An object that is bent at t1 and straight at t2 cannot be wholly and numerically identical at both times without violating Leibniz's Law, as Lewis argued in 'On the Plurality of Worlds'.

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David Lewis(the philosopher who created this theory): An influential American philosopher (1941-2001) who developed Counterpart Theory as a way to understand how we talk about objects in different possible worlds.
Leibniz's Law(Applied here to show that relative identity generates contradictions when sortals are treated as univocal.): The logical principle that if a = b, then whatever is truly predicated of a is truly predicated of b (the indiscernibility of identicals).
On the Plurality of Worlds(the specific work being discussed): A major book by David Lewis arguing that many different possible worlds actually exist as real entities, not just as abstract ideas we imagine.
metaphysical identity through time(the core problem being discussed in the statement): The philosophical question of whether an object remains the 'same' object when its properties change dramatically over time.

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