along its path from a fictional SF prop-idea to a well

founded physics concept that might one day be

realized. This improvement on the Alcubierre warp

drive was devised by general relativity theorist Chris

Van Den Broeck of the Catholic University of Leuven in

Belgium. He has eliminated seemingly insurmountable

problems with the Alcubierre warp-drive scheme. His

improvement employs topological gymnastics to keep the

interior of the warp bubble large while making its

external surface very small. But before describing Van

Den Broecks work, Ill summarize the Alcubierre warp

drive concept itself, first featured in my column

(#81) in the November-96 Analog.

Until 1994 a "warp drive" was one of the myths of

science fiction, a rubber-science concept used

principally to permit space-opera heroes to flit from

one star system to another at faster-than-light

speeds, moving the plot forward in the process. Those

familiar with the laws of physics saw the warp drive

as a flagrant violation of the principles of special

relativity, conservation of energy, and

physics-as-we-know-it. It was tolerated as an

excessive but perhaps necessary use of literary

license by SF authors.

The status of the warp drive changed dramatically in

1994, when Dr. Miguel Alcubierre published a paper

entitled "The Warp Drive: hyper-fast travel within

general relativity" in the journal Classical and

Quantum Gravity. Alcubierre is a theoretical physicist

from Mexico who in 1994 was working at the University

of Wales and is now at the Albert Einstein Institute

in Potsdam, Germany. Also a fan of SF, he was steeped

in the SF tradition and turned his physics expertise

to the task of considering how a warp drive might be

constructed within the restrictions of general

relativity, our present "standard model" of gravity.

Alcubierre constructed a "metric", a mathematical

specification of the curvature of space-time that had

all the characteristics of a SF warp-drive including

the capability for faster-than-light travel.

Surprisingly, Alcubierres warp-drive metric is a

solution of Einsteins equations of general relativity

and is completely consistent with them. Science

fictions warp drive had been given a consistent

theoretical and mathematical basis.

When theoretical physicist use general relativity,

their normal procedure is to start with some

distribution of massive objects and to calculate the

metric describing space-time curvature that such a

distribution would produce. Alcubierre reversed this

procedure. Without worrying about how it might be

formed, he constructed a metric that could transport

volume of flat space, perhaps containing a spaceship,

at superluminal speed. This was accomplished by

placing the volume of flat space inside a "bubble of

highly curved space, then destroying space in front of

the bubble while creating new space behind it.

Effectively, the warp bubble is driven forward by

creating and annihilating space as if a local Big Bang

were occurring at the rear of the space ship while a

local Big Crunch was occurring in front of it.

How does Alcubierres metric manage to move an object

faster than the speed of light? Isnt that in direct

contradiction to Einsteins special theory of

relativity? Actually, no. General relativity treats

special relativity as a restricted sub-theory that

applies locally to any region of space that is

sufficiently small that its curvature can be

neglected. General relativity does not forbid

faster-than-light travel or communication, but it does

require that the local restrictions of special

relativity must apply. In other words, light speed is

the local speed limit, but the broader context of

general relativity may provide ways of circumventing

this local statute. One example of this is a wormhole

(see my AV columns, Analog 6/89 and 5/90) connecting

two widely separated locations in space, say five

light-years apart. An object might take a few minutes

to move with at low speed through the neck of a

wormhole, observing the local speed-limit laws all the

way. However, by transiting the wormhole the object

has traveled five light years in a few minutes,

producing an effective speed of a million times the

velocity of light.

Another example of a faster than light phenomenon is

the expansion of the universe itself. As the universe

expands, new space is created between any two

separated objects. The objects may each be at rest in

their local space-time, but nevertheless the distance

between them may grow at a rate that is much greater

than the speed of light. According to the current

standard model of cosmology, most of the universe is

receding from us at FTL speeds and therefore is

completely isolated from us.

Alcubierres metric uses an analogous expansion of

space to drive the warp bubble forward. However, since

the ship within the bubble is at rest in its local

space, the occupants will feel no acceleration forces

when the forward speed of the bubble changes, nor will

they experience the "usual" relativistic effects of

mass increase and time dilation. If an Alcubierre

warp-drive ship travels 100 light years at 100 times

the velocity of light, to both the occupants and

outside observers the trip takes one year, no more and

no less.

--------------------------------------------------------------------------------

Alcubierres publication stimulated a flurry of

activity among general relativity theorists, who

investigated the implications of the new idea, It was

found, by himself and others, that Alcubierres

original warp-drive idea had a number of serious

problems. It violated the strong, dominant, and weak

energy conditions of general relativity. The net

energy of the warp bubble, as it turned out, was

extremely large and negative. For example, a warp

bubble 100 meters in radius that might contain a space

ship of reasonable size would have a net negative

energy that was roughly ten times larger in magnitude

than the entire (positive) energy of the visible

universe. Another problem was that the walls of the

bubble would have to be so thin that they could not be

constructed with matter, even "collapsed matter" of

nuclear density. It was also found that most of the

warp bubble is disconnected from a sizable part of the

external negative energy region. Therefore, the

surface part of the bubble could not be carried along

and would have to be continuously generated

externally. The drive could not be self-contained or

self-operated. These problems have seemed so

overwhelming that recent attention has been focused on

alternatives like the Krasnikov Tube (see my column

#86 in the September-97 Analog) that might present

fewer problems of implementation and control.

Now, however, Dr. Van Den Broeck has proposed an

improvement on Alcubierres scheme that appears to

solve many of its problems. Van Den Broeck observed

that most of the undesirable effects of Alcubierres

drive scale with the volume or surface area of the

warp bubble. Therefore, his simple solution is to make

the radius of the warp bubble so small that the

problems go away. In doing this, he makes use of

another trick from general relativity. The interior

volume of a region of space bounded by a closed

surface, because of space curvature, can be made much

larger than the flat-space volume bounded by its

surface. In curved space the inside volume of a sphere

of radius R can be much greater than 4/3pR3.

The new metric of the Van Den Broeck/Alcubierre warp

bubble is like a bulls-eye target with a center

(Region 1) surrounded by three concentric rings

(Regions 2-4). The central sphere in Region 1 is flat

space large enough to hold a spaceship. Region 2 is a

spherical shell containing distorted space that

connects the large interior volume of Region 1 to an

exterior region that is smaller in radius by a factor

of 1/a. Region 3 is a transition region of flat space,

a spherical shell with a volume much less than that of

Region 1. Region 4 is a spherical shell that is

Alcubierres warp bubble, but now with a very small

radius. Van Den Broeck makes the radius of Region 1

about 100 meters, and sets a to 1034, so that Region 4

is only about 3 ´ 10-32 meters in radius. With such a

small radius, if the warp bubble travels at 10 times

the velocity of light the amount of negative

mass-energy it would require is only about 0.06

grams. Even if it travels at 100 times the velocity of

light, it would require is only about 56 kilograms of

negative mass-energy. Region 2, where the volume of

space is compressed from inside to outside also

requires a quantity of negative mass-energy, but Van

Den Broeck calculates that it is only about 4 grams.

These small quantities of negative energy eliminate

many of the problems of Alcubierres original concept.

However, even with these improvements, there would

still be very severe "engineering problems" with any

implementation of the scheme. First, although the

interior of the warp bubble may be quite spacious, its

exterior is only 3 ´ 10-32 meters in radius, mush

smaller than a proton and approaching the Planck

length (1.62 ´ 10-35 meters) in size. This is close

enough to the minimum length-scale of the universe

that such a size reduction is doubtful due to quantum

effects. Moreover, since the diameter of the warp

bubble is many orders of magnitude smaller than a

wavelength of visible light (about 4 ´ 10-7 meters)

there would be no possibility of seeing out from

inside the bubble. Any trip would be a blind one, with

no possibility of seeing or steering. Moreover, while

the magnitude of energy required to form a warp bubble

becomes more reasonable in Van Den Broecks warp

drive, the energy density requirement remains

unphysically large.

And how could our space travelers enter the bubble or

exit again at the end of their trip? Van Den Broecks

calculations indicate that slowing the bubble to a

near stop might permit it to be expanded to any

desired size. However, such an expansion would

decrease the wall thickness, and it is not clear what

would happen if the wall thickness became smaller than

the Planck length. Van Den Broeck ends his paper by

commenting that while the first warp-drive space

flight remains a long way off, perhaps it has become

slightly less improbable with the new scenario for a

warp bubble.

--------------------------------------------------------------------------------

>From the point of view of science fiction, even the

application of general relativity to create a volume

of space that is larger on the inside than on the

outside is very appealing. It would, for example,

solve the book storage space problem for may of us.

Further, I cannot wait until this principle is applied

to airplane seats!

Van Den Broecks warp drive is a large volume of flat

space that is connected to normal space by a tiny

"neck". It therefore resembles the more familiar

general relativity topologies of wormholes or "baby

universes" and perhaps has a similar behavior. This

raises the issue of how the neck is prevented from

pinching off altogether, isolating our space travelers

in a new universe of their own rather than

transporting them to a new part of the old one.

I should also comment that these calculations were

performed without a proper understanding of the

unknown theory-to-be that we call "quantum gravity". A

warp bubble with a diameter near the Planck scale will

be affected by quantum gravity effects and

corrections. In particular, my previous column (12/99

Analog) described the possibility that extra space

dimensions affecting gravity may be rolled up into

loops about a millimeter in diameter. If this were the

case, it would modify general relativity at the

millimeter scale and would almost certainly render Van

Den Broecks metric unachievable.

Thus extra space dimensions might block the path to

faster-than-light travel. Ours is certainly an

interesting universe, and it grows more interesting as

we understand it more fully.

--------------------------------------------------------------------------------

AV Columns On-Line: Electronic reprints of over 100

"The Alternate View" columns by John G. Cramer, all

previously published in Analog, are available on-line

at the URL: http://www.npl.washington.edu/av. The

preprint referenced below can be obtained at:

http://xxx.lanl.gov

References:

General Relativity: C.W. Misner, K.S. Thorne, and J.A.

Wheeler, Gravitation, W.H. Freeman (1973).

The Alcubierre Warp Drive: Miguel Alcubierre,

Classical and Quantum Gravity, v. 11, L73-L77, (1994).

The Micro-Warp Drive: C. Van Den Broeck, preprint

hep-ph/9805217 , LANL Archive, (April 2, 1999).

Une injustice faite à un seul est une menace faite à tous

Montesquieu (1689-1755)