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starship-design: One more try...
>>You're right... according to what I said anyway. But there's a subtle
>>sign issue here, and I'm pretty sure I am right that FTL is equivalent to
>>staying in the same place and travelling backwards in time.
>What is this nonsense? No, FTL is not equivalent to staying in
>place and travelling backwards in time.
Yeah, I was getting pretty nonsensical there. Too many references to time,
space, speed, and other imprecise, frame-dependant terms that totally
obscured my underlying point. Here it goes from scratch.
There are four classes of journeys one can even consider making.
A) Within your forward time cone (All STL and light-speed falls in here)
B) Out of your forward light cone, but still (from Earth's perspective)
forward in time.
C) With your backwards time cone (Staying in the same place but travelling
backwards in time.
D) Our of your backwards light cone, but still (from Earth's perspective)
backwards in time.
The first point is that there is no difference between B and D. They are
both FTL and they are both identical. The only distinction is made from
Earth's perspective, so it is not a real distinction. For those of you who
think that B-type FTL journeys are okay and D-type are not, that is an
artifical separation that can only be true if there is a preferred
reference frame. You can't outlaw D without outlawing B, and therefore
outlawing all FTL.
My point about FTL (B and D) being equivalent to travelling backwards in
time in the same place (C) was obviously not literally correct. What I was
trying to say was that they are equivalent in the sense that if it is
possible to move out of your forward light cone with FTL (i.e. if B and D
are possible) then C becomes possible as well.
This is obvious; A D-type trip away from Earth, followed by a D-type trip
back to Earth, will add up to a C-type trip. Other examples include Adding
a B-type and a D-type trip to get a C-type. There are lots of ways to go
backwards in time once FTL (B and D) is allowed.
The only way to avoid C-type trips is to demand that D-type trips are
impossible. But Because D-type trips are equivalent to B-, if time travel
is forbidden, so is FTL.
That was all I was trying to say. Sorry for trying to do it in unspecific
terms; I confused even myself.