The implications for the substantivalist–relationalist controversy of Barbour and Bertotti's successful implementation of a Machian approach to dynamics are investigated. It is argued that in the context of Newtonian mechanics, the Machian framework provides a genuinely relational interpretation of dynamics and that it is more explanatory than the conventional, substantival interpretation. In a companion paper (Pooley [2002a]), the viability of the Machian framework as an interpretation of relativistic physics is explored. 1 Introduction 2 Newton versus Leibniz 3 Absolute space versus (...) an affine connection 4 Anti-relationalist arguments 5 Rehabilitating relationalism 6 Dynamics on the relative configuration space 7 Intrinsic particle dynamics 8 Conclusion. (shrink)

In this paper I wish to make some headway on understanding what \emph{kind} of problem the ``problem of time'' is, and offer a possible resolution---or, rather, a new way of understanding an old resolution. The response I give is a variation on a theme of Rovelli's \emph{evolving constants of motion} strategy. I argue that by giving correlation strategies a \emph{structuralist} basis, a number of objections to the standard account can be blunted. Moreover, I show that the account I offer provides (...) a suitable ontology for time in both classical and quantum canonical general relativity. (shrink)

Those who hold that all fundamental sparse properties have dispositional essences face a problem with structural (e.g. geometrical) properties. In this paper I consider a further route for the dispositional monist that is enabled by the requirement that physical theories should be background-free. If this requirement is respected then we can see how spatial displacement can be a causally active relation and hence may be understood dispositionally.

Starting from a generalized Hamilton-Jacobi formalism, we develop a new framework for constructing observables and their evolution in theories invariant under global time reparametrizations. Our proposal relaxes the usual Dirac prescription for the observables of a totally constrained system and allows one to recover the influential partial and complete observables approach in a particular limit. Difficulties such as the non-unitary evolution of the complete observables in terms of certain partial observables are explained as a breakdown of this limit. Identification of (...) our observables relies upon a physical distinction between gauge symmetries that exist at the level of histories and states, and those that exist at the level of histories and not states. This distinction resolves a tension in the literature concerning the physical interpretation of the partial observables and allows for a richer class of observables in the quantum theory. There is the potential for the application of our proposal to the quantization of gravity when understood in terms of the Shape Dynamics formalism. (shrink)

There is a widespread impression that General Relativity, unlike Quantum Mechanics, is in no need of an interpretation. I present two reasons for thinking that this is a mistake. The first is the familiar hole argument. I argue that certain skeptical responses to this argument are too hasty in dismissing it as being irrelevant to the interpretative enterprise. My second reason is that interpretative questions about General Relativity are central to the search for a quantum theory of gravity. I illustrate (...) this claim by examining the interpretative consequences of a particular technical move in canonical quantum gravity. (shrink)

Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to an ensemble of subsystems of the universe with identical constituents and similar preparations and environments. A new kind of interaction is posited amongst such similar subsystems which acts to increase their distinctiveness, by extremizing the variety. In the limit of large numbers of (...) similar subsystems this interaction is shown to give rise to Bohm’s quantum potential. As a result the probability distribution for the ensemble is governed by the Schroedinger equation. The measurement problem is naturally and simply solved. Microscopic systems appear statistical because they are members of large ensembles of similar systems which interact non-locally. Macroscopic systems are unique, and are not members of any ensembles of similar systems. Consequently their collective coordinates may evolve deterministically. This proposal could be tested by constructing quantum devices from entangled states of a modest number of quits which, by its combinatorial complexity, can be expected to have no natural copies. (shrink)

We make a first attempt to axiomatically formulate the Montevideo interpretation of quantum mechanics. In this interpretation environmental decoherence is supplemented with loss of coherence due to the use of realistic clocks to measure time to solve the measurement problem. The resulting formulation is framed entirely in terms of quantum objects without having to invoke the existence of measurable classical quantities like the time in ordinary quantum mechanics. The formulation eliminates any privileged role to the measurement process giving an objective (...) definition of when an event occurs in a system. (shrink)

Metaphysical orthodoxy holds that a privileged minority of properties carve reality at its joints. These are the so-called fundamental properties. This thesis concerns the contemporary philosophical debate about the nature of fundamental properties. In particular, it aims to answer two questions: What is the most adequate conception of fundamental properties? What is the “big picture” world-view that emerges by adopting such a conception? I argue that a satisfactory answer to both questions requires us to embrace a novel conception of powerful (...) qualities, according to which properties are at once dispositional and qualitative. By adopting the proposed conception of powerful qualities, an original theory of fundamental properties comes to light. I call it Dual-Aspect Account. In this thesis, I defend the Dual-Aspect Account and its superiority with respect to rival views of fundamental properties. I illustrate this claim by examining Dispositionalism, the view defended among others by Alexander Bird and Stephen Mumford, Categoricalism, which has been advocated notably by David Lewis and David Armstrong, and the Identity Theory of powerful qualities, primarily championed by C. B. Martin and John Heil. The latter is the standard conception of powerful qualities. However, in the literature, the Identity Theory faces the charge of contradiction. A preliminary task is therefore to show that a conception of powerful qualities is coherent. To accomplish this aim, I introduce the notion of an aspect of a property. On this interpretation, powerful qualities can be thought of as having dispositional and qualitative aspects. I show that such a conception allows us to disambiguate the claim that a property’s dispositionality is identical with its qualitativity, and evade the charge of contradiction. Aspects bring us other theoretical benefits. I illustrate this claim by showing how the Dual-Aspect Account offers us a promising theory of resemblance. I then compare its merits with David Armstrong’s theory of partial identity. The conclusion of this thesis is that the Dual-Aspect Account is better suited to capturing the world as we find it in everyday life and scientific investigation as compared to the theoretical positions examined. (shrink)

It is suggested, following a proposal made recently by Smolin, that the most fundamental law of the universe takes this form: Among the set of all possible universes compatible with an irreducibly minimal set of structural constraints, the actually realized universe is the one which maximizes a mathematically well-defined number (the variety) that measures the structural variety of the universe (in the totality of its history). This gives expression to Leibniz's idea that the actual universe gives “the greatest variety possible, (...) but with the greatest possible order.” Two models are proposed in which the idea can be realized and its consequences tested; both are discrete in nature and satisfy highly nonlocal laws. In such a scheme a unique (finite) universe is called into being by the fundamental requirement of maximal variety (for given definition of the variety), which it is conjectured could have such a powerful ordering effect that space, time, the currently known laws of physics, and the observed structure of the universe could all appear as emergent consequences of the single underlying law. (shrink)

The local Lorentz and diffeomorphism symmetries of Einstein's gravitational theory are spontaneously broken by a Higgs mechanism by invoking a phase transition in the early universe, at a critical temperature Tc below which the symmetry is restored. The spontaneous breakdown of the vacuum state generates an external time, and the wave function of the universe satisfies a time-dependent Schrödinger equation, which reduces to the Wheeler-deWitt equation in the classical regime for T (...) The conservation of energy is spontaneously violated for T>Tc, and matter is created fractions of seconds after the big bang, generating the matter in the Universe. The time direction of the vacuum expectation value of the scalar Higgs field generates a time asymmetry, which defines the cosmological arrow of time and the direction of increasing entropy as the Lorentz symmetry is restored at low temperatures. (shrink)

I explore Leibnizian themes in the theoretical physicist's pursuit of a quantum cosmology by examining Smolin's program based on the elimination of ideal elements. These constructs are formal mathematical structures of a physical theory that require for their interpretation the existence of objects external to the system treated by the theory. After introducing some necessary background information, I discuss the particulars of Smolin's definition of ideal elements and analyze his motivations and arguments for the elimination of ideal elements. I then (...) survey and assess his two specific proposals for the construction of a quantum cosmology. The former stems from the canonical approach to the development of a quantum theory of gravity; the latter consists of a series of hypotheses framing a speculative fundamental theory of the universe. Finally, I consider the explicit links and debts of Smolin's program to Leibniz's philosophy. (shrink)