We propose a new bound on a weighted average of the null energy along a finite portion of a null geodesic: the Smeared Null Energy Condition (SNEC). We believe our bound is valid on scales small compared to the radius of curvature in any quantum field theory that is consistently coupled to gravity. If correct, our bound implies that regions of negative energy density are never strongly gravitating, and that isolated regions of negative energy are forbidden.

Biological processes such as embryogenesis, wound healing and cancer progression, crucially rely on the ability of epithelial cells to coordinate their mechanical activity over length scales order of magnitudes larger than the typical cellular size. While regulated by signalling pathways, such as YAP (yes-associated protein), MAPK (mitogen-activated protein kinase) and Wnt, this behavior is believed to additionally hinge on a minimal toolkit of physical mechanisms, of which liquid crystal order is the most promising candidat. Yet, experimental and theoretical studies have given so far inconsistent results in this respect: whereas nematic order is often invoked in the interpretation of experimental data, computational models have instead suggested that hexatic order could in fact emerge in the biologically relevant region of parameter space. In this article we resolve this dilemma. Using a combination of in vitro experiments on Madin-Darby canine kidney cells (MDCK), numerical simulations and analytical work, we demonstrate that both nematic and hexatic order is in fact present in epithelial layers, with the former being dominant at large length scales and the latter at small length scales. In MDCK GII cells on uncoated glass, these different types of liquid crystal order crossover at 34 μm, corresponding approximatively to clusters of 21 cells. Our work sheds light on the emergent organization of living matter, provides a new set of tools for analyzing the structure of epithelia and paves the way toward a comprehensive and predictive mesoscopic theory of tissues.

The classic singularity theorems of General Relativity rely on energy conditions that can be violated in semiclassical gravity. Here, we provide motivation for an energy condition obeyed by semiclassical gravity: the smeared null energy condition (SNEC), a proposed bound on the weighted average of the null energy along a finite portion of a null geodesic. We then prove a semiclassical singularity theorem using SNEC as an assumption. This theorem extends the Penrose theorem to semiclassical gravity. We also apply our bound to evaporating black holes and the traversable wormhole of Maldacena-Milekhin-Popov, and comment on the relationship of our results to other proposed semiclassical singularity theorems.

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