Why do people think FTL allows for backwards time travel? It's called Special Relativity, and is much more convincing than people's general ideas.
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Suppose you're in a spaceship traveling at a speed relative to another spaceship such that time dilation is 2, meaning that for each of you time appears to pass at half speed for the other one. When you meet, you exchange ansible (instantaneous communicator) settings. An hour after, you put your coffee cup on the edge of the console, and it falls and breaks. You send a message to the other guy. You observe him getting it when, from his point of view, it's half an hour after meeting. He relays the message back, and observes you getting it when you are fifteen minutes from the meeting, and the message has therefore returned forty-five minutes before you sent it.
In order to argue with this, you need to at least understand it. You need to understand that "forward" and "back" are not determinate with any FTL phenomenon. (There is an objective forward and back as long as things stay under the speed of light. FTL is "sideways", using this classification, and has no "forward" or "back".)