Alcubierre drive
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 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 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 would eliminate those solutions in general relativity that allow for backward time travel and thus make the Alcubierre drive invalid.
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 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 more quickly than light, the mathematical formulation of the Alcubierre metric is consistent with the conventional claims of the laws of relativity 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.
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 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 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.
In general relativity, one often 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. The need for exotic matter raises questions about whether one can distribute the matter in an initial spacetime that lacks a warp bubble in such a way that the bubble is created at a later time, although some physicists have proposed models of dynamical warp-drive spacetimes in which a warp bubble is formed in a previously flat space. Moreover, according to Serguei Krasnikov, generating a bubble in a previously flat space for a one-way faster-than-light trip requires forcing the exotic matter to move at local faster-than-light speeds, something that would require the existence of tachyons, although Krasnikov also notes that when the spacetime is not flat from the outset, a similar result could be achieved without tachyons by placing in advance some devices along the travel path and programming them to come into operation at preassigned moments and to operate in a preassigned manner. Some suggested methods avoid the problem of tachyonic motion, but would probably generate a naked singularity at the front of the bubble. Allen Everett and Thomas Roman comment on Krasnikov's finding :
does not mean that Alcubierre bubbles, if it were possible to create them, could not be used as a means of superluminal travel. It only means that the actions required to change the metric and create the bubble must be taken beforehand by some observer whose forward light cone contains the entire trajectory of the bubble.
For example, if one wanted to travel to Deneb and arrive less than 2,600 years in the future according to external clocks, it would be required that someone had already begun work on warping the space from Earth to Deneb at least 2,600 years ago:
A spaceship appropriately located with respect to the bubble trajectory could then choose to enter the bubble, rather like a passenger catching a passing trolley car, and thus make the superluminal journey ... as Krasnikov points out, causality considerations do not prevent the crew of a spaceship from arranging, by their own actions, to complete a round trip from Earth to a distant star and back in an arbitrarily short time, as measured by clocks on Earth, by altering the metric along the path of their outbound trip.