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Re: starship-design: FTL idea

Timothy van der Linden writes:
 > Kyle,
 > >Causality violation:
 > >Stephen Hawking has speculated that at FTL speeds, particle-antiparticle
 > >anhialations dampen out chronal distortions, thus preventing causality
 > >violation. Perhaps FTL IS allowed in this way, preventing causality
 > >violation. In effect, the "naughty" part of your trip is prevented from
 > >creating CV's since it is hidden behind an event horizon.
 > I still don't understand why FTL creates causality problems. FTL doesn't
 > mean going back in time, it just means that you can get a places before
 > others can. For that matter you can't kill your mother before you are born
 > even if you can travel FTL.

Since you can do it, Timothy, do a Lorentz transformation on a FTL
worldline.  Note that for certain relative velocities the FTL worldline
swings from traveling forward in time to traveling backward in time, or
even for a particular sublight relative velocity appears to represent
infinite speed.

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.  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.

This is neatly summarized (with diagrams) in _Spacetime Physics_
(chapter L, I believe).

So far as I know, causality is not a derived principle in physics, but
merely an assumption; no one has proven that causal ordering has to
happen as a consequence of currently known physical laws.  However, it
appears to be a pretty good assumption, since no violations of causality
have been observed.  I wouldn't be surprised if someone eventually does
derive causality, though.

 > >P.S: If two objects APPROACH, each one travelling .99C, what is their
 > >combined velocity of approach? Is this done the same way as the regular
 > >velocity addition?
 > Ken gave you the relative velocity, which is what a person on one of the
 > objects would measure. For an observer to wich one objects is coming from
 > the right with 0.99c and one from the left with 0.99c, it is just a matter
 > of normal addition: The objects close eachother with 1.98c (If they are 1.98
 > lightsecond apart, it will take 1 second untill they collide.)

Relative velocity is a frame-dependent notion.  Ken's answer is correct
in the frame of either object given the measured velocities in a third
frame.  Your answer is correct in the frame in which both objects are
seen to travel at 0.99c in opposite directions.