Dilatant Dark Fluid: Toward a Unified Quantum-Hydrodynamic Origin of Lorentz Invariance, Gravity, and Cosmological Phenomenology

Abstract

This work introduces the dilatant dark fluid (DDF), a pervasive cosmic cold dark medium comprising two coupled ultralight bosonic sectors: a superfluid \( \phi \) and a heavier dispersed phase \( \varphi \) undergoing stress-induced shear jamming, distinguishing the framework from earlier superfluid-vacuum models. The DDF’s velocity-dependent dilatant response generates a jamming factor identical to the Lorentz factor, recovering Lorentz-form kinetic energy, clock rate, and length relations, alongside interferometric and resonator nulls. By governing both matter dynamics and operational measurement standards, the DDF provides a quantum-hydrodynamic material realization of geometric relativistic spacetime. Within the DDF, photons correspond to transverse \( \varphi \) excitations supported by the locally saturated jammed state and propagating at the universal speed \( c \). The superfluid sector supports quantized vortices representing fundamental massive particles, with spin encoded by their toroidal-to-poloidal circulation ratio. Their quantized circulation and near-core quantum potential generate a vortex-supported pressure deficit whose many-vortex coarse-graining yields the macroscopic gravitational field, so that gravity emerges as the Bernoulli force generated by DDF microphysics. Painlevé–Gullstrand river variables connect Bernoulli gravity to general relativity, assigning a material hydrodynamic origin to the corresponding exterior geometries, including leading Kerr–Lense–Thirring behavior. The model recovers classical weak- and strong-field benchmarks of general relativity. At galactic scales, an isothermal dark-fluid regime yields nearly flat rotation profiles, thereby providing a quantum-hydrodynamic route to MOND-like phenomenology. Cosmologically, the filamentary cosmic web is related to vortex-filament networks in doped laboratory superfluids. These results define a unified dark-medium framework, while the Appendices present a direct gravitational discriminator from general relativity, an astrophysical probe of the proposed superfluid interpretation of the cosmic web, and laboratory tests of the constitutive rheology underlying the DDF.