treehouse said:
I'm not being sarcastic when I tell you "I want to be lectured to on this."
But isn't momentum vectored? Can't the explosion push the spaceship one direction and the mass of the spent fuel going back into the spaceship push it in basically the same direction? Besides, when an electric car accelerates doesn't its momentum increase even though its resting mass doesn't change?
Yes, the momentum is a vector.
In order for the spaceship to move forward, the gases ejected must have a velocity with at least some component in the opposite direction.
If you want to somehow bring the gas back in the spaceship you need to reverse the direction of the momentum of these gases. The effect of this will be a deceleration of the spaceship.
The components of the momentum of the gas particles transverse to the direction of the motion are irrelevant. They cancel out all the time. Once the gas is ejected, no internal process can change its overall momentum.
A car of any kind moves due to the interaction with the road and the Earth. If you consider the system car-road, the motion of the car forward results in a change in the momentum of the Earth (or maybe just part of it) in the opposite direction.
Imagine you are in the middle of long boat. You can move towards one end of the boat and in the process the boat will move in the opposite direction because you are pushing it with your feet. You gain some forward momentum (relative to the water) and the boat an opposite momentum. If you replace the boat with the Earth, the velocity gained by the Earth is so much times smaller that we usually neglect it. But it is there.
Going back to the boat, your idea would be similar to a scenario in which once you reach one end of the boat, you try to pull the boat back (under your feet) so you are again in the middle and start all over.
Regarding phonons, you can read any book on introductory solid state or read a little on Wikipedia:
http://en.wikipedia.org/wiki/Phonon