I point out a simple sense in which the standard formulation of Curie’s principle is false when the symmetry transformation it describes is time reversal.

1.1 Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Tangent Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (...) . . . . . . . . . . . 7 1.3 Vector Fields, Integral Curves, and Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Tensors and Tensor Fields on Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.5 The Action of Smooth Maps on Tensor Fields . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.6 Lie Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.7 Derivative Operators and Geodesics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 1.8 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 1.9 Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 1.10 Hypersurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 1.11 Volume Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96.. (shrink)

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)

A reading is given of Curie''s Principle that the symmetry of a cause is always preserved its effects. The truth of the principle is demonstrated and its importance, under the proposed reading, is defended.As far as I see, all a priori statements in physics have their origin in symmetry. (Weyl, Symmetry, p. 126).

This paper is a tour of how the laws of nature can distinguish between the past and the future, or be T-violating. I argue that, in terms of the basic argumentative structure, there are basically just three approaches currently being explored. The first is an application of Curie's Principle, together with the CPT theorem. The second route makes use of a principle due to Pasha Kabir which allows for a direct detection. The third route makes use of a Non-degeneracy Principle, (...) and is related to the energy spectrum of elementary particles. I show how each provides a general template for detecting T-violation, illustrate each with an example, and discuss their prospects in extensions of particle physics beyond the standard model. (shrink)

Curie’s principle asserts that every symmetry of a cause manifests as a symmetry of the effect. It can be formulated as a tautology that is vacuous until it is instantiated. However instantiation requires us to know the correct way to map causal terminology onto the terms of a science. Causal metaphysics has failed to provide a unique, correct way to carry out the mapping. Thus successful or unsuccessful instantiation merely reflects our freedom of choice in the mapping.

In 1894 Pierre Curie announced what has come to be known as Curie's Principle: the asymmetry of effects must be found in their causes. In the same publication Curie discussed a key feature of what later came to be known as spontaneous symmetry breaking: the phenomena generally do not exhibit the symmetries of the laws that govern them. Philosophers have long been interested in the meaning and status of Curie's Principle. Only comparatively recently have they begun to delve into the (...) mysteries of spontaneous symmetry breaking. The present paper aims to advance the discussion of both of these twin topics by tracing their interaction in classical physics, ordinary quantum mechanics and quantum field theory. The features of spontaneous symmetry that are peculiar to quantum field theory have received scant attention in the philosophical literature. These features are highlighted here, along with an explanation of why Curie's Principle, though valid in quantum field theory, is nearly vacuous in that context. (shrink)

These notes discuss some aspects of the sort of symmetry considerations that arise in philosophy of physics. They describe and provide illustration of: (i) one common sort of symmetry argument; and (ii) a construction that allows one to eliminate symmetries from a given structure.

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)

This is the review paper for the section III ("Symmetry breaking") of the volume "Symmetries in physics: philosophical reflections", Cambridge University Press, 2003, edited by Katherine A. Brading and Elena Castellani. The paper's sections are: 1. Preliminaries (I); 2. Symmetry breaking and Curie's analysis; 3. Preliminaries (II); 4. Symmetry breaking of physical laws (4.1. Explicit symmetry breaking; 4.2. Spontaneous symmetry breaking); 5. Symmetry breaking and philosophical questions.