Abstract
In the philosophy of space and time, the “territory” is, of course, the ontology of space and time (i.e., its nature or being), whereas the principal “map” is the substantivalism (or absolutism) versus relationism dichotomy.
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Notes
- 1.
Throughout the remainder of our investigation, unless otherwise noted, the terms “space” and “spatial” will be used to designate both the standard 3-dimensional space as well as the 4-dimensional spacetime conception in modern relativity physics.
- 2.
The following abbreviations will be used for various cited works: AG = Leibniz (1989); NE = Leibniz (1996), referenced with book, chapter, section; N = Newton (2004); L = Leibniz and Clarke Leibniz (2000) (Leibniz letter), referenced with letter number and section; C = Leibniz and Clarke Leibniz (2000) (Clarke letter), referenced with letter number and section; Lm = Leibniz (1969).
- 3.
In the correspondence with Des Bosses, Leibniz states that “I hold every absolute to be substantial [a substance]” (Lm 608). Hence, “space as absolute being” is identical to “space as substance” as well.
- 4.
For the committed relationist, the vacuum solutions to GR without gravity waves might seem to undermine the suggestion made by Earman and Norton, since the absence of gravity waves means that there is no energy to convert into particles, etc. However, since the spacetime would still possess the capacity to generate waves, it is unclear that there is any real difference in this case for those who side with Einstein’s hypothesis that the g field is a physical field. A relationist could also accept Harré’s suggestion that the vacuum solutions to the field equations of GR have “no reasonable physical interpretations” (Harré 1986, 131), but this seems a rather unwarranted strategy since, as explained above, the vacuum solutions are mathematically meaningful. Some authors have attempted to account for the gravitational field, g, using the motions of point particles alone (Vasallo and Esfeld 2016), but the recent discovery of gravitational waves over the past few years completely undermines this approach. In the LIGO measurements from 2016, two black holes combined but lost roughly 3 solar masses that were converted into gravity waves. Hence, gravity waves exist, and so the claim by these authors, that an empty universe with gravity waves is merely “mathematical surplus structure” (Vasallo and Esfeld 2016, 104) is untenable. But there is an even more problematic issue at stake: Are Vasallo and Esfeld committed to the view that gravity waves exist if there is a particle somewhere in the universe that can be influenced by these waves, but that those same gravity waves just disappear if that particle is removed? This would be a highly implausible interpretation, needless to say.
- 5.
“Mach-lite” is the standard anti-substantivalist rejection of substantival space for a relationally acceptable alternative, such as the fixed stars, or, better yet, the center-of-mass reference frame of the world, which Mach stipulates must not accelerate (Mach 1960, 287). The most significant problem for Mach-heavy is the fact that the boundary conditions of GR’s field equations are not totally determined by T, but have to be specified with respect to a choice of g as well. Hence, Mach-heavy seems inconsistent with the mathematical structure of GR. Brown (2017) attempts to defend a substantivalist interpretation of the metric in GR by invoking the universe’s expansion: “If the universe expands but there is no material object expanding and there is no rearrangement of material objects relative to one another, then something non-material expands. This something is obviously space” (2017, 86). But, as Rovelli makes clear in the quotation above, “the metric/gravitational field has acquired most, if not all, the attributes that have characterized matter (as opposed to spacetime)”, so the claim that the metric, g, is non-material is simply untenable (and it also begs the question against the metric field relationist)
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Slowik, E. (2018). Substantivalism and Relationism as Bad Cartography: Why Spatial Ontology Needs a Better Map. In: Wuppuluri, S., Doria, F. (eds) The Map and the Territory. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-319-72478-2_10
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