spatiotemporal continuity a property of the careers, or space-time paths, of well-behaved objects. Let a space-time path be a series of possible spatiotemporal positions, each represented (in a selected coordinate system) by an ordered pair consisting of a time (its temporal component) and a volume of space (its spatial component). Such a path will be spatiotemporally continuous provided it is such that, relative to any inertial frame selected as coordinate system, (1) for every segment of the series, the temporal components of the members of that segment form a continuous temporal interval; and (2) for any two members ‹ti, Vi( and ‹tj, Vj( of the series that differ in their temporal components (ti and tj), if Vi and Vj (the spatial components) differ in either shape, size, or location, then between these members of the series there will be a member whose spatial component is more similar to Vi and Vj in these respects than these are to each other.
This notion is of philosophical interest partly because of its connections with the notions of identity over time and causality. Putting aside such qualifications as quantum considerations may require, material objects (at least macroscopic objects of familiar kinds) apparently cannot undergo discontinuous change of place, and cannot have temporal gaps in their histories, and therefore the path through space-time traced by such an object must apparently be spatiotemporally continuous. More controversial is the claim that spatiotemporal continuity, together with some continuity with respect to other properties, is sufficient as well as necessary for the identity of such objects – e.g., that if a spatiotemporally continuous path is such that the spatial component of each member of the series is occupied by a table of a certain description at the time that is the temporal component of that member, then there is a single table of that description that traces that path. Those who deny this claim sometimes maintain that it is further required for the identity of material objects that there be causal and counterfactual dependence of later states on earlier ones (ceteris paribus, if the table had been different yesterday, it would be correspondingly different now). Since it appears that chains of causality must trace spatiotemporally continuous paths, it may be that insofar as spatiotemporal continuity is required for transtemporal identity, this is because it is required for transtemporal causality.
See also PERSONAL IDENTITY, TIME SLICE. S.Sho.