Online research in philosophy

The concepts in the title refer to properties of physical theories (which are given, in this paper, a model-theoretic formulation and appropriate idealizations) and this paper investigates their nature and relations. The first three concepts, especially gauge invariance and indeterminism, have been widely discussed in connection to spacetime theories and the hole argument. Since the gauge invariance principle is at the crux of the issue, this paper aims at clarifying the nature of gauge invariance (either in general or as general covariance). I first explore the following chain of relations: gauge invariance $\Rightarrow $ the conservation laws $\Rightarrow $ the Cauchy problem $\Rightarrow $ indeterminism. Then I discuss gauge invariance in light of our understanding of the above relations and the possibility of spontaneous symmetry breaking.

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.

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.

This review is a critical discussion of three main claims in Debs and Redhead’s thought-provoking book Objectivity, Invariance, and Convention. These claims are: (i) Social acts impinge upon formal aspects of scientific representation; (ii) symmetries introduce the need for conventional choice; (iii) perspectival symmetry is a necessary and sufficient condition for objectivity, while symmetry simpliciter fails to be necessary.

Introduction Atoms theory and symmetry theory dominated physics. Symmetry propagation and interactions verify the Curie principle. But its violation by symmetry breaking is spontaneous.Fragility is creative. An information breaks a generalized symmetry. Results on symmetry breakings are not valid for fuzzy symmetries. The breaking of a fuzzy symmetry leads only to a pour symmetry (Fig.1).

Introduction Atoms theory and symmetry theory dominated physics. Symmetry propagation and interactions verify the Curie principle. But its violation by symmetry breaking is spontaneous.Fragility is creative. An information breaks a generalized symmetry. Results on symmetry breakings are not valid for fuzzy symmetries. The breaking of a fuzzy symmetry leads only to a pour symmetry (Fig.1).

We find symmetry attractive. It interests us. Symmetry is often an indicator of the deep structure of things, whether they be natural phenomena, or the creations of artists. For example, the most fundamental conservation laws of physics are all based in symmetry. Similarly, the symmetries found in religious art throughout the world are intended to draw attention to deep spiritual truths. Not only do we find symmetry pleasing, but its discovery is often also surprising and illuminating as well. For these reasons, we are inclined to think that symmetries are informative, and that symmetries contain information. On the other hand, symmetries represent a kind of invariance under transformation. Such invariance implies that symmetrical things contain redundancies. Redundancy, in turn, implies that the information content of a symmetrical structure or configuration is less than that of a similar nonsymmetrical structure. Symmetry, then, entails a reduction in information content. These considerations present us with somewhat of a paradox: On the one hand, many symmetries that we find in the world are surprising, and surprise indicates informativeness. On the other hand, the surprise value of information arises because it presents us with the unexpected or improbable, but symmetries, far from creating the unexpected, ensure that the known can be extended through invariant transformations. How can this paradox be resolved?

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.

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.

Given its importance in modern physics, philosophers of science have paid surprisingly little attention to the subject of symmetries and invariances, and they have largely neglected the subtopic of symmetry breaking. I illustrate how the topic of laws and symmetries brings into fruitful interaction technical issues in physics and mathematics with both methodological issues in philosophy of science, such as the status of laws of physics, and metaphysical issues, such as the nature of objectivity.