Recently I watched a good public lecture "Warp Drive and Aliens: Bryan Gaensler " provided by Perimeter Institute for Theoretical Physics. It is an overview of current technology and where we currently stand concerning human dream to travel to stars and maybe possibly find life.
After the talk, there was a block of questions and at 1:19:06 Bryan, like many other science videos I have seen, repeated the same argument, "when you travel faster than the speed of light all sort of paradoxes happen, you could travel back to time and face time-travelling paradox" and repeatedly that idea stuck in my mind.
So, let us imagine two humans, both astronauts. Each being in their spaceships, orbiting around the Earth.
They both point ships to Mars. First one, Ana beams laser toward Mars. Ben who is in second ships waits, 5 seconds and then turns on "Alcubierre warp drive" and travelling around 8 times faster than the speed of light, arrives in Mars in 20 seconds (total 25 seconds have passed since the start of the experiment).
As light needs 182 seconds to travel to Mars, Ben after arriving pointed ship toward Earth and start waiting.
After 182 seconds, after Ana has shot the laser toward Mars, Ben sees the laser coming from Earth.
Maybe for a Martian population, Ben will look like a prophet explaining things that have not yet happen, even watching his own reflection, but Ben has not violated time or space at any time. And there will be no travelling backwards in time.
Just for the sake of argument for a minute let's examine this using logic:
Regardless how many times faster than the speed of light we travel, 8 times or 100s times, we will always arrive (from the outside reference point of measure) fraction of the time second, minute, an hour... later than from the time, we started our journey.
Indeed, time does not flow the same for the person who is standing and the one who is travelling, but in this case astronaut Ben is shielded by space/time bubble of "Alcubierre warp drive".
Maybe mathematics for this case is a bit different. What if space/time in front and back wave cancel each other out, so inside the bubble, time would be the same as outside of the bubble? Therefore, astronaut Ben would not arrive younger then he was as he was travelling 8 times faster than the speed of light, but just usual 20 seconds older equally as he would be as he has not travelled at all - just waiting 20 seconds.
And in fact, if we think about it, inside of the bubble Ben is not travelling - space is moving.
As space/time was curved during "Alcubierre warp drive" travel, we could maybe guess how would light bounce of that curved-cancelling-out space/time bubble, but again `time` would not be violated and there will be no `time` going backwards. Only, things that would happen were rather strange light effects similar to those pilots can experience with sound, breaking the sonic barrier, and then hearing the sound of their engine after a few seconds.
I would appreciate if some among you kind professional astrophysicists answer, or share this with someone knowledgable enough to answer, what am I missing in the above idea? How would "Alcubierre warp drive" faster then light travel - cause a time travel paradox?