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

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electrons (electrons and positrons) or when one state has one more electron
(electron-positron pair) than the other.
Cosmological inflation [9], cosmological particle production [9], classical scalar fields
[9], the conformal anomaly [9], and gravitational vacuum polarization [12-15] are
among many other examples that also violate the energy conditions. Since the laws of
quantum field theory place no strong restrictions on negative energies and fluxes, then
it might be possible to produce exotic phenomena such as faster-than-light travel [31­
33], traversable wormholes [8, 9, 34], violations of the second law of thermodynamics
[35, 36], and time machines [9, 34, 37]. There are several other exotic phenomena
made possible by the effects of negative energy, but they lie outside the scope of this
report. In what follows, we consider only items 2 and 4 in the previous list for the
purpose of this report due to their ready applicability and technical maturity. We will
not examine the other items in the list because they are theoretical curiosities that
remain under study by investigators.
Basic Notions of the Quantum Field Theory of Light
Before going further, it will be helpful to briefly outline the basic notions and
terminology of the quantum field theory of light (i.e., quantum optics) because the
content of this report focuses on those aspects.
Classically, light is electromagnetic radiation that can be pictured as waves flowing
through space at the speed of light, c (= 3.0 x 108 m/s). The waves are not waves of
anything substantive, but are in fact ripples in the state of a field. These waves carry
energy, and each wave has a specific direction, frequency and polarization state. This
is called a "propagating mode of the electromagnetic field." A simple model for this is
the electromagnetic oscillator. One complex-valued vector function u(x,t) called a
spatial-temporal mode comprises all classical wave aspects including polarization. The
simplest example of a spatial-temporal mode is a plane wave
u(x,t) = u0 exp[i(kx-wt)] of polarization vector uo, angular frequency co, and wave
vector k (definition: k2 =u}/c2), where i is the unit complex number, and x is the
space coordinate and tis the time coordinate.
This mode defines a framework in space and time that may be excited by the quantum
field "light." The mode function quantifies the strength of one excitation in space and
time. Also, the mode function obeys the laws of classical waves given by Maxwell's
equations of electrodynamics. The choice of u(x,t) is made by the observer. The
observer singles out one mode, one quantum object from the rest of the world to make
a specific observation or measurement. This object turns out to be a harmonic
oscillator described by the annihilation operator a. A useful tool for modeling the
propagating mode of the electromagnetic field in quantum mechanics is the ideal
quantum mechanical harmonic oscillator: a hypothetical charged mass on a perfect
spring oscillating back and forth under the action of the spring's restoring force. The
operator astands for the quantized amplitude with which u(x,t) can be excited. In
classical optics it would be just a complex number a of magnitude lal and phase
arg(a) . The quantized amplitude a is neither predetermined nor given by the observer
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