Time Travel and the Immutability of the Past within B-Theoretical Models


The goal of this paper is to defend the general tenet that time travelers cannot change the past within B-theoretical models of time, independently of how many temporal dimensions there are. Baron Pacific Philosophical Quarterly, 98(1), 129–147 (2017) offered a strong argument intended to reach this general conclusion. However, his argument does not cover a peculiar case, i.e. a B-theoretical one-dimensional model of time that allows for the presence of internal times. Loss Pacific Philosophical Quarterly, 96, 1–11 (2015) used the latter model to argue that time travelers can change the past within such model. We show a way to debunk Loss’s argument, so that the general tenet about the impossibility of changing the past within B-theoretical models is maintained.

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  1. 1.

    Bernstein (2017) offers an A-theoretical model that features a Movable Objective Present to make van Inwagen’s point more general. There, time travel does not necessarily feature the annihilation of some portions of reality, but it necessarily features a shift of the Objective Present. The result is that past-changing time travel within an A-theoretical framework is compatible not only with the growing-block theory like in van Inwagen’s, but also with presentism and the moving spotlight view.

  2. 2.

    Baron’s argument to this conclusion is quite long and complex, and thus we don’t try to summarize it here in few words. The interested reader is redirected to his paper to know more.

  3. 3.

    With regard to the dialectic of this debate, Baron (2017: 131) is worried about whether or not there are philosophers who can qualify as his opponents in virtue of holding a B-theoretical 2D view of time to make a case for changing the past, for that position is the intended target of his argument. He then individuates Goddu (2003, 2011) and Hudson and Wasserman (2010). However, this does not seem correct with regard to Hudson and Wasserman. In fact, Hudson and Wasserman are responding to van Inwagen (2010) A-theoretical growing-block 2D model, and one of their points is that the spirit of van Inwagian model can be cashed out also by assuming eternalism in place of the growing block. Even though most eternalists endorse the B-theory of time, eternalism is compatible with the A-theory. And this latter combination is precisely what Hudson and Wasserman have in mind while proposing their model. In fact, in their model, past-changing time travel occurs when the objective present hits the T-slice within the eternalist block where the time traveler pushes the button of her time machine. See also Wasserman (2017, Ch. 3) for more details on such A-theoretical eternalist 2D model. At any rate, the position Baron discusses is general enough that, we think, there is no need to look for someone holding that position in order to make a case for the changing past.

  4. 4.

    The earlier-later relation does this job for any pair of T-slices, as long as time is linear. In branching-time models we might have pairs of times which are not related by such relation. We set aside this case, given that Loss’s example is a case where time is linear. We are setting aside also considerations from special theory of relativity, where what is primitive are spatio-temporal intervals.

  5. 5.

    For the sake of simplicity and exposition, we shall assume throughout the paper that time is discrete. This way we can safely talk of the first, second and last instant of a given interval. The points we are making do not depend on this assumption.

  6. 6.

    Loss implicitly assumes that external time always has its own metric. But external time is here just the earlier-later relation, and it’s at least open what stance one should have with respect to metric determinations. Roughly, an objectivist with respect to temporal metric takes as primitive a metric version of the earlier-later relation. Thus, according to the objectivist there are fact of the matter not only about what comes before or after what, but also about the length of temporal intervals. Whereas, according to a conventionalist with respect to temporal metric, there are only facts of the matter about what comes earlier or later what, but no facts of the matter concerning temporal distances. Facts concerning distances are given only relative to a chosen measurement device, that is a clock. Depending on the variety of conventionalism, the choice of the clock can be more or less constrained by reliability considerations (See Newton-Smith 1980). Since Loss appeals liberally to temporal distances of the earlier-later relation even when measuring systems get abruptly annihilated and replaced, like in the case of the spheres break, his account assumes an objectivist metric version of the earlier-later relation. For the sake of discussion, we will stick to this assumption.

  7. 7.

    The reference to the time z as a “common ancestor” at the same internal temporal distance from both x and y is crucial for Loss to make his point. Without it, any possible world with two T-slices similar enough to count as counterparts of each other would be a case where a (past) time changes. And this would be wrong. A possible world might just end up in a state very similar to an earlier one.

  8. 8.

    Actually, as Loss observes, V1b is quasi-regular. In fact, in V1b Tim appears out of thin air. This kind of local irregularity should not bother us, though. Tim’s case is supposed to be a time-travel case. Hence, some local irregularity has to be expected.

  9. 9.

    We are aware that days are not the most appropriate units of time to refer to the length of time intervals in a scenario where there are just micro-particles. One can replace days with other units. Obviously, the gist of our argument is not affected by that.


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For helpful comments on earlier drafts of this paper, we would like to thank Samuele Iaquinto, Roberto Loss, Nicola Piras, Jonathan Tallant, Achille C. Varzi, and members of the Centre for Philosophy of Time in Milan.

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Correspondence to Giacomo Andreoletti.

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Andreoletti, G., Torrengo, G. Time Travel and the Immutability of the Past within B-Theoretical Models. Philosophia 47, 1011–1021 (2019). https://doi.org/10.1007/s11406-018-0028-0

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  • Time travel
  • Time
  • Hyper-time
  • B-theory
  • Changing the past