Online research in philosophy

This paper is devoted to examining the relevance of Dirac's view on the use of transformation theory and invariants in modern physics --- as it emerges from his 1930 book on quantum mechanics as well as from his later work on singular theories and constraints --- to current reflections on the meaning of physical symmetries, especially gauge symmetries.

It is argued that awareness of the distinction between dynamical and variational symmetries is crucial to understanding the significance of Noether's 1918 work. Specific attention is paid, by way of a number of striking examples, to Noether's first theorem, which establishes a correlation between dynamical symmetries and conservation principles.

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?

The paper discusses the invariance view of reality: a view inspired by the relativity and quantum theory. It is an attempt to show that both versions of Structural Realism (epistemological and ontological) are already embedded in the invariance view but in each case the invariance view introduces important modifications. From the invariance view we naturally arrive at a consideration of symmetries and structures. It is often claimed that there is a strong connection between invariance and reality, established by symmetries. The invariance view seems to render frame-invariant properties real, while frame-specific properties are illusory. But on a perspectival, yet observer-free view of frame-specific realities they too must be regarded as real although supervenient on frame-invariant realities. Invariance and perspectivalism are thus two faces of symmetries. Symmetries also elucidate structures. Because of this recognition, the invariance view is more comprehensive than Structural Realism. Referring to broken symmetries and coherence considerations, the paper concludes that at least some symmetries are ontological, not just epistemological constraints.

The basic dynamical quantities of classical mechanics, such as position, linear momentum, angular momentum and energy, obtain their fundamental epistomological content by means of their intimate relationship to the symmetries of the space-time manifold which is the arena of physics. The program of canonical quantization can be understood as a two stage process. The first stage is Bohr's Correspondence Principle, whereby the basic dynamical quantities of the quantum theory are required to retain precisely the same relationship to the symmetries of the space-time manifold as do their classical counterparts, thereby preserving their epistemological, as well as measurement-theoretic, significance. Having so identified the basic dynamical variables, functions of these may now be used to identify the subtler symmetries of the proper canonical group. The second and determining stage of the quantization program requires the establishment of a correspondence between some of these subtler symmetries of the classical theory and related symmetries of the quantum theory, the relationship being determined by a common algebraic form for their defining functions.

The quality of potential symmetries of the similarity structure of the Basic Colour Terms has been assessed. The assessment was made on the basis of a database of similarity judgements, made by subjects in response to linguistically expressed questions. All potential symmetries can be statistically rejected, although the well-known and some novel interpretable symmetries are shown to be approximately correct.

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.

Spontaneously broken symmetries are often called hidden or secret symmetries. They are symmetries in the laws of nature that do not show up in observable phenomena. This raises the basic epistemological question: Is there reason to believe that these hidden symmetries are real features of nature rather than artifacts of theorizing. This paper clarifies the epistemic status of spontaneously broken symmetries. It presents the details of an argument by analogy that suggests the spontaneously broken gauge symmetry of electroweak interactions, and the subsequent hypothetico-deductive testing of the hypothesis. It is a story of how dubious means can lead to a credible end.

Symmetries in physics are most commonly recognized and discussed in terms of their function in the mathematical formalism of the theories. Discussion of the observation of symmetries in nature is less common. This paper analyses the observation of particular symmetries such as Lorentz and gauge symmetries, distinguishing between direct observation of the symmetry itself and indirect evidence, the latter being the observation of some consequence of the symmetry are, in an important sense, directly observed, while local symmetries such as gauge symmetry are not.

I examine the debate between Michel Janssen and Harvey Brown over the arrow of explanation in special relativity. Brown argues that the symmetries of the dynamical laws explain the symmetries of space-time, whereas Janssen argues for the converse. Janssen has recently argued against Brown's position on the grounds that it recommends trying to infer information from the relativistic effects, e.g., length contraction, in a way wasteful of time and resources. I show how Brown can respond to Janssen and trace the dispute not to a methodological difference, but to opposing positions on the meaning of spatio-temporal symmetries. According to Janssen, the symmetries of space-time are constraints on dynamical laws. According to Brown, symmetries of space-time arise jointly from matter distributions and the laws governing matter. Finally, I provide some considerations in favor of Brown's position.