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In Cyborg 2087, Garth travels back in time and ends up preventing his own existence, a prime example of the Grandfather Paradox in action. If that's the case, how was he able to even go back in time to perform this action? Does this mean that robots can travel through time with impunity?

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Since time travel itself is not really possible, different authors use different time travel mechanics. In this case, the mechanic is of the 'delayed' variety used in Back to the Future; you can take any historical action you like as a time traveler, because it doesn't remove you from existence until after a delay.

Alternative theories of time travel that might allow this include the multiple universe theory... you travel back in time, and create a new timeline that no longer includes you in the future, but there is no paradox because you are from a different universe than the one you alter.

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