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The Krasnikov Tube: A Subway to the Stars

by John G. Cramer

Alternate View Column AV-86
Keywords: Krasnikov Tube Alcubierre Warp Drive general relativity space time metric FTL subway
Published in the September-1997 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 04/12/97 and is copyrighted ©1997 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

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About a year ago I wrote a column about the Alcubierre Warp Drive (see the 11/96 issue of Analog). The Alcubierre Warp Drive is a distortion of space, a solution to the equations of general relativity that forms a sphere of flat space surrounded by a warped-space "bubble". At the front edge of the bubble, space is contracting (like a collapsing black hole, and at the rear edge space is expanding like a mini-Big-Bang. This space warp transports the contents of the spherical volume forward at velocities that can be much larger than the velocity of light. This was proposed in 1994 by Miguel Alcubierre in the physics journal Classical and Quantum Gravity.

It has taken quite a while for the physics community to digest Alcubierre's ingenious space warp, criticize it, and suggest improvements, but now this is beginning to happen. In this column I want to discuss some of this recent work.


S. V. Krasnikov is a theoretical Physicist at the Central Astronomical Observatory at Pulkovo in St. Petersburg, Russia. He has examined Alcubierre's proposal and found what seems to be a near-fatal flaw in the scheme: if the space warp moves faster than the velocity of light, it cannot be controlled from inside. Krasnikov's analysis shows that at superluminal speeds the interior of the bubble is causally isolated from its surface and exterior. Photons cannot pass from the inside to the outside. Therefore, there would be no way of controlling the space warp, of stopping, starting or steering. And it would not be a very interesting trip because passengers inside the bubble would be isolated from the outside world and unable to see where they were going.

Of course, these problems might be circumvented by entering and exiting an Alcubierre space warp while it was traveling slowly, arranging for some automatic mechanism to raise the bubble velocity above the speed of light for a programmed period, and then lower the speed again in order to exit. This scheme is unworkable because material objects (like control computers and a warp generators) in the skin of the bubble would be destroyed by the enormous forces generated from space annihilation or creation, while outside the bubble they would not travel at the superluminal speed of the interior and would be left behind.

Therefore, Krasnikov proposes an alternative: create a space warp behind the space ship as it travels at near lightspeed to some distant star system, and then use the "tube" thus created for the return trip. He suggests a particular "metric", a distortion of space that has an interesting property for the return trip: it gets you back home shortly after you left, no matter how far you go. Perhaps this is best illustrated with an example.

Suppose we have a starship that can travel at speeds that are 0.00005% (5 parts in 10,000,000) less than the speed of light (about the speed of particles in our largest particle accelerators), which means that within the ship time slows down by a factor of 1000 (the clock ticks that much slower than a clock on Earth.)

The ship makes a trip to the star system of Deneb, the brightest star in the constellation Cygnus, approximately 1,630 light-years from Earth. For earth-based observers watching the trip through a telescope, the trip would take essentially 1,630 years. However, because of relativistic time dilation the trip only takes 1.63 years for those aboard the ship.

But as SF readers understand, the short duration of the trip is only a relativistic illusion, the lightspeed equivalent of sleeping in a deep freeze while time goes on outside. We know from stories like Ursula LeGuin's Rocannon's World and Joe Haldeman's The Forever War that when the astronauts return from a trip to Deneb, they can expect to find that 3,260 years have passed, everyone they knew is dead, and the world has changed beyond recognition, right? Well, not quite. The Krasnikov Tube that was created in the wake of the spaceship now forms a return pathway within which time "unwinds. Because of the temporal properties of the Krasnikov metric, if the ship travels home at near lightspeed in the space enclosed by this tube, the astronauts can return home just a bit over 3 years after they left.

In effect the Krasnikov Tube is a tunnel through time, connecting the departure time of the ship with the time of its arrival at Deneb. Inside the tube space-time is "flat", i.e., unwarped, but the path limits of light through space-time has been opened out so that it permits superluminal travel in one direction only, e.g., back to the starting point on Earth.

In its impact on interstellar travel, the Krasnikov Tube is similar to that of a hypothetical wormhole mouth launched with an near-lightspeed velocity, a concept that I described in a previous AV column ("Wormholes II: Getting There in No Time", Analog, June, 1990). In both cases the distortion of space-time provides a shortcut that subverts the relativistic rules of interstellar travel. However, there is an important difference: the traveling wormhole provides a shortcut through time and space, so that once the wormhole path was established one could literally walk from one star system to another. On the other hand, the Krasnikov Tube is only a shortcut through time. The distance to Deneb and back must still be traversed by a fast starship with enormous relativistic time dilation.

Krasnikov argues that despite the time-machine-like aspects of his metric, it cannot violate the Law of Causality (that a cause must always precede its effects in all coordinate systems and along all space-time paths) because all points along the round-trip path of the spaceship always have an ordered timelike separation interval [in algebraic terms, c2(t1-t2)2 is always larger than (x1-x2)2 + (y1-y2)2 + (z1-z2)2]. This means, for example, that a light-beam message sent along a Krasnikov Tube cannot be used for back-in time signaling.

Therefore, aside from the "engineering problem" of actually building a hyperfast starship that can leave a Krasnikov Tube in its wake, this all sounds very promising as a way around the lightspeed limit. What, then, are the problems, if any, with Krasnikov's proposal for fast-turnaround interstellar travel?


Allen E. Everett and Thomas A. Roman of Tufts University have recently written a paper criticizing the Krasnikov scheme on several grounds. First, they show that while one Krasnikov Tube presents no problems with Causality, two Krasnikov Tubes going in opposite directions can create timelike loops and violations of Causality.

For example, suppose that on the return trip from Deneb to Earth the astronauts lay down Tube II rather than traveling back in Tube I, the first tube they produced. In about 1.63 years of ship time they will arrive back on Earth, but at a time 3260 years in the future of their departure. But now that two Krasnikov Tubes are in place, astronauts from the future can travel to Deneb in Tube II, then to Earth in Tube I and will arrive 3260 years earlier than their departure. The Krasnikov Tube system has become a time machine.

In a previous column (Analog, Mid-December, 1994, "NASA Goes FTL - Part 1: Wormhole Physics") I had discussed the emerging view first advocated by Stephen Hawking that "Nature abhors a time machine" and that exponentially growing vacuum fluctuation will rise up and destroy any attempt to create a timelike loop in which Causality is violated. If that was so, it would be possible to construct Tube I, but vacuum fluctuations would destroy Tube II before it could be used. Therefore, as long as Krasnikov Tube were used for "proper" activities like interstellar travel and not for "improper" activities like time travel, all would be right with the universe.

Everett and Roman further demonstrate another problem with the Krasnikov Tube: it has a net energy that is negative. They also argue that within the thin walls of the tube the local energy density is not only negative but also is so enormous as to be physically impossible to achieve with any conceivable machine constructed of matter.

Producing a region of space with a negative net energy would actually offer some advantages, in that you could use the surplus energy you remove to drive your space ship or perhaps beam it back to Earth to be sold to the light and power company. However, while we currently know how to use the Casimir effect to produce a small region of space that has a small negative energy density, the total overall energy of any Casimir device is positive. Creating large regions of space that have a negative energy density is well beyond our present technological abilities.

The issue, however, is not whether we can construct a Krasnikov Tube (we certainly can't), but whether it is physically possible for some advanced civilization, one that can carry out works of engineering on the scale of star systems and user friendly space-time metrics. Typically, the interesting but exotic solutions to Einstein's equations of general relativity such as wormholes, warp drives, and the Krasnikov Tube considered here all require some negative energy density and violate what is called "the weak energy condition" (that the overall energy of a metric should be positive). This is a rule often used in general relativity. It may or may not have the status of a natural law. I feel, with some encouragement from considerations of quantum gravity, that the weak energy condition is not a law of nature and can be violated.

In a previous column (Analog, Mid-December, 1994) I described Visser wormholes which are connected regions of flat space framed by an exotic metric of general relativity called a cosmic string, a one-dimensional string-like discontinuity in the structure of space. The comic string framing a Visser wormhole must have negative energy and negative string tension, giving it a tendency to expand which balances the wormhole's tendency to contract and disappear. This seems to be a general property of exotic metrics. They would otherwise be unstable, attempting to pinch together and vanish. The negative energy component in general represents a tendency to expand, thus counteracting the intrinsic tendency of the metric to collapse.

The two dimensional analog of the cosmic string solution of general relativity is the "cosmic wall" a two dimensional sheet discontinuity in space. If we imagine this cosmic wall formed into a circular tube and having a negative "hoop tension" around its circular cross section, then we have a suitable wall for a Krasnikov Tube, cincentrated negative energy density and all. Whethere this works on closer scrutiny I will leave to the mathematical theorists, but it is at least a plausible way in which an advanced civilization might build such a tube.

This, then raises an interesting question. Are there such Krasnikov Tubes connecting star systems in our neighbor hood of the galaxy? How could they be detected at interstellar distances? Would they have any distinctive physical properties (like deflection of light passing near or through them) that would constitute a unique detection signature?

At least, the existence of Krasnikov Tubes between the stars might provide a neat solution to the Fermi Paradox. We get no interstellar visitors because there is no Krasnikov Tube coming to the Solar System, so it its too inconvenient. We receive no interstelar communications because all such communications are beamed through Krasnikov Tubes, so that the sender does not have to wait years or centuries for an answer.

I think that, at the very least, we have some good material for hard SF stories here.


AV Columns On-line: Electronic versions of more than eighty past "The Alternate View" columns by John G. Cramer are available on-line on WorldWideWeb at the URL: http://www.npl.washington.edu/AV. The LANL preprintsreferenced below can obtained on WorldWideWeb at: http://xxx.lanl.gov.


References:

The Krasnikov Tube:

S. V. Krasnikov, LANL Preprint Archive gr-qc/9511068 (1995);

Allen E. Everett and Thomas A. Roman, LANL Preprint Archive gr-qc/9702049 (1997).

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This page was created by John G. Cramer on 07/10/97.