We study a long-recognised but under-appreciated symmetry called dynamical similarity and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a system where the unit of Hamilton’s principal function is rescaled, and therefore represent a kind of dynamical scaling symmetry with formal properties that differ from many standard symmetries. To study this symmetry, we develop a general framework for symmetries that distinguishes the observable and surplus structures of a theory by using the (...) minimal freely specifiable initial data for the theory that is necessary to achieve empirical adequacy. This framework is then applied to well-studied examples including Galilean invariance and the symmetries of the Kepler problem. We find that our framework gives a precise dynamical criterion for identifying the observables of those systems, and that those observables agree with epistemic expectations. We then apply our framework to dynamical similarity. First we give a general definition of dynamical similarity. Then we show, with the help of some previous results, how the dynamics of our observables leads to singularity resolution and the emergence of an arrow of time in cosmology. (shrink)

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)

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 argue that the fundamental assertion underlying Mach's critique of Newton's first law is that inertial motion is not motion in the absence of causes; rather, it is motion whose cause lies in some homogeneous aspect of the environment. We distinguish this formal requirement (Mach's principle) from two hypotheses which Mach considers concerning the origin of inertia: that the distant stars play (1) a merely “collateral” or (2) a “fundamental” role in the causal determination of inertial motion. -/- In his (...) later writings, Mach deliberately avoids referring to the concept of causation, and indeed, this has made the interpretation of Mach's principle a subject of widespread controversy. However, in his earlier writings, the substance of Mach's critique is less ambiguously expressed. Therefore, close attention is given to Mach's early writings and the evolution of his thought. Various accounts in the secondary literature on Mach's principle, in particular those of Norton and DiSalle, are assessed on this basis. We end with a defence of the Machian status and legitimacy of the early Einstein's research program. (shrink)

Substantivalists believe that spacetime and its parts are fundamental constituents of reality. Relationalists deny this, claiming that spacetime enjoys only a derivative existence. I begin by describing how the Galilean symmetries of Newtonian physics tell against both Newton's brand of substantivalism and the most obvious relationalist alternative. I then review the obvious substantivalist response to the problem, which is to ditch substantival space for substantival spacetime. The resulting position has many affinities with what are arguably the most natural interpretations of (...) special and general relativity. I move on to consider and reject two recent antisubstantivalist lines of thought. The interim conclusion is that the best argument for relationalism is an appeal to Ockham's razor. However, for this to be successful there must be genuine relationalist theories that share the theoretical virtues of their substantivalist rivals but without the additional ontological commitment. The bulk of the paper is therefore an investigation of various concrete relationalist proposals. I distinguish three options for the relationalist in the face of the success of Galilean invariant physics and trace how these generalise to relativistic physics. One of the options is particularly promising but, since its basic objects end up being spacetime points, this does not help the prospects of relationalism as traditionally conceived. I end with some reflections on the fate of substantivalism in the aftermath of the Hole Argument, concluding that we have as yet to be given good reasons to abandon the natural, substantivalist interpretation of current physics. (shrink)

After a brief introduction to issues that plague the realization of a theory of quantum gravity, I suggest that the main one concerns defining superpositions of causal structures. This leads me to a distinction between time and space, to a further degree than that present in the canonical approach to general relativity. With this distinction, one can make sense of superpositions as interference between alternative paths in the relational configuration space of the entire Universe. But the full use of relationalism (...) brings us to a timeless picture of Nature, as it does in the canonical approach. After a discussion of Parmenides and the Eleatics' rejection of time, I show that there is middle ground between their view of absolute timelessness and a view of physics taking place in timeless configuration space. In this middle ground, even though change does not fundamentally exist, the illusion of change can be recovered in a way not permitted by Parmenides. It is recovered through a particular density distribution over configuration space which gives rise to 'records'. Incidentally, this distribution seems to have the potential to dissolve further aspects of the measurement problem that can still be argued to haunt the application of decoherence to Many-Worlds quantum mechanics. I end with a discussion indicating that the conflict between the conclusions of this paper and our view of the continuity of the self may still intuitively bother us. Nonetheless, those conclusions should be no more challenging to our intuition than Derek Parfit's thought experiments on the subject. (shrink)