A moving spherical cavity must shrink in a specific way or the waves inside it will literally fall apart.
Lorentz-FitzGerald contraction is the famous relativistic effect where moving objects appear shorter. This proof shows that this contraction is the only possible way a moving resonant cavity can stay stable. If the cavity didn't deform exactly this way, the internal wave structure would be destroyed. This suggests that relativity is not just a weird property of time and space, but a mechanical requirement for matter to exist while moving. It links the behavior of light and waves directly to the physical shape of the containers they inhabit.
Lorentz-FitzGerald Contraction as the Unique Closure Condition for Moving Spherical-Harmonic Cavities
arXiv · 2604.27525
We prove that the Lorentz--FitzGerald contraction is the unique deformation of a resonant cavity moving through a mechanical wave medium that preserves spherical-harmonic phase closure. For a cavity moving at speed $v = \beta c$ through a medium supporting nondispersive wave propagation at speed $c$, the round-trip phase of an internal ray at angle $\theta$ to the motion depends on the boundary radius $r(\theta)$ according to $\Phi(\theta) = 2k\,r(\theta)\sqrt{1-\beta^2\sin^2\theta}/(1-\beta^2)$