## Indeterminism

The main interpretive problem facing direct interpretations of gauge theories is the underdetermination that results from the gauge freedom. How one chooses to deal with this problem leads quickly into many distinct interpretive problems indeterminism, non-locality and frozen dynamics (to name the most important for our purposes). I save the latter to a detailed examination in Chapter 7 the non-locality problem that results from a particular attitude to this problem is reviewed in the next...

## Leibniz Versus Clarke

In the course of his debate with Clarke, Leibniz presents an argument (a reduc-tio) directed against Newtonian substantivalism.66 In this case, as van Fraassen ( 1990 , p. 239) nicely expresses it, Leibniz's God was Buridan's ass magnified (see also Earman 1989 , p. 118) given certain features about the nature of Newtonian space, it is impossible for God to make a reasoned decision regarding the placement of the world within it. Here, in its entirety, is the oft-quoted argument designed to...

## Maxwellian Electromagnetism

As traditionally conceived, Maxwell's equations for electromagnetism describe the behaviour of a pair of vector fields E (the electric field) and B (the magnetic field) that are (1) defined at each point of space (taken to possess the structure represented by R3) (2) functions of time t e R and (3) dependent upon the electric charge density p and current density . Setting the speed of light c to 1, Maxwell's equations are 89 In other words, underdetermination is not sufficient for indeterminism...

## What Is an Observable in General Relativity

It is a curious fact about the hole argument that the indeterminism is not an observable feature it is not an empirical kind of indeterminism that we could in any way detect. Even if it was true that general relativity was indeterministic in the sense that Earman and Norton say the manifold substantivalist is committed to, it is of such a strange kind that we could never tell one way or the other whether we lived in a world that ran according to such a scheme. For example, Hoefer writes Note...

## Connection to spacetime theory

The presentation of 1.1 showed that the most common sorts of spacetime theory represent spacetime by means of a 'bare' differentiable manifold M over which certain structures, called geometric-object fields, are defined. The types of geometric-object fields split into two distinct categories the absolute objects (or what, following contemporary physicists' parlance, I have been calling background structures) Bi and dynamical objects . The interpretation usually given to these objects (e.g....

## Interpretation And Ontology

Can philosophers really contribute to the project of reconciling general relativity and quantum field theory Or is this a technical business best left to the experts . General relativity and quantum field theory are based on some profound insights about the nature ofreality. These insights are crystallized in the form of mathematics, but there is a limit to how much progress we can make by just playing around with this mathematics. We need to go back to the insights behind general relativity...

## What Is The Significance Of Relational Localization

The standard view amongst physicists is that a gauge-theoretical understanding of diffeomorphism invariance implies that the localization of fields is relational (i.e. grounded by relations between fields rather than manifold points), and that this in turn implies spacetime relationalism, or at least anti-substantivalism. Rovelli sketches the supposed implication as follows Diffeomorphism invariance implies that spacetime localization is relational, for the following reason. If ( , Xn) is a...

## Defining Observables

It is observables that give us our connection to the world in the context of physics they are the things we measure and whose values we predict. They form the qualitative character of a world in the sense that two worlds that are duplicates in terms of the observables they contain, and in terms of their assigned values, are qualitatively indistinguishable. I think that the resolution of the hole argument can only come about once we have a proper grasp on what the theory of general relativity is...

## Symmetry And Structure

Let us begin by distinguishing between a structure and the elements or objects of a structure. A structure S may be defined as an ordered tuple of the form (D, R), where D is a (non-empty) set of individuals (the domain of S), and R is a (non-empty) set of relations over (or on') D (including 1-place' relations i.e. predicates). The objects of a structure are simply the elements of D, and they are characterized by the Ri. Now suppose we have two structures, S (D, Ri) and S' (D', Ri), and an...

## Manifold Substantivalism

It is the manifold that Earman and Norton claim is the best candidate for what represents spacetime for a substantivalist. Hence, it is the M component of the spacetime models that we discussed in 1.1 that the substantivalist should be committed to. This commitment to the manifold amounts to a realism about the points of spacetime along with their topological and differential properties. Note that this part of the model classes as a background structure in that it is fixed across the physically...

## Three Types Of Structuralism

Most flavours of structuralism are united on the point that relations are important where they differ is on the issue of the extent of their importance. We have seen in our discussion of the hole argument that many responses work precisely by invoking some relations not all of these were relationalist, strictly speaking. However, much of the division between relationalists and those who call themselves structuralists, and indeed substantivalists, turns on the question of the status of the...

## Troubles With Determinism

What is Earman and Norton's minimal definition of determinism Butterfield states it like this one physically possible world is singled out by the specifica- 149 These are borrowed and modified versions of those given by Butterfield 1988 and Pooley in press note that But-terfield calls Haec Each I prefer Pooley's since it makes the connection to the metaphysics of modality more explicit. 150 This fact forms the basis of one of Norton's criticisms of Maudlin's metrical essentialism, a response...

## The gauge argument

For simplicity, consider the example of a free non-relativistic particle with wave-function f(x). Invariance under U(1) means that if we act (by multiplication) on this wave-function by an element of el0 e U(1) (i.e., a phase factor), the resulting wave-function is physically equivalent98 to the original, i.e. In this case a global U(1) transformation was applied to the wave-function. What this means is that the same operation is applied at every point in space at some time (i.e. 0 does not...

## Empty space and fields

Before I move on to the Leibniz-shift argument, I should first deal briefly with a potential difficulty faced by relationalism, which is sometimes glossed over in 61 I mention this aspect briefly in the next subsection, and consider its bearing on the substantivalism-relationalism debate. the literature. Namely, that the requirement that there be no spatial and temporal vacua might seem to be too stringent a condition for the relationalist to meet. There are two questions to be asked here (1)...

## Denying primitive identity

Recall that the manifold substantivalist was supposed to get into bother with inde-terminism because of the alleged commitment to the existence of worlds that are qualitatively identical but differ with respect to how the geometrical properties are spread over the points of space. The general covariance of general relativity implies that the equations of the theory cannot uniquely determine this spreading of the geometrical properties over the points. If the manifold substantivalist is so...

## Surplus Semantic Universalism And Minimal Structuralism

Following Ismael and Van Fraassen 2003 , p. 371 , let us distinguish between 'elements' and 'structure' where the latter is defined by a set of relations on the elements, as I defined in 1.2. If we use a structure to represent a physical system or an aspect of a physical system i.e., if the structure is a mathematical model , then any surplus will, if it manifests itself at all, manifest itself through a many-to-one relationship between model and system. One and the same physical state of...

## Varieties Of Relationalism

The final class of response we consider comprises those that see the lesson of the hole argument as implying an endorsement of LE, and see that as implying rela-tionalism. We have already seen that there are forms of substantivalism that fall 176 Though he uses the terminology Lockean and non-Lockean to denote the anti-haecceitistic and haecceitistic brands of substantivalism. under this mantle too. Hence, it is possible for both relationalists and substan-tivalists to endorse LE. I begin with...

## Sophisticated Substantivalism And Unsophisticated Relationalism

The two claims I wish to question are 1 that the substantivalist is committed to taking I as representing possibility space and 2 that the relationalist is committed to taking D as representing possibility space. This pair of claims are stated quite forcibly by Belot. Thus, he writes modified to suit the example of the previous section I require substantivalists to maintain that there are a large number of such embeddings of point particles in Euclidean space, with their relative distances...

## References

Primitive thisness and primitive identity, The Journal of Philosophy 1979, LXXVI 1 , 5-26. Aharonov and Bohm, 1959 Aharonov, Y., Bohm, D. Significance of electromagnetic potentials in the quantum theory, Physical Review 1959, 115 3 , 485-91. Alexander, 1956 Alexander, H.G. The Leibniz-Clarke Correspondence, Manchester University Press, 1956. Amelino-Camelia, 1999 Amelino-Camelia, G. Are we at the dawn of quantum-gravity phenomenology Kowalski-Glikman, J., editor....

## Maudlins metrical essentialism

At the heart of Maudlin's scheme 1988 1990 is the idea that only one model from an equivalence class of hole diffeomorphs represents a physically possible world.160 Butterfield too takes this line, though he grounds it in a different way, using counterpart theory. For Maudlin the hole diffeomorphism or any non-trivial diffeomorphism does not allow one to generate physically admissible models from models. And the reason for this is that a diffeomorphic copy of a model does not, in general,...

## Preface

Symmetry is increasingly becoming a central, and indeed 'hot' topic for philosophers of physics it is linked to various metaphysical issues having to do with space, time, motion, change, identity, modality, ontology and much more besides. This book examines the current interpretive landscape of symmetry in physics with the emphasis on those issues just listed. I consider a number of physical theories for which symmetry poses a particular and universal interpretive difficulty the same difficulty...