AAWSAP DIRD, Quantum Tomography of Negative Energy States in the Vacuum, January 2011

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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.
However, real physical matter is not "reasonable" because the energy conditions are in
general violated by semiclassical quantum effects ( occurring at order Tl) [9].* 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 [3]. This violates the WEC, which postulates that the local energy density is non­
negative for all observers. And there are also general theorems of differential geometry
that guarantee that there must be a violation of one, some, or all of the energy
conditions (meaning exotic matter is present) for all FTL and antigravity spacetimes.
However, all of the energy condition hypotheses have been experimentally tested in the
laboratory and experimentally shown to be false - 25 years before their formulation
[11].
In quantum field theory, negative energy is a manifestation of what is now called the
"sub-vacuum" levels of the quantum zero-point (or vacuum ground state) fluctuations
that correspond to any particular quantum field of matter under study. Hence, the
energy corresponding to sub-vacuum quantum fluctuations is now called "sub-vacuum
energy": sub-vacuum energy= negative energy. Further investigation into this technical
issue showed that violations of the energy conditions are widespread for all forms of
both "reasonable" classical and quantum matter [12-16]. Furthermore, Visser [9)
showed that all (generic) spacetime geometries violate all the energy conditions. So
the condition that PE> Pi and/or PE~ 0 must be obeyed by all forms of matter in nature
is spurious. Negative energy has been produced in the laboratory and this will be
discussed in the following sections.
Examples of Negative (Sub-Vacuum) Energy Found in Nature
The exotic (energy condition-violating) fields that are known to occur in nature are:
1. Static, radially-dependent electric or magnetic fields. These are borderline exotic,
if their tension were infinitesimally larger, for a given energy density [10, 17].
2. Squeezed quantum vacuum states: electromagnetic and other (non-Maxwellian)
quantum fields [8, 18].
3. Gravitationally squeezed electromagnetic vacuum fluctuations [19).
4. Casimir effect, i.e., the Casimir vacuum in flat, curved, and topological spaces
[20-28).
5. Other quantum fields/states/effects. In general, the local energy density in
quantum field theory can be negative due to quantum coherence effects [3].
Other examples that have been studied are Dirac field states: the superposition
of two single particle electron states and the superposition of two multi-electron­
positron states [29, 30]. In the former (latter), the energy densities can be
negative when two single (multi-) particle states have the same number of
* Planck's reduced constant, TJ "' 1.055 x 10-34 J.s.
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