Time Travel Research Center © 2005 Cetin BAL - GSM:+90 05366063183 - Turkey/Denizli
Alcubierre Warp Drive
Physics Modern Relativity and is the calculation of a Covariant G_pq Einstein Tensor to be used for Alcubierre Warp Drives.....with a time dilatation coefficent to lower the negative energy densities of the equation Miguel 19 of the paper arXiv.org@gr-qc/0009013 5 Sep 2000 "The Warp Drive : Hyper-Fast Travel within General Relativity" Miguel Alcubierre University of Wales in Cardiff UK Some good advices for the reader of this page from ZcPhysics "The interval there was cut and paste from what I input into GRTensor II for Maple 6. The Einstein tensor there was cut and paste from the output. It's an excellent program for this kind of work. GRTensor II is also downloadable for free and I highly recommend it." Maple Site in this club we developed a metric similar to the one of Miguel Alcubierre the ESAA Metric.
The ESAA is the club motto "EX SOMNIUM AD ASTRA" which means to say "From a Dream to the Stars"...
ZcPhysics Loupwarp(i am Loupwarp) and Halgravity are the club members behind this page here is a brief discussion of what we found in the club: in 1994 when Miguel Alcubierre discovered the warp drive he wrote in his Legendary work (images taken from the work arXiv.org@gr-qc/0009013 5 Sep 2000 the warp drive:hyper fast travel within general relativity)
He used the quantum field and the casimir effect to supply the negative energy densities and WEC violations to power his warp drive then some scientists appeared with the so called quantum inequalities to rule out the Alcubierre Warp Drive based over large and absurd negative energy density requirements these scientists are good scientists but their work is placing in danger the future of the entire Human Race and our Destiny in the Outer Space these scientists are denying the space exploration beyond the borders of our tiny planetary system. But we know from the work arXiv.org@gr-qc/0009076 21 Sep 2000 Classical Scalar Fields and Violations of the Second Law from Lawrence Ford and Thomas Roman that scalar fields can allow large negative energy densities while outside the scope of the quantum inequalities..scalar fields can power a warp drive. See the images below
in the opinion of the club members the Alcubierre Warp Drive is still alive and the club members developed a time dilatation coefficient a similar to the one in equation 1 of Miguel 1994 work and this term have the following features:
a=1 in the ship and far from it a have large values in the bubble walls to lower the negative energy densities this will affect the stress energy momentum tensor below the new Einstein Curvature Tensor is presented and this tensor is covariant Miguel wrote the equation Miguel 19 contravariantly and the scientists that ruled out Miguel also worked contravariantly there is differences between contravariance and covariance below there is a message from Halgravity "sigma can be given in the form d sigma^2=delta_ik d_i d_k for future reference delta will be given as "d" there is something different in the alpha term of the ESAA metric when one compares and contrast covariant and contravariant fields as suggest by Loupwarp. The proper relation between the two is g_uv=g^uv=-"d"{.... so for the Alcubierre top hat the delta term can be give from ("d")-("d")/2("d")--->-"d" which is identical to the covariant form g_uv at a first approximation however for the f(rs)^ (sigma*R) term, we have just "d"_uv, so that the relation between the two sigma terms is "d"_uv and g_uv for proper time one can have -ds^2=d tau=-(dx_1^2+dx_2^2+dx_3^2)-dx_4^2 thus the "d"_uv term can appear to take away energy from proper time when interacting with the g_uv term.
However for the case when "d" is contravariant it will contribute to the proper time coordinates,so for this special case the covariant and contravariant terms are different as previously suggested by Loupwarp".
Halgravity the club members calculated the Einstein tensor covariantly there is another comment from ZcPhysics
"Where the covariant Einstein tensor is presented, I think it would be better to refer to it as the covariant Einstein tensor instead of the stress energy tensor because is is different from the covariant stress energy tensor by a 8*pi*G/c^4. I think it would also be important to remind the reader that it is the covariant solution because the classical energy pressure etc densities actually come from the contravariant stress energy tensor."
ZcPhysics this G_pq Einstein Curvature tensor will be linked to a T_pq from Scalar fields proving the the warp drive is possible and Miguel work must be placed in his right place allowing the Space Exploration beyond the borders of our tiny planetary system. The club expertise in Scalar Fields will come from the work of great scientists of the Los Alamos National Laboratory e-print service known as arXiv.org and to name the works are these:
arXiv.org@gr-qc/0009076 21 Sep 2000 Classical Scalar Fields and Violations of Second Law Lawrence Ford and Thomas Roman
arXiv.org@gr-qc/0001099 28 Jan 2000 Energy Conditions and their Cosmological Implications Matt Visser and Carlos Barcelo
arXiv.org@gr-qc/0003025v2 14 Jul 2000 Scalar Fields Energy Conditions and Transversable Wormholes Matt Visser and Carlos Barcelo
arXiv.org@gr-qc/9908029 9 Aug 1999 Transversable Wormholes from Massless Conformally Coupled Scalar Fields....Matt Visser and Carlos Barcelo
the Einstein Curvature Tensor in these works is covariant and not contravariant
Here is an excellent comment from ZcPhysics about Scalar Fields
"Conserning scalar fields, I have doubts that the consept of a scalar field really applies to the Alcubierre spacetime globally. In Hiscock's 2d calculation a scalar field could easily be found because of the form the metric took. ds^2 = (1 +2phi/c^2)dct^2 - dz^2/(1 + 2phi/c^2) But I don't think "only" one exists that is globally descriptive for the alcubierre spacetime in 4 dimensions. If it did, I think we should be able to globally transform the spacetime to that form in 4 dimension which can't be done. The scalar field is a "linearized" and weak field approximation for this particular form of a spacetime metric. The energy density can classically by arrived at by t^00 = -(7c^2/8piG)(phi,j*phi,j) using Einstein summation. But this relation has only been derived for this particular form of spacetime or for those spacetimes that approximate it. In general there are actually 16 potentials for gravitation which are the elements of the metric tensor. Of these there are only 10 that are independent potentials because it is symmetric. In doing a linearized weak field approximation four more restrictions can be placed on the potentials in linearizing the result that reduces the number of independed potentials to 6. The restriction that has to be done to linearize the result allows for 4 more restrictions because there remained some choices of frame. In the end this still leaves 2 independent scalar potentials. Fortunately the classical result as calculated by the ship frame is that the energy density is given only by one element of the contravariant Einstein tensor G^00. We know what that is and so we know what GR says the energy density is. Coordinate frame energy density = T^00 = (c^4/8piG)G^00. We don't need a scalar potential to get this. We already have it."
ZcPhysics
Another good one from ZcPhysics
"I can think of how to define 2 potentials for the Alcubierre spacetime with the time dilation term included, but without dropping the term, I can't think of a "single" descriptive scalar potential."
ZcPhysics
here is another comment from ZcPhysics slightly modified by Loupwarp
"Alcubierre's original more general metric had a time dilation term in the remote observer's frame A(ct,r). We will reintroduce such a term into the ship frame's interval. Only we will use different boundary conditions for it. We will keep A = 1 both at the location of the ship, and far from it, but allow it to become large in the warped region.
Numerical Simulation of A(ct,rho)
The solution for T^pq or T_pq are given in function of the G^pq or G_pq in the following GrTensor II MAPLE 6 OUTPUT
Now we see that T^pq or T_pq can be arbitrarily lowered by making A arbitrarily large in the warped region. Since the ship frame energy density term can be arbitrarily lowered while there are other terms in the stress-energy tensor that do not vanish in the limit that we neglect 1/A4 , it appears that it is not the energy density term that is important to the warp drive characteristics of the spacetime at all. Thus we might be able to build a warp drive that has the terms are not order 1/A4 and not concern ourselves with obtaining negative energy that violates the weak energy condition and we might still result in a working warp drive spacetime. Notice that with the use of the trig identity sin2q + cos2q = 1 all the denominators can be greatly simplified."
ZcPhysics slightly modified by Loupwarp. ZcPhysics originally wrote the comment above focusing contravariance. Loupwarp modified the comment to focuse also covariance to keep pace with the Visser-Barcelo Ford-Roman Stress Energy Momentum Tensors for Scalar Fields. ZcPhysics was the original creator of the ESAA metric Loupwarp and Halgravity studied the metric in the club postings. The ESAA WARP DRIVE METRIC preceedes the Einstein Curvature Tensors.
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