scientific explanation. (shrink)

We survey and clarify some recent appearances of the term ‘emergence’. We distinguish epistemological emergence, which is merely a limitation of descriptive apparatus, from ontological emergence, which should involve causal features of a whole system not reducible to the properties of its parts, thus implying the failure of part/whole reductionism and of mereological supervenience for that system. Are there actually any plausible cases of the latter among the numerous and various mentions of ‘emergence’ in the recent literature? Quantum mechanics seems (...) to offer one, in the Bell properties of entangled particles, but other apparently promising candidates, such as non‐linear dynamical systems investigated by complexity studies and chaos theory, seem on careful analysis to display only epistemological emergence. We examine the consequences for physicalism of admitting ontological emergence in the micro‐physical. (shrink)

This article examines ontological/dynamical aspects of emergence, specifically the micro-macro relation in cases of universal behavior. I discuss superconductivity as an emergent phenomenon, showing why microphysical features such as Cooper pairing are not necessary for deriving characteristic properties such as infinite conductivity. I claim that the difficulties surrounding the thermodynamic limit in explaining phase transitions can be countered by showing how renormalization group techniques facilitate an understanding of the physics behind the mathematics, enabling us to clarify epistemic and ontological aspects (...) of emergence. I close with a discussion of the impact of these issues for questions concerning natural kinds. (shrink)

This paper looks at emergence in physical theories and argues that an appropriate way to understand socalled “emergent protectorates” is via the explanatory apparatus of the renormalization group. It is argued that mathematical singularities play a crucial role in our understanding of at least some well-defined emergent features of the world.

I argue against the currently prevalent view that algebraic quantum field theory (AQFT) is the correct framework for philosophy of quantum field theory and that “conventional” quantum field theory (CQFT), of the sort used in mainstream particle physics, is not suitable for foundational study. In doing so, I defend that position that AQFT and CQFT should be understood as rival programs to resolve the mathematical and physical pathologies of renormalization theory, and that CQFT has succeeded in this task and AQFT (...) has failed. I also defend CQFT from recent criticisms made by Doreen Fraser. (shrink)

I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (QFT) (that is, the ‘naive’ (QFT) used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian (QFT) has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least (...) as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work. (shrink)

We discuss from a philosophical perspective the way in which the normal concept of time might be said to `emerge' in a quantum theory of gravity. After an introduction, we briefly discuss the notion of emergence, without regard to time. We then introduce the search for a quantum theory of gravity ; and review some general interpretative issues about space, time and matter. We then discuss the emergence of time in simple quantum geometrodynamics, and in the Euclidean approach. Section 6 (...) concludes. (shrink)

I give an informal outline of the hole argument which shows that spacetime substantivalism leads to an undesirable indeterminism in a broad class of spacetime theories. This form of the argument depends on the selection of differentiable manifolds within a spacetime theory as representing spacetime. I consider the conditions under which the argument can be extended to address versions of spacetime substantivalism which select these differentiable manifolds plus some further structure to represent spacetime. Finally, I respond to the criticisms of (...) Tim Maudlin and Jeremy Butterfield. (shrink)

The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is (...) Heisenberg's `quantum-theoretical Umdeutung (reinterpretation) of classical observables', which lies at the basis of quantization theory. Similarly, Bohr's correspondence principle (in somewhat revised form) and Schroedinger's wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit N goes to infinity of a large system with $N$ degrees of freedom (at fixed h), and through decoherence and consistent histories. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain ``classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are ``einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories. This combination of ideas and techniques does not quite resolve the measurement problem, but it does make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it. (shrink)

Further arguments are offered in defence of the position that the variant of quantum field theory (QFT) that should be subject to interpretation and foundational analysis is axiomatic quantum field theory. I argue that the successful application of renormalization group (RG) methods within alternative formulations of QFT illuminates the empirical content of QFT, but not the theoretical content. RG methods corroborate the point of view that QFT is a case of the underdetermination of theory by empirical evidence. I also urge (...) caution in extrapolating interpretive conclusions about QFT from the application of RG methods in other contexts (e.g., condensed matter physics). This paper replies to criticisms advanced by David Wallace, but aims to be self-contained. (shrink)

This paper explicates two notions of emergencewhich are based on two ways of distinguishinglevels of properties for dynamical systems.Once the levels are defined, the strategies ofcharacterizing the relation of higher level to lower levelproperties as diachronic and synchronic emergenceare the same. In each case, the higher level properties aresaid to be emergent if they are novel or irreducible with respect to the lower level properties. Novelty andirreducibility are given precise meanings in terms of the effectsthat the change of a bifurcation (...) or perturbation parameterin the system has. (The same strategy can be applied to otherways of separating levels of properties, like themicro/macro distinction.)The notions of emergence developed here are notions of emergencein a weak sense: the higher level emergent properties wecapture are always structural properties (or are realized insuch properties), that is, they are defined in terms of the lowerlevel properties and their relations. Diachronic and synchronicemergent properties are distinctions within thecategory of structural properties. (shrink)

Quantum field theory (QFT) presents a genuine example of the underdetermination of theory by empirical evidence. There are variants of QFT—for example, the standard textbook formulation and the rigorous axiomatic formulation—that are empirically indistinguishable yet support different interpretations. This case is of particular interest to philosophers of physics because, before the philosophical work of interpreting QFT can proceed, the question of which variant should be subject to interpretation must be settled. New arguments are offered for basing the interpretation of QFT (...) on a rigorous axiomatic variant of the theory. The pivotal considerations are the roles that consistency and idealization play in this case. *Received June 2009; revised August 2009. †To contact the author, please write to: Department of Philosophy, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada; e‐mail: [email protected]. (shrink)

Weak emergence has been offered as an explication of the ubiquitous notion of emergence used in complexity science (Bedau 1997). After outlining the problem of emergence and comparing weak emergence with the two other main objectivist approaches to emergence, this paper explains a version of weak emergence and illustrates it with cellular automata. Then it explains the sort of downward causation and explanatory autonomy involved in weak emergence.

Weak emergence is the view that a system’s macro properties can be explained by its micro properties but only in an especially complicated way. This paper explains a version of weak emergence based on the notion of explanatory incompressibility and “crawling the causal web.” Then it examines three reasons why weak emergence might be thought to be just in the mind. The first reason is based on contrasting mere epistemological emergence with a form of ontological emergence that involves irreducible downward (...) causation. The second reason is based on the idea that attributions of emergence are always a reflection of our ignorance of non-emergent explanations. The third reason is based on the charge that complex explanations are anthropocentric. Rather than being just in the mind, weak emergence is seen to involve a distinctive kind of complex, macro-pattern in the mind-independent objective micro-causal structure that exists in nature. The paper ends by addressing two further questions. One concerns whether weak emergence applies only or mainly to computer simulations and computational systems. The other concerns the respect in which weak emergence is dynamic rather than static. (shrink)

We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general relativity), as a 4-dimensional manifold equipped with a Lorentzian metric. After an introduction (Section 1), we briefly review the conceptual problems of the ingredient theories (Section 2) and introduce the enterprise of quantum gravity (Section 3). We then describe how three main research programmes in quantum (...) gravity treat four topics of particular importance: the scope of standard quantum theory; the nature of spacetime; spacetime diffeomorphisms, and the so-called `problem of time' (Section 4). These programmes are the old particle-physics approach, superstring theory, and canonical quantum gravity. By and large, these programmes accept most of the ingredient theories' treatment of spacetime, albeit with a metric with some type of quantum nature; but they also suggest that the treatment has fundamental limitations. This prompts the idea of going further: either by quantizing structures other than the metric, such as the topology; or by regarding such structures as phenomenological. We discuss this in Section 5. (shrink)

Intuitively, a classical field theory is background-in- dependent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. Background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully background-independent relative to an interpretation (...) if each physical possibility corresponds to a distinct spacetime geometry; and it falls short of full background-independence to the extent that this condition fails. (shrink)

More often than not, recently popular structuralist interpretations of physical theories leave the central concept of a structure insufficiently precisified. The incipient causal sets approach to quantum gravity offers a paradigmatic case of a physical theory predestined to be interpreted in structuralist terms. It is shown how employing structuralism lends itself to a natural interpretation of the physical meaning of causal set theory. Conversely, the conceptually exceptionally clear case of causal sets is used as a foil to illustrate how a (...) mathematically informed rigorous conceptualization of structure serves to identify structures in physical theories. Furthermore, a number of technical issues infesting structuralist interpretations of physical theories such as difficulties with grounding the identity of the places of highly symmetrical physical structures in their relational profile and what may resolve these difficulties can be vividly illustrated with causal sets. (shrink)

This is a contribution to a book on quantum gravity and philosophy. I discuss nature and origin of the problem of quantum gravity. I examine the knowledge that may guide us in addressing this problem, and the reliability of such knowledge. In particular, I discuss the subtle modification of the notions of space and time engendered by general relativity, and how these might merge into quantum theory. I also present some reflections on methodological questions, and on some general issues in (...) philosophy of science which are are raised by, or a relevant for, the research on quantum gravity. (shrink)

The AdS/CFT duality has been a source of several strong conceptual claims in the physics literature that have yet to be explored by philosophers. In this paper I focus on one of these: the extent to which spacetime geometry and locality can be said to emerge from this duality, so that neither is fundamental. I argue: that the kind of emergence in question is relatively weak, involving one kind of spacetime emerging from another kind of spacetime; inasmuch as there is (...) something conceptually interesting to say about the emergence of spacetime and locality , it is no different from that already well known to those within canonical quantum gravity; that at the core of AdS/CFT is an issue of representation and redundancy in representation. (shrink)

In recent years, a change in attitude in particle physics has led to our understanding current quantum field theories as effective field theories. The present paper is concerned with the significance of this EFT approach, especially from the viewpoint of the debate on reductionism in science. In particular, it is a purpose of this paper to clarify how EFTs may provide an interesting case-study in current philosophical discussion on reduction, emergence and inter-level relationships in general.

Unlike the overall framework of Ernest Nagel's work on reduction, his theory of intertheoretic connection still has life in it. It handles aptly cases where reduction requires complex representation of a target domain. Abandoning his formulation as too liberal was a mistake. Arguments that it is too liberal at best touch only Nagel's deductivist theory of explanation, not his condition of connectability. Taking this condition seriously gives a powerful view of reduction, but one which requires us to index explanatory power (...) to sciences as they are formulated at particular times. While we may thereby reduce more than philosophers have supposed, we must abandon hope (as Nagel did) of saying anything useful about reductionism. (shrink)