Aether Spin/Entanglement Coupling Lagrangians

$$L_{spin} = -\frac{1}{2}\bar{\psi}(i\gamma^\mu D_\mu - m)\psi + \xi\, \bar{\psi}\, \gamma^5 \gamma^\mu u_\mu \psi, \quad L_{ent} = \eta\, \bar{\psi}1 \gamma^\mu u\mu \psi_2$$

Status: Unproven.

The first term of $L_{spin}$ (the Dirac Lagrangian, $-\frac12\bar\psi(i\gamma^\mu D_\mu-m)\psi$) is real, standard relativistic quantum field theory — the correctly-quantized Lagrangian for a spin-1/2 fermion field. The rest — the $\xi$-coupling term binding spin to the aether field $u^\mu$, and the entire $L_{ent}$ entanglement-coupling term — are PBT’s own additions, with coupling constants ($\xi$, $\eta < 10^{-15}$) chosen to be small enough to satisfy real observational bounds, but not derived from or confirmed by any independent measurement.

What would make this proven: a genuine experimental signature of these specific coupling terms — a measurable deviation from standard QFT’s Dirac Lagrangian alone, at a magnitude consistent with $\xi,\eta<10^{-15}$, that current or near-future instruments could actually detect and that has been detected. Paper 5 proposes decoherence-anomaly and Bell-experiment tests but reports no such detection.

Used in: Paper 5.