I offer an account of how the quantum theory we have helps us explain so much. The account depends on a pragmatist interpretation of the theory: This takes a quantum state to serve solely as a source of sound advice to physically situated agents on the content and appropriate degree of belief about matters concerning which they are currently inevitably ignorant. The general account of how to use quantum states and probabilities to explain otherwise puzzling regularities is then illustrated by (...) showing how we can explain single particle interference phenomena, the stability of matter, and interference of Bose-Einstein condensates. Finally I note some open problems and relate this account to alternative approaches to explanation that emphasize the importance of causation, of unification, and of structure. (shrink)
Atomistic metaphysics motivated an explanatory strategy which science has pursued with great success since the scientific revolution. By decomposing matter into its atomic and subatomic parts physics gave us powerful explanations and accurate predictions as well as providing a unifying framework for the rest of science. The success of the decompositional strategy has encouraged a widespread conviction that the physical world forms a compositional hierarchy that physics and other sciences are progressively articulating. But this conviction does not stand up to (...) a closer examination of how physics has treated composition, as a variety of case studies will show. (shrink)
A closer look at some proposed Gedanken-experiments on BECs promises to shed light on several aspects of reduction and emergence in physics. These include the relations between classical descriptions and different quantum treatments of macroscopic systems, and the emergence of new properties and even new objects as a result of spontaneous symmetry breaking.
While its applications have made quantum theory arguably the most successful theory in physics, its interpretation continues to be the subject of lively debate within the community of physicists and philosophers concerned with conceptual foundations. This situation poses a problem for a pragmatist for whom meaning derives from use. While disputes about how to use quantum theory have arisen from time to time, they have typically been quickly resolved, and consensus reached, within the relevant scientific sub-community. Yet rival accounts of (...) the meaning of quantum theory continue to proliferate . In this article I offer a diagnosis of this situation and outline a pragmatist solution to the problem it poses, leaving further details for subsequent articles. (shrink)
According to conventional wisdom, local gauge symmetry is not a symmetry of nature, but an artifact of how our theories represent nature. But a study of the so-called theta-vacuum appears to refute this view. The ground state of a quantized non-Abelian Yang-Mills gauge theory is characterized by a real-valued, dimensionless parameter theta—a fundamental new constant of nature. The structure of this vacuum state is often said to arise from a degeneracy of the vacuum of the corresponding classical theory, which degeneracy (...) allegedly arises from the fact that “large” (but not “small”) local gauge transformations connect physically distinct states of zero field energy. If that is right, then some local gauge transformations do generate empirical symmetries. In defending conventional wisdom against this challenge I hope to clarify the meaning of empirical symmetry while deepening our understanding of gauge transformations. I distinguish empirical from theoretical symmetries. Using Galileo’s ship and Faraday’s cube as illustrations, I say when an empirical symmetry is implied by a theoretical symmetry. I explain how the theta-vacuum arises, and how “large” gauge transformations differ from “small” ones. I then present two analogies from elementary quantum mechanics. By applying my analysis of the relation between empirical and theoretical symmetries, I show which analogy faithfully portrays the character of the vacuum state of a classical non-Abelian Yang-Mills gauge theory. The upshot is that “large” as well as “small” gauge transformations are purely formal symmetries of non-Abelian Yang-Mills gauge theories, whether classical or quantized. It is still worth distinguishing between these kinds of symmetries. An analysis of gauge within the constrained-Hamiltonian formalism yields the result that “large” gauge transformations should not be classified as gauge transformations; indeed, nor should “global” gauge transformations. In a theory in which boundary conditions are modeled dynamically, “global” gauge transformations may be associated with physical symmetries, corresponding to translations of these extra dynamical variables. Such translations are symmetries if and only if charge is conserved. But it is hard to argue that these symmetries are empirical, and in any case they do not correspond to any constant phase change in a quantum state. (shrink)
I think van Fraassen is right to see the development of quantum mechanics as a turning point for physical science with a profound moral for philosophy, and not just for the philosophy of science. But the moral is not that even a completely successful physical theory may fail to account for the appearances by showing how they arise within the reality it represents. The moral is more radical: it is that a physical theory – even a fundamental theory – may (...) be completely successful in all its applications without offering a representation of reality at all. (shrink)
This document records the discussion between participants at the workshop "Philosophy of Gauge Theory," Center for Philosophy of Science, University of Pittsburgh, 18-19 April 2009.
Gauge theories have provided our most successful representations of the fundamental forces of nature. How, though, do such representations work? Interpretations of gauge theory aim to answer this question. Through understanding how a gauge theory's representations work, we are able to say what kind of world our gauge theories reveal to us. -/- A gauge theory's representations are mathematical structures. These may be transformed among themselves while certain features remain the same. Do the representations related by such a gauge transformation (...) merely offer alternative ways of representing the very same situation? If so, then gauge symmetry is a purely formal property since it reflects no corresponding symmetry in nature. -/- Gauging What's Real describes the representations provided by gauge theories in both classical and quantum physics. Richard Healey defends the thesis that gauge transformations are purely formal symmetries of almost all the classes of representations provided by each of our theories of fundamental forces. He argues that evidence for classical gauge theories of forces (other than gravity) gives us reason to believe that loops rather than points are the locations of fundamental properties. In addition to exploring the prospects of extending this conclusion to the quantum gauge theories of the Standard Model of elementary particle physics, Healey assesses the difficulties faced by attempts to base such ontological conclusions on the success of these theories. (shrink)
While empirical symmetries relate situations, theoretical symmetries relate models of a theory we use to represent them. An empirical symmetry is perfect if and only if any two situations it relates share all intrinsic properties. Sometimes one can use a theory to explain an empirical symmetry by showing how it follows from a corresponding theoretical symmetry. The theory then reveals a perfect symmetry. I say what this involves and why it matters, beginning with a puzzle that is resolved by the (...) subsequent analysis. I conclude by pointing to applications and implications of the ideas developed earlier in the paper. (shrink)
It has sometimes been suggested that quantum phenomena exhibit a characteristic holism or nonseparability, and that this distinguishes quantum from classical physics. One puzzling quantum phenomenon arises when one performs measurements of spin or polarization on certain separated quantum systems. The results of these measurements exhibit patterns of statistical correlation that resist traditional causal explanation. Some have held that it is possible to understand these patterns as instances or consequences of quantum holism or nonseparability. Just what holism and nonseparability are (...) supposed to be has not always been made clear, though, and each of these notions has been understood in different ways. Moreover, while some have taken holism and nonseparability to come to the same thing, others have thought it important to distinguish the two. Any evaluation of the significance of quantum holism and/or nonseparability must rest on a careful analysis of these notions. (shrink)
Gauge theories have provided our most successful representations of the fundamental forces of nature. This book describes the representations provided by gauge theories in both classical and quantum physics. I defend the thesis that gauge transformations are purely formal symmetries of almost all the classes of representations provided by each of our theories of fundamental forces. Evidence for classical gauge theories of forces (other than gravity) gives us reason to believe that loops rather than points are the locations of fundamental (...) properties. In addition to exploring the prospects of extending this conclusion to the quantum gauge theories of the Standard Model of elementary particle physics, I assess the difficulties faced by attempts to base such ontological conclusions on the success of these theories. (shrink)
All change involves temporal variation of properties. There is change in the physical world only if genuine physical magnitudes take on different values at different times. I defend the possibility of change in a general relativistic world against two skeptical arguments recently presented by John Earman. Each argument imposes severe restrictions on what may count as a genuine physical magnitude in general relativity. These restrictions seem justified only as long as one ignores the fact that genuine change in a relativistic (...) world is frame-dependent. I argue on the contrary that there are genuine physical magnitudes whose values typically vary with the time of some frame, and that these include most familiar measurable quantities. Frame-dependent temporal variation in these magnitudes nevertheless supervenes on the unchanging values of more basic physical magnitudes in a general relativistic world. Basic magnitudes include those that realize an observer's occupation of a frame. Change is a significant and observable feature of a general relativistic world only because our situation in such a world naturally picks out a relevant class of frames, even if we lack the descriptive resources to say how they are realized by the values of basic underlying physical magnitudes. (shrink)
Those looking for holism in contemporary physics have focused their attention primarily on quantum entanglement. But some gauge theories arguably also manifest the related phenomenon of nonseparability. While the argument is strong for the classical gauge theory describing electromagnetic interactions with quantum “particles”, it fails in the case of general relativity even though that theory may also be formulated in terms of a connection on a principal fiber bundle. Anandan has highlighted the key difference in his analysis of a supposed (...) gravitational analog to the Aharonov-Bohm effect. By contrast with electromagnetism in the original Aharonov-Bohm effect, gravitation is separable and exhibits no novel holism in this case. Whether the nonseparability of classical gauge theories of non-gravitational interactions is associated with holism depends on what counts as the relevant part-whole relation. Loop representations of quantized gauge theories of non- gravitational interactions suggest that these conclusions about holism and nonseparability may extend also to quantum theories of the associated fields. (shrink)
The conceptual and technical difficulties involved in creating a quantum theory of gravity have led some physicists to question, and even in some cases to deny, the reality of time. More surprisingly, this denial has found a sympathetic audience among certain philosophers of physics. What should we make of these wild ideas? Does it even make sense to deny the reality of time? In fact physical science has been chipping away at common sense aspects of time ever since its inception. (...) Section 1 offers a brief survey of the demolition process. Section 2 distinguishes a tempered from an extremely radical form that a denial of time might take, and argues that extreme radicalism is empirically self-refuting. Section 3 begins an investigation of the prospects for tempered radicalism in a timeless theory of quantum gravity. (shrink)
Classically, a gauge potential was merely a convenient device for generating a corresponding gauge field. Quantum-mechanically, a gauge potential lays claim to independent status as a further feature of the physical situation. But whether this is a local or a global feature is not made any clearer by the variety of mathematical structures used to represent it. I argue that in the theory of electromagnetism (or a non-Abelian generalization) that describes quantum particles subject to a classical interaction, the gauge potential (...) is best understood as a feature of the physical situation whose global character is most naturally represented by the holonomies of closed curves in space-time. (shrink)
Quantum mechanics predicted the Aharonov-Bohm effect and violations of Bell inequalities before either phenomenon was experimentally verified. It is now commonly taken to explain both phenomena. Maudlin has pointed out significant disanalogies between these phenomena. But he has failed to appreciate the striking analogy that emerges when one examines the structure of their quantum mechanical explanations. The fact that each may be explained quantum mechanically in terms of a locally-acting, but nonseparable process suggests that the lesson of quantum nonlocality may (...) be that while there is no action at a distance, the world is nonseparable. (shrink)
Is there a vacuum in nature? This is a question which preoccupied natural philosophers for millennia. Great thinkers including Democritus and Newton maintained the existence of a vacuum, while Aristotle, Descartes and Leibniz argued strongly that there was not, and perhaps could not be, any such thing. A casual glance at the literature of contemporary physics may leave the impression that scientific progress has produced a definitive positive answer, so that the philosophers' debates are now of only historical interest. Not (...) only is the attainment of high vacua a multimillion dollar industry, but almost every text and research paper in theoretical high energy or condensed matter physics or cosmology includes multiple references to the vacuum and its often surprising properties. And yet we have it on the authority of no less a scientist than Einstein himself that his general theory of relativity vindicates Descartes' conclusion that there could be no vacuum since the idea of space without matter is unintelligible! Does this mean that there is after all no scientific consensus on this issue, and that the ancient philosophical debate should simply be resumed with renewed vigor? I shall argue that it does not. The progress of physics has given rise to such a proliferation of different (though related) uses of the word 'vacuum' as to irretrievably alter the terms of that debate. Rather than asking whether there is a vacuum in nature, one should ask how well what counts as the vacuum in some physical theory represents reality. This in turn splits up into a semantic question (What aspect of which model counts as the vacuum in this theory?) and an empirical question (How strong is the evidence that nature is faithfully represented by this aspect of the model?) I shall focus mainly on the prior, semantic question here. (shrink)
At first sight the Aharonov-Bohm effect appears nonlocal, though not in the way EPR/Bell correlations are generally acknowledged to be nonlocal. This paper applies an analysis of nonlocality to the Aharonov-Bohm effect to show that its peculiarities may be blamed either on a failure of a principle of local action or on a failure of a principle of separability. Different interpretations of quantum mechanics disagree on how blame should be allocated. The parallel between the Aharonov-Bohm effect and violations of Bell (...) inequalities turns out to be so close that a balanced assessment of the nature and significance of quantum nonlocality requires a detailed study of both effects. (shrink)
The integration of recent work on decoherence into a so-called modal interpretation offers a promising new approach to the measurement problem in quantum mechanics. In this paper I explain and develop this approach in the context of the interactive interpretation presented in Healey (1989). I begin by questioning a number of assumptions which are standardly made in setting up the measurement problem, and I conclude that no satisfactory solution can afford to ignore the influence of the environment. Further, I argue (...) that there are good reasons to believe that on a modal interpretation environmental interactions rapidly ensure that a quantummechanically describable apparatus indeed records a definite result following a measurement interaction. (shrink)
In his recent work, Michael Redhead (1986, 1987, 1989, 1990) has introduced a condition he calls robustness which, he argues, a relation must satisfy in order to be causal. He has used this condition to argue further that EPR-type correlations are neither the result of a direct causal connection between the correlated events, nor the result of a common cause associated with the source of the particle pairs which feature in these events. Andrew Elby (1992) has used this same condition (...) as a premise in an independent argument for the conclusion that EPR-type correlations cannot be causally explained (except, perhaps, by a nonlocal hidden variable theory). I wish to argue here that robustness is itself too fragile a notion to support such conclusions. (shrink)
This is one of the most important books on quantum mechanics to have appeared in recent years. It offers a dramatically new interpretation that resolves puzzles and paradoxes associated with the measurement problem and the behavior of coupled systems. A crucial feature of this interpretation is that a quantum mechanical measurement can be certain to have a particular outcome even when the observed system fails to have the property corresponding to that outcome just prior to the measurement interaction.
Everett's interpretation of quantum mechanics has been criticized for failing to account for what one experiences when performing quantum measurements. This paper investigates the extent of the general responsibility of physics to explain experiences, as distinct from the phenomena that produce them. The conclusions are that while no scientific theory can be required to explain experiences fully, a fundamental physical theory is required to explain how certain actual experiences are possible and that imposing this requirement on quantum mechanics under Everett's (...) interpretation forces one to some perhaps unanticipated metaphysical extremes. (shrink)
