Vorticity Spin Quantization

$$\omega = \nabla \times v \approx \frac{1}{r}\frac{\partial(r v_\theta)}{\partial r}, \quad v_\theta = \frac{\Gamma}{2\pi r}, \quad \Gamma \propto \hbar\sqrt{s(s+1)}$$

Status: Unproven.

This is PBT’s own proposal that quantum spin $s$ is literally aether vorticity (fluid-dynamical rotation), with circulation $\Gamma$ quantized in units related to $\hbar$. It borrows real fluid-dynamics vocabulary (vorticity, circulation) but applies it to a hypothesized subatomic medium, not a measured fluid.

What would make this proven: an independent derivation showing this specific quantization condition follows necessarily from the theory’s other postulates (rather than being fit to match the known real spin-quantization result), plus an experimental test distinguishing “spin is literally vorticity” from the standard quantum-mechanical treatment of spin as an intrinsic, non-classical property (which has no classical vorticity analog — a point particle spinning classically to match measured electron spin would need faster-than-light surface velocity, a known problem with any “spin is literally rotation” picture). Simulated results (mean quantized spin 0.251, max vorticity 0.839 in Paper 5’s own code) aren’t independent confirmation of the underlying physical claim, since the simulation is built to produce quantized-looking output by construction.

Used in: Paper 5.