According to the third law of motion, you van't have an mass move in a particular direction unless there is a proportional opposite mass/acceleration ratio in the opposite direction.
No-one has been able to provide a convincing argument otherwise, but the best one to date is Shawyer's EM Drive. He claims some fancy relativistic effects are what allows his engine to work, but I have read some papers which claim he is a fraud.
My question is, why is it impossible to move a mass in a given direction without a proportional change in the opposite direction?
I'm not talking about a perpetual motion machine, or anything. Sure, the device would need to consume at least the amount of energy proportional to the energy required to accelerate the mass.
Here's a highly hypothetical example: Say we either can project a gravity well in front of our vehicle, and/or project a gravity hill behind. In empty space, the effects of the gravity will be near-negligible by the time they reach any other object, however close to the vehicle they will be more significant. The end result would be the vehicle would move in the given direction, and nothing else around would really move at all.
An even cruder example would be to shine a bright torch out the back of your vehicle. Even though the photons have no mass, wouldn't the vehicle move forward?