The Universal Fluid: A Deterministic Formulation of the Universe through Four Pressure-Induced Phase Transitions

AbstractThis work introduces a hydrodynamic and deterministic formulation of the Universe,based on the Polarized Membrane Model (PM-Model), as an alternative to the probabilisticand perturbative frameworks of the Standard Model, continuing the fundamentalcritique of local reality incompleteness [4] through a continuous wave-mechanicsapproach [5, 6]. We postulate the existence of a single, fundamental continuousmedium—the Universal Fluid—whose macroscopic and microscopic behavior is governedexclusively by four phase transitions induced by variations in local pressure density,as structurally mapped in our preliminary topological framework [3]. Through astrict hyperelastic constitutive relation and the introduction of the Bulk Modulus of thecondensed vacuum (Kv ≈ 2.09 × 10^36 N/m^2), we bypass the formalism of Lattice QCDfor determining the internal structure of baryons. The peak internal pressure of theproton at 0.603×10^35 Pa, experimentally measured at Jefferson Lab [9], is here analyticallyderived via an exact linear calculation [1], establishing a precise convergence withempirical shear forces localization [7] and mechanical radius constraints [8, 10]. Finally,the hydraulic extension of the relativistic hydrostatic equilibrium equations of Tolman-Oppenheimer-Volkoff (TOV) maps the macroscopic gravitational collapse limit, settingthe transition toward the dielectric saturation phase (Phase III) at a critical mass of2.5–3.0M⊙. The obtained numerical results confirm the validity of the hydrodynamicformalism as a key for a purely geometric and self-contained unification of cosmologicalevolution.The appendix dedicated to the predictive capabilities of the Universal Fluid modelincludes:• A classical analysis of the kinetic instability of the free neutron, interpreting β−decay not as a stochastic event, but as a structural failure due to mechanicalfatigue induced by a residual torsional misalignment (Anisotropic PolarizationGap equal to −0.013 μN). This asymmetry generates a normal mode of standingmagneto - elastodynamic-mechanical oscillation at the natural frequency of ≈198 kHz.• Providing an elegant and analytical solution to the systematic ”Beam vs Bottle”anomaly.• A geometric reinterpretation of the ”mass defect” in Deuterium fusion as mechanicalwork of contraction of the membrane interfaces.• Predicting the asymptotic rigidity of the neutron magnetic form factor (GMn),comparing the current state of research with the introduction of the assumptionof the elasticity modulus of the containment shell for the internal pressure of theproton/neutron.CORE DEVIATION FROM STANDARD FIELD FORMALISM:“Mass is analytically derived as the geometric work of volumetric strain against thecondensed vacuum elastic modulus (Kv), eliminating probabilistic quantum fieldparameters.”