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Another approach is to accept special relativity, but to posit that mechanisms allowed by general relativity ( e. g., wormholes ) will allow traveling between two points without going through the intervening space.
While this gets around the infinite acceleration problem, it still would lead to closed timelike curves ( i. e., time travel ) and causality violations.
Causality is not required by special or general relativity, but is nonetheless generally considered a basic property of the universe that cannot be sensibly dispensed with.
Because of this, most physicists expect that quantum gravity effects will preclude this option.
An alternative is to conjecture that, while time travel is possible, it never leads to paradoxes ; this is the Novikov self-consistency principle.

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