Bubble Control With Horizons

This page will evolve ongoing construction, it was only posted as suggested by a peer, all consideration on this are purely based on some rough thought  experiments.  The problem discuses is the problem of controlling a warp drive spacetime once it has gone beyond the classic Einstein barrier of light.

I have to believe if the warp drive is possible it must occur naturally somewhere in the cosmos, here is a special case.  Let's imagine that by chance the collision of two black holes will spawn some arbitrary warp drive spacetime in  the form of gravitational waves, which will propel the bodies forward further than what can be expected by the local momentum.  Well one wouldn't be to surprised by this because a partial amount of mass is lost through gravitational waves themselves.  To get to the typical view of how the warp drive should work is rather simple, one needs negative mass to be radiated away, so that the ships mass would remain unaffected, and v'ola warp drive.

Now the "control problem" arises because we view the warp drive somewhat like the figure below:

horzion problem graphical

We are in a speed boat in a vast ocean and decide the best way to get the further for our buck, is to have a bowie displace water behind our speed boat, and have a large barge ride in front of us, so we can ride a wave to our destination.  The rear horizon is not a problem for controlling the bubble because it is simply towed with us, however when the barge is out of range of our imaginary walkie-talkie we can not signal the barge to slow down and it continues on, this is the "horizon problem" of the warp drive.  If one were to look more carefully at this example the ship would also notice that if the ship is moving within the bubble that there will be a rather peaked blue shift, so the levels of deadly radiation would seem to put a limit on this kind of warp drive.  This is a consequence of the static field, it just as equivalent to say the boat is moving at c, as it is for the system, the problem is that the boat doesn't experience proper time and v'ola, radiation, and lots of it (when comparing this example to the black holes one can also see that this curvature nullifies some of the effects of special relativity), talk about barriers.

Possible Solution?

The reason this problem exist is because we again assume that the warp shells are static structures in spacetime, i.e. the booie and the barge in the above figure (act as planetary bodies if you will).  To resolve this problem we can go back to the colliding black holes example, the key is that the spacetime curvature only exist temporally and radiates away at the speed of light.  Now if we replace replace the static geometry with that of radiating gravitational waves the warp drive looks more like:

gravitatioanl wave inspiration
vg=velocity of gravitational waves, c=speed of light, vs=velocity of ship.

In this model we can not control the bubble of t=1, at time t=2, the warp shells are still causally disconnected from t=2.  However, this is not a concern as we can simply generate a new set of gravitational waves (t=2 above) which will give us our desired speed, when we slow our ship's velocity (in this case the USS Enterprise NCC-1701-E).  Here the warp shells are no more controllable than gravitational waves but our desired result is carried out, now a problem results from this solution being yet another energy problem.  If you produce one set of gravitational waves (say by colliding two bodies of large negative mass for this paradigm), after the mass has been radiated, how does one require more mass to continue the trip, this is now the new problem.  Thus to maintain control of the bubble one must exchange the Alcubierre warp shells with that correspond to parametric functions (corresponding to the figure above), and have access to some kind of imaginary energy well to keep replenishing the energy needed that is seen from recalling the black hole example.

Clarifications and New Findings

Much time after I have posted this short little article about the the horizon problem, a few of my peers have put together a possible solution to this.  The above possible solution has a very negative consequence, it is only possible to relinquish control if starting off superluminal.  If one starts off of subluminally one encounters the same problem illustrated within the first figure, and recently a research found and discussed more in depthly about the lethal radiation I mentioned above [1].  Although some of the problem discussed  by the author have been put into question by some recent research, its still a good read for the horizon problem and for general warp geometries.  So how do you get rid of the control and horizon problem, you can't!  The only thing you can do is modify when the horizon appears for the warp bubble (click for animation zipped avi file), our peer group found a way which to do just that [2]:

ds2=-[A2-(vsS(rs))2]dt2+2vsS(rs)dx'dt+dx'2

Which is a warp drive set in two-dimensional space to treat the horizons more easily, in essence an extension of Hiscock's work [3].  This spacetime is built on a piecewise function that makes it possible to move where the horizon form when a warp drive tries to go superluminal below is a simple graphic of this "trick."

The double shell design means that when the warp drives tries to go superluminal the horizon forms at the outershell, as mentioned before the horizon still forms.  However that is not the important part, its how the whole thing looks to an outside observer.  When the shells move through space at sublight speeds they interact to make portion of space disappear in front of the ship.  So to when the shells travel at 90% of c (relative to the ship), it would seem that space was disappearing in front of the ship in such a way that the ship would seem to travel at superluminal velocities (this is perhaps the only good thing the exotic energy does for the warp drive).  So the extra shell can act to turn of an initially superluminal warp drive, or subluminaly it can control when the ship appears to go superluminal from the perspective of an outside observer.

[1] J. Natario. Warp Drive with Zero Expansion Class. Quant. Grav 19 2002 gr-qc/0110086.
[2] F. Loup, et. al. A Causally Connected Warp Drive Spacetime gr-qc/0202021 (HTML note poor image translation)
[3] W. Hiscock. Quantum effect in the alcubierre warp drive spacetime. Class. Quant. Grav 14 gr-qc/9707024


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