 Unless this is the case, the causal past for a single observer, and even a collection of causal pasts, place very weak constraints on the global properties of spacetime. The global properties of a spacetime characterize its causal structure, such as the presence or absence of  singularities.[21]  General relativity tolerates a wide variety of global properties, since EFE impose only a local constraint on the spacetime geometry. One way to make this question precise is to consider whether there are any global properties shared by spacetimes that are constructed as follows. For a given spacetime, construct an indistinguishable counterpart that includes the collection of causal pasts \(\{J^-(p)\}\) for all points in the original spacetime. The constructed spacetime is indistinguishable from the first, because for any observer in the first spacetime there is a “copy” of their causal past in the counterpart. It is possible, however, to construct counterparts that do not have the same global properties as the original spacetime. The property of having a Cauchy surface, for example, need not be shared by an indistinguishable  counterpart.[22]  More generally, the only properties that are guaranteed to hold for an indistinguishable counterpart are those that can be established based on the causal past of a single point. This line of work establishes that (some) global properties cannot be established observationally, and raises the question of whether there are alternative justifications.