The Alcubierre drive () is a speculative warp drive idea according to which a spacecraft could achieve apparent faster-than-light travel by contracting space in front of it and expanding space behind it, under the assumption that a configurable energy-density field lower than that of a vacuum (that is, negative mass) could be created. Proposed by theoretical physicist Miguel Alcubierre in 1994, the Alcubierre drive is based on a solution of Einstein's field equations. Since those solutions are metric tensors, the Alcubierre drive is also referred to as Alcubierre metric.
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 more quickly than light would in normal space without breaking any physical laws.
Although the metric proposed by Alcubierre is consistent with the Einstein field equations, construction of such a drive is not necessarily possible. The proposed mechanism of the Alcubierre drive implies a negative energy density and therefore requires exotic matter or manipulation of dark energy. If exotic matter with the correct properties does not exist, then the drive cannot be constructed. At the close of his original article, however, 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.
Another possible issue is that, although the Alcubierre metric is consistent with Einstein's equations, general relativity does not incorporate quantum mechanics. Some physicists have presented arguments to suggest that a theory of quantum gravity (which would incorporate both theories) would eliminate those solutions in general relativity that allow for backward time travel and thus make the Alcubierre drive invalid.
Solitons offer a mathematical "loophole" in general relativity to theoretically create a warp bubble with positive energy. They move through spacetime, while the bubble itself could move faster than the speed of light.
History In 1994, Miguel Alcubierre proposed a method for changing the geometry of space by creating a wave that would cause the fabric of space ahead of a spacecraft to contract and the space behind it to expand. The ship would then ride this wave inside a region of flat space, known as a warp bubble, and would not move within this bubble but instead be carried along as the region itself moves due to the actions of the drive. The local velocity relative to the deformed spacetime would be subluminal, but the speed at which a spacecraft could move would be superluminal, thereby rendering possible interstellar flight, such as a visit to Proxima Centauri within a few days.
Alcubierre's original paper noted that the stress–energy tensor required by the metric violates the energy conditions, so that the drive would need exotic matter of negative energy density. Much of the subsequent literature has addressed whether that requirement can be reduced or removed. In 1999 Chris Van Den Broeck showed that modifying the geometry of the bubble could lower the total energy requirement by many orders of magnitude, and in 2002 José Natário described a variant in which the volume of space is neither expanded nor contracted, demonstrating that the common description of the drive as expanding space behind the ship and contracting it in front is not an essential feature of the geometry.
Research activity increased markedly after 2020. Between 2020 and 2021, Osvaldo Santos-Pereira, Everton Abreu and Marcelo Ribeiro published a series of papers analysing which matter models—dust, perfect fluids, charged dust and fluids with a cosmological constant—are compatible with the warp-drive geometry. In 2021, Erik Lentz, Alexey Bobrick and Gianni Martire, and Shaun Fell and Lavinia Heisenberg separately proposed warp geometries whose energy density is non-negative as measured by a particular family of observers. A 2022 analysis by Jessica Santiago, Sebastian Schuster and Matt Visser argued that such tests examine only one preferred family of observers, and that the spacetimes concerned still violate the energy conditions once all observers are taken into account.
From 2024, work shifted towards numerical methods and towards asking whether a warp geometry could be produced by a physically reasonable source, rather than inferred from a metric chosen in advance. A numerical toolkit released that year made it possible to compute the curvature, stress–energy content and energy-condition maps of metrics that are not analytically simple, and was used to construct a subluminal configuration, moving at constant velocity, that was reported to satisfy all of the classical energy conditions. Other work has examined warp bubbles embedded in curved backgrounds such as black hole and de Sitter space geometries, and the evolution of warp-like initial data as a solution of the Einstein equations rather than as a permanently imposed geometry.
Alcubierre metric 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 at effectively faster-than-light speed. The interior of the bubble is an inertial reference frame and inhabitants experience no proper acceleration. This method of transport does not involve objects in motion at faster-than-light speeds with respect to the contents of the warp bubble; that is, a light beam within the warp bubble would still always move more quickly than the ship. Because objects within the bubble are not moving (locally) more quickly 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.
An extension of the Alcubierre metric that eliminates the expansion of the volume elements and instead relies on the change in distances along the direction of travel is that of mathematician José Natário. In his metric, spacetime contracts towards the prow of the ship and expands in the direction perpendicular to the motion, meaning that the bubble actually "slides" through space, roughly speaking by "pushing space aside".
The Alcubierre drive remains a hypothetical concept with seemingly difficult problems, although the amount of energy required is no longer thought to be unobtainably large. However, Alexey Bobrick and Gianni Martire claim that, in principle, a class of subluminal, spherically symmetric warp drive spacetimes can be constructed based on physical principles presently known to humanity, such as positive energy. Furthermore, a study by Remo Garattini and Kirill Zatrimaylov shows that the amount of negative energy density required to sustain a warp bubble can in principle be reduced if the bubble is moving in an external gravitational field, such as that of a black hole.
Mathematics Using the ADM formalism of general relativity, the spacetime is described by a foliation of space-like hypersurfaces of constant coordinate time , with the metric taking the following general form:
where is the lapse function that gives the interval of proper time between nearby hypersurfaces, is the shift vector that relates the spatial coordinate systems on different hypersurfaces, is a positive-definite metric on each of the hypersurfaces.
The particular form that Alcubierre studied is defined by:
where
with arbitrary parameters and . Alcubierre's specific form of the metric can thus be written:
With this particular form of the metric, it can be shown that the energy density measured by observers whose 4-velocity is normal to the hypersurfaces is given by:
where is the determinant of the metric tensor.
Thus, because the energy density is negative, one needs exotic matter to travel more quickly than the speed of light. The existence of exotic matter is not theoretically ruled out; however, generating and sustaining enough exotic matter to perform feats such as faster-than-light travel (and to keep open the "throat" of a wormhole) is thought to be impractical. According to writer Robert Low, within the context of general relativity it is impossible to construct a warp drive in the absence of exotic matter.
Connection to dark energy and dark matter Astrophysicist Jamie Farnes from the University of Oxford has proposed a theory, published in the peer-reviewed scientific journal Astronomy & Astrophysics, that unifies dark energy and dark matter into a single dark fluid, and which is expected to be testable by the Square Kilometre Array around 2030. Farnes found that Albert Einstein had explored the idea of gravitationally repulsive negative masses while developing the equations of general relativity, an idea which leads to a "beautiful" hypothesis where the cosmos has equal amounts of positive and negative qualities. Farnes' theory relies on negative masses that behave identically to the physics of the Alcubierre drive, providing a natural solution for the current "crisis in cosmology" due to a time-variable Hubble parameter.
As Farnes' theory allows a positive mass (i.e. a ship) to reach a speed equal to the speed of light, it has been dubbed "controversial". If the theory is correct, which has been highly debated in the scientific literature, it would explain dark energy, dark matter, allow closed timelike curves , and suggest that an Alcubierre drive is physically possible with exotic matter.
Physics With regard to certain specific effects of special relativity, such as Lorentz contraction and time dilation, the Alcubierre metric has some apparently peculiar aspects. In particular, Alcubierre has shown that a ship using an Alcubierre drive travels on a free-fall geodesic even while the warp bubble is accelerating: its crew would be in free fall while accelerating without experiencing accelerational g-forces. Enormous tidal forces, however, would be present near the edges of the flat-space volume because of the large space curvature there, but a suitable specification of the metric would keep the tidal forces 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 might 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 could be misleading, since the contraction and expansion actually refer to the relative motion of nearby members of the family of ADM observers.