Wells (1895) has a thoroughly Newtonian background. Newtonian space and time are mutually independent, eternal substances. Newtonian time is absolute and uniform—passing everywhere in the same direction, at the same rate. Newtonian worlds as a whole possess unambiguous time functions and absolute simultaneity, i.e. have a universal ‘now’. In relativity, space and time are not independent existents but twin aspects of spacetime. General relativity predicts matter’s presence affects spacetime itself and allows time (in effect) to ‘curve’. Gödel (1949) describes spacetimes so curved as to allow ‘closed timelike curves’ (CTCs): journeys that are always (locally) future-directed yet eventually rendezvous with their own spatiotemporal starting points. Parts of Gödel universes (e.g. galaxies) can have well-defined time-functions but Gödel universes in toto cannot: they have no universal ‘now’. (Simultaneity relations cannot be defined for their entirety.) Gödel universes neither begin nor end but simply are: infinite, four-dimensional blocks with strange geometrical ‘twists’ that let travelers visit any (externally) earlier or later times. Wellsians take peculiar journeys in otherwise conventional universes; Gödelians are otherwise conventional travelers in strangely-structured spacetimes. Wellsians actively go against time’s local flow; Gödelians passively follow time’s local direction. (Wellsians resemble helicopters in a uniform breeze; Gödelians, balloons in a cyclone.) In effect, Gödelians merely persist in idiosyncratic directions. Gödelians thus don’t much resemble time travelers in fiction, who can generally go anywhere in history. Indeed, some (notably Le Poidevin 2005) think Gödelians’ relative lack of room for maneuver means they cannot genuinely time-travel. If so, problems for Wellsians doom physical time travel.
Newtonian worlds are temporally well-behaved. Gödel (1949) universes have CTCs through every point. CTCs have well-defined past and future directions locally (in the traveler’s vicinity) but not globally (viewed as a whole). Gödelians can re-encounter their own pasts by traveling into their local future. Past and future are only relatively distinct on CTCs, rather as ‘up’ and ‘down’ are not absolute distinctions but relative to the Earth’s center. (Similarly, clock-faces have well-defined clockwise and anti-clockwise directions at every point yet a sufficiently prolonged clockwise journey revisits its starting point.) Reversing direction against external time gives Wellsian travel clear start- and end-points. Such reversals present the problems which are the main focus here. Starts and finishes for Gödelian travel are less clear, as temporal oddities show up only for the whole journey: “In Gödel’s space-time the local temporal and causal order will not differ from the one we are familiar with in our world; deviations can only occur for global distances”, (Pfarr 1981: p. 1090, emphasis original).
Wells (1895) features no processes recognized by relativity. Relativistic time travel (time dilation or CTCs) requires movement and/or gravitational differences between personal and external reference frames. However, Wells’ (1895) Traveller sits at rest (relative to the Earth) with his personal time varying in direction and/or rate of travel relative to all surrounding objects. Everything outside Wells’ (1895) machine registers one external time, while the machine enjoys a unique personal time without motion or gravitational differences relative to its surroundings. During backward time-travel, Wells’ (1895) Traveller sees everything outside the Machine seemingly go into reverse. Unlike Wellsians, Gödelians see no apparent failures of entropy (or other temporal anomalies) in their immediate extra-vehicular surroundings. Wellsian travel requires locally and globally backward causation; Gödel travel requires only the latter.
Below are depicted one Gödelian and seven Wellsians in various one-dimensional and two-dimensional spaces, (‘Linelands’ and ‘Flatlands’ respectively).Footnote 3 All illustrations have one time-dimension.Footnote 4\(\hbox {Wellsian}_\mathrm{(a)}\) is an unextended (point-like) object which reverses temporal direction twice (first at \(\upphi \) and then at \(\upomega \)) but otherwise persists normally (Fig. 1).
External time increases and personal time decreases \(\upomega \)-to-\(\upphi \). Each personal moment holds one Wellsian. Each external moment \(\upomega \)-to-\(\upphi \) (e.g. m1) holds three Wellsians, the midmost growing younger as external time increases. Viewed externally, two Wellsians seem to converge on \(\upphi \) and disappear, while two seemingly appear ex nihilo at \(\upomega \) and diverge. If these phases form parts of one history, physical continuity (and personal time) must survive \(\upphi \) and \(\upomega \)—otherwise, they are three separate objects and not one continuant. Wellsian round-trips require both \(\upphi \)-style and \(\upomega \)-style reversals. Wells’ (1895) Traveller departs from/returns to external times around 10 am and 7.30 pm respectively on one day early in 1894. Meantime, he spends eight personal days visiting 802,701 AD and then c. thirty million AD. He presumably reverses \(\upphi \)-style leaving the future and then \(\upomega \)-style re-entering 1894.Footnote 5
Wellsian reversals seem temporally peculiar but spatially benign—at least for unextended objects. However, extended Wellsians risk overlapping later and earlier selves. What Grey (1999: pp. 60–61) baptizes double occupancy looms pre-\(\upphi \) and post-\(\upomega \), with “not one but two machines—one going backwards and the other forwards—each apparently occupying (or attempting to occupy) the same location”. Wellsians face identical difficulties at \(\upphi \)-style ‘apex-instants’ or \(\upomega \)-style ‘nadir-instants’—it’s changing direction that poses problems. Can extended concrete objects make such transitions?
Dowe (2000: p. 446) suggests reversing Wellsians avoid self-overlap if they also move in space: “To do this sort of time travel you have to take a run up”. Passers-by might see a departing Wellsian machine “moving across a field, and ... its reversed later self moving towards it (perhaps an antimatter time machine, perhaps not)”, until “the two collide, apparently annihilating both”, (ibid., emphasis added). However, as Le Poidevin (2005: p. 344) shows and Fig. 2 illustrates, movement during reversal still leaves some overlap inevitable. (At least movement at finite velocity. Infinite velocity, even if coherent, threatens discontinuous existence or multiple overlapping stages.) Moving is not enough.
Stationary \(\hbox {Wellsian}_\mathrm{(b)}\) reverses once at \(t_{2}\) so two copies overlap completely at every moment shown. Co-occupancy is more localized and transitory for moving \(\hbox {Wellsian}_\mathrm{(c)}\). The leading and trailing edges of \(\hbox {Wellsian}_\mathrm{(c)}\) are ‘B’ and ‘A’ respectively. In external time, two of \(\hbox {Wellsian}_\mathrm{(c)}\) first meet at \(t_{1}\), when the forward phase’s edge B meets the backward phase’s edge A. These two \(\hbox {Wellsians}_\mathrm{(c)}\) then progressively overlap until they coincide at \(t_{2}\) and vanish thereafter. \(\hbox {Wellsians}_\mathrm{(b, c)}\) are extended objects which multiply occupy the same spaces for extended periods. If one Wellsian can’t exclude another from its space \(t_{1}-t_{2}\), is it still concrete at such times? Genuine solutions to double occupancy must at least let Wellsians behave like concrete objects that have continuous histories.
Time travelers who are Gödelian, unextended or spatiotemporally discontinuous all evade double occupancy. Likewise, diverse tropes, universals, fields or sortalsFootnote 6 can co-occupy. However, “two [concrete] objects of the same kind (persons, chairs, iron spheres)”, (Le Poidevin 2005: pp. 336–337) cannot co-occupy. Napoleon and his dress-sense can co-occupy but Napoleon and Wellington cannot, and nor can two Napoleons.
Interestingly, Le Poidevin (2005: p. 350) thinks backward time travel should be something travelers do (or initiate), and should proceed against time’s global direction:
It is, I think, a moot point whether simply following a closed time-like curve in worlds where there is no global earlier-later direction constitutes genuine time-travel. Arguably, time travel is something that, as we might put it, goes against the grain of space-time, rather than simply following it.
If Gödelians are mere slaves of curved spacetimes (with no global time direction to buck), only Wellsians could truly time-travel. (For similar sentiments, see Torretti 1999: p. 79, n. 20.) Even Gödel thought Gödelians weren’t strictly time travelers. He thought the possibility of CTCs proved that dynamic time has no objective analogue, therefore our temporal experience tracks only an ‘ideal’ (apparent or non-objective) time and relativity’s ‘t’ co-ordinate is not truly timelike. (See Yourgrau 1999). Hence a dilemma: without global time, Gödelians can’t time-travel; Wellsians could (per impossibile) time-travel but spatial problems (e.g. co-occupancy) foil them.
But must time travel be Wellsian? Lewis’s (1976) necessary and sufficient condition for time travel, i.e. discrepancy between external and personal time-registers, covers Wellsian and Gödelian alike. Lewis (1976) defines time travel by outcomes, not topologies or methods, and leaves unspecified how discrepancies arise. Pace Gödel, suppose a wormhole takes your (apparent) personal history from 2045 to execution for witchcraft in 1645. If so, being told you hadn’t really time-traveled (and/or time is ideal) seems cold comfort. However, Le Poidevin (2005) raises relevant issues even if Gödelians truly time-travel. Gödel universes may lack universal times but other relativistic models permit them.Footnote 7 If future physics restores global times, only Wellsian travel remains. Sections 1–3 surveyed Lewisian time travel, Gödelian/Wellsian differences and double occupancy. Next, Sect. 4 differentiates double occupancy from bilocation and persistence problems. Sections 5–11 outline and refine candidate answers to double occupancy.