From the Null Ray to the Massive Particle from a principle of ontological continuity

The principle of ontological continuity takes the null boundary of the light cone — wave- like in nature — as the primary object, and requires by continuity that the timelike interior too, the realm of massive particles, inherit a wave structure: mass is the sole door that joins the boundary to the interior. On this basis the optical dictionary is developed: the worldline of a particle is read as a ray in a conformal medium of refractive index 𝑛(𝑥), with a pole on the horizons — the light cone, the Rindler horizon, the horizon of a black hole. In this reading, the Klein–Gordon equation in the conformal medium generates of itself the coupling to the index gradient, and mass appears as the coupling that breaks conformal invariance: the boundary of the cone does not “feel” the refractive medium. Analogously one derives the optical Dirac equation, in which the spin–refraction coupling and an effective mass 𝑛𝑚 emerge naturally. Spin imposes itself with greater clarity than in its canonical derivation: a null four-momentum factorizes into a spinor, and spin 1 2 is the spinorial root of the null ray, half-integer by the topology ℤ2 = 𝜋1 (𝑆𝑂(3)). The massive particle is built from two null Weyl halves glued by mass — Penrose’s zig-zag; and mass is also read as the frequency of the internal clock, 𝜔 = 𝑚, which ticks only where proper time advances. The falsifiable target — Thomas precession — is here actually computed (§8), with an outcome that is a partial confirmation: the precession is recovered as the holonomy of the hyperbolic space of velocities, but spin transport must be relocated to that space, not to the conformal medium of spacetime. Finally the whole reading is placed on the celestial sphere — the Riemann sphere of null directions, on which 𝑆𝐿 (2, ℂ) acts — as a unifying conformal boundary, showing that every quantized quantity (orbital angular momentum ℓ, helicity 𝜆, spin) is a topological winding number, while their values come from interaction. The affinity with the active programme of celestial holography and with Penrose’s twistor programme is openly declared. We stress the kind of continuity — hard in velocity, soft in mass — as the generative root: through the sole door of mass there emerges a dispersive wavefunction, that is the form of wave mechanics, but not yet complete quantum mechanics, which further requires the scale ℏ and the Born rule. gianroccoguerriero@libero.it