Endurantism, Perdurantism and Special Relativity

The Philosophical Quarterly, Vol. , No. October ISSN – ENDURANTISM, PERDURANTISM AND SPECIAL RELATIVITY B S D. H T A. J There are two main theories about the persistence of objects through time. Endurantists hold that objects are three-dimensional, have only spatial parts, and wholly exist at each moment of their existence. Perdurantists hold that objects are four-dimensional, have temporal parts, and exist only partly at each moment of their existence. We argue that endurantism is poorly suited to describe the persistence of objects in a world governed by special relativity, and it can accommodate a relativistic world only at a high price not worth paying. Perdurantism, on the other hand, fits beautifully with our current scientific understanding of the world. We use only the implications of the Lorentz transformations, without appeal to geometrical interpretations, dimensional analogies or auxiliary premises like temporal eternalism. I. INTRODUCTION Philosophical puzzles about the persistence and change of physical objects have received much recent attention from metaphysicians. There are two main competing theories about how non-momentary objects relate to time: endurantism (or three-dimensionalism), and perdurantism (or four- dimensionalism). David Lewis roughly characterizes these terms thus: Let us say that something persists iff, somehow or other, it exists at various times; this is the neutral word. Something perdures iff it persists by having different temporal parts, or stages, at different times, though no part of it is wholly present at more than one time; whereas it endures iff it persists by being wholly present at more than one time.1 Endurantism, then, is the view that objects have three spatial dimensions and move through time. Persistence in three dimensions means that an object is at one time, then the next time, then the next time, and so on; things are wholly present at each time at which they exist. An object that is here now is entirely here now, and only here now. Nothing that is a part of an object now is somehow still around in the past, or waiting for us in the 1 D. Lewis, On the Plurality of Worlds (Oxford: Blackwell, ), p. © The Editors of The Philosophical Quarterly, . Published by Blackwell Publishing, Garsington Road, Oxford , UK, and Main Street, Malden, , USA. ENDURANTISM, PERDURANTISM AND SPECIAL RELATIVITY future. The second approach, perdurantism, is the denial of endurantism: objects are not wholly present at each time at which they exist. This may be positively characterized as the view that objects are composed of so-called temporal parts. When we see an object here and now, we are seeing the parts of it that are now – but there are other parts of it at other times that we might have encountered or might yet encounter. The usual arguments on either side are a priori, and attempt to show that one or the other view solves more effectively mereological conundrums such as Heraclitus’ river, the ship of Theseus, the sorites paradox, and the like.2 Recently there has been a revival of interest in whether there are a posteriori reasons to prefer perdurantism over endurantism, and in particular whether Einstein’s theory of special relativity (hereafter SR) supports a temporal-parts ontology. We shall argue that while endurantism can be reworked so as to be consistent with SR, the result is a profligate, Byzantine ontology with few redeeming qualities. Perdurantism, on the other hand, has a natural and elegant fit with the physical facts of our world. Philosophers who have considered the relationship of SR to the meta- physics of persistence have thought that either () SR has no relevance to the purely a priori endurantism debate, or () SR undermines endurantism, but only if one can first establish intermediate propositions, for example, that temporal eternalism is true, or that Minkowski space-time is the correct geometrical interpretation of SR. We shall argue that both () and () are false. The empirical inseparability of space and time under SR is quite relevant to the nature and persistence of objects. We contend that given the uncontroversial central theses of SR, namely, (i) physics is the same in all inertial reference frames, and (ii) the speed of light in a vacuum is a constant, endurantism, an ontology more suited to an outmoded Galilean relativity, is revealed as inadequate to what are generally regarded as the facts of our Einsteinian world. Furthermore, our conclusions will not depend on the debate over eternalism or the findings of differential geometers. We are well aware that not everyone accepts (i) and (ii). Around the time Einstein developed special relativity, various scientists investigated various non-relativistic alternatives, particularly an æther compensatory theory. 2 Those who defend perdurantism in this way include W.V.O. Quine, ‘Identity, Ostension, and Hypostasis’, Journal of Philosophy, (), pp. –; D.M. Armstrong, ‘Identity through Time’, in P. van Inwagen (ed.), Time and Cause (Dordrecht: Reidel, ), pp. –; M. Heller, The Ontology of Physical Objects (Cambridge UP, ); T. Sider, Four-Dimensionalism (Oxford UP, ). A priori defenders of endurantism include R. Chisholm, Person and Object (La Salle: Open Court, ); J.J. Thomson, ‘Parthood and Identity across Time’, Journal of Philosophy, (), pp. –; J. Van Cleve, ‘Mereological Essentialism, Mereological Conjunctivism, and Identity through Time’, in P. French et al. (eds), Midwest Studies in Philosophy, Vol. (Univ. of Minnesota Press, ), pp. –; P. van Inwagen, ‘Four-Dimensional Objects’, Noûs, (), pp. –. © The Editors of The Philosophical Quarterly, STEVEN D. HALES AND TIMOTHY A. JOHNSON Often associated with this view are Henri Poincaré and H.A. Lorentz. However, even they were hardly devoted defenders of the æther. For example, in La science et l’hypothèse (), Poincaré writes ‘We don’t care whether the æther really exists ... a day will doubtless come when the æther will be discarded as useless’. Similarly, Lorentz, in his Columbia Lectures of , gives Einstein credit ‘for making us see, in the negative result of ex- periments like those of Michelson, Rayleigh, and Brace, not a fortuitous compensation of opposing effects, but the manifestation of a general and fundamental principle’.3 This ‘fundamental principle’ is of course Einstein’s principle of relativity, the first premise of special relativity, and accepted as canonical among the vast majority of physicists for the past century. Here we simply register our agreement with, and acceptance of, the established view. In §II we give a quick sketch of the features of SR relevant to issues of persistence. In §III we canvass the recent literature addressing the relationship of SR to endurance vs perdurance, and show that it does not quite get matters right. In §IV we present our own argument that endurantism should be rejected in the light of SR. In §V we offer our conclusion. II. SPECIAL RELATIVITY AND THE LORENTZ TRANSFORMATION Special relativity, when it was introduced almost years ago, profoundly changed scientists’ understanding of space and time. Without developing the theory and its results in detail, we shall briefly outline those aspects of SR that are fundamental to our argument: the relationship between the temporal and spatial co-ordinates of objects in inertial reference frames in relative motion. Within a local approximation, at least, the universe is governed by special relativity. The geometry of space-time, as understood within general relativity, is a four-dimensional space-time manifold, curved by the presence of mass. The local approximation is a region of that space small enough to approximate the flat space-time of special relativity. (This is analogous to treating the surface of the earth as if it were flat, a good approximation of human-scale interactions with the earth.) In a world governed by SR, co- ordinates in different inertial reference frames are related through the Lorentz transformation. The Lorentz transformation falls naturally out of the two fundamental premises of SR, and derivations or demonstrations can 3 Both these quotations are cited from R. Torretti, Relativity and Geometry (New York: Dover, ), pp. , . © The Editors of The Philosophical Quarterly, ENDURANTISM, PERDURANTISM AND SPECIAL RELATIVITY be found in any number of introductory texts on special relativity.4 We shall consider two reference frames in relative motion in a spatial direction which we identify with the x-axis in both frames; the constant relative velocity is v. It is not possible to determine which frame is in motion and which is ‘at rest’, but both frames agree on their relative velocity. If we take a point in space-time which, in one reference frame, has spatial co-ordinates x, y and z and temporal co-ordinate t, the Lorentz transformation allows us to determine the co-ordinates of that point in the other reference frame. The Lorentz transformation for the space and time co-ordinates of these reference frames can be expressed thus: x = γ(x´ + β(ct´)) y = y´ z = z´ t = γ(ct´ + βx´) where the primed co-ordinates are the co-ordinates as measured in the other frame, c is the speed of light, β = (v/c), and γ = ( – β2)–½. (|β| is always less than , since nothing can move faster than light, and thus γ is always greater than . For a relative velocity of approximately ⋅c, β2 = ⋅, and γ = .) We shall examine a few special cases of these transformations. First, simultaneous measurements of a distance in one frame from the other frame: ∆x = γ∆x´. That is, a distance measured in one frame is measured smaller in a frame moving with respect to that frame: length contraction. Next, time elapsed at a fixed point: (c∆t) = γ (c ∆t´). In the time it takes a clock in one frame to tick off one second, a clock in a frame moving with respect to that frame will have ticked off less than one second: time dilation.

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