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RE: starship-design: FTL

L. Parker writes:
 > Steve,
 > > Now, Isaac has been chiding me for being somewhat confused about the
 > > notions of unique time ordering and causality, which I'll admit to
 > > having played too loosely with.  Observer-dependent time ordering isn't
 > > the same as causality violation, and Isaac has explained that difference
 > > pretty well in recent examples.  However, I do think it's accurate to
 > > say that if you claim to be able to link events separated by a spacelike
 > > interval, then you can construct causality violation under the right
 > > conditions.

 > Umm, by any chance does time have a negative value under FTL? That seems to 
 > be what is happening. If it is strictly a product of frame of reference I
 > don't get it. 

First of all, I'm not entirely sure what you mean by a negative time
value.  The only observer-independent notion of time in relativity is
"proper time", i.e. the time that an object experiences itself.  In at
least one (probably oversimplified) analysis, FTL motion requires that
the object experience _imaginary_ proper time.  If an object is measured
to move without acceleration for a time t through a displacement x, then
the proper time experienced by the object (say read off a clock carried
by it) will be sqrt(t^2 - x^2), and this proper time will be the same
for all observers; all of the possible times and displacements that they
observe will produce the same value of sqrt(t^2 - x^2).  However, if the
object moves FTL, the value of t^2 - x^2 will be negative, its
experienced proper time will be an imaginary number, and we could
probably argue for a very long time about what that might mean.

 > Definitions of instantaneous vs. simultaneous aside, unless time can assume 
 > a negative value, I don't see how you can get back before you left even with 
 > FTL. For that matter, something someone said about photons travelling at 
 > infinite speed which totally confused me comes back to mind, something about
 > NOW...never mind, I can't stand relativity, probably why I am only an 
 > engineer.

Photons experience no proper time at all -- for them, t^2 - x^2 is zero,
meaning that they always move through the same amount of time as space.
So to a photon everything is simultaneous.  This is, however, something
of a degenerate case.

For any FTL-moving object, there is one observer moving at a particular
speed relative to the events in question who will see the object's
motion as infinitely fast and the events as simultaneous.  Consequently
any FTL motion will look like infinite speed to someone.  Does that
help?  :-)

Again in an oversimplified nutshell, FTL can be used to create a
causality loop if you send an FTL signal to an object moving fast enough
to see your FTL signal as moving backwards in time, and then it sends
another FTL signal back to you which you see as moving backwards in
time.  Consquently you receive a signal before the signal you sent that
you claim caused the received signal.  And if the signal you receive is
the destruct code for the transmitter equipment, you can work on the
headache from there.