A Dark Material Model of the Universe
A substrate formed of microscopic orbital systems fills the gaps in physics
AI disclosure: I used Claude (Anthropic PBC) for content, graphics, and help with equations.
About This Project
This is a compilation of the work of many great scientists. I’m a 61 year old Engineering Fellow at Posit PBC - a code first data science company that supports open source. I’m pretty good at software, but a novice when it comes to Physics and this is an open source, solo side project.
In late June, 2025 after seeing one of the first Vera Rubin photos on a hi-res monitor, I intuited that dark matter had to be dark material orbital systems, they had to be in the atom and in space. In my mind’s eye, I saw why it has to be this way. The universe is not weird, and there’s an explanation for cellular dynamics, the gulf stream, magnetic fields.
I eventually found these five amazing theories that when combined paved the last mile:
- Pilot wave hydrodynamics by Bush, Oza, et al.1
- Volovik’s theories from “The Universe in a Helium Droplet”2
- Simeonov’s mapping of the Madelung equations as a fluid form of the Schrödinger equation3
- Khoury’s papers on Dark Matter Superfluidity4
- Larichev & Reznik, Saffman, Aftalion, Fetter for the math behind modons and vortices5
From this foundation I built a model and in dialog with Claude, refined it till it started to click. At this point, the model describes the world in a more unified and satisfying way, but some challenges remain.
What changes
| Standard physics | Substrate framework | |
|---|---|---|
| Spacetime | Warped geometry (no medium) | Acoustic geometry of a superfluid |
| Time dilation | Fundamental, unexplained | Pressure-dependent clock rate in the medium |
| Gravity | Curvature of spacetime | Ebbing current through orbital boundaries |
| Dark matter | Unknown particle (not yet detected) | The substrate itself (n_1 m_1 = \rho_{DM}) |
| Galaxy rotation curves | Dark matter halos (not yet detected) or modified gravity (MOND, ad hoc) | Boundary parity → quadratic CPR → MOND field equation; a_0 = c\sqrt{G\rho_\text{DM}} |
| Dark energy | Fine-tuned to 10^{-122} | Zero at equilibrium; observed \Lambda from residual disequilibrium |
| Quantum vacuum | Abstract field with 10^{122}\times too much energy | Superfluid at measured \rho_{DM} |
| Wave–particle duality | Complementarity principle | Vibrating particle in a responsive medium |
| Wave function collapse | Measurement problem (unresolved) | Orbital system reorganization at boundary |
| Spin | “Intrinsic” (no classical analog) | Counter-rotating boundary layer angular momentum |
| Quantization | Postulated (Born rule) | Standing-wave boundary matching (geometric) |
| Entanglement | Nonlocal correlations | Topologically protected vortex channel |
| Mathematical frameworks | Two (QFT + GR), incompatible | One (fluid dynamics at all scales) |
Framework Thesis
If dark matter is really a dark material, composed of at least two particles — dc1 (“dark carbon”) and dag (“dark silver”) — much smaller than an electron and of sufficiently different mass, they would have formed orbital systems during the creation event, the lighter particles spinning around the heavier ones with enormous energy. There is no mechanism that could have removed this material from the atom, or from space.
Model these particles as orbital systems in a frictionless substrate, colliding elastically to create a superfluid environment. Atomic nuclei become orbital system complexes that balance into the lowest-energy stable state, despite high internal rotational velocity, stabilized by counter-spinning vortices that bind these systems together at energy boundaries. Within the same energy region, counter-spinning vortices of dc1 form between same-spinning orbital systems.
How light travels through the substrate, and crossing boundaries without losing energy:
Energy transfer follows the boundary equations for modons — dipole vortex streams that travel long distances against the flow in ocean currents. These “dark modons” are orbital system pair complexes (dipole vortex streams) absorbed and emitted between systems, conveying packets of energy. They are transmitted freely in (and propelled by) the energy of the substrate, crossing boundary layers frictionlessly by flip-flopping spin direction, producing the lowest-energy transmission: Lorentz Invariance.
The substrate framework asks: how do co-rotating systems in low-dissipation environments create and maintain boundary layers, and what is the energy budget of those boundaries? In all analogous macro-scale systems — binary star collisions, vortex streets, Jupiter’s atmosphere, modons, pilot wave pairs — counter-rotating structures form spontaneously at boundaries between co-rotating regions. They self-organize into the lowest-energy configuration consistent with the boundary conditions, and they transport excess energy away as propagating vortex pairs (modons). The math is the same across scales: Euler equations with a vorticity source term at boundaries.
This same mechanism operating at the Planck scale in a dc1/dag superfluid reproduces quantum mechanics à la Madelung/Bohm6, where the quantum potential is the reaction force of the counter-rotating boundary layer. Quantized states emerge from wave interference in the dc1/dag medium, not from imposed quantum rules. Quantization is a geometric consequence of oscillatory solutions enclosed by decaying solutions, joined at a boundary.
Spacetime is not fundamental. It is the acoustic geometry of the dc1/dag substrate. Curvature is not fundamental. It is the gradient of the current that ebbs through the boundary, then falls in the laminar stream in the substrate by the energetic system inbetween. And Einstein’s equations are not just postulated — they are understood at a deeper level. The substrate does not just mimic General Relativity - it generates GR as the low-energy effective theory of quasiparticle propagation.7 Spacetime geometry is the acoustic geometry of the dc1/dag substrate. Einstein’s equations are the self-consistency condition for the substrate’s response to organized energy. And the features of our universe that ΛCDM takes as given — \Lambda, dark matter, flatness, inflation — emerge from the material properties of the substrate.
The equations show how effective mass disappears, and how a dipole vortex spinning at 0.776c will flow through an orbital system substrate at a constant c.
the substrate forms 2D lattices of orbital systems and counter-spinning vortices
But I cannot find math to model the incredible 3D system, so we are left with a big gap due to this amazing math challenge. Within a localized region, the substrate forms into 2D lattices, dc1/dag orbital systems with the same chirality, bound by counter-spinning dc1 substrate vortices.
The sheets stack so an orbital system is over a vortex
In 3D, the lattices stack, but offset so that each dc1/dag orbital system spins above and below a counter-spinning dc1 vortex. The polar stream jets from the dc1/dag orbital systems form a feedback loop with the counter-spinning vortices. It’s a perfectly energy efficient dynamical system, tied together with feedback loops between: the polar jets, the counter-spinning vortices, and the co-rotating orbital systems - all intertwined, and regulated by their interaction, and spaced at the value we computed two ways - using the bridge equation: \approx 100\;\mum. The same dimensions of the photon/modon’s. My intuition, and the model says they travel through energetic springing mattress, at constant speed, with perfect energy efficiency, no matter which direction. It’s also perfectly clear why the math is so challenging.
The dc1/dag substrate is dark matter. The “missing mass” in galaxy rotation curves, cluster dynamics, and CMB anisotropies is the substrate itself.
- Collisionless: counter-rotating boundary layers do not interact with electromagnetic modons
- Pressureless on galactic scales: bulk flow is coherent, P_\text{eff} \approx 0 for structure formation
- Self-gravitating: orbital system rotational energy generates ebbing currents
What it predicts
From one measured input (\sin^2\theta_W = 0.2312) and zero new free parameters:
| Quantity | Predicted | Measured | Discrepancy |
|---|---|---|---|
| Fine structure constant \alpha | 1/135.1 | 1/137.036 | +1.45% |
| Anomalous magnetic moment (g-2)/2 | 0.001178 | 0.001160 | +1.6% |
| Core-boundary asymmetry \eta | 0.03432 | 0.03406 | +0.8% |
From the substrate parameters alone — with zero new free parameters — the MOND acceleration scale is predicted:
| Quantity | Predicted | Measured | Discrepancy |
|---|---|---|---|
| MOND acceleration a_0 | c\sqrt{G\rho_\text{DM}} = 1.200 \times 10^{-10} m/s² | (1.20 \pm 0.02) \times 10^{-10} m/s²8 | < 1\% |
| Flat rotation curves | Derived from boundary parity | Observed universally | — |
| Baryonic Tully-Fisher M_b \propto v^4 | Derived | M_b \propto v^{3.98 \pm 0.06} | — |
| a_0/(cH_0) ratio | \sqrt{3\Omega_\text{DM}/(8\pi)} = 0.179 | 0.179 | 0.15% |
The MOND field equation emerges from the parity symmetry of the counter-rotating boundary layers: because the boundary contains both rotation directions equally, its current-phase relation is quadratic (not linear) at leading order, which produces \nabla \cdot [|\nabla\Phi|\nabla\Phi] \propto \rho_b — the deep-MOND equation.9 The Hubble expansion breaks the parity and induces a linear (Newtonian) term. The crossover between the two regimes is a_0 = c\sqrt{G\rho_\text{DM}}. See Galactic Dynamics for the full derivation.
From three measured constants (\hbar, c, \rho_{DM}) the coherence length is determined by two independent routes — one from particle physics, one from cosmology — that agree through a single relation with no adjustable parameters:
| Route | Formula | Value |
|---|---|---|
| Cosmology (close-packing) | \xi = (\hbar/\rho_{DM} c)^{1/4} | 110 μm |
| Particle physics (SC2) | from \alpha_{mf}, m_e, j_{11} | 96.9 μm |
| Bridge equation | \xi_{SC2}/\xi_{CP} = (4\pi/K\sqrt{2})^{1/4} | 0.047% match (ξ ratio) |
The bridge equation decomposes into three factors, each from a different domain of physics: 4\pi from general relativity (the Gauss’s law solid-angle factor in \nabla^2\Phi = 4\pi G\rho), K = j_{11}^2+1 from the Bessel function matching at the modon boundary, and 1/\sqrt{2} from the quantum kinetic energy operator \hbar^2\nabla^2/(2m). A fourth factor — \eta = 1, confirming no 3D geometric correction to the lattice packing — is established by a five-pillar stability argument from classical vortex dynamics (Tkachenko, Jimenez, Moffatt, Onsager).10 Together they form a zero-parameter relation connecting \sin^2\theta_W, m_e, \rho_\text{DM}, \hbar, c, and j_{11} — electroweak physics, quantum mechanics, gravity, cosmology, and now galactic dynamics linked through one superfluid.
Free parameters: The Standard Model + ΛCDM requires ~25 free parameters. The substrate framework has 3 truly unconstrained parameters (M_d, n_d, \delta), none of which appear in any current prediction. All quantitative results above use only measured constants as inputs.
*This model has not been independently validated. All results are tree-level; discrepancies are consistent with missing radiative corrections. See the bridge equation for the derivation, galactic dynamics for the MOND result, and constraint system for open derivations and theoretical gaps.
The key identifications:
| Standard Physics | Substrate Framework |
|---|---|
| Quantum vacuum | dc1/dag orbital system substrate |
| Photon | Modon (counter-rotating vortex dipole) |
| Electron | One effective quantum (\sim 10^9 dc1, mass m_\text{eff} = 1.7 MeV/c^2) orbiting at r_\text{eff} = 150 fm with \hbar angular momentum, dressed by coherence soliton at \xi \approx 100\;\mum |
| Quantum potential Q | Reaction force from counter-rotating layer |
| Planck’s constant \hbar | 2m \cdot D (diffusion constant of counter-rotating layer) |
| Speed of light c | \hbar/(m_1 \cdot \xi) — ratio of Planck’s constant to dc1 mass times coherence length (Volovik quasiparticle speed in BEC regime) |
| Gravitational constant G | Parametrizes dc1 leak current through boundaries |
| Wave function \psi | \sqrt{\rho} \cdot \exp(iS/\hbar) — amplitude + phase of co-rotating layer |
| Spin | Angular momentum of effective quantum about its axis |
| Chirality | Direction of spin relative to direction of motion |
| Higgs field | Local chirality state of the dc1/dag substrate |
| Measurement | Interaction that couples particle orbital system to detector field |
| Wave function collapse | Orbital system reorganization upon boundary interaction |
Fermions are polarized orbital systems — with a central unbalanced energy and an odd number of counter-rotating boundary layers separating their internal co-rotating flow from the external substrate. They repel each other according to the Pauli exclusion principle because two same-state fermions would create an irreconcilable boundary conflict.
Bosons are balanced opposite-spinning pairs that have formed an orbital system complex. They move through the fluid with zero forward momentum — massless — due to the counter-balancing energetic effects and even boundary parity.
Mass is rotational energy - the orbital kinetic energy of substrate particles spinning in organized systems. An electron’s 0.511 MeV is entirely accounted for by one effective quantum (~8.3 × 10⁸ condensed dc1 particles) orbiting at 0.776c.
The speed of light is a substrate property: c = \hbar/(m_1 \cdot \xi), the ratio of Planck’s constant to the dc1 mass times the coherence length. It is the maximum speed at which organized disturbances propagate through the superfluid — set by the medium, not by geometry.
Planck’s constant is the minimal action of a counter-rotating boundary layer: \hbar = 2m \cdot D, where D is the diffusion constant of the counter-spinning eddies. Quantization is not imposed — it emerges because only discrete standing-wave patterns survive the boundary matching between co-rotating interior and decaying exterior.
Photons are modons — counter-rotating vortex dipoles ejected when an orbital system reorganizes across boundary layers. They form from the electron’s coherence dress (already at the ~100 μm soliton scale), accelerate to c because their counter-spinning topology is always opposite to the substrate flow, and transit boundaries frictionlessly by flip-flopping spin direction. Their energy is set by the transition; their structure is set by the lattice.
In standard QM, the wavefunction \psi is a probability amplitude with no agreed-upon physical meaning. In the substrate framework, \psi = \sqrt{\rho}\,\exp(iS/\hbar) decomposes into two measurable quantities — \rho is the co-rotating substrate density, and S is the phase of the pilot wave flow. The quantum potential Q emerges from the interaction between the co-rotating flow and the counter-rotating eddies at its boundaries. Nothing is mysterious. Nothing requires interpretation. It’s fluid dynamics.
And this results in these phenomena:
- Free-flowing, Lorentz Invariant energy transport; gravitational lensing based on pressure/energy changes in the substrate; a way to model subtle observed CMB effects without warping space-time or invoking nonlocality — instead creating hidden pathways of wave energy in an active dynamic substrate that reacts like pilot-wave hydrodynamics.
- Gravity acts like an “ebbing” or tidal force applied to boundaries, not individual particles. It applies to the contained mass of the orbital system enclosed by that boundary. The theory predicts gravity’s weakness as a consequence of boundary layer efficiency. And once the boundary layer has been penetrated, it accelerates through the boundary to the next layer.
- QFT is incredibly accurate but combines two dynamical layers into one effective description, producing terms (Q, \mathbf{A}) whose physical origin is obscured because the counter-rotating layer’s degrees of freedom have been integrated out. This framework proposes the microscopic content that would make QFT a complete theory — analogous to how kinetic theory provides the microscopic content behind thermodynamics.
- Tunneling occurs because the counter-rotating layer at the turning point isn’t a perfect wall. It’s a dynamic, fluctuating boundary whose eddies occasionally create momentary gaps.
- Entanglement occurs because a singlet’s topology guarantees signal fidelity through a topologically protected vortex channel — the half-integer winding protects information in transit the same way it protects a qubit in a topological quantum computer. The substrate predicts a drop-off in Bell correlations beyond long distances.
- The spin-statistics connection — fermion/boson distinction, Pauli exclusion, 720° rotation — emerges as a topological consequence of how many counter-rotating boundary layers separate a particle’s internal flow from the external substrate.
- The Higgs mechanism is the local chirality ordering of the dc1/dag substrate, with spontaneous symmetry breaking arising from same-chirality clustering.
- The Aharonov-Bohm effect shows that the substrate field polarity is an almost immeasurable difference in a field that makes a big difference in electron spin.
- The Big Bang as classically conceived is a singular origin with no place to be — spacetime expanding everywhere all at once. The substrate framework’s bang is a local bubble popping in a universe that boils. It pops wherever the pressure has built up enough to nucleate a pocket of the other phase. There is no contradiction between this and what we observe. There is, instead, a different relationship between the observer and the cosmos: we are not surveying the aftermath of a unique creation. We are inside one of the substrate’s normal relaxations, looking outward at the wall that made us, and asking — reasonably, but mistakenly — where it came from. It came from the substrate boiling. That is the whole story. The rest is hydrodynamics.
The framework now has a consistent story from the Planck scale (substrate particles) through nuclear physics (quark confinement), atomic physics (hydrogen orbitals), condensed matter (conductivity, superconductivity), particle physics (electroweak symmetry breaking, Higgs mechanism, weak force chirality), and galactic dynamics (flat rotation curves, the MOND acceleration scale, Tully-Fisher — all from boundary parity with zero new parameters).
Footnotes
Bush, J.W.M. & Oza, A.U., “Hydrodynamic Quantum Analogs,” Annual Review of Fluid Mechanics 52, 2020. A vibrating particle in a responsive medium reproduces quantized orbits, tunneling, and interference — the template for the electron. See also Dagan & Bush, “Hydrodynamic quantum field theory: the free particle,” Comptes Rendus Mécanique, 2020. [R1, R1b]↩︎
Volovik, G.E., The Universe in a Helium Droplet, Oxford University Press, 2003. The single most important source: emergent speed of light (Ch. 7), two-fluid model (Ch. 4–5), gauge fields from vortex cores (Ch. 22–25), and cosmological constant self-tuning (Ch. 29–30). [R2]↩︎
Simeonov, L., “Quantum mechanics as a two-fluid stochastic theory,” arXiv:2509.02868, 2025. Shows that the osmotic velocity of a counter-rotating fluid derives from the HVBK mutual friction force, formally bridging superfluid hydrodynamics to quantum mechanics. [R3]↩︎
Khoury, J., “Dark Matter Superfluidity,” arXiv:1507.01860, 2015; Berezhiani, L. & Khoury, J., “Theory of Dark Matter Superfluidity,” Phys. Rev. D 92, 103510, 2015. Dark matter as a superfluid on galactic scales, with a MOND-like phonon-mediated force and CDM-to-MOND transition at the Landau critical velocity. [R4, R26]↩︎
Larichev, V.D. & Reznik, G.M., “Two-dimensional solitary Rossby waves,” Doklady Akademii Nauk SSSR 231, 1976 (modon boundary matching, K = j_{11}^2+1); Saffman, P.G., Vortex Dynamics, Cambridge, 1992 (dipole dynamics, lattice stability); Aftalion, A. et al., Phys. Rev. A 71, 023611, 2005 (vortex lattice energy functional); Fetter, A.L., Rev. Mod. Phys. 81, 647, 2009 (GP healing length, 1/\sqrt{2} factor). [R5, R6, R7, R8]↩︎
Nelson, E., “Derivation of the Schrödinger Equation from Newtonian Mechanics,” Phys. Rev. 150, 1079, 1966; Bohm, D. & Vigier, J.-P., Phys. Rev. 96, 208, 1954. The formal bridge from superfluid hydrodynamics to QM is completed by Simeonov [R3]. [R18, R19]↩︎
Barceló, C., Liberati, S. & Visser, M., “Analogue gravity,” Living Reviews in Relativity 8, 12, 2005. Any barotropic, irrotational, inviscid fluid produces an acoustic metric formally identical to curved Lorentzian spacetime. The substrate satisfies this. [R13]↩︎
McGaugh, S.S., Lelli, F. & Schombert, J.M., “Radial Acceleration Relation in Rotationally Supported Galaxies,” PRL 117, 201101, 2016. Measured from 2693 data points across 153 galaxies. [R24]↩︎
This is the Bekenstein-Milgrom AQUAL formulation: Bekenstein, J. & Milgrom, M., ApJ 286, 7, 1984 [R63]. The original MOND proposal: Milgrom, M., ApJ 270, 365, 1983 [R25]. The substrate derives rather than postulates this equation.↩︎
Tkachenko, V.K., Soviet Phys. JETP 23, 1049, 1966 (triangular lattice optimality); Jimenez, J., J. Fluid Mech. 68, 49, 1975 (co-rotating pair stability); Moffatt, H.K., J. Fluid Mech. 35, 117, 1969 (helicity conservation); Onsager, L., Nuovo Cimento Suppl. 6, 279, 1949 (negative-temperature clustering). The fifth pillar — energy-optimal parallel filaments — is from Saffman [R6]. [R27–R30]↩︎