Highlighting main issues and controversies, this book brings together current philosophical discussions of symmetry in physics to provide an introduction to the subject for physicists and philosophers. The contributors cover all the fundamental symmetries of modern physics, such as CPT and permutation symmetry, as well as discussing symmetry-breaking and general interpretational issues. Classic texts are followed by new review articles and shorter commentaries for each topic. Suitable for courses on the foundations of physics, philosophy of physics and philosophy of science, (...) the volume is a valuable reference for students and researchers. (shrink)

Symmetry considerations dominate modern fundamental physics, both in quantum theory and in relativity. Philosophers are now beginning to devote increasing attention to such issues as the significance of gauge symmetry, quantum particle identity in the light of permutation symmetry, how to make sense of parity violation, the role of symmetry breaking, the empirical status of symmetry principles, and so forth. These issues relate directly to traditional problems in the philosophy of science, including the status of the laws of nature, the (...) relationships between mathematics, physical theory, and the world, and the extent to which mathematics suggests new physics.This entry begins with a brief description of the historical roots and emergence of the concept of symmetry that is at work in modern science. It then turns to the application of this concept to physics, distinguishing between two different uses of symmetry: symmetry principles versus symmetry arguments. It mentions the different varieties of physical symmetries, outlining the ways in which they were introduced into physics. Then, stepping back from the details of the various symmetries, it makes some remarks of a general nature concerning the status and significance of symmetries in physics. (shrink)

Du Châtelet’s 1740 text Foundations of Physics tackles three of the major foundational issues facing natural philosophy in the early eighteenth century: the problem of bodies, the problem of force, and the question of appropriate methodology. This paper offers an introduction to Du Châtelet’s philosophy of science, as expressed in her Foundations of Physics, primarily through the lens of the problem of bodies.

In a recent paper in this journal, Kosso ([2000]) discussed the observational status of continuous symmetries of physics. While we are in broad agreement with his approach, we disagree with his analysis. In the discussion of the status of gauge symmetry, a set of examples offered by 't Hooft ([1980]) has influenced several philosophers, including Kosso; in all cases the interpretation of the examples is mistaken. In this paper, we present our preferred approach to the empirical significance of symmetries, re-analysing (...) the cases of gauge symmetry and general covariance. Direct and indirect empirical significance Global and local continuous symmetries Gauge symmetry 3.1 Local gauge symmetry 3.1.1 Discussion of the first claim 3.1.2 Discussion of the second claim 3.2 Global gauge symmetry Space-time symmetries Direct and indirect empirical significance again Conclusion. (shrink)

Symmetry, intended as invariance with respect to a transformation (more precisely, with respect to a transformation group), has acquired more and more importance in modern physics. This Chapter explores in 8 Sections the meaning, application and interpretation of symmetry in classical physics. This is done both in general, and with attention to specific topics. The general topics include illustration of the distinctions between symmetries of objects and of laws, and between symmetry principles and symmetry arguments (such as Curie's principle), and (...) reviewing the meaning and various types of symmetry that may be found in classical physics, along with different interpretative strategies that may be adopted. Specific topics discussed include the historical path by which group theory entered classical physics, transformation theory in classical mechanics, the relativity principle in Einstein's Special Theory of Relativity, general covariance in his General Theory of Relativity, and Noether's theorems. In bringing these diverse materials together in a single Chapter, we display the pervasive and powerful influence of symmetry in classical physics, and offer a possible framework for the further philosophical investigation of this topic. (shrink)

Analysis of Emmy Noether’s 1918 theorems provides an illuminating method for testing the consequences of “coordinate generality”, and for exploring what else must be added to this requirement in order to give general covariance its far-reaching physical significance. The discussion takes us through Noether’s first and second theorems, and then a third related theorem due originally to F. Klein. Contact will also be made with the contributions of, principally, J.L. Anderson, A. Trautman, P.A.M. Dirac, R. Torretti and the father of (...) the whole business, A. Einstein (an apparent shift in Einstein’s thinking on the significance of general covariance between 1916 and 1918 is highlighted). (shrink)

In this paper I argue that reading history of physics as a contribution to history of philosophy is important for contemporary philosophy of physics. My argument centers around a particular case: special relativity versus presentism. By means of resources drawn from reading aspects of Newton's work as contributions to philosophy, I argue that there is in physics an alternative way to approach what we mean by "present" such that presentism remains an open empirical question whose refutation requires resources that go (...) beyond those of special relativity. I offer this as an example of one fruitful way in which we pursue integrated HPS. (shrink)

Taking Bogen and Woodward's discussion of data and phenomena as his starting point, McAllister presents a challenge to scientific realism. I discuss this challenge and offer a suggestion for how the scientific realist could respond to both its epistemic and ontological aspects. In so doing, I urge that the scientific realist should not reject ontological pluralism from the start, but should seek to explore versions of scientific realism that leave open the possibility of certain kinds of pluralist ontology. I investigate (...) the available options and use a law-constitutive approach to offer a strategy for the scientific realist who is open-minded about ontological pluralism. (shrink)

Recent discussions of structuralist approaches to scientific theories have stemmed primarily from Worrall's, in which he defends a position whose historical roots he attributes to Poincare. In the renewed debate inspired by Worrall, it is thus not uncommon to find Poincare's name associated with various structuralist positions. However, Poincare's structuralism is deeply entwined with both his conventionalism and his idealism, and in this paper we explore the nature of these dependencies. What comes out in the end is not only a (...) clearer picture of Poincare's position regarding structuralism, but also two arguments for versions of epistemic structuralism different in kind from that given by Worrall. (shrink)

Analysis of Emmy Noether's 1918 theorems provides an illuminating method for testing the consequences of coordinate generality, and for exploring what else must be added to this requirement in order to give general covariance its far-reaching physical significance. The discussion takes us through Noether's first and second theorems, and then a third related theorem due originally to F. Klein. Contact will also be made with the contributions of, principally, J.L. Anderson, A. Trautman, P.A.M. Dirac, R. Torretti and the father of (...) the whole business, A. Einstein. (shrink)

I discuss the three distinctions “absolute and relative”, “true and apparent”, and “mathematical and common”, for the specific case of time in Newton’s Principia. I argue that all three distinctions are needed for the project of the Principia and can be understood within the context of that project without appeal to Newton’s wider metaphysical and theological commitments. I argue that, within the context of the Principia, the three claims that time is absolute rather than relative, true rather than apparent, and (...) mathematical rather than common, are to be evaluated with respect to the needs of, and relative to the success of, the project of the Principia. I claim that Newton is thereby offering a new, and empirical, philosophy of time. (shrink)

The focus of this paper is the recent revival of interest in structuralist approaches to science and, in particular, the structural realist position in philosophy of science . The challenge facing scientific structuralists is three-fold: i) to characterize scientific theories in ‘structural’ terms, and to use this characterization ii) to establish a theory-world connection (including an explanation of applicability) and iii) to address the relationship of ‘structural continuity’ between predecessor and successor theories. Our aim is to appeal to the notion (...) of shared structure between models to reconsider all of these challenges, and, in so doing, to classify the varieties of scientific structuralism and to offer a ‘minimal’ construal that is best viewed from a methodological stance. (shrink)

Within philosophy of physics it is broadly accepted that presentism as an empirical hypothesis has been falsified by the development of special relativity. In this article, I identify and reject an assumption common to both presentists and advocates of the block universe and then offer an alternative version of presentism that does not begin from spatiotemporal structure, which is an empirical hypothesis, and which has yet to be falsified. While some features of familiar presentism are lost, a sufficient core remains (...) to warrant the label. (shrink)

This book is a wonderful resource for historians and philosophers of mathematics and physics alike, not just for Hilbert's own work in physics, but also because Corry sets Hilbert in context, bringing out the people with whom Hilbert had contact, describing their work and possible links with Hilbert's work, and describing the activities going on around Hilbert. The historical thesis of this book is that Hilbert worked on a wide range of issues in physics for a period lasting more than (...) two decades, employing and developing his axiomatic approach throughout. One conclusion that follows from this is that Hilbert's 1915–1917 work relating to Einstein's General Theory of Relativity was a natural continuation of Hilbert's pre-existing interests and activities, and not a one-off foray into foreign territory. 1Of especial interest to philosophers of mathematics are two further theses. Corry stresses that for Hilbert geometry is an empirical science, and related to this argues first, that Hilbert intends the axiomatic method to be used in enhancing our understanding of the content of a given theory via relating the results of the axiomatic investigation back to the intuitive content of the axioms; and, second, that to understand Hilbert's axiomatic approach in mathematics we must pay serious attention to his work in physics.Corry also hopes to show ‘the significant and unique contribution of Hilbert to certain important developments in twentieth-century physics’ . 2 In the end, this assessment of Hilbert's contribution to physics is far from clear cut: the two cases where Hilbert goes into the details of a physical theory show him lacking feel for what is important physically with respect to that theory. Nevertheless, philosophers and historians of physics will find a great deal to interest them in the story of Hilbert's involvement in physics, and in the details …. (shrink)

This book argues that the Enlightenment was a golden age for the philosophy of body, and for efforts to integrate coherently a philosophical concept of body with a mathematized theory of mechanics. Thereby, it articulates a new framing for the history of 18th-century philosophy and science. It explains why, more than a century after Newton, physics broke away from philosophy to become an autonomous domain. And, it casts fresh light on the structure and foundations of classical mechanics. Among the figures (...) studied are Malebranche, Leibniz, Du Châtelet, Boscovich, and Kant, alongside d’Alembert, Euler, Lagrange, Laplace and Cauchy. (shrink)

In this paper we argue that the primary issue in Descartes’ Principles of Philosophy, Part II, articles 1-40, is the problem of individuating bodies. We demonstrate that Descartes departs from the traditional quest for a principle of individuation, moving to a different strategy with the more modest aim of constructing bodies adequate to the needs of his cosmology. In doing this he meets with a series of difficulties, and this is precisely the challenge that Newton took up. We show that (...) Descartes’ questions and his strategy influenced not only Newton’s account of physical bodies, but also the structure of his mechanics. (shrink)

I discuss the three distinctions “absolute and relative”, “true and apparent”, and “mathematical and common”, for the specific case of time in Newton’s Principia. I argue that all three distinctions are needed for the project of the Principia and can be understood within the context of that project without appeal to Newton’s wider metaphysical and theological commitments. I argue that, within the context of the Principia, the three claims that time is absolute rather than relative, true rather than apparent, and (...) mathematical rather than common, are to be evaluated with respect to the needs of, and relative to the success of, the project of the Principia. I claim that Newton is thereby offering a new, and empirical, philosophy of time. (shrink)

Here is a problem at the heart of the metaphysics of the natural world: How, if at all, can a unity undergo change? This problem incorporates two questions. First, in virtue of what is a thing a genuine unity? And second, the issue that’s more obvious in the formulation of the question: how, if at all, can such a unity undergo change? There are two basic approaches to this problem present in Newton’s physics. The more familiar grounds unity and change (...) in space and time, the second in the laws of nature. The latter approach is set out in this paper. I argue that a law-constitutive approach to the entities that are the subject-matter of Newton’s physics offers a principle of unity for things, be they simple or composite, and for the parts of composites, such that we also gain an account of what it is for a genuine unity to undergo change in its properties whilst retaining its numerical identity. I end by arguing that the law-constitutive approach favors endurantism over perdurantism. This paper is intended as an example of a particular approach to the relationship between metaphysics and philosophy of physics, according to which, as a philosopher, one engages with physics as a part of the history of philosophy, beginning with our deepest philosophical questions and using the development of physics read as a contribution to natural philosophy to explore how these questions are transformed, re-worked, addressed, and sometimes rendered non-questions. (shrink)

The papers posted under the heading 'Symmetries in Physics, New Reflections: Oxford Workshop, January 2001' were presented and discussed at the corresponding workshop. As the organisers, we give a brief summary of the purpose of the workshop, and list the talks and the participants.