Why is there no action at a distance?
One of the bedrock principles underlying modern physics is locality. In other words, there can be no action at a distance: in order to influence something over there, something over here must travel to over there. This is of course built into the fabric of special relativity, where no information can travel faster than the speed of light, and also finds a home in quantum field theory, where forces are mediated by force-carrying particles like the photon (electromagnetism) or graviton (gravity). Another bedrock principle of modern physics is unitarity. Quantum mechanics and quantum field theory calculations output probabilities, which must always add up to 1.
It is a deep fact that these two principles, despite looking very different, are fundamentally related. In the AdS/CFT correspondence, locality in the bulk gravity theory is related to unitarity of the boundary gauge theory. A third property, analyticity of scattering amplitudes, ties locality and unitarity together in a beautiful way and has inspired research programs from the S-matrix of the 1960's through the "Amplituhedron" of 2013.
This is not my main area of research but it's been fun to dabble in. I've focused on the question: is locality "preferred" by unitarity? Specifically, Jesse Thaler and I found that in the framework of dimensional deconstruction, a Lagrangian which is purely local in the compactified extra dimension has a higher cutoff than any theory obtained by perturbing the Lagrangian by interactions which are nonlocal in the extra dimension. Said another way, one could imagine that the spectrum and interactions of KK modes in a nonlocal theory could unitarize the scattering matrix up to a higher cutoff than a local theory - we found that this was not the case. This is a tree-level statement, though, and the corresponding one-loop question is still outstanding: does a nonlocal theory in the UV become a local theory in the IR under renormalization group flow?