A Krasnikov tube is a speculative mechanism for space travel involving the warping of

spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...

into permanent

superluminal Faster-than-light (also FTL, superluminal or supercausal) travel and communication are the conjectural propagation of matter or information faster than the speed of light (). The special theory of relativity implies that only particles with z ...

tunnels. The resulting structure is analogous to a

wormhole A wormhole ( Einstein-Rosen bridge) is a hypothetical structure connecting disparate points in spacetime, and is based on a special solution of the Einstein field equations. A wormhole can be visualized as a tunnel with two ends at separate ...

or an immobile Alcubierre drive (and like them requires exotic matter with negative energy density) with the endpoints displaced in time as well as space. The idea was proposed by

Sergey Krasnikov Serguei Vladilenovich Krasnikov (russian: Серге́й Владиле́нович Кра́сников; 1961) is a Russian physicist. Life Krasnikov obtained a doctorate ( CSc.) in physics and mathematics from Saint Petersburg University. He is c ...

in 1995.

Structure

The tube is a distortion of spacetime that can be intentionally created (using hypothetical technology) in the wake of travel near the speed of light. The Krasnikov tube allows for a return trip that takes travelers back to the time right after they left. Experiencing the effect requires that the traveler race along the tube at speeds close to that of light.

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, is always larger than ). 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 Tufts University is a private research university on the border of Medford and Somerville, Massachusetts. It was founded in 1852 as Tufts College by Christian universalists who sought to provide a nonsectarian institution of higher learning. ...

that two Krasnikov tubes going in opposite directions can create a

closed timelike curve In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime, that is "closed", returning to its starting point. This possibility was first discovered by Willem Jacob van ...

, which would violate

causality Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cau ...

. For example, suppose that a tube is built connecting Earth to a star 3000 light years away. The astronauts are travelling at relativistic velocities, so that the journey through this Tube I only takes 1.5 years from their perspective. Then the astronauts lay down tube II rather than travelling 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 the star 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. In 1993, Matt Visser argued that the two mouths of a wormhole with an induced clock difference could not be brought together without causing quantum field and gravitational effects that would either make the wormhole collapse or the two mouths repel each other. (See Time travel using wormholes and the

Chronology protection conjecture The chronology protection conjecture is a hypothesis first proposed by Stephen Hawking that laws of physics beyond those of standard general relativity prevent time travel on all but microscopic scales - even when the latter theory states that it ...

.) It has been suggested that a similar mechanism would destroy time-machine Krasnikov tubes. That is, vacuum fluctuation would grow exponentially, eventually destroying the second Krasnikov tube as it approaches the timelike loop limit, in which causality is violated.

References

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