Alcubierre drive
Concept of the Alcubierre drive, showing the opposing regions of
expanding and contracting spacetime that propel the central region
The
Alcubierre drive (or
Alcubierre metric /
Metric tensor) is a speculative idea based on a valid solution of the Einstein field equations as proposed by
Miguel Alcubierre by which a spacecraft might be accelerated to speeds greater than the
speed of light in order to achieve the objective of interstellar flight.
History
In 1994 Alcubierre proposed a way of changing the geometry of space
by creating a wave which 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 as a consequence of the actions of the drive. If
this is so, conventional
relativistic effects such as
time dilation
would not apply in the way they would in the case of a ship moving at a
very great velocity through flat spacetime, relative to other objects.
This method of propulsion would not involve objects in motion at speeds
faster than light with respect to the contents of the
warp-bubble; that is, a light beam within the
warp-bubble would still always move faster than the ship. Thus the mathematical formulation of the
Alcubierre metric
does not contradict the conventional claim that the laws of relativity
do not allow a slower-than-light object to accelerate to
faster-than-light speeds. The Alcubierre drive, however, remains a
hypothetical concept with seemingly insuperable problems: The amount of
energy required is unobtainably large, there is no method to create a
warp bubble in a region that does not already contain one, and there is
no method to move from the warp-bubble once having arrived at a supposed
destination.
Alcubierre metric
The Alcubierre metric defines the warp drive spacetime. This is a
Lorentzian manifold which, if interpreted in the context of
general relativity, allows a
warp bubble to appear in previously flat spacetime and move off at effectively
superluminal speed. Inhabitants of the bubble feel no
inertial
effects. The object(s) within the bubble are not moving (locally)
faster than light, instead, the space around them shifts so that the
object(s) arrives at its destination faster than light would in normal
space.
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.
Mathematics of the Alcubierre drive
Using the
ADM 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 metric described within the context of this formalism is:
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
and
with
and
arbitrary parameters. 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, as the energy density is negative, one needs
exotic matter to travel faster than the speed of light.
The existence of exotic matter is not theoretically ruled out; 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 has argued 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 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. In
particular, 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.
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 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. Yet another problem is that, according to
Serguei Krasnikov,
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. Some 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.
Difficulties
Significant problems with the metric of this form stem from the fact that all known warp drive spacetimes violate various
energy conditions.
It is true that certain experimentally verified quantum phenomena, such as the
Casimir effect,
when described in the context of the quantum field theories, lead to
stress-energy tensors which also violate the energy conditions, such as
negative mass-energy, and thus one can hope that Alcubierre-type warp
drives can be physically realized by clever engineering taking advantage
of such quantum effects. However, if certain
quantum inequalities conjectured by Ford and Roman hold,
then the energy requirements for some warp drives may be absurdly gigantic, e.g. the energy equivalent of -10
67 grams might be required
to transport a small spaceship across the Milky Way galaxy. This is orders of magnitude greater than the
estimated mass of the universe. Counter-arguments to these apparent problems have also been offered.
Chris Van Den Broeck, in 1999, has tried to address the potential issues.
By contracting the 3+1 dimensional surface area of the 'bubble' being
transported by the drive, while at the same time expanding the 3
dimensional volume contained inside, Van Den Broeck was able to reduce
the total energy needed to transport small atoms to less than 3
solar masses. Later, by slightly modifying the Van Den Broeck metric,
Krasnikov reduced the necessary total amount of
negative energy to a few milligrams.
Krasnikov proposed that, if tachyonic matter cannot be found or used,
then a solution might be to arrange for masses along the path of the
vessel to be set in motion in such a way that the required field was
produced. But in this case, the Alcubierre Drive vessel is not able to
go dashing around the galaxy at will. It is only able to travel routes
which, like a railroad, have first been equipped with the necessary
infrastructure. The pilot inside the bubble is causally disconnected
with its walls and cannot carry out any action outside the bubble. Thus,
because the pilot cannot place infrastructure ahead of the bubble while
"in transit", the bubble cannot be used for the
first trip to a distant star. In other words, to travel to
Vega
(which is 25 light-years from the Earth) one first has to arrange
everything so that the bubble moving toward Vega with a superluminal
velocity would appear and these arrangements will always take more than
25 years.
Coule has argued that schemes such as the one proposed by Alcubierre are infeasible as matter placed
en route
of the intended path of a craft has to be placed at superluminal speed.
Thus, according to Coule, an Alcubierre Drive is required in order to
build an Alcubierre Drive. Since none have been proven to exist already
then the drive is impossible to construct, even if the metric is
physically meaningful. Coule argues that an analogous objection will
apply to
any proposed method of constructing an Alcubierre Drive.
A paper by José Natário published in 2002 argued that it would be
impossible for the ship to send signals to the front of the bubble,
meaning that crew members could not control, steer or stop the ship.
A more recent paper by Carlos Barceló, Stefano Finazzi, and Stefano
Liberati makes use of quantum theory to argue that the Alcubierre Drive
at FTL velocities is impossible; mostly due to extremely high
temperatures caused by
Hawking radiation
destroying anything inside the bubble at superluminal velocities and
leading to instability of the bubble itself. These problems do not arise
if the bubble velocity is kept subluminal, but it is still necessary to
provide exotic matter for the drive to work.
More difficulties emerge in regards to the amount of exotic matter
required for such a propulsion. According to Pfenning and Allen Everett
of Tufts, a warp bubble traveling at 10 times light-speed must have a
wall thickness of no more than 10
−32 meters. This is only slightly longer than the
Planck length, 10
−35.
A bubble macroscopically large enough to enclose a ship 200 meters
across would require a total amount of exotic matter equal to 10 billion
times the mass of the observable universe. Straining the exotic matter
to an extremely thin band of 10
−32 meters is considered
impractical. Similar constraints apply to Krasnikov's superluminal
subway. A modification of Alcubierre's model was recently constructed by
Chris van den Broeck of the Catholic University of Louvain in Belgium.
It requires much less exotic matter but places the ship in a curved
space-time "bottle" whose neck is about 10
−32 meters.
So-called cosmic strings, hypothesized in some cosmological theories,
involve very large energy densities in long, narrow lines. But
[clarification needed]
all known physically reasonable cosmic-string models have positive
(positive space-time warping effects) energy densities. These results
seem to make it rather unlikely that one could construct Alcubierre warp
drives using exotic matter generated by quantum effects.
The Alcubierre drive and science fiction
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. Some science-fiction works, particularly of the 'hard' genre,
have explicitly made use of the Alcubierre theory, such as
Stephen Baxter's novel
Ark.
The Alcubierre drive theory is proposed as a possible reason for events occurring in the graphic novel "
Orbiter" by
Warren Ellis and
Colleen Doran.
The
Ian Douglas "
Star Carrier" series exclusively uses the Alcubierre drive as the main mode of interstellar travel.
Also, in
M. John Harrison's novel
Light,
the character Ed Chianese, while trying to get a job with the Circus of
Pathet Lao, claims that he "rode navigator on Alcubierre ships."
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