Online research in philosophy

Using a model quantum clock, I show how the velocity of a relativistic particle can be measured. The results are used to analyse the long-standing problem of the velocity..

On stage theory, ordinary continuants are instantaneous stages which persist by exduring—by bearing temporal counterpart relations to other such stages. Exduring objects lack temporal extension and there is a sense in which they are wholly present at multiple instants. How then is exdurance different from endurance? I offer a definition of ‚exdurance’ that clearly sets it apart from other modes of persistence.

The rotating discs argument (RDA) against perdurantism has been mostly discussed by metaphysicians, though the argument of course appeals to ideas from classical mechanics, especially about rotation. In contrast, I assess the RDA from the perspective of the philosophy of physics. I argue for three main conclusions. The first conclusion is that the RDA can be formulated more strongly than is usually recognized: it is not necessary to ‘imagine away’ the dynamical effects of rotation. The second is that in general relativity, the RDA fails because of frame-dragging. The third conclusion is that even setting aside general relativity, the strong formulation of the RDA can after all be defeated, namely, by the perdurantist taking objects in classical mechanics (whether point-particles or continuous bodies) to have only temporally extended (i.e. non-instantaneous) temporal parts, which immediately blocks the RDA. Admittedly, this version of perdurantism defines persistence in a weaker sense of ‘definition’ than pointilliste versions that aim to define persistence assuming only instantaneous temporal parts. But I argue that temporally extended temporal parts (i) can do the jobs within the endurantism–perdurantism debate that the perdurantist wants temporal parts to do and (ii) are supported by both classical and quantum mechanics. Introduction The story so far 2.1 The RDA 2.2 Intrinsic properties and the idea of velocity 2.2.1 The intrinsic–extrinsic distinction 2.2.2 Velocity to the rescue? 2.3 ‘Naturalism’ 2.4 The accompaniments of rotation 2.5 Two kinds of reply: against the consensus Describing rotation 3.1 Rotation is kinematic 3.2 Beware of rigidity 3.3 An improved RDA: allowing the actual accompaniments 3.4 The RDA fails in general relativity Perdurantism without tears: the classical case 4.1 Rejecting instantaneous temporal parts 4.2 Replying to the RDA 4.2.1 ‘Kinematics’ 4.2.2 ‘Dynamics’ 4.2.3 An ‘anti-pointilliste’ objection and reply 4.3 Intrinsic properties of non-instantaneous temporal parts 4.3.1 Can the perdurantist appeal to them? 4.3.2 Temporal intrinsicality at an instant is rare 4.3.3 A better reason for temporal intrinsicality 4.4 Non-instantaneous parts can do the jobs 4.4.1 Humean supervenience revisited 4.4.2 The problem of change 4.4.3 Puzzles of coincidence 4.5 Instantaneous velocity is hardly extrinsic Support from decoherence in quantum theory 5.1 Classical and quantum: relativizing the intrinsic–extrinsic distinction 5.1.1 Unitarity: momentum as temporally intrinsic 5.2 Position and existence as nomically extrinsic.

There is a longstanding definition of instantaneous velocity. It saysthat the velocity at t 0 of an object moving along a coordinate line is r if and only if the value of the first derivative of the object's position function at t 0 is r. The goal of this paper is to determine to what extent this definition successfully underpins a standard account of motion at an instant. Counterexamples proposed by Michael Tooley (1988) and also by John Bigelow and Robert Pargetter (1990) are reinforced and illuminated by considering the presence or absence of changes to the object's motion.

In this essay, I first set out the principles of change, paying particular attention to the need for a support for all changes and to the need for prime matter. I then discuss the nature of time, arguing that time is not actually composed of durationless instants but that instants can be understood as limits to an infinite process of potential division. I then give a definition of instants in terms of intervals and propose a way of modeling them. In the next section I bring together the two previous sections by explaining change as an instantaneous process that does not involve actual instants. In the final section I draw out a larger metaphysical moral that emphasizes the role of potentiality and sees the potentiality in change and the potentiality in time as but different aspects of the same radical potentiality in nature.

Extending on an earlier paper [Found. Phys. Ltt., 16(4) 343–355, (2003)], it is argued that instants of time and the instantaneous (including instantaneous relative position) do not actually exist. This conclusion, one which is also argued to represent the correct solution to Zeno’s motion paradoxes, has several implications for modern physics and for our philosophical view of time, including that time and space cannot be quantized; that contrary to common interpretation, motion and change are compatible with the “block” universe and relativity; and that time, space, and space-time too, cannot exist. Instead, motion and change become the major players.

Frank Arntzenius has recently suggested that we should reject the standard view that the instantaneous state in classical mechanics consists of both the position and the velocity. In his view, the velocity as ordinarily defined-as the derivative of position with respect to time-cannot be genuinely instantaneous, and, thus, it should be excluded from the instantaneous state. After reviewing Bertrand Russell's traditional objections to the notion of an instantaneous velocity and suggesting that Russell's concerns can be effectively answered, I argue that Arntzenius' attempt to show that the standard definition of velocity fails to yield an instantaneous property is not compelling either. Although I review several suggestions that Arntzenius makes against the existence of instantaneous velocity, much of his case rests upon an intuition, which has also appeared in the work of David Albert, about what is required of genuine instantaneous states. I argue in part that there is no reason to accept this intuition, and, thus, no reason to revise standard physical practice when it comes to the classical, instantaneous state.