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Philosophy of Space and Expanding Universe in G. J. Whitrow

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Abstract

One of the few authors to have explicitly connected the physical issue of the expansion of the universe with the philosophical topic of the metaphysical status of space is Gerald James Whitrow. This paper examines his view and tries to highlight its strong and weak points, thereby clarifying its obscure aspects. In general, this really interesting philosophical approach to one of the most important phenomena concerning our universe, and therefore modern cosmology, has been very rarely tackled. This unicity increases the value, from a physical, philosophical and historical point of view, of Whitrow’s attempt and calls for new research.

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Notes

  1. Also the philosophical terminology has partially changed: the more recent term “substantivalism” is adopted instead of “absolutism”. Both designate realist views on space, but the former has an Einsteinian “flavour” (space is a sort of substance influenced by matter), whereas the latter has a Newtonian, but physically outdated, “overtone” (space is an immutable entity).

  2. The exceptions are few. For example: Baryshev and Teerikorpi (2002, sect. 12.4.1), Misner et al. (1973, pp. 739–740), Schutz (2003, p. 365).

  3. I will quote and comment on only the second edition, but the parts I am interested in here are practically identical in the first edition (§ V.4). In order to better elucidate Whitrow’s view on this topic, I also examined all his books (Bondi et al. 1960; Jones et al. 1956; Whitrow 1949,1959; 1967; 1972; 1980; 1988) and most of his papers, unfortunately without finding any comments related to the philosophy of space.

  4. According to Misner et al. (1973, p. 740) “to speak of the ‘creation’ of space is a bad way of speaking [...]. The right way of speaking is to speak of a dynamic geometry”. It is true that the term “creation”, and similars, does not smack of “good science”, but I agree with Baryshev and Teerikorpi (2002, p. 197): “To say that space expands is close to saying that space is created. To the space within the Hubble radius a volume like that of our Local Group of galaxies is added every second. [...] There is the physical phenomenon of increasing volume, no matter which word, ‘expansion’ or ‘creation’, is used. If the distance between two galaxies increases, but the galaxies do not move inside space, then a natural way to understand this is that space emerges in the region between them”.

  5. Note that by “space structure”, Infeld and Schild mean “the curvature \(kR^{-2}(\tau )\) of the 3-space \(\tau \) = constant” (Infeld and Schild 1945, p. 251).

  6. For an introduction to these notions see Sect. 4.2.

  7. Infeld and Schild, in the paper quoted by Whitrow himself, more generally affirm: “By kinematical cosmology is usually understood that part of relativistic cosmology which deals with the metric form of our universe, characterized by a four-dimensional space-time manifold, and with the motion of free particles and light rays in this universe” (Infeld and Schild 1945, p. 250). So kinematical cosmology ignores the dynamical aspects of cosmology, namely “the connection between the Riemannian curvature tensor on the one hand and the energy-momentum tensor on the other” (ibid.).

  8. Significantly, Whitrow, in the book under scrutiny here, speaks exclusively of the Doppler shift. Actually, in just one case (p. 296) he uses the formula of the cosmological redshift, i.e. the so-called Lemaître’s equation, in which redshift is determined by the ratio of the scale factors (giving the variations in size of the metric) at emission and reception of the electromagnetic wavelength. But he does not attach any importance to such an equation, neither in terms of the physical phenomenon underlying it, nor in terms of its possible philosophical consequences.

  9. I am thinking here of the “traditional” Leibnizian view of relationism, i.e. the one Whitrow initially refers to. I will also briefly consider those somewhat more “slippery” positions which, by accepting the existence of a space(time) ontologically dependent on matter, tend to blur the traditional metaphysical distinction between relationism and absolutism/substantivalism, in particular with regard to the separation between container and contained.

  10. As a reviewer interestingly underlines, according to Rugh and Zinkernagel (2009), the vacuum solutions cannot provide a material basis for the physical time (or length) scale, so that, without such a scale, the very idea of the expansion could be undermined. This is a deep issue and would deserve closer and longer inspection. However, I am not completely convinced that the time duration is the only way to capture the expansion and I suspect that other factors, such as the time order and the curvature given by the cosmological constant, could do it.

  11. This is not the place to go into the details or the possible criticisms of this view. I will cover these aspects in another paper.

  12. Remember that Whitrow was, with A. G. Walker, Milne’s main collaborator from 1932 to 1950, particularly in the development of this cosmological model.

  13. See, for instance, Milne (1934). For a brief overview of Milne’s view on space see Macchia (2014, sect. 7).

  14. For an example see Friedman (1983, p. 32).

  15. Coleman and Korté (1980) and Nerlich (1994, pp. 216–218), for instance, think that conventionalism is defeated, whereas Sklar (1985, pp. 129–149) sees no reason for this conclusion.

  16. For example, see Bondi (1960), Narlikar (2010), Pauri (1995), Raychaudhuri (1979).

  17. Note that small-scale objects (galaxies, planets, etc.) have chaotic peculiar motions. Nonetheless, their very low velocities (less than one-thousandth of the light velocity in the vacuum \(c\)) make them negligible when compared to the large-scale recessional velocities of clusters (comparable to \(c\)).

  18. Although the particles of EPS and of Weyl’s Principle are conceptually similar, I am not claiming that this inverse approach should necessarily be that of EPS, nor that an inverse approach is immune to problems (see, for instance, Macchia 2011). Mine is just a qualitative not a quantitative analysis in order to meet Whitrow’s standpoint.

  19. Milne (1948, p. 8).

  20. I think that North deduces his consideration from the following reflection. With regards to the “weak view”, when one looks at “the material correlates of the fundamental particles” rather than at the particles themselves, as he says, one finds that the real universe does not possess at least one important characteristic of the substratum: continuity. It is the continuity that would make such a space (deduced from the fundamental particles) a set of relata devoid of spatial relations (as in the “strong view”) due to the continuous distribution of fundamental particles considered like a fluid. But this distribution does not fit the real universe, where clusters form a discrete set, namely there is “space” (or void, or, in a sense, only spatial relations) among clusters. Thus, this weak view is, as it were, purely relational. Instead, with regards to the “strong view”, this discreteness problem does not subsist insofar as only the material correlates (not the voids among them) of the universe are taken into account to identify space, so that space is a kind of “almost Cartesian” plenum coming from the continuity of matter itself. However, let me remark that in the Cartesian view the identification between matter and space seems completely arbitrary.

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Acknowledgments

This work was completed with the assistance of the Government of Canada. I am also grateful to Chris Smeenk and his students in the Rotman Institute’s cosmology group for some helpful comments on an earlier draft of this paper. Finally, I thank the anonymous referees for their helpful remarks.

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Macchia, G. Philosophy of Space and Expanding Universe in G. J. Whitrow. Found Sci 20, 233–247 (2015). https://doi.org/10.1007/s10699-014-9363-1

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