The Alcubierre metric defines the so-called warp drive spacetime introduced by Miguel Alcubierre in 1994. 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 awkward inertial effects, and travelers making a round trip inside a warp bubble experience no time dilation of the kind known from the famous twin paradox from special relativity. Because of the basic geometry of spacetime, however, any means of traveling faster than light can be used to travel backward in time; that is, faster than light travel is necessarily equivalent to time-travel. Dr. Miguel Alcubierre Miguel Alcubierre (Born 1964) is a Mexican theoretical physicist. ... 1994 was a common year starting on Saturday of the Gregorian calendar, and was designated the International year of the Family. ... In differential geometry, a pseudo-Riemannian manifold is a smooth manifold equipped with a smooth, symmetric, tensor which is nondegenerate at each point on the manifold. ... Two-dimensional visualization of space-time distortion. ... The Enterprise-D goes into warp. ... http://www. ... Faster-than-light (also superluminal or FTL) communications and travel are staples of the science fiction genre. ... In simple terms, Inertia is a physical property of matter, namely, a resistance to change in motion, and it is related to the mass of an object. ... The twin paradox is a thought experiment in special relativity of two twin brothers, one undertaking a long space journey with a very high-speed rocket at almost the speed of light, the other remaining on Earth. ... Time travel is a concept that has long fascinated humanity—whether it is Merlin experiencing time backwards, or religious traditions like Mohammeds trip to Jerusalem and ascent to heaven, returning before a glass knocked over had spilt its contents. ...

The bubble velocity is defined as the velocity, as seen from the point of view of a flat space observer, of any matter contained within the curved space created by the faster-than-light drive.

The Alcubierre metric may be written

where

and

.

Alcubierre chose a specific form for the function f, but other choices give a simpler spacetime exhibiting the desired "warp drive" effects more clearly and simply.

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.

All known warp drive spacetimes violate various energy conditions. It is true that certain experimentally verified quantum phenomena, such as the Casimir effect, when approximated in the context of relativistic classical field theories, lead to stress-energy tensors which also violate the energy conditions. This initially led some to hope that Alcubierre type warp drives could perhaps be physically realized by clever engineering taking advantage of such quantum effects. Unfortunately, it turns out that a rather general class of warp drive spacetimes also violates certain quantum inequalities, and such violations are much harder to dismiss. The energy conditions in general relativity were never more than rough rules of thumb, but the quantum inequalities are generalizations of the uncertainty principle and seem to stand on solid ground in quantum field theory. Another problem with a large class of warp drive spacetimes is that even if the violations of the quantum inequalities were acceptable, the energy requirements may be absurdly gigantic, e.g. the mass-energy content of a star might be required to transport a small spaceship across the Milky Way galaxy. Counterarguments to these apparent problems have been offered, but not everyone is convinced they can be overcome. (If they could be, it has been suggested that an intense flux of blue shifted starlight would fry any inhabitants of the bubble.) The energy conditions refer to various constraints which can be imposed on a spacetime that any physically reasonable matter distributions in physics are expected to satisfy. ... In 1948 Dutch physicist Hendrik B. G. Casimir of Philips Research Labs predicted that two uncharged parallel metal plates will be subject to a force pressing them together. ... Albert Einsteins theory of relativity is a set of two theories in physics: special relativity and general relativity. ... A classical field theory is a field theory which does not take into account quantum phenomena. ... In quantum physics, the Heisenberg uncertainty principle, sometimes called the Heisenberg indeterminacy principle (a title prefered by Niels Bohr - see quantum indeterminacy), expresses a limitation on accuracy of (nearly) simultaneous measurement of observables such as the position and the momentum of a particle. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ...

Perhaps the most troubling objection of all is that if warp drives were genuinely possible, we would expect to see, even in toy models such as the Alcubierre warp drive, some indication of mass-energy being gathered up, transported, concentrated, reorganized and used to create and operate the warp bubble. But by their very nature, current warp drive metrics seem to have a very different character: the bubble appears (and may eventually disappear) "spontaneously". We can observe a kind of "circulation" of energy-momentum around the bubble, but nothing which suggests a phenomenon which can be created or controlled by physical means.

At present it seems fair to say that the consensus among physicists is that warp drive spacetimes of type considered here are probably impossible to realize. Some general counteraguments have been offered to the construction of any warp drive (not just ones of the Alcubierre or Natario forms). Nevertheless, a few physicists continue to hold out hope that some kind of warp drive might after all be physically possible, at least in principle.

See also

• Alcubierre drive
• Exact solutions in general relativity (for more on why the Alcubierre spacetimes are not solutions).

It has been suggested that this article or section be merged with Alcubierre metric. ... // Introduction In general relativity, an exact solution is a Lorentzian manifold equipped with certain tensor fields which are taken to model states of ordinary matter, such as a fluid, or classical nongravitational fields such as the electromagnetic field. ...

References

• Lobo, Francisco S. N.; & Visser, Matt (2004). Fundamental limitations on 'warp drive' spacetimes. Class. Quant. Grav. 21: 5871-5892. See also the "eprint". arXiv. URL accessed on June 23, 2005.

• Natario, Jose (2002). Warp drive with zero expansion. Class. Quant. Grav. 19: 1157-1166. See also the "eprint". arXiv. URL accessed on June 23, 2005.

• Broeck, Chris Van Den (1999). A `warp drive' with more reasonable total energy requirements. Class. Quant. Grav. 16: 3973-3979. See also the "eprint". arXiv. URL accessed on June 23, 2005.

• Low, Robert J. (1999). Speed Limits in General Relativity. Class. Quant. Grav. 16: 543-549. See also the "eprint version". arXiv. URL accessed on June 30, 2005.

• Hiscock, William A. (1997). Quantum effects in the Alcubierre warp drive spacetime. Class. Quant. Grav. 14: L183-L188. See also the "eprint". arXiv. URL accessed on June 23, 2005.

• Pfenning, Michael J.; Ford, L. H. (1997). The unphysical nature of 'Warp Drive'. Class. Quant. Grav. 14: 1743-1751. See also the "eprint". arXiv. URL accessed on June 23, 2005.

• Alcubierre, Miguel (1994). The warp drive: hyper-fast travel within general relativity. Class. Quant. Grav. 11: L73-L77. See also the "eprint version". arXiv. URL accessed on June 23, 2005.