Hyperfast Travel: Warp Drives

Fernando Loup Home Page on Alcubierre Warp Drives

The text below was taken from the 1994 historical Alcubierre paper.
The Warp Drive of the future starships must obey these features because these features are correct.
Even without the negative energy density and without the exotic matter that prevents the Alcubierre Warp drive to be fully functional Alcubierre did an excellent work.
I found a solution of the Einstein Field Equations that allows exactly the existance of a Warp Drive in much similar to the Alcubierre and retaining the Alcubierre features but without negative energy densities.
I am writing a paper to be published in the Los Alamos e-print service known as general relativity and quantum cosmology.
My email adress is:[email protected]

"Class Quant Grav 11 (1994) 73-77 ISSN 0264-9381"

The Warp Drive: Hyper-Fast Travel Within General Relativity

Miguel Alcubierre
Class. Quantum Grav. 11 (1994), L73-L77.

Abstract:
It is shown how, within the framework of general relativity and without the introduction of wormholes, it is
possible to modify a spacetime in a way that allows a spaceship to travel with an arbitrarily large speed. By a
purely local expansion of spacetime behind the spaceship and an opposite contraction in front of it, motion faster than the speed of light as seen by observers outside the disturbed region is possible. The resulting distortion is reminiscent of the ``warp drive'' of science fiction. However, just as it happens with wormholes, exotic matter will be needed in order to generate a distortion of spacetime like the one discussed here.

When we study special relativity we learn that nothing can travel faster than the speed of light. This fact is still true in general relativity, though in this case one must be somewhat more precise: in general relativity, nothing can travel locally faster than the speed of light. Since our everyday experience is based on an Euclidean space, it is natural to believe that if nothing can travel locally faster than light then given two places that are separated by a spatial proper distance , it is impossible to make a round trip between them in a time less than measured by an observer that remains always at the place of departure. Of course, from our knowledge of special relativity we know that the time measured by the person making the round trip can be made arbitrarily small if his (or her) speed approaches that of light. However, the fact that within the framework of general relativity and without the need to introduce non-trivial topologies (wormholes), one can actually make such a round trip in an arbitrarily short time as measured by an observer that remained at rest will probably come as a surprise to many people.

Here I wish to discuss a simple example that shows how this can be done. The basic idea can be more easily understood if we think for a moment in the inflationary phase of the early Universe, and consider the relative speed of separation of two comoving observers. It is easy to convince oneself that, if we define this relative speed as the rate of change of proper spatial distance over proper time, we will obtain a value that is much larger than the speed of light. This doesn't mean that our observers will be travelling faster than light: they always move inside their local light-cones. The enormous speed of separation comes from the expansion of spacetime itself.This superluminal speed is very often a source of confusion. It is also a very good example of how an intuition based on special relativity can be deceiving when one deals with dynamical spacetimes.}

The previous example shows how one can use an expansion of spacetime to move away from some object at an arbitrarily large speed. In the same way, one can use a contraction of spacetime to approach an object at any speed. This is the basis of the model for hyper-fast space travel that I wish to present here: create a local distortion of spacetime that will produce an expansion behind the spaceship, and an opposite contraction ahead of it. In this way, the spaceship will be pushed away from the Earth and pulled towards a distant star by spacetime itself. One can then invert the process to come back to Earth, taking an arbitrarily small time to complete the round trip.
The author wishes to thank Bernard F. Schutz and Gareth S. Jones for many useful comments.

REFERENCES

C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation W.H. Freeman, 1973.

J.W. York, ``Kinematics and Dynamics of General Relativity'' in:Sources of Gravitational Radiation, ed. L.L. Smarr, pp. 83-126, Cambridge University Press, 1979.

S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Spacetime, Cambridge University Press, 1973.

B.S. DeWitt, in General Relativity: An Einstein Centenary Survey, edited by S.W. Hawking and W. Israel, Cambridge University Press, Cambridge, 1979.

I removed all the mentions to exotic matter and negative energy densities but i kept the fist part of Alcubierre work because this is the correct behaviour of a faster than light Warp Drive.
I can reproduce this behaviour without exotic matter and i am commited to publish my work in the [email protected] in order to be seen by the entire World.
My purpose is to win the challenge posed by the NASA BREAKTHROUGH PROPULSION PHYSICS PROGRAM and WARP DRIVE WHEN and PROJECT GREENGLOW.