The **Alcubierre metric**, also known as the **Alcubierre drive** or **warp drive**, is a speculative mathematical model of a spacetime exhibiting some features reminiscent of the fictional faster than the speed of light warp drive from Star Trek; hence the name. The Alcubierre Drive is often called a 'solution' of Einstein's field equations in general relativity, but this is inaccurate; see Alcubierre metric.

The physicist Miguel Alcubierre proposed a method of stretching space in a wave, causing the space "ahead" of a spacecraft to contract along the axis the spacecraft wishes to travel in 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 actually moving within this bubble, but rather being carried along as the region itself moves, conventional relativistic effects do not apply. There is no known way to induce such a wave, however, or to leave it once started; thus, the Alcubierre drive remains a theoretical concept at this time.

## Mathematics of the Alcubierre drive Edit

Using the 3+1 formalism of general relativity, the spacetime is described by a foliation of space-like hypersurfaces of constant coordinate time

$ t $ . The general form of the Alcubierre metric is:

- $ ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j $

where

$ \alpha $ is the lapse function that gives the interval of proper time between nearby hypersurfaces,

$ \beta^i $ is the shift vector that relates the spatial coordinate systems on different hypersurfaces and

$ \gamma_{ij} $ is a positive definite metric on each of the hypersurfaces. The particular form that Alcubierre studied (1994) is defined by:

- $ \alpha=1\, $

- $ \beta^x=-v_s(t)f\left(r_s(t)\right), $
- $ \beta^y = \beta^z =0 $
- $ \gamma_{ij}=\delta_{ij} $

where

- $ v_s(t)=\frac{dx_s(t)}{dt}, $
- $ r_s(t)=[(x-x_s(t))^2+y^2+z^2]^{\frac{1}{2}} $

and

- $ f(r_s)=\frac{\tanh(\sigma (r_s + R))-\tanh(\sigma (r_s - R))}{2 \tanh(\sigma R)} $

with

$ R > 0 $ and

$ \sigma > 0 $ arbitrary parameters. 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

- $ -\frac{c^4}{8 \pi G} \frac{v_s^2 (x^2+y^2)}{4 g^2 r_s ^2} \left(\frac{df}{dr_s}\right)^2 $

where

$ g $ is the determinant of the metric tensor. Thus, as the energy density is negative, 'one needs exotic matter to travel faster than the speed of light' (Alcubierre, 1994). The existence of exotic matter is not theoretically ruled out and the Casimir effect lends support to the proposed existence of such matter; however, generating enough exotic matter and sustaining it to perform feats such as faster-than-light travel (and also to keep open the 'throat' of a wormhole) is thought to be impractical. Low (1999) has shown that within the context of general relativity, it is impossible to construct a warp drive in the absence of exotic matter. It is generally believed that a consistent theory of quantum gravity will resolve such issues once and for all.

## Physics of the Alcubierre driveEdit

For those familiar with the effects of special relativity, such as Lorentz contraction, mass increase 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.

##### Manipulated spacetimeEdit

String theory (and all other theories involving hidden dimensions) predict that gravity and electromagnetism unify in hidden dimensions and that the hidden dimensions are indetectible because of their small size. It does also predict that sufficiently short-waved photons, with wavelengths shorter than the size of the hidden dimensions, can enter them. Producing ultra-short photons can thus manipulate gravity, with revolutionizing space travel applications such as cheap anti-gravity launches. The problem that it would require high energy can be practically solved by concentrating several laser beams on a nanoparticle, heating it to locally extreme temperatures. An Alcubierre metric can be created by ejecting multiple nanoparticles from the craft and then beam perfectly timed laser beams on them (fire at the most distant first so that they are hit simultaneously), so each nanoparticle contributes a slower than light effect but together add up to faster than light, creating no discrete event horizon and thus no Hawking radiation.

### The Alcubierre drive and science fiction Edit

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, analogously 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).

Although it precedes Alcubierre drive, the anime version of Captain Future featured a similar mechanism, called *undulating mode*.

## See alsoEdit

## ReferencesEdit

- Template:Cite book Apparently a popular book by a science writer, on space travel in general.

## External linksEdit

- Journal of Advanced Theoretical Propulsion
- Problems with Warp Drive Examined
- http://w210.ub.uni-tuebingen.de/dbt/volltexte/2001/240/pdf/09warp.html provides a short video clip of the hypothetical effects of the warp drive.