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Re: starship-design: FTL idea
Timothy van der Linden writes:
> >If you have a collection of events connected by worldlines representing
> >velocities less than or equal to c, then all observers at any relative
> >velocity to those events will agree on the time ordering of the events,
> >if not the time intervals between them.
> True. (Assuming they remember that what they see is not what actually happens.)
The qualification is unnecessary, even incorrect in some senses. What
those observers see can be used to accurately reconstruct the intervals
between events. The local measurements of different observers may
differ, but they can all apply appropriate transforms to reconstruct the
events and intervals
> >If there are events connected
> >by FTL worldlines, they can no longer agree on the time ordering, and
> >hence they will not agree on the causal order of events.
> Why not? Please give me an example.
One observer fires a projectile that travels at 3 c, and strikes a
target 3 light-years away. Consider the firing of the projectile as
event A and the projectile striking the target as event B. What is the
spacetime location of event B relative to event A as seen by an observer
travelling at 0.1 c relative to the first observer? At 0.5 c?
observer? At 0.9 c? At what velocity does a moving observer have to
travel to measure those events as simultaneous in his reference frame?
Now repeat this exercise for the case where the projectile travels at
1/3 c and strikes a target 1 light-year away, and determine the measured
spacetime locations as seen by the same three moving observers.