The most fundamental puzzle about identity is the problem of change.
Calosi (2010b) suggests that the problem of change for multilocated objects becomes especially serious in the context of Minkowski spacetime.
Ehring (2002) develops a variant of the problem of change that involves incompatible spatial relations rather than incompatible intrinsic properties.
Some authors have objected to this consequence of the definition of action, and they might be right if we were dealing with the general philosophical problem of change.
It is an interesting question to what extent the friend of multilocation can invoke other responses to the problem of change.
For more on relativizing responses to the traditional problem of change, see Haslanger (2003), Hawley (2010), and Carroll (2011), who focuses on time travel.
Presentism seems to dissolve the problem of change: since only the overripe banana is present, its unripe state does not exist, so there's nothing to worry about.
But unless there are independent reasons for accepting presentism (see the separate entry on time), it seems like a drastic response to the problem of change.
And, as with the problem of change, endurantists may reply that temporal parts don't help, or that there is a perfectly good endurantist alternative, or both.
Merricks (1995) and Hinchliff (1996) argue that eternalism rules out endurantism, because of the problem of change; see the suggested reading at the end of section 3 for endurance-friendly eternalist accounts of change.
