A general local causality principle of space-time

We propose a generalisation of the local causality principle of space-time, asserting that it holds for all regimes of motion, including superluminal motions. It assumes the existence of a countably infinite set of metrical null cone speeds, $c_k$, where the first one, $c_1=c$, corresponds to the speed of light in vacuum. Our associated space-time measures do not diverge at the maximum speed of each interval of speeds and implies a generalisation of Einstein's rule for velocities addition. We construct a causal structure for each regime of motion. After introducing a simple dynamical measure, we derive an expression for the energy of material particles, which approaches the relativistic one when $v<c$. An experiment to energise photons in an 1-1 process is proposed as a test of our interpretation of the non divergence at the speed of light of present space-time measures. We discuss also the possible transition of a material particle from the subluminal regime $v<c$ to the first superluminal regime and vice versa, making discrete changes in $v^2/c^2$ around the unit in terms of a very tiny constant, $\epsilon^2$, which we introduce to prevent the divergence of the Lorentz $\gamma$ factor at the speed of light in vacuum.