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Compact spaces and privileged times; what the video game asteroids can teach us about the present

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Abstract

The A-Theory of time has long struggled with the results of special relativity. One proposed solution is to stipulate the existence of a physically or metaphysically privileged frame which defines the global present for all observers. Recently this proposal has cropped up in literature on spatially closed universes (SCUs) which seem to naturally instantiate such structures. This paper examines the privileged frame proposal through the lens of SCUs, arguing that even in these space-times which seem overwhelmingly friendly to A-theoretic accounts the theory face insurmountable challenges.

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Notes

  1. There are a number of different ways this can be cashed out, ranging from theories which hold that all past, present and future events exist but only present objects are ‘metaphysically real’ (Moving Spotlight), that the present converts a non-existing future into an existing past (Growing Block), or that only the present exists (Presentism). On all accounts it is critical that the present be metaphysically distinct from the past and future such that it possesses the property of being ‘now’. (Emery et al., 2020).

  2. None of these are necessary properties of such universes. Time could also be circular, for example, or space curved. For this paper, however, I follow the topologies used by previous authors including Weeks (2001), Peters (1983), and Luminet (2009)

  3. It should be noted here that the sudden discontinuity in x-coordinates is an artifact of the metric we are using, and is no more significant than the fact that people standing on the line of zero longitude on our own planet seem to be able to step from 0◦ to 360◦.

  4. I am hesitant to use this language as it implies there is something special about the points of identification within the universe. Recall, however, that this is a remnant of the metric being used, and the location of the discontinuity is a matter of convenience and choice rather than a real break in the world.

  5. It is worth noting that even though we have a system with significant restrictions on the Cauchy surfaces available, there are still multiple viable Cauchy surfaces for Alice’s frame. ‘Wavy’ surfaces, for example, are still valid solutions provided they never have an angle greater than 45◦ from the xc direction.

  6. This is in contrast with theories like cosmic time which, in some cases, attempt to define a universal present by methods like the statistical averaging of galactic motion, or the mean motion of the cosmic background radiation (Bourne, 2004; Swinburne, 2007).

  7. Many thanks to a reviewer who pointed out that in the presence of generic curvature radar synchronisation often does remain useful as demonstrated by Perlick (2008).

  8. It is worth noting that there does exist some literature within physics on our ability to determine large-scale topological features using local properties, but most of it focus on orientability (Bielińska & Read, 2023) or mapping the cosmic background radiation (Gomero, Mota, & Reboucas, 2016).

  9. This objection has also been raised for cosmic time, which suffers similar weaknesses (Read & Qureshi-Hurst, 2021).

  10. There are other types of cosmic time which get used in the literature. See Smeenk (2013) for a good overview. Here I am using Swinburne’s (2007) one, however, because it is simple, easy to intuit, and clearly demonstrates the property I am trying to highlight.

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Acknowledgements

Many thanks to Craig Callender for his help in refining this paper, and to the anonymous reviewer who gave such helpful and detailed feedback.

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  1. McCoy Family Center for Ethics in Society, Stanford University, 450 Jane Stanford Way, Palo Alto, CA, 94305, USA

    Ann C. Thresher

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Thresher, A.C. Compact spaces and privileged times; what the video game asteroids can teach us about the present. Synthese 202, 161 (2023). https://doi.org/10.1007/s11229-023-04325-w

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