The Alcubierre Drive is another intriguing concept that proposes bending spacetime around a spacecraft to facilitate faster-than-light travel. By creating a 'warp bubble', this theoretical propulsion system could potentially propel a spaceship to speeds exceeding the speed of light, while technically not violating the laws of physics.

In 1996, NASA founded a research project known as the Breakthrough Propulsion Physics Project (BPP) to study various spacecraft proposals and technologies. In 2002, the project's funding was discontinued, which prompted the founder – Marc G. Millis – and several members to create the Tau Zero Foundation. Named after the famous novel of the same name by Poul Anderson, this organization is dedicated to researching interstellar traveL.

The Alcubierre warp drive is a speculative idea based on a solution of Einstein's field equations in general relativity as proposed by Mexican theoretical physicist Miguel Alcubierre, by which a spacecraft could achieve apparent faster-than-light travel if a configurable energy-density field lower than that of vacuum (that is, negative mass) could be created.

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Rather than exceeding the speed of light within a local reference frame, a spacecraft would traverse distances by contracting space in front of it and expanding space behind it, resulting in effective faster-than-light travel. Objects cannot accelerate to the speed of light within normal spacetime; instead, the Alcubierre drive shifts space around an object so that the object would arrive at its destination faster than light would in normal space without breaking any physical laws.

Two-dimensional visualization of an Alcubierre 'Space-Time Warp' drive

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Although the metric proposed by Alcubierre is consistent with the Einstein field equations, it may not be physically meaningful, in which case a drive will not be possible. Even if it is physically meaningful, its possibility would not necessarily mean that a drive can be constructed. The proposed mechanism of the Alcubierre drive implies a negative energy density and therefore requires exotic matter. So if exotic matter with the correct properties can not exist, then the drive could not be constructed. However, at the close of his original article Alcubierre argued (following an argument developed by physicists analyzing traversable wormholes) that the Casimir vacuum between parallel plates could fulfill the negative-energy requirement for the Alcubierre drive. A collaboration between researchers from the University of Western Australia and the University of California Merced has provided a new way to measure tiny forces and use them to control objects. https://phys.org/news/2020-08-casimir.html

Note: Exotic matter can now be created as described in the article below:

https://www.space.com/exotic-matter-quantum-world-on-space-station.html

An Engineer Artist's  Interpretation of an Alcubierre FTL Space Craft

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​The Alcubierre metric defines the warp-drive spacetime. It is a Lorentzian manifold that, if interpreted in the context of general relativity, allows a warp bubble to appear in previously flat spacetime and move away effectively faster than lightspeed. The interior of the bubble is an inertial reference frame and inhabitants suffer no proper acceleration. This method of transport does not involve objects in motion at speeds faster than light with respect to the contents of the warp bubble; that is, a light beam within the warp bubble would still always move faster than the ship. Because objects within the bubble are not moving (locally) faster than light, the mathematical formulation of the Alcubierre metric is consistent with the conventional claims of the laws of relativity (namely, that an object with mass cannot attain or exceed the speed of light) and conventional relativistic effects such as time dilation would not apply as they would with conventional motion at near-light speeds. Some warp drive mathematics is described on: https://en.wikipedia.org/wiki/Alcubierre_drive#Mathematics.

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The Alcubierre drive, however, remains a hypothetical concept with seemingly difficult problems, though the amount of energy required is no longer thought to be unobtainably large. Believe it or not, NASA is serious about creating faster than light travel, and have released a new concept image (see above) showing exactly what a spacecraft equipped with a star-hopping warp drive might look like. The video link also provides an explanation of the FTL drive:     https://www.youtube.com/watch?v=Xlmdtf3UbmQ

There has been a lot of serious thought given to this type of warp drive. See below: