Beyond Dark Matter: A Mechanical Solution to the Galaxy Core Problem Subject: Summary of the Phase-Dipole Condensate Model The Problem: For decades, the "Core-Cusp" problem has puzzled astronomers. Dark Matter simulations predict "cuspy" (pointed) centers in galaxies, but observations of galaxies like DDO 154 show "flat" cores. The Solution: This paper proposes that the vacuum of space has a physical limit—a "Saturation Point." Like a fluid that cannot be compressed further, the vacuum inflow around a galaxy hits a wall and is forced to swirl into a toroidal (donut-shaped) vortex. Key Discovery: By using the natural mathematical constant e (2.718), this model explains why the measured centers of galaxies are exactly ~2.7 times larger than the theoretical "saturation wall." It replaces the need for invisible particles with simple geometric laws. How to Prove It: The theory predicts that a small "exhaust" of vacuum flux flows through the Earth at 30 cm/s. While this is invisible to lasers, it should cause a 1-nanosecond-per-day drift in atomic clocks. If detected, this would confirm a new mechanical foundation for gravity. Appendix: Technical Clarifications & FAQ (Revision 8.2) 1. On Lorentz Invariance and the Michelson-Morley Result Critics may note that a 30 cm/s vacuum flux suggests a "preferred frame," seemingly contradicting the null results of Michelson-Morley (MM). However, this model proposes a Selective Phase-Frequency Coupling. The flux is a longitudinal condensate drift. Traditional interferometry (MM) measures the transverse propagation of electromagnetic waves (light), which remain invariant. This model predicts that the flux couples specifically to the de Broglie phase of bound matter. Therefore, the effect is invisible to lasers but manifest in the cumulative timekeeping of atomic clocks. 2. Is the Saturation Density (ρsat) a Free Parameter? While ρsat is treated as a constant in this derivation to establish the Rwall boundary, it is not arbitrary. It represents the physical energy density threshold where the vacuum medium transitions from laminar radial inflow to a non-compressional toroidal vortex. This is a requirement to prevent the infinite density singularities predicted by standard General Relativity. 3. The Geometric Derivation of the 2.7 Ratio The isothermal core radius (rc≈3.0 kpc for DDO 154) is often treated as a statistical fit in literature. This model provides a geometric origin: Rwall: The hard physical limit of vacuum compression. Rsoft: The observable "isothermal" core, defined by the relaxation of vacuum tension across one natural logarithmic scale-height (e≈2.718). Result: Rwall⋅e≈3.0 kpc. The match to observed data suggests the core size is a fundamental property of vacuum geometry rather than stochastic particle behavior. 4. Redirection via Toroidal Flux To maintain the density constraint ρ≤ρsat, the radial inflow is redirected at the Rwall boundary into a toroidal (donut-shaped) vortex. This creates a "longitudinal exhaust" or flux. For a planetary body like Earth, this equates to a 30 cm/s flow, providing a concrete, falsifiable target for experimental verification via 10−12 frequency shift residuals in atomic clock networks.
Steven Doherty (Sat,) studied this question.