This review of Julian Barbour's The End of Time ([1999]) discusses his Machian theories of dynamics, and his proposal that a Machian perspective enables one to solve the problem of time in quantum geometrodynamics, viz. by saying that there is no time! 1 Introduction 2 Machian themes in classical physics 2.1 The status quo 2.2 Machianism 2.2.1 The temporal metric as emergent 2.2.2 Machian theories 2.2.3 Assessing intrinsic dynamics 3 The end of time? 3.1 Time unreal? The classical case 3.1.1 (...) Spontaneity 3.1.2 Barbour's vision: time capsules 3.2 Evidence from quantum physics? 3.2.1 Mott scattering as a model for time capsules 3.2.2 Solving the problem of time? (shrink)

Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about 'matter' moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of (...) space-time points. The role of the wave function then is to govern the motion of the matter. (shrink)

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)

The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction - the direct quantisation of Einstein's general theory of relativity and string theory - are covered. Whereas the first attempts to construct a viable theory for the gravitational field alone, string theory assumes that (...) a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantisation of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is a detailed presentation of the main approaches employed in quantum general relativity: path-integral quantisation, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of string theory centres around its quantum-gravitational aspects and the comparison with quantum general relativity. Physical applications discussed at length include the quantisation of black holes, quantum cosmology, the indications of a discrete structure of spacetime, and the origin of irreversibility. This book will be of interest to researchers and students working in relativity and gravitation, cosmology, quantum field theory and related topics. It will also be of interest to mathematicians and philosophers of science. (shrink)

The paper presents an inquiry into the question regarding the compatibility of Bohmian mechanics, intended as a non-local theory of moving point-like particles, with background independence. This issue is worth being investigated because, if the Bohmian framework has to be of some help in developing new physics, it has to be compatible with the most well-established traits of modern physics, background independence being one of such traits. The paper highlights the fact that the notion of background independence in the context (...) of spacetime physics is slippery and interpretation-laden. It is then suggested that the best-matching framework developed by Julian Barbour might provide a robust enough meaning of background independence. The structure of Bohmian dynamics is evaluated against this framework, reaching some intermediate results that speak in favor of the fact that Bohmian mechanics can be made background independent. (shrink)

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)

Abraham Stone recently has published an argument purporting to show that David Bohm's interpretation of quantum mechanics fails to solve the measurement problem. Stone's analysis is not correct, as he has failed to take account of the conditions under which the theorems he cites are proven. An explicit presentation of a Bohmian measurement illustrates the flaw in his reasoning.

I consider a quantum system that possesses key features of quantum shape dynamics and show that the evolution of wave-packets will become increasingly classical at late times and tend to evolve more and more like an expanding classical system. At early times however, semiclassical effects become large and lead to an exponential mismatch of the apparent scale as compared to the expected classical evolution of the scale degree of freedom. This quantum inflation of an emergent and effectively classical system, occurs (...) naturally in the quantum shape dynamics description of the system, while it is unclear whether and how it might arise in a constrained Hamiltonian quantization. (shrink)

I want to consider some features of the position put forward by Julian Barbour in The End of Time that seem to me of particular philosophical interest. At the level of generality at which I'll be concerned with it, the view is relatively easy to describe. It can be arrived at by thinking of time as decomposing in some natural way linearly ordered atomic parts, ‘moments’, and combining an observation about the internal structure of moments with an epistemological doctrine about (...) our access to the past. The epistemological doctrine, which I'll call ‘Presentism’, following Butterfield, is the view that our access to the past is mediated by records, or local representations, of it. The observation is that the state of the world at any moment has the structure of what Barbour calls a ‘time capsule’, which is to say that it constitutes a partial record of its past, it is pregnant with interrelated mutually consistent representations of its own history. (shrink)

A version of relationism that takes spatiotemporal structures—spatial geometry and a standard of inertia—to supervene on the history of relations between bodies is described and defended. The account is used to explain how the relationist should construe models of Newtonian mechanics in which absolute acceleration manifestly does not supervene on the relations; Ptolemaic and Copernican models for example. The account introduces a new way in which a Lewis-style ‘best system’ might capture regularities in a broadly Humean world; a defence is (...) given against a charge of indeterminism that applies to any such approach to laws. (shrink)

Numerous approaches to a quantum theory of gravity posit fundamental ontologies that exclude spacetime, either partially or wholly. This situation raises deep questions about how such theories could relate to the empirical realm, since arguably only entities localized in spacetime can ever be observed. Are such entities even possible in a theory without fundamental spacetime? How might they be derived, formally speaking? Moreover, since by assumption the fundamental entities cannot be smaller than the derived and so cannot ‘compose’ them in (...) any ordinary sense, would a formal derivation actually show the physical reality of localized entities? We address these questions via a survey of a range of theories of quantum gravity, and generally sketch how they may be answered positively. (shrink)

On one popular view, the general covariance of gravity implies that change is relational in a strong sense, such that all it is for a physical degree of freedom to change is for it to vary with regard to a second physical degree of freedom. At a quantum level, this view of change as relative variation leads to a fundamentally timeless formalism for quantum gravity. Here, we will show how one may avoid this acute ‘problem of time’. Under our view, (...) duration is still regarded as relative, but temporal succession is taken to be absolute. Following our approach, which is presented in more formal terms in, it is possible to conceive of a genuinely dynamical theory of quantum gravity within which time, in a substantive sense, remains. 1 Introduction1.1 The problem of time1.2 Our solution2 Understanding Symmetry2.1 Mechanics and representation2.2 Freedom by degrees2.3 Voluntary redundancy3 Understanding Time3.1 Change and order3.2 Quantization and succession4 Time and Gravitation4.1 The two faces of classical gravity4.2 Retaining succession in quantum gravity5 Discussion5.1 Related arguments5.2 Concluding remarks. (shrink)

We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical dynamics of the system and must therefore be deemed inappropriate. We propose a new strategy for consistently quantizing systems with a relational notion of time that does capture the full classical dynamics of the system and allows for evolution parametrized by an equitable internal (...) clock. This proposal contains the minimal temporal structure necessary to retain the ordering of events required to describe classical evolution. In the context of shape dynamics (an equivalent formulation of general relativity that is locally scale invariant and free of the local problem of time) our proposal can be shown to constitute a natural methodology for describing dynamical evolution in quantum gravity and to lead to a quantum theory analogous to the Dirac quantization of unimodular gravity. (shrink)

This paper sets out a moderate version of metaphysical structural realism that stands in contrast to both the epistemic structural realism of Worrall and the—radical—ontic structural realism of French and Ladyman. According to moderate structural realism, objects and relations (structure) are on the same ontological footing, with the objects being characterized only by the relations in which they stand. We show how this position fares well as regards philosophical arguments, avoiding the objections against the other two versions of structural realism. (...) In particular, we set out how this position can be applied to space-time, providing for a convincing understanding of space-time points in the standard tensor formulation of general relativity as well as in the fibre bundle formulation. (shrink)

The paper points out that the modern formulation of Bohm’s quantum theory known as Bohmian mechanics is committed only to particles’ positions and a law of motion. We explain how this view can avoid the open questions that the traditional view faces according to which Bohm’s theory is committed to a wave-function that is a physical entity over and above the particles, although it is defined on configuration space instead of three-dimensional space. We then enquire into the status of the (...) law of motion, elaborating on how the main philosophical options to ground a law of motion, namely Humeanism and dispositionalism, can be applied to Bohmian mechanics. In conclusion, we sketch out how these options apply to primitive ontology approaches to quantum mechanics in general. (shrink)

Quantum philosophy, a peculiar twentieth-century malady, is responsible for most of the conceptual muddle plaguing the foundations of quantum physics. When this philosophy is eschewed, one naturally arrives at Bohmian mechanics, which is what emerges from Schrodinger's equation for a nonrelativistic system of particles when we merely insist that 'particles' means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. The quantum formalism emerges when measurement situations are (...) analyzed according to this theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with quantum theory simply evaporate.Bohr's ... approach to atomic problems ... is really remarkable. He is completely convinced that any understanding in the usual sense of the word is impossible. Therefore the conversation is almost immediately driven into philosophical questions, and soon you no longer know whether you really take the position he is attacking, or whether you really must attack the position he is defending. (shrink)

In Dirac-Bergmann constrained dynamics, a first-class constraint typically does not _alone_ generate a gauge transformation. By direct calculation it is found that each first-class constraint in Maxwell's theory generates a change in the electric field E by an arbitrary gradient, spoiling Gauss's law. The secondary first-class constraint p^i,_i=0 still holds, but being a function of derivatives of momenta, it is not directly about E. Only a special combination of the two first-class constraints, the Anderson-Bergmann -Castellani gauge generator G, leaves E (...) unchanged. This problem is avoided if one uses a first-class constraint as the generator of a _canonical transformation_; but that partly strips the canonical coordinates of physical meaning as electromagnetic potentials and makes the electric field depend on the smearing function, bad behavior illustrating the wisdom of the Anderson-Bergmann Lagrangian orientation of interesting canonical transformations. The need to keep gauge-invariant the relation dot{q}- dH/dp= -E_i -p^i=0 supports using the primary Hamiltonian rather than the extended Hamiltonian. The results extend the Lagrangian-oriented reforms of Castellani, Sugano, Pons, Salisbury, Shepley, _etc._ by showing the inequivalence of the extended Hamiltonian to the primary Hamiltonian even for _observables_, properly construed in the sense implying empirical equivalence. Dirac and others have noticed the arbitrary velocities multiplying the primary constraints outside the canonical Hamiltonian while apparently overlooking the corresponding arbitrary coordinates multiplying the secondary constraints _inside_ the canonical Hamiltonian, and so wrongly ascribed the gauge quality to the primaries alone, not the primary-secondary team G. Hence the Dirac conjecture about secondary first-class constraints rests upon a false presupposition. The usual concept of Dirac observables should also be modified to employ the gauge generator G, not the first-class constraints separately, so that the Hamiltonian observables become equivalent to the Lagrangian ones such as the electromagnetic field F. (shrink)

The most puzzling issue in the foundations of quantum mechanics is perhaps that of the status of the wave function of a system in a quantum universe. Is the wave function objective or subjective? Does it represent the physical state of the system or merely our information about the system? And if the former, does it provide a complete description of the system or only a partial description? We shall address these questions here mainly from a Bohmian perspective, and shall (...) argue that part of the difficulty in ascertaining the status of the wave function in quantum mechanics arises from the fact that there are two different sorts of wave functions involved. The most fundamental wave function is that of the universe. From it, together with the configuration of the universe, one can define the wave function of a subsystem. We argue that the fundamental wave function, the wave function of the universe, has a law-like character. (shrink)

We derive for Bohmian mechanics topological factors for quantum systems with a multiply-connected configuration space Q. These include nonabelian factors corresponding to what we call holonomy-twisted representations of the fundamental group of Q. We employ wave functions on the universal covering space of Q. As a byproduct of our analysis, we obtain an explanation, within the framework of Bohmian mechanics, of the fact that the wave function of a system of identical particles is either symmetric or anti-symmetric.