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The Alcubierre metric, also known as the Alcubierre drive or Warp Drive, is a speculative mathematical model of a spacetime exhibiting features reminiscent of the fictional "warp drive" from Star Trek, which can travel Faster-than-light. The Alcubierre Drive is occasionally referred to as a solution of Einstein's field equations in general relativity, but this is misleading. In 1994, the Mexican physicist Miguel Alcubierre proposed in the Journal of Classical and Quantum Gravity a method of stretching space in a wave which would in theory cause the fabric of space ahead of a spacecraft to contract and the space behind it to expand. The ship would ride this wave inside a region known as a warp bubble of flat space. Since the ship is not moving within this bubble, but carried along as the region itself moves, conventional relativistic effects do not apply. However, there are no known methods to induce such a wave or to leave it once it starts, so the Alcubierre drive remains a theoretical concept at this time. Mathematics of the Alcubierre drive
Alcubierre Metric The Alcubierre Metric defines the so-called warp drive spacetime. This is a Lorentzian manifold which, if interpreted in the context of general relativity, exhibits features reminiscent of the warp drive from Star Trek: a warp bubble appears in previously flat spacetime and moves off at effectively superluminal speed. Even more striking, inhabitants of the bubble feel no inertial effects. Travelers making a round trip inside a warp bubble would experience no time dilation of the kind known from the famous twin paradox from special relativity. Most physicists familiar with general relativity consider this metric to be physically unrealizable. Mathematical representation The Alcubierre metric may be written ight),dt^2 where and . Alcubierre chose a specific form for the function , but other choices give a simpler spacetime exhibiting the desired "warp drive" effects more clearly and simply. Physics of the Alcubierre drive For those familiar with the effects of special relativity, such as Lorentz contraction and time dilation, the Alcubierre metric has some apparently peculiar aspects. Since a ship at the center of the moving volume of the metric is at rest with respect to locally flat space, there are no relativistic mass increase or time dilation effects. The on-board spaceship clock runs at the same speed as the clock of an external observer, and that observer will detect no increase in the mass of the moving ship, even when it travels at FTL speeds. Moreover, Alcubierre has shown that even when the ship is accelerating, it travels on a free-fall geodesic. In other words, a ship using the warp to accelerate and decelerate is always in free fall, and the crew would experience no accelerational g-forces. Enormous tidal forces would be present near the edges of the flat-space volume because of the large space curvature there, but by suitable specification of the metric, these would be made very small within the volume occupied by the ship. The original warp drive metric, and simple variants of it, happen to have the ''ADM form'' which is often used in discussing the initial value formulation of general relativity. This may explain the widespread misconception that this spacetime is a solution of the field equation of general relativity. Metrics in ADM form are adapted to a certain family of inertial observers, but these observers are not really physically distinguished from other such families. Alcubierre interpreted his "warp bubble" in terms of a contraction of "space" ahead of the bubble and an expansion behind. But this interpretation might be misleading, since the contraction and expansion actually refers to the relative motion of nearby members of the family of ADM observers. Natario has suggested a significantly different kind of warp bubble metric which does not feature expansion. Whether the Alcubierre metric can be considered physically realistic is questionable. Normally in general relativity, one first specifies a plausible distribution of matter and energy, and then finds the geometry of the spacetime associated with it; but it is also possible to run the Einstein field equations in the other direction, first specifying a metric and then finding the energy-momentum tensor associated with it, and this is what Alcubierre did in building his metric. This practice means that the solution can violate various energy conditions and require exotic matter, and even if exotic matter is possible it also leads to questions about whether it is actually possible to find a way to distribute the matter in an initial spacetime which lacks a "warp bubble" in such a way that the bubble will be created at a later time. Some analyses suggest that it would be impossible to generate the bubble without being able to force the exotic matter to move at locally FTL speeds, which would require the existence of tachyons. Other methods have been suggested which would avoid the problem of tachyonic motion, but would probably generate a naked singularity at the front of the bubble. ** The Alcubierre drive and science fiction Note that faster-than-light travel is often used in science fiction to denote a wide variety of imaginary propulsion methods, most of which have nothing to do with the Alcubierre drive or any other physical theory. Star Trek fans claim that, in Star Trek, the Alcubierre theory has largely been accepted due to the similarity of the appropriate terms, in order to explain the apparent breaking of the laws of physics in most of the series. In fact, the physics of warp drive in Star Trek have never been defined specifically onscreen and none of the "technical manuals" based on the show has made any reference to Dr. Alcubierre's theory. As a fictional construct, the warp drive in Star Trek is vague in its specifics and changeable to suit the needs of dramatic storytelling. In a 1978 production memo, Dr. Jesco von Puttkamer, technical advisor for Star Trek: The Motion Picture, proposed a model of warp drive which bears some striking similarities to Dr. Alcubierre's later theory, employing the same principle of a distortion in spacetime moving a ship faster than light inside a pocket of spacetime within it. (The memo is reprinted on pp. 153-4 of the book The Making of Star Trek: The Motion Picture.) However, later Star Trek technical advisors did not follow this model, and modern Star Trek productions tend to follow a warp-drive model based on the use of "subspace" as an alternate dimensional realm through which a ship may travel at hyperlight speeds, analogous to the use of hyperspace in much science fiction. However, the specifics remain vague enough that some consider it possible to reconcile Star Trek warp drive with the Alcubierre theory (for example, see Aftermath by Christopher L. Bennett in the Starfleet Corps of Engineers Ebook series). Another, more recent book called Warp Speed by Dr. Travis S. Taylor delves more into detail about the Alcubierre theory, as well as using it as the basis for the entire book. Although it precedes Alcubierre drive, the anime version of Captain Future featured a similar mechanism, called undulating mode. Alcubierre drive theory is also mentioned in Orbiter, a graphic novel by Warren Ellis. Warp fields Warp fields are a literary device, common in modern science fiction, which "warp" spacetime to allow something to be done which is not otherwise possible. Most commonly, they allow the transport of physical objects or the transmission of information faster than the speed of light, which is currently understood to be impossible under most circumstances in the real universe. The most famous use of "warp" terminology is in the Star Trek universe, where warp fields are produced by warp drives. Star Trek-type warp fields make possible warp travel - travel faster than the speed of light - and allow other useful effects, such as manipulating the mass of objects. Current scientific theory postulates the existence of phenomena which could be referred to as warp fields, such as the discontinuity at the Schwartzchild radius of a black hole. (See also the concept physicists refer to as a "singularity," especially the sort known as a "wormhole.") However, no plausible proposal for the creation of a manmade warp field has yet been put forward. Possible drawbacks Expansion on the work of Alcubierre See also | |||||||||
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