observers only encounter positive energy densities. However, it has been known since 1965 that, unlike most classical physics models, no (Wightman) quantum field theory can obey pointwise energy conditions [@epstein]. Moreover, it is possible to show that the negative energy density arising from a quantum field theoretic source is unbounded (from below) in magnitude [@fewster; @lisbon]. This startling feature of quantum field theory is often used, in the context of the semi-classical Einstein equation $G_{ab}=8\pi G\langle T^{\mathrm{ren}}_{ab}\rangle_\omega$, to support so-called ‘designer spacetimes’ like Alcubierre’s warp drive [@alcubierre] or traversable worm hole geometries. Following Ford’s [@ford] observation that it is possible to bound the magnitude and duration of the flux of negative energy of a quantum field source, work began in earnest to prove that the averaged (expectation value of the) energy density of a quantum field was bounded from below. A suitable definition, sufficient for our purposes[^2], is that a worldline *quantum weak energy inequality* (QWEI) is a result of the form $$\label{wqwei}
\int_{\mathbb{R}}{\mathrm{d}}\tau \, \langle \rho^\mathrm{ren} \rangle_\omega (\gamma(\tau)) F(\tau) \geq
- \mathcal{B} > -\infty$$ where $F$ is some appropriately chosen sampling function, $\gamma:{\mathbb{R}}\mapsto {\mathcal{M}}$ is a timelike worldline and $\langle
\rho^\mathrm{ren}\rangle_\omega$ is the (expectation value of the) energy density 