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From these different roles we can draw some preliminary conclusions about the status of symmetries. It is immediately apparent that symmetries have an important heuristic function, indicating a strong methodological status. Is this methodological power connected to an ontological or epistemological status for symmetries? According to an ontological viewpoint, symmetries are seen as a substantial part of the physical world: the symmetries of theories represent properties existing in nature, or characterize the structure of the physical world.

It might be claimed that the ontological status of symmetries provides the reason for the methodological success of symmetries in physics. A concrete example is the use of symmetries to predict the existence of new particles. See Bangu, , for a critical analysis of the reasoning leading to this prediction. Or, as in more recent cases, via the unificatory role: the paradigmatic example is the prediction of the W and Z particles experimentally found in in the context of the Glashow-Weinberg-Salam gauge theory proposed in for the unification of the weak and electromagnetic interactions.

These impressive cases of the prediction of new phenomena might then be used to argue for an ontological status for symmetries, via an inference to the best explanation. The question of exactly what a realist would be committed to on such a view of internal spaces remains open, and an interesting topic for discussion. One approach to investigating the limits of an ontological stance with respect to symmetries would be to investigate their empirical or observational status: can the symmetries in question be directly observed?

We first have to address what it means for a symmetry to be observable, and indeed whether all symmetries have the same observational status. Kosso arrives at the conclusion that there are important differences in the empirical status of the different kinds of symmetries. In particular, while global continuous symmetries can be directly observed — via such experiments as the Galilean ship experiment — a local continuous symmetry can have only indirect empirical evidence. In particular, Teh argues that this phenomenon is responsible for the empirically significant symmetries of topological soliton solutions.

Physics in the complex domain

On the other hand, Friederich contends that on one plausible axiomatization of the schema introduced by Greaves and Wallace, it is possible to deduce that local symmetries do not have direct empirical significance. The direct observational status of the familiar global spacetime symmetries leads us to an epistemological aspect of symmetries. For Wigner, this conception of symmetry principles is essentially related to our ignorance if we could directly know all the laws of nature, we would not need to use symmetry principles in our search for them.

There is another reason why symmetries might be seen as being primarily epistemological. As we have mentioned, there is a close connection between the notions of symmetry and equivalence, and this leads also to a notion of irrelevance: the equivalence of space points translational symmetry , for example, may be understood in the sense of the irrelevance of an absolute position to the physical description. There are two ways that one might interpret the epistemological significance of this: on the one hand, we might say that symmetries are associated with unavoidable redundancy in our descriptions of the world, while on the other hand we might maintain that symmetries indicate a limitation of our epistemic access — there are certain properties of objects, such as their absolute positions, that are not observable.

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The view that symmetries are connected with the presence of non-observable quantities in the physical description, with the corollary that the empirical violation of a symmetry is intended in the sense that what was thought to be a non-observable turns out to be actually an observable, was particularly defended by one of the discover of parity violation, T. Lee see section 2. See on this and, more generally, on the relation between symmetry, equivalence and irrelevance Castellani Dasgupta defends an epistemic interpretation of symmetry on a similar basis as Lee.

Finally, we would like to mention an aspect of symmetry that might very naturally be used to support either an ontological or an epistemological account. It is widely agreed that there is a close connection between symmetry and objectivity , the starting point once again being provided by spacetime symmetries: the laws by means of which we describe the evolution of physical systems have an objective validity because they are the same for all observers.

The old and natural idea that what is objective should not depend upon the particular perspective under which it is taken into consideration is thus reformulated in the following group-theoretical terms: what is objective is what is invariant with respect to the transformation group of reference frames, or, quoting Hermann Weyl , p. They point out p. Growing interest, recently, in the metaphysics of physics includes interest in symmetries. Baker offers an accessible introduction, and Livanios , connecting discussions of symmetries to dispositions and essences, is an example of this work.

To conclude: symmetries in physics offer many interpretational possibilities, and how to understand the status and significance of physical symmetries clearly presents a challenge to both physicists and philosophers. The Concept of Symmetry 2. Symmetry Principles 2. Symmetry Arguments 4. Symmetry Breaking 4. As we have seen, the scientific notion of symmetry the one we are interested in here is a recent one.

If we speak about a role of this concept of symmetry in the ancient theories of nature, we must be clear that it was not used explicitly in this sense at that time. The second is between the two main ways of using symmetry. First, we may attribute specific symmetry properties to phenomena or to laws symmetry principles.

It is the application with respect to laws, rather than to objects or phenomena, that has become central to modern physics, as we will see. Second, we may derive specific consequences with regard to particular physical situations or phenomena on the basis of their symmetry properties symmetry arguments. Symmetry Principles The first explicit study of the invariance properties of equations in physics is connected with the introduction, in the first half of the nineteenth century, of the transformational approach to the problem of motion in the framework of analytical mechanics.

Within the philosophical literature, work relating symmetries to dualities generally responds to one of the following three questions: What is an appropriate formal framework for understanding the inter-theoretic relationship realized by duality symmetries? And within the far simpler context of classical mechanics, Teh and Tsementzis explore the use of the quintessential symmetry of classical phase space viz.

What is the relationship between the local symmetry of a theory and the symmetries of its dual theory?

Concrete applications for accelerator science

One reason that this question is pressing is that as we mentioned in Section 2. However, de Haro, Teh, and Butterfield argue that this conjecture is not true in full generality: there is a special class of diffeomorphisms which do not vanish in the boundary theory, but instead correspond to conformal transformations of the boundary CFT.

Symmetry Arguments Consider the following cases. What do they have in common? What is needed for its occurrence i. The symmetry elements of the causes must be found in their effects, but the converse is not true; that is, the effects can be more symmetric than the causes. Symmetry Breaking A symmetry can be exact, approximate, or broken. General Philosophical Questions Much of the recent philosophical literature on symmetries in physics discusses specific symmetries and the intepretational questions they lead to.

Bibliography Anderson, J. Ashtekar, A. Baker, D. Bangu, S. Belot, G. Brading and E. Castellani eds. Batterman ed. Born, M. Reprinted in E. Castellani ed.


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