If time travel is possible, it seems to inevitably lead to paradoxes. These include consistency paradoxes, such as the grandfather paradox, and bootstrap paradoxes, where something is created out of nothing. One proposed class of resolutions to these paradoxes allows for multiple histories(or timelines), such that any changes to the past occur in a new history, independent from the one where the time traveler originated. In this paper we introduce a simple model for a spacetime with a time machine and multiple histories, and suggest three possible physical manifestations of multiple histories: one branching universe, many parallel universes, or one universe with many parallel histories. We use our model to study questions such as how many histories are needed to resolve time travel paradoxes and whether one can ever come back to a previously visited history. Interestingly, we find that the histories may be cyclic under certain assumptions, in a way which combines the Novikov self-consistency conjecture with the multiple-histories approach. We give an example of this novel hybrid scenario in the context of the grandfather paradox, and discuss its consequences. Finally, we discuss how observers may experimentally distinguish between the different manifestations of multiple histories, and between multiple histories and the Hawking and Novikov conjectures.

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