TAP-2: A Full Theory of Hidden Quadrupole Vacuum Anisotropy

We formulate and derive a phenomenological theory of hidden quadrupole anisotropy of the vacuum (TAP-2), effective only for macroscopic coherent quantum modes. A dynamic axis n and a small deformation parameter \Delta\theta \ll 1 are introduced. Weak couplings to the photon and condensate sectors lead to angular-dependent corrections to dispersion relations. The key result is the orientational energy shift: \Delta E(\varphi) = \Lambda \, \Delta\theta \, \frac{hc}{\lambda} \cos(2\varphi)\, S\!\left(\frac{\ell_{\mathrm{coh}}}{\ell_*}\right), where S(x) = (x/(1+x))^p acts as a coherence filter. This framework predicts measurable signatures in: Optical resonators — sidereal modulation of relative frequency shifts at the 10^{-18} level. Anisotropic Casimir effect — quadrupolar dependence of vacuum pressure. Superconducting rings — torque proportional to \sin(2\varphi). The theory is falsifiable: a null result would constrain \Lambda \Delta\theta S, while a positive detection would require revising the assumption of isotropy of the vacuum. TAP-2 thus provides a minimal extension of relativity with direct laboratory tests and potential cosmological implications.