p2

∇
2
K −
( c K)
0
1
2
∂ K
∂t
2 2
⎧
⎪
( mc
0 0
K)
⎡ ⎤
=− + −
⎪ ⎛ v ⎞ ⎣ ⎝ ⎠ ⎦
⎪ 1−
⎜ ⎟
⎪⎩ ⎝c0
K ⎠
2 2
8π
G ⎪
1 ⎛ v ⎞
3
K
4 ⎨ ⎢ 1 ⎜ ⎟ ⎥δ
( r r
2
0 )
c0 2 ⎢ c0
K ⎥
2
4
2
2 c ⎡
0
2 ⎛ K ⎞ ⎤⎫
Kε0E
( K)
2
⎢
2
⎥⎬
0 ⎢ ( c0
K)
⎝ ∂ ⎠ ⎥
1⎛ B ⎞ 1 1 ∂ ⎪
+ ⎜ + ⎟− ∇ + ⎜ ⎟
2⎝Kµ ⎠ 32πG K
⎣
t
⎦⎭ ⎪
(2.33).
This equation describes the generation of general relativistic vacuum polarization effects due to the
presence of matter and fields. By inspecting the right-hand side of the equation, we observe that changes
in K are driven by the mass density (1 st term), electromagnetic energy density (2 nd term), and the vacuum
polarization energy density itself (3 rd term). In fact, the 3 rd term emulates the gravitational field selfenergy
density. Note that the 2 nd and 3 rd terms in (2.33) appear with opposite signs with the result that
electromagnetic field effects can counteract the gravitational field effects. Puthoff found that (2.33) gives
the solution K = exp(2GM/rc 0 2 ) in the vicinity of a static spherically symmetric (uncharged) mass M (in
the low velocity limit v 1 near mass concentrations.
Of major importance to the present study are solutions giving K < 1 so that teleportation can be
realized. Puthoff has found one such solution by studying the case of a static spherically symmetric mass
M with charge Q familiar from the study of the Reissner-Nordstrφm spacetime metric. In this case
Puthoff found the result
⎡ ⎛ 2 2 2 2
b −a ⎞ a ⎛ b −a
⎞⎤
K = ⎢cos
+ sin
⎥ b > a
r
2 2
⎢ ⎜ ⎟ b a ⎜ r ⎟
⎣ ⎝ ⎠ − ⎝ ⎠⎥⎦
2
2 2
( )
(2.34),
where a 2 = (GM/c 0 2 ) 2 , b 2 = Q 2 G/4πε 0 c 0 4 , and r is the radial distance from the center of M. And in this case
(2.34) gives K < 1, which shows that FTL solutions are available in the PV-GR approach (as they are also
in the Einstein theory). (For a 2 > b 2 the solution is hyperbolic-trigonometric and describes the standard
Reissner-Nordstrφm metric where K > 1.)
Generally speaking, in Einstein general relativity the Reissner-Nordstrφm metric can be manipulated
along with two shells of electrically charged matter to form a traversable wormhole (Schein and
Aichelburg, 1996). But there are two drawbacks to this. The first is that the scheme involves dealing
with the collapsed state of the stellar matter that generates the metric (a.k.a. Reissner-Nordstrφm black
hole) along with the unpleasant side effects that are encountered, such as the crushing singularities and
multiple (unstable) event horizons. Second, the traversable wormhole is an eternal time machine
connecting remote regions of the same universe together. Now there are no black hole solutions found in
the PV-GR model because in that approach stellar matter collapses smoothly to an ultra-dense state and
without the creation of singularities and event horizons (Puthoff, 1999b).
In either case, the Reissner-Nordstrφm metric does not offer a viable mechanism for vm-
Teleportation. We are more interested in examining other PV-GR cases (where K < 1 or even K