deletions | additions       diff --git a/subsection_General_Relativity_Quantum_Field__.tex b/subsection_General_Relativity_Quantum_Field__.tex  index 8929182..7425083 100644  --- a/subsection_General_Relativity_Quantum_Field__.tex  +++ b/subsection_General_Relativity_Quantum_Field__.tex 
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\begin{equation}  \usepackage{physics}  \xi_{ave}\left( \lvert{\Omega^{\prime}}\rangle \right) = \xi_{ave}\left( \lvert{\Omega}\rangle \right) - f \frac{\int_{V}\left( \vec{J}_{e} \cdot \vec{A}_{cl}(\vec{x}\vec{\chi}_{1}) \right) d\vec{x} }{V} }{V},  \end{equation}  where an $f$ can always be found that makes $\xi_{ave}\left( \lvert{\Omega^{\prime}}\rangle \right)$ a negative number with an arbitrarily large magnitude.  For the purpose of Alcubierre experimentation, we assume that negative energy densities in Quantum Field Theory are in fact similar to General Relativity's own interpretation. This assumption allows us to perform Alcubierre and negative energy experiments with the expectation that by mixing Quantum Field Theory, General Relativity, and semi-classical theory, we can obtain real results.  Although Quantum Field Theory introduces negative energy, the magnitude and duration of negative energy is limited by quantum inequalities (Pfenning et al., 1998). This becomes an issue for scaling an Alcubierre drive. Assuming the quantum inequalities apply to the scale of a spaceship, a warp bubble 200 meters across would require a total amount of negative energy equal to 10 billion times the mass of the observable universe (Ford et al., 2000). General Relativity does not have such limits similar to the quantum inequalities, with the exception of localized negative energy density potentially violating the weak energy condition. However, when energy conditions are measured in a non-localized way, it is possible to uphold the weak energy condition (Roman, 1986). It remains to be seen how the quantum inequalities would affect implementation at a larger scale, and it begs the question of whether negative energy in Quantum Field Theory is the same as its General Relativity counterpart. If the two are dissimilar, any experiment built on Quantum Field Theory aiming to produce negative energy may not actually lead to construction of an Alcubierre drive at a large scale. We accept this as a potentail risk to experimentation.