THE UNIVERSAL LAW OF PRESSURE: Unifying Forces through Elastic Superfluid Hydrodynamics (10⁴³ Pa)

Author: Barbu, Ilie Date: February 4, 2026 Field: Fundamental Physics / Unified Theory 1. ABSTRACT This paper proposes a radical unification of physics by redefining the Vacuum as an Elastic Superfluid Continuum. We demonstrate through dimensional analysis that Energy and Force are manifestations of Pressure (J/m³ = Pa). The model resolves the "Aether" paradox by postulating a zero-viscosity superfluidity with a finite Bulk Modulus (B) of 10⁴³ Pa. This inherent elasticity accounts for the propagation of light at a finite velocity (c). Furthermore, the Gravitational Constant (G) is analytically derived from vacuum density, framing gravity as a hydrodynamic pressure gradient rather than a fundamental force. 2. DIMENSIONAL IDENTITY AND VACUUM CONSTANTS We postulate that the Vacuum is not "nothingness" but a medium with specific physical parameters: Bulk Modulus (B):10⁴³ Pa (Resistance to compression). Vacuum Density (ρ_vac): 7.91 × 10²⁶ kg/m³ (Inertial mass of the medium). The Michelson-Morley Solution: By treating the vacuum as a Superfluid, we invoke D’Alembert’s Paradox: a body moving at a constant velocity through an ideal fluid experiences zero drag. This explains the null result of ether-wind experiments while maintaining the medium's existence. 3. DERIVATION OF c AND G The speed of light is redefined as the speed of a longitudinal/shear wave through this elastic medium, governed by the Newton-Laplace formula: c = √(B / ρ_vac) Substituting B = 10⁴³ Pa and ρ_vac ≈ 10²⁶ kg/m³ yields c ≈ 3 × 10⁸ m/s. Gravitational Derivation: Gravity is the pressure deficit flux toward matter (cavitation zones). G is derived as: G = (3π · c²) / (16 · ρ_vac) The mathematical alignment with the experimental value of G (6.67 × 10⁻¹¹) validates the proposed vacuum density. 4. MATTER AS CAVITATION VORTICES In this framework, Matter is a geometric structure (Vortex) maintaining a localized low-pressure zone. Stability: Maintained by the equilibrium between the Vacuum Pressure (10⁴³ Pa) and the Centrifugal Force of the spin. Dissipation: As a superfluid, the vortex rotation (Spin) is non-dissipative, allowing for stable, long-lived particles without thermal decay. 5. CONCLUSION The Barbu-Ilie model provides a causal, mechanical, and unified explanation for physical reality. By replacing abstract space-time curvature with Elastic Hydrodynamics, we simplify the universal architecture to a single principle: F = ΔP · S