Comments by "Edward Cullen" (@edwardcullen1739) on "Why Going Faster-Than-Light Leads to Time Paradoxes" video.
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Hi, your use of the diagram is erroneous.
You claim that, according to the STL ship, the notification arrived before the notification was sent. This is a misunderstanding of time dilation.
At relativistic speeds, time slows for the ship, but not for the "rest of the universe". While the occupants of the ship travelling close to the speed of light may have only aged a few days or weeks, the time would have passed outside their frame by years, something that would not be apparent unless and until they "synchronise" their frame.
The CHILDS film Flight of the Navigator explains this perfectly.
The fundamental issue is perception - the perception of a ship travelling at relativistic speeds is that time slows, but the reality is that it's going along "normally" for everyone else.
In your example, causality is only broken iff the STL ship were able to transmit a message back to Earth before the message were sent.
Your diagram demonstrates that this is not possible, as the message returned at the speed it was received would not reach Earth until after it was sent.
These diagrams are interesting, but they can be misleading. I never understood why until now.
Regardless of any line drawn in your example, the only way to break causality is to transmit backwards in time, so that the response to a message is received before the original is transmitted.
I know that there's actually a mathematical proof of what I'm saying in the Lorentz equations (for translating a spacetime co-ordinate from one frame of reference to another), but I haven't gotten around to demonstrating it.
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