RE: starship-design: Relativity

[Steve VanDevender <stevev@darkwing.uoregon.edu>]

L. Parker writes:
 > I kind of thought so...
 > 
 > Okay, first question:
 > 
 > If the limit of T (the time required to go from point A to point B) as v
 > approached c equals zero, why isn't the limit of ABbar (the length of the
 > worldline) as v approaches c equal to zero? I sort of understand how and why
 > it is actually shorter even though it isn't a straight line, but why doesn't
 > it go to zero as v approaches arbitrarily close to c? Or have I simply not
 > read far enough yet? Maybe I'm just totally confused?
 > 
 > Lee

Is this in reference to a particular exercise or passage in _Spacetime
Physics_?  If so, which one?  It would help me understand the context.
I hope you have the second (1989) edition; otherwise it may be a bit
hard to connect with the copy I have.

It depends on what you mean by "the length of the worldline".  The
definition that is invariant for all observers is that the "length" of
the worldline (typically called the interval in _Spacetime Physics_) is
is equal to the elapsed time experienced by the object that travels
along that worldline between event A and event B.  Depending on their
relative velocities to that object other observers will see event A and
event B as being different distances from each other and the object as
taking different amounts of their time to travel from event A to event
B.  The ratio between the amount of time shown on a clock carried with
the object and the amount of their time they measure for the passage
from point A to point B goes to zero as the relative velocity of the
object approaches c.