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This article provides a new context for an established metaphysical debate regarding the problem of persistence. I contend that perdurance, a popular view about persistence which maintains that objects persist by having temporal parts, can be formulated in quantum mechanics due to the existence of a formal analogy between temporal and spatial location. However, this analogy fails due to a ‘no-go’ result which demonstrates that quantum systems cannot be said to have temporal parts in the same way that they have spatial parts. Therefore, if quantum mechanics describes persisting physical objects then those objects cannot be said to perdure.

This paper investigates the use of theories of mechanics (classical and quantum) to provide answers to questions in the metaphysics of spatial location and persistence. Investigating spatial location, I find that in classical physics bodies pertend the region of space at which they are exactly located, while a quantum system spans a region at which it is exactly located. Following this analysis, I present a 'no-go' result which shows that quantum mechanics (conventionally interpreted) restricts the available options for locational persistence theories in an interesting way: it demonstrates that the spatiotemporal path of a persisting thing is discrete (or discontinuous) in time. This leads to unpalatable consequences for both perdurantists and endurantists. In particular, I argue that Butterfield's 'anti-pointilliste' perdurantism is ruled out, and show that endurantists relying on immanent causation run into trouble. I conclude by suggesting the revival of Whitehead's alternative mode of persistence called 'reiteration.'

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First I want to thank Prof. Fleming for his detailed, thoughtful, and thought-provoking remarks, and particularly for his generous advice on how to improve successive versions of the conference paper presented here in its final form. While our continuing correspondence has led to something of a convergence of views, there are several differences of opinion that resist this reconciliation. In this reply I will present my side of two of these remaining disputes, which are particularly relevant for understanding how accepting my account of event time observables (sketched in the final section of the paper) leads to a distinctive view of quantum theory. The core of what is distinctive about my view is that it restores a certain symmetry between time and space with respect to what is observable according to the theory. The empirical motivation for this view is that often the outcomes of an experiment may be located in time as well as in space. The theoretical consequence of this view is that time covariant POVMs must be provided which have this specific empirical interpretation.