A visualization of an Alcibierre warp drive, which is expanding and contracting space-time. (Image Credit: AllenMcC/Wikimedia, Creative Commons)
We might be seeing warp drives that would enable faster space travel in the future. I doubt any time soon though. 
Two researchers at Applied Physics claim they have created the first physical model for a warp drive, which could allow spacecraft to travel faster than the speed of light. They say this could be achieved without breaking the laws of physics. Their proposed theory is based on the Alcubierre warp drive, named after Miguel Alcubierre. He stated that the drive could work by warping space-time.
The term warp drive originates from Star Trek. In this sci-fi world, the Federation's warp drive works by colliding both matter and antimatter together and transforming the explosive energy into propulsion. As a result, the ships travel at faster-than-light speeds.
Theoretically, warp drives work by bending and modifying space-time to distort differences in time and distance. By applying this concept, space travelers would then be able to trek across distances faster than the speed of light. In 1994, Alcubierre outlined one of those circumstances. He proposed that a spacecraft powered by an Alcubierre drive would achieve faster-than-light speeds by contracting space-time in front of the craft while expanding it from behind. The downside is that it would need huge amounts of negative energy, which isn't feasible.
Negative energy is a huge deal because it's used as a workaround for some problems that arise from faster-than-light travel. Generally, it allows space to expand and contract faster than light. This is achieved while maintaining its warping within speed limits.
Alexey Bobrick and Gianni Martire have found a way around this. They say that a huge gravitational field could be used instead of negative energy. Gravity would bend space-time, which means that the passage of time inside and outside the warp drive would be very different. However, this requires compressing a planet-sized mass to use its gravity so that it can affect space-time. Due to those difficulties, building a warp drive from the researcher's proposed model isn't possible. Their paper suggests that it could be achieved in the future.
Even though traveling to far-away stars and planets is a long way off, this new research suggests that the warp drive principles are reasonable in scientific terms.
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