AAWSAP DIRD, Warp Drive, Dark Energy, and the Manipulation of Extra Dimensions, April 2010

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2.1 WARP DRIVE REQUIREMENTS
Implementation of FTL interstellar travel via warp drives requires engineering of
spacetime into very specialized local geometries as shown by Equation (2.1). The
analysis of these via the general relativistic field equation plus the resultant source
matter equations of state demonstrates that such geometries require the use of
"exotic" matter in order to produce the requisite FTL spacetime modification. Exotic
matter is generally defined by general relativity (GR) physics to be matter that
possesses (renormalized) negative energy density and/or negative stress-tension (=
positive outward pressure, aka gravitational repulsion). The term is widely
misunderstood and misapplied by the non-GR community. Also, it has been claimed
that FTL spacetimes are not plausible because exotic matter violates the general
relativistic energy conditions. 2 However, this has been shown to be a spurious issue
(Reference 11).
The energy density for the Alcubierre (Reference 1) warp drive that is derived from the
general relativistic field equation is complex, so we instead use a more simple formu la
to express the net energy required, E.varp , to build a warp bubble around a spaceship
(Reference 12):
v2
c4 R2 cr
=_ warp
Ewarp
G
(2.3)
=-(l.21 x 1044 ) v:,,up R2 cr,
where G is Newton's universal gravitation constant (6.673 x 10-11 N·m2/kg 2), Vwarp is the
dimensionless speed of the warp bubble, R (> 0) is the radius of the warp bubble, and cr
(> 0) is proportional to the inverse of the warp bubble wall thickness L'. (i.e., cr ~ 1/L'.).
Equation (2.3) characterizes the amount of negative energy that one needs to localize
in the walls of the warp bubble. Table 2 presents a tabulation of the required negative
energy as a function of the "warp factor," Vwarp , One can compare the values of E.varp in
the table with the (positive) rest-energy contained in the Sun (1.79 x 1047 J). The
consequence of Equation (2.3) and Table 2 is that if one wants to travel at hyperlight
speeds, then the warp bubble energy requirement will be an enormous negative
number. And this remains true even if one engineers an arbitrarily low sublight speed
warp bubble. Engineering a warp drive bubble is quite daunting given these results.
2 The condition for ordinary, classical (non-exotic) forms of matter that we are familiar with in nature is that PE > p
and/or PE ;:: 0, where PE is the energy density and p is the pressure/stress-tension of some source of matter. These
conditions represent two examples of what are variously called the "standard" energy conditions: Weak Energy
Condition (WEC: PE.?: 0, PE + p .?: 0), Null Energy Condition (NEC: PE + p ~ 0), Dominant Energy Condition (DEC),
and Strong Energy Condition (SEC). These energy conditions forbid negative energy density between material
objects to occur in nature, but they are mere hypotheses. The energy conditions were developed to establish a
series of mathematical hypotheses governing the behavior of collapsed-matter singularities in the study of
cosmology and black holes.
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