This article is from the Relativity and FTL Travel FAQ, by Jason W. Hinson jason@physicsguy.com with numerous contributions by others.
First, we might want to consider the four provisions and try to decide
which one would best fit Trek so that everyday warp travel couldn't be used
to produce unsolvable paradoxes.
So, let's consider both the first and second provisions. In these
cases, neither of the two FTL trips in our FTL bullet example will
necessarily be forbidden. So, if we consider that example yet again, we can
make the following argument: Let Op be the Enterprise. Then, rather than
sending a bullet, the Enterprise could itself travel from the origin to "*".
It could then (through ordinary acceleration) change its frame of reference
to match O's. Then it could travel from "*" (or just after "*"--we have to
give them a little time to do their acceleration) back to the O observer,
and it could get to O BEFORE it ever left for its first FTL trip (i.e. we
put the Enterprise in place of the FTL signal sent by the third observer).
Thus, since neither the first or second provision has to forbid any of these
actions, the Enterprise could use everyday warp travel via this method to
easily travel back in time without having to do something as dangerous as
zipping around the sun (as they have had to do on the show).
In addition, if the first provision governed normal warp travel, then
making different trips from different frames of reference would introduce
the possibility that you would find yourself being transferred to another
parallel universe to prevent unsolvable paradoxes. Also, if the second
provision governed normal warp travel, it would require Star Trek ships to
be careful as to which frames of reference they were in when they decided to
enter warp. After all, they may not want to accidentally meet themselves
from a previous trip (in which case the universe may destroy them to protect
self consistency). So, there seems to be some daunting arguments against
using either the first or second provision to keep ordinary warp travel from
producing unsolvable paradoxes in Trek.
Okay, what about the third provision? With that provision it would be
impossible to use ordinary warp travel as a "time machine". However, this
provision does cause certain noticeable restrictions on some FTL trips
(remember, it allows certain FTL trips to prevent other FTL trips). There
could be cases where the Enterprise would be prevented from completing its
warp trip on time because of an FTL signal sent by someone else. We
certainly don't see that on the show (not surprisingly). So, considering
this provision, I can't easily point out any arguments to support using it
to keep warp travel from being self inconsistent.
This leaves us with the fourth provision, and I think you will see that
it the provision of choice for the purposes of Trek. Of course, this fourth
provision must involve some special frame of reference; therefore, we might
first ask about where this special frame might come from. Thus, I will make
a proposal for answering such a question in the next section, and then I
will present what I believe are strong arguments for using the fourth
provision to keep normal warp travel from being self inconsistent in Trek.
 
Continue to: