[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: starship-design: FTL idea
>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?
t' = gamma (t - -----)
x' = gamma (x - v t)
Spacetime coordinate convention: (t',x',y',z')
v=0 A(0,0,0,0) B( 1.000,3.000,0,0)
v=0.1 A(0,0,0,0) B( 0.704,2.915,0,0)
v=0.3 A(0,0,0,0) B( 0.105,2.830,0,0)
v=1/3 A(0,0,0,0) B( 0.000,2.828,0,0)
v=0.9 A(0,0,0,0) B(-3.900,4.818,0,0)
>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.
v=0 A(0,0,0,0) B( 3.000,1.000,0,0)
v=0.1 A(0,0,0,0) B( 2.714,0.905,0,0)
v=0.3 A(0,0,0,0) B( 2.201,0.734,0,0)
v=0.9 A(0,0,0,0) B( 0.688,0.229,0,0)
v=1.0 A(0,0,0,0) B( 0.000,0.000,0,0)
OK, I catch your drift. But... knowing that you move this fast with respect
to the observed phenomenon, you can reconstruct what really(=in a frame at
rest) happens and remove the apparent causality reversal.
For those few that happen to see everything at once, they are at a loss,
they will never be able to reconstruct what happened.
OK, now for a horizontal bar falling down on a parallel floor. The event
that one end touches the floor is called A, the event that the other bar
touches the floor is called B.
(If you like, assume the bar is 1 lightsecond long)
v=0 A(0,0,0,0) B( 0.000,1.000,0,0)
v=0.1 A(0,0,0,0) B(-0.101,1.005,0,0)
v=0.9 A(0,0,0,0) B(-2.065,2.294,0,0)
v=-0.1 A(0,0,0,0) B( 0.101,1.005,0,0)
So even for very small velocities without FTL, you can measure a reversal in
time ordering. Does my example differ from yours?