>Perhaps there is no persistent identity at all; in every moment in time there is a single separate identity.
That view is known as perdurantism (opposed to endurantism).
> Perhaps time itself is an illusion: perhaps the universe is just one single snapshot in time.
Not sure what you mean here, but if you're assuming determinism then you're scientifically wrong (which is to say that there's now a scientific answer to what was historically a philosophical conundrum). The universe is indeterministic. This is more because of entropy ("determinism is fundamentally a denial of the arrow of time") than chaos theory (which is still deterministic). Ilya Prigonine is notable for emphasizing this worldview as a third departure from Newton, first two being quantum mechanics and general relativity.
> Does anyone have a recommendation for reading more about this topic?
That view is known as perdurantism (opposed to endurantism).
> Perhaps time itself is an illusion: perhaps the universe is just one single snapshot in time.
Not sure what you mean here, but if you're assuming determinism then you're scientifically wrong (which is to say that there's now a scientific answer to what was historically a philosophical conundrum). The universe is indeterministic. This is more because of entropy ("determinism is fundamentally a denial of the arrow of time") than chaos theory (which is still deterministic). Ilya Prigonine is notable for emphasizing this worldview as a third departure from Newton, first two being quantum mechanics and general relativity.
> Does anyone have a recommendation for reading more about this topic?
http://en.wikipedia.org/wiki/Ship_of_Theseus
http://en.wikipedia.org/wiki/Philosophy_of_space_and_time