AAWSAP DIRD, Traversable Wormholes, Stargates, and Negative Energy, April 2010

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UNCLASSIFIED/fFOA OFFl&I.t..k YS& 8Ptk\f
2
} throat c
M wh =
G
= -(1. 35 X 1027 kg) J throat
(9)
1 meter
= - (0.71MJ) ] throat
1 meter
where Mwh is the (equivalent) mass required to build the wormhole, A.throat is a suitable
measure of the linear dimension (width or diameter) of the throat, and M1 is the mass
of the planet Jupiter. One can also obtain the required energy, E..,1i, by multiplying both
sides of Equation (9) by c2 . Equation (9) shows that a mass of -0. 71 M1 will be required
to build a wormhole 1-m in size. As the wormhole size increases, the mass requirement
grows negative-large. Table 2 presents a tabulation of the required negative
( equivalent) mass as a function of sample wormhole throat sizes. After being alarmed
by the magnitude of the results, one should note that M wh is not the total mass of the
wormhole as seen by remote observers. The non-linearity of the general relativistic field
equation dictates that the total mass is zero (actually, the total net mass being positive,
negative or zero in the Newtonian approximation depending on the details of the
negative energy configuration constituting the wormhole system). Finally, Visser et al.
(Reference 59) demonstrated the existence of spacetime geometries containing
traversable wormholes that are supported by arbitrarily small quantities of negative
energy, and this was proved to be a general resu lt. The next section will expand on this
further.
Table 2. Negative Equivalent Mass Required for
Traversable Wormhole
A.throat (m}
Mwh
1000
- 709.9 MJ
100
- 71 MJ
10
-7.1 MJ
1
- 0. 71 MJ
0.1
-22.6 M©
0.01
- 2.3 M©
M1 = 1.90 x 1027 kg, Mo= 5.98 x 1024 kg
B. PHYSICAL CONSTRAINTS ON NEGATIVE ENERGY
The Quantum Inequalities (QI) conjecture is an extension of the Heisenberg Uncertainty
Principle to curved spacetimes. Much research has been conducted around this one
topic alone. The literature is too numerous to cite here but the reader should consult
(Reference 10) and (Reference 46) for detailed information. The QI conjecture relates
(via model dependent time integrals of the energy density along geodesics) the energy
density of a free quantum field and the time during which this energy density is
observed. This conjecture was devised as an attempt to quantify the amount of
UNCLASSIFIEQ { {FOR OFFICIAL YS& 8HLY
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