For operations up to .25c (.25 the speed of light) the impulse
engines are used. This is for general maneuvering during docking
and destination travel. On the
Enterprise there are two impulse engines on the saucer
module and one on the main body of the craft. There are deuterium
tanks and antimatter tanks for use
as fuel in multiple places. If the
speeds were too high during impulse there would be relativistic
concerns to be dealt with.
Einstein's theory of relativity has to do with space and time
being interwoven and that massive objects such as the earth can
bend the space-time, felt as gravity.
The speed of light is the same to someone observing it
regardless of the speed that person is traveling. "Imagine setting
a large body in the center of a
trampoline. The body would press down into the fabric, causing it
to dimple. A marble rolled around the edge would spiral inward
toward the body, puling in
much the same way the the gravity of a planet pulls at rocks
in space."-Nola Taylor Redd, Space.com There have been several
ways of confirming Einstein's
theory of relativity, one being gravitation lensing. When you look
at a massive object at a distance is space, such as a black hole,
the light bends as it goes around
that object with the dimple in space-time. The image below
show the a black hole acting as a lens, bending a quasar from the
Pegasus constellation so four
images of the same thing appear as a result of the light
being bent. This certain quasar is 8 billion light-years away
sitting behind a galaxy that is only 400
million light-years away. Another validation is that Mercury is
changing orbit as a result of the sun. A really interesting
experiment done by Robert Pound and
Glen Rebka at Harvard University was an experiment with the
Doppler Effect. They shot gamma rays of radioactive iron up a
tower at the University and they
were found to be less than their natural frequency because gravity
caused distortions. Currently research is being done to try to
find evidence of gravitational
waves from the collision of 2 massive bodies like black holes.
This research is being done by the Laser Interferometer
Gravitational Wave Observatory (LIGO)
in Washington.
Warp speed and factor are purely made up for the series and movies
so that the crews can travel large distances quickly. There
doesn't seem to be any base in
real science except that with increasing speed the energy required
to do so increases exponentially. The speeds are accomplished
through the reaction of matter
and antimatter.The nacelles generate the warp field allowing
for the faster than light travel and also collect helium that is
floating in space to put back into the
gas tank basically.