Krasnikov tube

The Krasnikov Tube is a speculative mechanism for space travel involving the permanent warping of spacetime into superluminal tunnels.

Origins and theory

Serguei Krasnikov is a theoretical physicist at the Central Astronomical Observatory at Pulkovo in St. Petersburg, Russia. He identified what he saw as a critical flaw in Miguel Alcubierre's space warp proposal for space travel: 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.

These problems might be circumvented by entering and exiting an Alcubierre space warp while it was travelling 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 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.

Krasnikov's alternative is to 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. This distortion of space has an interesting property for the return trip: it gets you back home shortly after you left, no matter how far you go.

In effect the Krasnikov tube is a tunnel through time, connecting the departure time of the ship with the time of its arrival. Inside the tube space-time is flat, but the path limits of light through space-time have been opened out so that it permits superluminal travel in one direction only; for example, back to the starting point on Earth.

Causality violations

One-tube case

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, $c^2\; dt^2$ is always larger than $dx^2\; +\; dy^2\; +\; dz^2$] . This means, for example, that a light-beam message sent along a Krasnikov tube cannot be used for back-in-time signaling.

Two-tube case

While one Krasnikov tube can be seen to present no problems with causality, it was proposed by Allen E. Everett and Thomas A. Roman of Tufts University that two Krasnikov tubes going in opposite directions can create timelike loops and violations of causality.

For example, suppose that a tube is built connecting Earth to a star 3000 light years away. The astronauts are traveling at relativistic velocities, so that the journey only takes 1.5 years from their perspective. Then the astronauts lay down tube II rather than traveling back in tube I, the first tube they produced. In another 1.5 years of ship time they will arrive back on Earth, but at a time 6000 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 6000 years earlier than their departure. The Krasnikov tube system has become a time machine.

It is presumed that a similar mechanism which destroys time-machine wormholes will destroy the time-machine Krasnikov tubes.Fact|date=May 2008 That is, vacuum fluctuation will grow exponentially and eventually destroy the Second Krasnikov tube as it approaches the timelike loop limit, in which causality is violated.Fact|date=May 2008

ee also

* Wormhole

External links

* [http://arxiv.org/pdf/gr-qc/9702049 Exposition and criticism of the Krasnikov Tube by Allen E. Everett and Thomas A. Roman ]
* [http://arxiv.org/abs/gr-qc/0603060 Superluminal motion in (semi)classical relativity by Serguei Krasnikov (In Russian) ]