"or that its cross-section is zero under every interaction except the gravitational one."
What if we are looking at it backwards, that mass is an effect of what we refer to as gravity, rather than gravity a property of mass?
All that can be said of gravity is that it's a centripetal effect, associated with this dense state we refer to as mass. Wouldn't it seem reasonable to consider both sides of the equation, rather than assuming one is primary, primarily because our primate brains like things we can pick up? Nodes before networks.
When waves synchronize, the effect is centripetal. Lasers are synchronized light waves and it's safe to say the effect is focal. While the center of galaxies are thought of in terms of the eye of the storm, referred to as black holes, most of what actually falls in can be accounted for, by the quasars shooting out the poles. Even smaller black holes are not so much dark lumps of matter, as they are spiraling vortices.
This ties back into what is one of the biggest mistakes in modern theory, treating time as narrative flow, from past to future, codified as measures of duration, rather than change turning future to past.
Our faunal brains are evolved to navigate our situation, so this sequence of perceptions, by which we experience it, is a logical consequence of navigation, but there is no dimension of time. The past is consumed by the present, to inform and drive it. Causality and conservation of energy. Cause BECOMES effect.
Energy is "conserved," because it manifests the present, creating time, as well as temperature, pressure, color and sound. Time is frequency, events are amplitude.
So energy, as present, goes past to future, while the patterns generated go future to past. Energy drives the wave, while the fluctuations rise and fall. No tiny strings necessary.
Consciousness also goes past to future, while the perceptions and thoughts giving it form and structure go future to past. Explaining why there is this focus on patterns, measurements, distilled reductionist information, rather than the dynamic generating it.
So if waves are the initial pattern, generated by energy, the two effects resulting would be synchronization, as path of least resistance for the waves, as well as harmonization, as the energy radiates out, distributing energy across the entire field. Consequently, nodes and networks, organisms and ecosystems, particles and fields.