Buckets of Water and Waves of Space

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1 by Tim Maudlin 1. Introduction Maudlin reviews the substantivalism/relationism controversy. This material should seem quite familiar. 2. The Bucket Newton s bucket and the two globes arguments are rehearsed, with Maudlin taking them to be arguments for the existence of absolute space. Relationists are challenged to account for the

2 results of the experiment without postulating absolute space. But what tools are they allowed to use? What relations (and what forms of construction, one might add) are relationists allowed to invoke? Suppose one believes that the only spatiotemporal facts are facts about the temporal duration between events and about the spatial distance between material bodies at a given time. (186) Given this stock of relations, relationists cannot account for the various tensions in the cord between the globes when (as we say) they rotate at various speeds. But if in addition to the relations mentioned above we add distance relations between nonsimulteneous events, then we have a view Maudlin calls Newtonian relationism. This view: (1) would avoid one of Leibniz s objections against Newtonian substantivalism (187) [the argument that substantivalism requires the existence of a 2

3 multitude of empricially equivalent but physically distinct situations] and (2) It demonstrates that Newton s bucket argument is not effective against relationism per se. (187) 3. The Relationist Counterattack. There are two relationist arguments that are often conflated but, according to Maudlin, are quite distinct. The static Leibniz shift argument. The whole world might have existed with everything shifted some distance d (in the same direction) from where it is now. The kinematic Leibniz shift. The whole world may be moving with any constant velocity v with respect to space (as Newton conceived it). It is typically argued that in both cases substantivalists must say that there are infinitely many distinct models of Newtonian dynamics while relationists are unable, and usually unwilling, to distinguish them. 3

4 As we have seen before, if it is only relations between bodies that are empirically determinable, then substantivalists are forced to embrace the existence of many empirically indistinguishable models, possibly violating P IdIn and/or the Principle of Sufficient Reason (PSR). In short, both the static and kinematic shifts, if real possibilities, would result in ontologically distinct but observationally indistinguishable states of affairs, and these are supposed to be metaphysically objectionable. (189) Maudlin thinks that the kinematic shift argument shows that Newton must postulate that the universe has a physically real but empirically inaccessible property (190), but he claims that the static shift argument shows no such thing. Various positional states of the universe as a whole are possible: It could be created so my desk is here, or three meters north of here, or 888 meters from here in the direction from Earth to Betelgeuse, and so on. Which is the actual state of the world? Now the answer is easy: In its actual state, my desk is here, not three meters north or anywhere else. So in the kinematic case, 4

5 unlike the static case, sensible physical questions can be asked but cannot be answered by observations. To even formulate the appropriate question in the static case one must indexically pick out a spatiotemporal location, and it is then no great trick to observe what material body that location actually contains. (190) But think back to Maudlin s fanciful scenario. After I indicate where my desk is--here!--god chloroforms me. Is Maudlin saying that when I wake up I can tell whether or not God has left everything where it was or moved everything, so that my desk is no longer at the spatial location that I indicated indexically before? How could I do this? Maudlin s reply is that we should eliminate the fanciful scenario, because (I suppose) it is fanciful. What we are left with is this: The world described by the shift may be qualitatively indistinguishable from the actual world in the sense that no purely qualitative predicate is true of the one which is false of the other. But we have more than purely qualitative vocabulary to describe the actual world; we have, for example, the 5

6 indexicals, without which the Leibniz shift cannot be described. So in the context of the static shift, the PII is of no use. (191) Maudlin thinks the crux of the matter is that indexicals can be used to pick out spatial locations in the actual world, and then we can formulate counterfactual assertions about these locations. We can also be assured that they are counterfactuals, that they do not describe the world as it is. (190) He states his view in a very evocative way. For the substantivalist, terms such as here or now can be used to drive linguistic pegs into the fabric of absolute space and time. Without such pegs, that static Leibniz shift cannot even be formulated. (191) In the case of the kinematic shift, only the PSR is relevant. To counter it, substantivalists can retreat to neo-newtonian spacetime in which, as we have seen, the notion of absolute velocity does not make sense. 4. Some New Arguments Maudlin argues that substantivalists can escape 6

7 the kinematic shift arguments by changing from full Newtonian to neo-newtonian spacetime. Relationists have a hard time mimicking this move. And Maudlin endorse Hartry Field s argument that in this case relationists are stuck with an ideology consisting of an infinite set of primitive distance predicates. 5. The Special Theory In Minkowski spacetime, relationism fares well. There is one basic relation, the interval. It is possible to embed the occupied points in M up to various symmetries in a way that makes it possible to do physics and and answer Leibnizian critisisms as well as substantivalists. 6. The Final Round In GR a relationist committed to a particle ontology inherits a hopeless task (199) because the geometry of a GR spacetime is not fixed independently of the matter in it. The set of all spatiotemporal relations between occupied event locations [which are all that are available to relationists] cannot generally provide enough information to uniquely settle the geometry of the embedding spacetime. (199) 7

8 The natural way for a relationist to cope with this difficulty is to switch to a field ontology and plenism. But then what is the difference between this view and substantivalism (since all points are occupied)? Even though substantivalism and plenist relationism are not per se mere notational variants, the difference between them becomes elusive to the point of evaporation in the context of the GTR. ((200) 7. Some Morals Nevertheless, Maudlin thinks that relationists have given up more than substantivalists in the dialectic that leads to the melding of the two views argued for in 6. The only plausible everywhere nonvanishing field, in Maudlin s view, is the metric tensor, and the metric tensor inherits all the merits and problems of space itself. The conception of spacetime at which we have arrived is much more the heir of Newton than of Leibniz. (202) Two final points: Modern physical theories are couched in terms of partial differential equations. Systems require continuous or non-gappy spacetime in order to evolve. This technical fact makes nonplenist relationism seem a decidedly uphill struggle. [And 8

9 anyway particle ontologies were outmoded by the end of the 19th century.] Second, the important advances in understanding or evaluating the substantivalist/relationist dispute have come from physics, not conceptual analysis. [Is this true for the Hole Argument? How clean is the separation when one is looking at foundational issues in physics?] So advances in physics may well change the complexion of this dispute in ways we cannot now anticipate. But so what? As always, we can only do the best with what physical and conceptual materials we have now. 9