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Can time flow at different rates? The differential passage of A-ness

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Abstract

According to the No Alternate Possibilities (NAP) argument, (1) if time passes then the rate at which it passes could be different but (2) time cannot pass at different rates, and hence (3) time cannot pass. Typically, defenders of the NAP argument have focussed on defending premise (1), and have taken the truth of (2) for granted: they accept the orthodox view of rate necessitarianism. In this paper we argue that the defender of the NAP argument needs to turn her attention to (2). We describe a series of worlds that appear to contain differential passage: worlds where time passes at different rates in different subregions. If the NAP argument is to succeed, rate necessitarians must show that each of these worlds is either metaphysically impossible, or does not contain differential passage.

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Notes

  1. Hence, by temporal passage here we mean roughly what Skow (2015) means by robust (rather than anemic) temporal passage. Both these are to be contrasted with more recent deflationary views of passage which take passage to be something compatible with the truth of the B-theory. For instance, Savitt (2001, 2002) defends the view that temporal passage consists there being a sequence of temporally ordered events, and Maudlin (2007) defends the view that temporal passage consists in there being an intrinsic asymmetry in the temporal structure of the world. Leininger (2018) argues, contra Skow, that moving A-ness—i.e. robust passage, rather than anemic passage is the kind of passage that A-theorists ought want (though Leininger herself thinks that deflationary passage of the sort consistent with the B-theory deserves the name temporal passage).

  2. Notably, not all presentists subscribe to there being temporal passage. Tallant (2012) for instance, defends a version of presentism that does not posit temporal passage.

  3. This idea can be found as early as Williams (1951, 463–464), who writes that “as soon as we say that time or the present or we move in the odd extra way which the doctrine of passage requires, we have no recourse but to suppose that this movement in turn takes time of a special sort: time1 move at a certain rate in time2, perhaps one second1 per one second2, perhaps slower, perhaps faster. Or, conversely, the moving present slides over so many seconds of time1 in so many seconds of time2.”.

  4. Or some equivalent rate such as 60 s per minute.

  5. For further discussion of the NRA see Olson (2009), Phillips (2009), Skow (2011) and Tallant (2010).

  6. See also Raven (2010, 464): “The necessity of the rate of time’s passage entails that there are no possible alternative rates, hence (allegedly) entailing the incoherence of the rate itself”. This argument also appears in Maudlin (2002), Markosian (1993), Price (1996).

  7. We take metaphysical possibility to be the widest genuine kind of possibility (i.e. possibility that is not merely doxastic or epistemic).

  8. See for instance Raven (2010).

  9. For instance one can, in many cases, translate talk of the differential growth of the block into talk of the differential movement of the spotlight, to get similar results for the moving spotlight theory. Or, in the context of a dropping branches model, one could have branches dropping off the tree at different rates in different parts of the tree. We won’t speak to the issue of whether that is also true given a presentist model.

  10. Perhaps there could be space-time atoms that have internal mereological structure without having temporal extension. But if so, the space-time atoms in the worlds we consider are not like this.

  11. According to causal set theory space-time atoms progressively come into existence, and this constitutes the passage of time. The view is known as the causal sets approach because on this view the causal structure of space-time—i.e. the light-cone structure of space time—which entails that at any space-time point, we can partially order all other points into the absolute past, absolute future or absolute elsewhere of the point in question is paramount. It is this partial ordering of points, at a space-time point, which allows us to model the ‘causal sets’, and which, in turn, generates the order of accretion of space-time atoms. See Dowker (2006) and Sorkin (1990).

  12. This seems in keeping with what many growing block theorists want to say. Forrest (2004, 358) for instance, says that for no-futurists ‘nowb’ refers to times on the boundary of reality. Forbes (2016) says that present events are succeeded by nothing.

  13. While it is not our aim to do so here, we note that positing the existence of hypertime provides a ready response to the NRA: time passes not at 1 second of time per 1 second of time, but at 1 second of time per 1 second of hypertime. As the numerator and denominator are different, there seems to be no issue in saying that this is a rate, and thus that it is possible for time to pass at some rate in worlds with hypertime.

  14. Something like this idea, though not framed in terms of hypertime, can be found in Forrest (2008, Sect. 1), who suggests that the passage of time can be measured in terms of ‘seconds per layer’ or (as he prefers) ‘layers per second’.

  15. See for instance Skow (2015), Correia and Rosenkrantz (2013), Van Inwagen (2010), Bernstein (2017), Hudson & Wasserman (2010).

  16. See for instance Smart (1949), McTaggart (1908), Broad (1938), Crisp (2003).

  17. Perhaps thinking of rates of passage in terms of s/s is infelicitous. Instead, perhaps we ought measure temporal passage in terms of something like average elapsed time per new time, or per next (thanks to an anonymous referee for this suggestion). While we have not specified the temporal width of the temporal atoms in our models, suppose for the sake of this thought that they are a nanosecond long. Then we can say that time passes at 1 nanosecond per next in Fast and 0.5 nanoseconds per next in Slow. Nevertheless, the NAP is framed in terms of s/s, and we think the below succeeds in responding to it on its own terms.

  18. There is a third option. Freddie might depart S7 when t13 is present, and arrive at F14 when t14 is present. This option is unattractive because when t14 is present, S7 is still present. Thus Freddie’s arrival and departure will be co-present!

  19. See Forrest (2004, 2006) and Forbes (2016).

  20. See for instance Forbes (2016).

  21. For discussion of this issue see Miller (2006).

  22. To reframe this in terms of the idea we floated in footnote 17, we could talk of the number of nexts between nextn and nextn+, per some temporal interval as defined by the distance between events on nextn and nextn+.

  23. We also discuss these models in Miller and Norton (2020).

  24. With thanks to an anonymous referee for pressing us to consider this possibility.

  25. Of course, if the actual world is a growing block world, then this kind of differential passage is actual. We make the weak claim that it is probably nomologically possible in order to leave open that if our world is, say, a block universe world, then this kind of differential passage might not be nomologically possible, insofar as it may not be nomologically possible that there is a correct foliation of hyper-planes into privileged hyper-planes.

  26. The idea that non-parallel hyper-planes will result in differential passage appears in Forrest (2008, 247), who notes that “If the Absolute Foliation consists of hyperplanes, that is flat hypersurfaces, then Time passes uniformly with respect to one frame of reference if and only if it passes uniformly with respect to every other and this occurs if and only if the hyperplanes are parallel”.

  27. Moreover, in this model (and those we subsequently consider) the transitivity of simultaneity and co-presence is preserved.

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  1. Department of Philosophy, The University of Sydney, Sydney, Australia

    Kristie Miller

  2. Department of Philosophy, Háskóli Íslands, Reykjavík, Iceland

    James Norton

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Miller, K., Norton, J. Can time flow at different rates? The differential passage of A-ness. Philos Stud 178, 255–280 (2021). https://doi.org/10.1007/s11098-020-01430-1

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