starship-design: Raise the limit?

[Steve VanDevender <stevev@efn.org>]

kyle writes:
 > I was wondering about FTL travel, and ask myself "why do we really need
 > it?" To get somewhere fast. Why not abandon FTL until physics gets that
 > far and simply travel without traversing the space between two points?
 > You could theoretically travel from any point to any point without
 > having to exceed the speed of light, AND taking a very short travel time
 > in earth's reference point. 

The problem with this is that so far the only known way to curve space
is to concentrate mass.  Furthermore, curving space doesn't easily allow
for the sort of curvature

 > One other possibility: the speed of light can be raised, so why bother
 > with FTL? Just boost the speed of light to say, 150,000,000,000 m/sec?
 > One question: how much energy is needed?

In the case of the Casimir effect, the speed of light is increased in a
region between two charged plates.  Even if you could get rid of the
plates, the problem with this is either making the region large enough
to allow travel over a great distance, or getting the region itself to
travel faster than c.

>From my study of the physics involved, my suspicion is that any FTL
technique will probably take much more energy than relativistic travel.
I think that if FTL is ever developed it will probably only be used for
the most critical applications, because it will be so much more
expensive.

 > One last thing: relativity does NOT (for me) explain superluminal
 > velocity of quasars. I know the velocity trick, but isn't that
 > contradiction with the Lorentz transformation addition of velocity?
 > Maybe they just didn't want to get into something real hard to explain.
 > Or maybe I misunderstood.

Let's consider a simplified version of this phenomenon.

Using a powerful telescope, you observe a craft depart from a distant
planet headed toward you for another planet a light-year closer to you.
Using measurements of doppler-shifted light from the craft, you can tell
that it's moving at 0.8 c.  Continuing to observe the craft, you see
that it reaches its destination after only 0.25 years of observation.
So it moved one light-year in 0.25 years, meaning it traveled at 4 c,
right?

Well, not really.  This doesn't even really require relativity to
resolve, because it's really just an effect of the finite speed of
light.

When you observe the craft departing the planet and (in a negligible
time, for our purposes) accelerating to 0.8 c, the ship itself is
lagging not too far behind the light that it emitted on departure.  When
it reaches its destination planet a light-year closer to you, it's
traveled 1 light-year in 1.25 years (1 / 0.8) of your time; in that time
the light it emitted on departure has travelled 1.25 light years, so
those approaching photons are only 0.25 light-years ahead of the photons
it emitted on reaching its destination, and you see those photons arrive
only 0.25 years apart.

For something headed directly toward you, the apparent velocity you see
is v / (1 - v).  For any v > 0.5 c, this produces an apparent velocity
of approach greater than c, and as the object approaches the speed of
light, the apparent velocity of approach goes to infinity, as the object
lags less and less behind the light that you're using to perceive it.
Note that the apparent superluminal motion happens only when the object
approaches you; the converse result is that an object moving away
appears to recede at no more than 1/2 c even when its velocity is close
to -1 c.

Exercises 3-15 and 3-16 (pp. 89-92) in _Spacetime Physics_ go into more
detail on this phenomenon.  Exercise 3-16 specifically covers the
analysis of a "superluminal" jet from a quasar and the more general case
of objects approaching at an angle rather than straight-on.