Defense Intelligence Reference Document Antigravity For Aerospace Applications

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because repulsive force terms are second and higher-order in the source mass velocity.
To invent a relativistic driver for a captured astronomical body in order to use it to
launch payloads into relativistic motion presents a large technical challenge for future
experimenters. For this reason, this paper will not consider this concept any further.
However, it does serve the useful purpose of illustrating the unusual antigravity forces
that can appear in Einstein's general relativity theory.
NEGATIVE ENERGY-INDUCED ANTIGRAVITY
Negative energy density and negative pressure are acceptable results both
mathematically and physically in general relativity and quantum field theories, and
negative energy/pressure manifests as gravitational repulsion (that is, antigravity).
Negative energy is also known as a form of "exotic matter."
In classical physics the energy density of all observed forms of matter (fields) is non-
negative. What is exotic about negative energy is that it must have negative energy
density and/or negative flux (Reference 20). The energy density is "negative" in the
sense that a given (exotic) matter field must have an energy density, PE(= pc2, where
p is the rest-mass density), that is less than or equal to its pressures/tensions, P1
(Reference 21,22). 3 In many cases, these equations of state are also known to possess
an energy density that is algebraically negative; that is, the energy density and flux are
less than zero. It is on the basis of these conditions that this material property is called
"exotic." The condition for ordinary, classical (non-exotic) forms of matter that one is
familiar with in nature is that PE> p; and/or PE :c: 0. These conditions represent two
examples of what are variously called the "standard" energy conditions: Weak Energy
Condition (WEC: pE 2 0, pE + Pi 2 0), Null Energy Condition (NEC: pE + Pi 2 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. Hawking and Ellis (Reference 23) formulated the energy
conditions in order to establish a series of mathematical hypotheses governing the
behavior of collapsed-matter singularities in their study of cosmology and black hole
physics. More specifically, classical general relativity allows one to prove lots of general
theorems about the behavior of matter in gravitational fields.
The bad news is that real physical matter is not "reasonable" because the energy
conditions are in general violated by semiclassical quantum effects (occurring at order
11) (Reference 22). 4 More specifically, quantum effects generically violate the average
NEC (ANEC). Furthermore, it was discovered in 1965 that quantum field theory has the
remarkable property of allowing states of matter containing local regions of negative
energy density or negative fluxes (Reference 24). This violates the WEC, which
postulates that the local energy density is non-negative for all observers. "Negative
energy" has the unfortunate reputation of alarming physicists. This is unfounded since
all the energy condition hypotheses have been experimentally tested in the laboratory
and experimentally shown to be false - 25 years before their formulation (Reference
25).
3 Latin indices (e.g.,,, J, k = 1...3) that are affixed to physical quantities denote the usual 3-d1mens1onal space
coordinates, x' x 3, indicating the spatial components of vector or tensor quantities.
4 Planck's reduced constant, '1 = 1.055 x 10-34 J.s.
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