Physics. Here is an idea to accelerate matter to the speed of light
without using any fuel. My question is what would happen if this
expermiment were possible.
Assume there was a pole connected to the earth's equator on a hinge.
The pole is unbreakable and of sufficient length to extend very far
beyond the orbit of the moon. The pole is pointed east at the horizon
out into space and is lying directly in the path of the moon. As the
moon's
orbit brings the moon in contact with the pole it will begin to move, or
push, the entire pole with it. The pole is sufficiently long such that
the far end of the pole will approach, and reach, the speed of light.
With the moon moving forward, and the rotation of the earth moving the
base of the pole in the opposite direction, the far end of the pole
would accelerate very quickly. (This would essentially be a very long
lever) What would happen assuming the pole couldn't break. Would the
far end of the pole explode in an atomic reaction? (Of course it would
depend upon what the pole is made of) Would it slow the moon down?
(With disasterous consequences.) Would it cut into the moon and split
it in two? Would the far end of the pole be accellerated beyond the
speed of light. (remember this pole is sufficiently long, to have the
far end of the pole theoretically surpass the speed of light given
the speed of the moon and the opposite rotation of the earth.
What would happen?

The far end of the pole cannot exceed the speed of light. Lightspeed
limits apply to such things as well.

Postulate a solid pole from Earth to Pluto, and ignore all the fiddly
little problems with that. Now wiggle the pole left to send a "dit"
and right to send a "dah." Instant communication, right?

Nope.

Let someone else explain it. It will only take years of advanced math
and physics, and then some wag will forget to carry the one...

Well, the fundamental point is pretty simple.

The moon only has a certain amount of kinetic energy to pump into your
pole. It would require an infinite amount of energy to get the far end
of the pole up to the speed of light, so what will happen is that the
moon will come to a halt with the far end of the pole going very fast,
but not up to the spped of light. Then the moon will drop onto the
base of the pole and break it. ;-)

In any case, forgetting about going anywhere near the speed of light,
you're not using fuel only because you're tapping into the moon's
stored energy. That's not really very exciting from a physics point of
view, any more than if you said you'd found a way to run your laptop
without mains power - all you have to do is put a battery pack in it.

From an engineering view, either your pole or the moon will break at
first contact, depending on which is stronger. You can avoid this only
by accelerating the pole to nearly the same velocity as the moon (at
the level of the moon's orbit, of course), which makes the whole
exercise pretty pointless really. You could possibly use some sort of
variant of this idea to give ships a small speed boost on their way,
but I don't really think it would be worth it.

Please see the following thread:
 Question ID: 73321

No matter what your poll is made out of it will curve as the motion
travels out to the end of the lever. On a scale that big the poll
would look like a stream of water coming from a hose if it was viewed
from high abov the moons orbital plane.

Motion can only propogate through solid matter as fast as the speed of
sound in that medium.

This is a GREAT little read on FTL travel
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#4