Stability analysis of the uniform motion of electrodynamic bodies

Abstract

We show that when an electrodynamic body is perturbed from a state of uniform motion, it starts to perform fast oscillations, irrespective of the frequency of the perturbation. It has been demonstrated in previous works that the state of uniform motion can be Lyapunov unstable for particles having a prolate geometry with respect to the direction of motion. Here we show that the limit cycle oscillations are destabilized through a Hopf bifurcation as the geometry of the electrodynamic body gradually switches from prolate to oblate. The resulting symmetry breaking of the Lorentz group implies that the principle of inertia only holds on average, suggesting that the default state of matter is not uniform motion, but self-oscillation as well. We propose that the excitability of electrodynamic bodies under external perturbations is at the basis of the wave-particle duality and its related quantum effects.