Theoretically, just two week to reach Alpha Centuri with this interstellar formula one race car, but it would burn enough anti-matter getting there to equal a small moon. While we might be able to construct something like this within the next fifty years, powering it could remain challenging for much longer. In the meantime, China has supposedly successfully tested their own microwave version of a reactionless drive in orbit and is working towards producing thrusters for satellites. For their part, NASA is making progress with their own propellentless Woodward "Mach Drive", moving from the first rudimentary experiments to attempting to improve the engine's performance and testing the first models in orbit. Like the warp drive proposal, it obeys General Relativity, but require a lot less power and either design could, theoretically, reach the moon in as little as 4 hours and Mars in about 10 weeks. A mature version of the Woodward drive could also, theoretically, be used as a warp drive. In my own opinion, nobody really has a clue how any of this technology works just yet, but it most certainly appears to work. The Woodward drive use piezo electric crystals to push particles forward when they are heavy, and pull them back in when they are light by, more less, vibrating space-time at the right frequency. These warp drives would all vibrate space-time in a similar fashion, making it easier to warp.
The Woodward Effect is for the inertial drive and assumes transient mass fluctuations occur as electrons assume different orbitals. In other words, the more energy you pump into a crystal, the more its mass fluctuates as it releases the energy and its electrons teleport from one orbital to another. By vibrating large banks of them in this manner, you produce thrust in a vacuum. Theoretically, electrons are composed of negative matter and the cloud of virtual particles surrounding them is what actually gives them positive mass, making it possible to extract negative energy from space-time itself and create a warp drive. At least, that's the easiest way to conceptualize the concept that I know of, and obeys currently established physics. You can think of it as Quantum Field theory, where particles are actually waves of intersecting fields. Vibrating them in a manner analogous to the Woodward Effect merely saves energy in pulling space-time towards you and pushing it away behind you.
