Rest observer watching a massive particle. The total speed along the helix is always c; only its partition between the observable base (vₓ) and the internal fiber (v₀) changes.
At rest (vₓ = 0) the wave is pure internal rotation — the wavefronts are rings turning in place, and the internal clock ticks at its maximum rate. As vₓ increases, part of the motion is diverted along x: the helix stretches, and the internal rotation (hence the particle's own clock) slows as v₀ = c/γ. As vₓ → c the helix straightens toward the axis and the internal clock freezes. The bright point rides a single wavefront throughout.The complex wavefield Ψ(x,θ,t)=exp[i(kₓx + kθθ-ωt)] is mapped to the surface in two-tone blue through Re[ψ].