Edward Halerewicz, Jr.

LLCC Library 10/16/2001

 

 Alcubierre Warp Drive Spacetime

 

 

 

Graph of the Alcubierre Warp Drive Spacetime as produced with Derive version 4.02:

 

 

The used version of the Derive program is very limited so I had to post the generated graphic into a Word file (as these were the two programs available to me while on campus).  In order to produce the above graph a bivariant function of order  was needed (referring to the 3-D plot definitions of the Derive Program), this also prevented the definition of  from being obeyed in reference to the Alcubierre Article (to do so would require a lot of unnecessary programming).  If one has access to Derive 4.02, 5.02, or some other 3-D mathematical program one should be able to plot a graph similar to the one shown above by using the following equation:

 

                                                    

[Note:  in reference to the Alcubierre paper the arbitrary numbers in the above equation are symbolically given as with , 2=R,

 

Again in reference to the Alcubierre paper the graph is meant to be a function of .   I hope this file helps to aid in the picturing of the Alcubierre Warp Drive Spacetime.

 

The purpose of this graph is to illustrate the appearance of how the Alcubierre Warp Drive Spacetime would appear in three-dimensions, so as to be within the range of human understanding.  The graph shows a gravitational spacetime distortion of an arbitrary “top-hat” function:

                                                                

                                                

                                                                            

Which yields a visual demonstration for a basic proof of concept.  This specific nature of this spacetime is described with the following metric:

 

                                                

 

This equation describes the motion of the arbitrary “top-hat” function through flat Minkowski spacetime.  As it can be seen this is a highly idealistic model, which uses the contraction of spacetime in front of a spaceship as well as an expansion behind it in order to use gravitation as a form of propulsion.  This document was only meant to give a very general overview of what is meant by a warp drive spacetime, for more details please refer to the 1994 paper of Miguel Alcubierre (the reference for that work is provided below).

 

Reference:

M. Alcubierre Class. Quant. Grav. 11 (1994) L73-77

At the time this document was produced an online version of this paper was available at the following address: http://xxx.lanl.gov/abs/gr-qc/0009013, via the General Relativity and Quantum Cosmology Archive of the Los Alamos National Laboratories, preferred address of the “arXiv” is http://arxiv.org/

Acknowledgement:

Special thanks are accredited to “Ufokier,” from the Yahoo club Alcubierre Warp Drive: http://clubs.yahoo.com/clubs/alcubierrewarpdrive, for providing the details necessary in order to display the “warp drive” equation and its graph within the Derive program.

Copyrighted © 2001: Edward Halerewicz, Jr.

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