AAWSAP DIRD, Concepts for Extracting Energy from the Quantum Vacuum, April 2010

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Gravitational Squeezing of the Vacuum
In their study of traversable wormholes, Hochberg and Kephart (Reference 84)
discovered that the gravitational field of any astronomical body produces a zone of
negative energy around it by "dragging" some of the virtual quanta (a.k.a. vacuum
ZPF) downward. They applied their discovery to the problem of creating and stabilizing
traversable wormholes. Their quantum optics analysis showed that there is a distortion
of the vacuum electromagnetic ZPF due to the interaction with a prescribed
gravitational background, which results in "squeezed" vacuum states that possess a
negative energy density. Squeezing of the vacuum is a quantum process that is roughly
analogous to the compression of an ordinary fluid. This means that as the vacuum field
is continuously being squeezed by the gravitational field of a body, its energy is
continuously being degraded with respect to the undisturbed remote vacuum field.
The magnitude of the gravitational squeezing of the vacuum can be estimated from the
quantum optics squeezing condition for given transverse (to the direction of
gravitational acceleration) momentum and (equivalent) energy eigenvalues, j =
8rrrs/ 1 13 of two electromagnetic ZPF field modes, subject to the squeezing condition j
,1
➔ 0, where ).. is the ZPF mode wavelength and rs is the Schwarzschild radius of the
astronomical body under study (Reference 84). 14 This condition simply states that
substantial gravitational squeezing of the vacuum occurs for ZPF field modes with "A, z
8rrrs. The corresponding local vacuum state energy density that this effect produces is
pE-gsvac = -2n2ric/A.4 .
It is not clear whether this mechanism can be exploited to extract energy from the
vacuum. Conservation of energy suggests one of two possible outcomes: 1) the lost
energy is injected into the gravitational energy of the body, or 2) the lost energy
reappears as an accumulation of positive energy density ZPF modes elsewhere in the
universe. Further research will be needed to address this question.
Redshifting the Vacuum
Calloni et al. (Reference 85, 86) explored the possibility of verifying the equivalence
principle for the zero-point energy of QED. They used semi-classical quantum gravity
theory to evaluate the net force produced by the quantum vacuum ZPF acting on a rigid
Casimir cavity in a weak gravitational field which is modeled using the standard
Schwarzschild spacetime metric geometry. 15 They evaluated the regularized (or
renormalized) stress-energy tensor (r:c') of the quantized vacuum electromagnetic field
between two plane-parallel ideal metallic plates lying in a horizontal plane. (r,i;,)
encodes the Casimir effect, which has a negative energy density and a negative
pressure along the vertical (gravitational acceleration) axis between the plates. Bimonte
13 Note that j contains an extra factor of two ( compared to the j derived in Reference 84) in order to account for
the photon spin.
14 rs = 2GM/c2 is the critical radius at which a body of mass M collapses into a black hole. It is used here as a
convenient distance parameter to simplify the inequality, but there is no actual black hole collapse involved in this
mechanism. G is Newton's universal gravitation constant {6.673 x 10-11 Nm2/kg 2).
15 A spacetime metric is a Lorentz-invariant distance function between any two points in spacetime, which is
defined in terms of a metric tensor, g µv, that encodes the geometry of spacetime (Greek indices p,v = 0.. .3 denote
spacetime coordinates, x:'...x3 , such that x1...x3 = space coordinates and ><°= time coordinate).
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