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The Possibility of Flawed Logic

It looks like somebody doesn't understand relativity. Our current understanding of physics dictates that we cannot travel faster than the speed of light. Even with an extremely fast acceleration, from at least one reference frame, if an object has mass, it will never reach the speed of light. Accelerating an object with a mass's speed to the speed of light would require an infinite (read: extremely massive) amount of energy that we just aren't capable of producing. Sure putting a gravitational field in front of an object would produce a force, but just how massive would would the object have to be to produce a gravitational field that produces enough force to actually accomplish something within a limited amount of time? It would appear that the only hypothetically feasible object to use would be a black hole, and even those are not known well enough to do anything useful with them. It's useless talking about how we are going to accomplish time-travel if we don't even have all of the (mathematical) tools available to evaluate the situation.

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