The Photon as Modon
Structure
A photon is a modon — a counter-rotating vortex dipole propagating through the dc1 substrate. Two orbital systems of opposite chirality, bound together as a solitonic pair, self-propel through the medium at exactly the speed of light.
The modon has zero rest mass because it is an excitation of the substrate, not a localized concentration of substrate material. The two counter-rotating systems carry equal and opposite angular momentum perpendicular to the propagation direction, so the net mass flow along the direction of travel is zero. The energy is entirely kinetic — stored in the rotational motion of the vortex pair. This is structurally identical to a Lamb-Chaplygin dipole in an ideal fluid, which carries momentum and energy but involves no net mass transport.
The two counter-rotating cores are the same anti-phase pair the substrate keeps everywhere else. In Conductors two electrons bind by breathing in anti-phase about a shared counter-rotating seam, and the lattice itself breathes in pairs, each vortex shadowed by a counter-rotating partner. The Cooper pair is that pairing held standing; the photon is the same pairing set propagating — the lattice’s breath let loose to travel. It is why the smallest modon carries exactly one full breath of a single cell, E_\text{min} = 2\pi m_1 c^2: a propagating breath cannot carry less than the standing one it is made of.
In the substrate, this explains why photons are massless: the modon’s internal orbital angular momentum cancels, leaving only the translational energy E = h\nu propagating at speed c.
Why Photons Travel at c
In the strong-coupling BEC regime (\Delta_0 \gg E_F), the quasiparticle spectrum is automatically Dirac-like:
E^2 = \mu^2 + c^2 p^2
with a single isotropic speed c = \hbar/(m_1 \xi) set by the dc1 mass and the coherence length, the perturbation envelope. All low-energy excitations — scalar (phonons), vector (modons/photons), and tensor (gravitational wave metric perturbations) — inherit this speed from the BEC medium. The speed of light is not a postulate. It is the maximum group velocity of organized disturbances in a superfluid with particle mass m_1 \approx 2 meV/c^2 and coherence length \xi \approx 110\;\mum.
This makes a concrete prediction: gravitational waves and electromagnetic waves travel at exactly the same speed. GW170817 confirmed |c_\text{GW}/c - 1| < 6 \times 10^{-15}; the substrate predicts exact equality, since both are quasiparticle excitations of the same medium.
The Modon Matching Condition
The internal structure of a photon is governed by the Larichev-Reznik modon solution — the same boundary-matching mathematics that governs the entire framework. Inside the modon (r < \xi), the streamfunction is oscillatory, built from Bessel functions J_1. Outside (r > \xi), it decays exponentially via modified Bessel functions K_1. Matching at the boundary r = \xi produces a discrete spectrum:
\text{Interior:}\quad \psi \sim J_1(pr), \qquad \text{Exterior:}\quad \psi \sim K_1(qr)
The matching condition at the separatrix involves j_{11} \approx 3.83, the first zero of J_1, and determines the modon structure constant K = j_{11}^2 + 1 = 15.67. Requiring the modon to propagate at c against the substrate’s background vorticity gradient is the modon existence condition; written honestly — the dipole riding the dc1-circulation gradient \kappa_1 = 2\pi\hbar/m_1 — it collapses to the Volovik speed c = \hbar/(m_1\xi), an identity that carries no \omega_0 (see Emergent Speed of Light).
The outer-scale lattice rotation \omega_0 \approx 7.8 \times 10^9 rad/s is instead fixed in the gravity sector; its velocity v_\text{rot,outer} = \omega_0 \xi \approx 0.0025\,c is orders of magnitude below the inner-scale orbital velocity v_\text{rot,inner} = c\sqrt{2\alpha_{mf}} = 0.776\,c that governs particle physics. Photon propagation is an outer-scale phenomenon: the modon rides on the lattice, not on the inner orbital dynamics.
Propagation Through the Layered Lattice
The substrate’s vortex lattice is not a uniform 3D gas — it is organized into chirality-coherent 2D sheets stacked along a perpendicular axis, with counter-rotating intermediate vortex layers between them. Yet the photon propagates freely in all three dimensions. The mechanism is the modon’s self-propulsion: its energy is entirely internal, carried by the counter-rotating vortex pair, and the substrate neither injects nor extracts energy during transit.
Self-propulsion. A modon is not pushed by the medium — it pulls itself through it. The two counter-rotating vortices advect each other forward: each vortex sits in the velocity field of the other, and their mutual induction drives the pair at a speed determined by the medium’s equation of state. The substrate provides the confinement (the exponential decay at scale L_R = c/f_0) but the propulsion is internal. This is why the modon’s speed is c regardless of direction: the EOS P = \rho c^2 has a single characteristic speed, and any steadily propagating localized disturbance in this medium travels at that speed.
Boundary crossing by spin flip. When a modon encounters the boundary between adjacent chirality sheets, it reverses its spin orientation to match the local chirality — the “flip-flop” mechanism. The counter-rotating topology of the modon is always opposite to the local substrate flow, so it always finds a propulsion channel. What changes at each boundary is the handedness; what is preserved is the topological relationship between the modon and its medium. The energy cost of the flip is zero: the modon’s two vortices simply exchange roles (the one that was co-rotating with the sheet becomes counter-rotating, and vice versa), and the total energy is unchanged. This is the lowest-energy transit path — any other trajectory would require the modon to fight the substrate flow.
Why energy is conserved in transit. The modon displaces the substrate as it passes: the dc1 fluid is pushed aside by the vortex pair, flows around it, and returns to its equilibrium position behind it. The net energy transfer is zero — the substrate acts as an elastic medium that deforms and recovers. This is fundamentally different from a sound wave, which is a collective oscillation that gradually dissipates. The modon is a topological excitation: its vortex structure is protected by the same boundary-matching mathematics (Bessel interior, exponential exterior) that makes it stable. The only thing that can destroy a modon is encountering an anti-modon — a vortex pair with the opposite topology whose vorticity destructively interferes.
The matching condition holds in any plane. The L-R modon matching operates in a 2D plane — but this plane is defined by the modon’s own propagation direction and dipole axis, not by the lattice planes. A modon moving perpendicular to the sheets satisfies the same Bessel boundary condition (K = j_{11}^2 + 1 = 15.67) as one moving parallel to them, because the medium is isotropic at the modon’s scale \xi \gg d (where d is the inter-sheet spacing). The scale separation ensures that the modon cannot resolve the layered microstructure — it sees only the effective homogeneous BEC. This is the same dimensional crossover identified by Blatter et al. (1994) for layered superconductors: 2D behavior at short wavelengths, 3D isotropic behavior at long wavelengths, with the crossover at the inter-layer spacing.
These four properties — self-propulsion, spin-flip boundary crossing, elastic transit, and plane-independent matching — are the substrate’s complete account of why photons travel at c in all directions without losing energy. Lorentz invariance is not imposed; it emerges from the combination of an isotropic BEC spectrum and a modon topology that is compatible with every layer it enters.
Vertical Lattice Dynamics: Motion Across the Grain
The spin-flip mechanism above handles a modon propagating perpendicular to the chirality sheets without net energy cost. A separate question — and one WIP-15 needs in order to close — is how the lattice itself responds to perpendicular forcing: what equation governs vertical mass motion in the substrate, what sets the vertical period d of the chirality-coherent stack, and under what conditions the lattice can be deformed up or down. Two classical results in superfluid vortex dynamics — now woven into the framework’s foundations (the stacking geometry and the spacing d_\text{GJO} are introduced in Substrate Particles § The Vertical Scale) — supply the missing pieces.
Saffman bending modes — the vertical analogue of Tkachenko. In the 2D triangular cross-section of co-rotating vortex lines, the lowest-frequency shear mode is the Tkachenko wave (1966). Out-of-plane, where the five-pillar argument requires the lattice to be a fiber bundle of parallel filaments, each filament can bend, and the array supports a long-wave bending mode whose dispersion follows from Saffman’s local induction approximation (Vortex Dynamics, 1992):
\omega_\text{bend}^2(k_\perp) \;\sim\; \frac{\kappa_q^2}{4\pi^2}\,k_\perp^4\,\ln\!\frac{1}{k_\perp a_c}
The k_\perp^4 scaling is the key feature. The bending mode is much softer than the Tkachenko wave (\omega_\text{Tk}\propto k_\parallel) and far softer than modon propagation (\omega_\text{modon}\propto k). At astronomical L_\text{system}, the gap to the bending branch is vanishingly small — which is why the substrate can adapt to local mass distributions (planets, stars, galaxies) without measurable resistance, and why a modon traversing the grain decouples from the bending branch cleanly (the modon sits orders of magnitude above it in frequency). Tkachenko and LIA together form the substrate’s complete linear response of the vortex lattice: in-plane shear within each chirality sheet, out-of-plane bending across them. The LIA branch is the substrate’s vertical mass-motion equation — classical fluid dynamics applied to a lattice geometry the framework already requires.
The GJO wavelength sets the inter-sheet spacing. The Glaberson-Johnson-Ostermeier instability (Glaberson, Johnson & Ostermeier 1974; Sonin, Dynamics of Quantized Vortices in Superfluids, §3.10) shows that axial superflow along vortex lines becomes unstable above a Landau-like critical velocity v_\text{cr} = 2\sqrt{2\Omega\nu}, with the unstable Kelvin mode at critical wavenumber
k_c \;=\; \sqrt{2\Omega/\nu}
— the wavelength 1/k_c is the natural vertical scale picked out by the dispersion. Substituting the in-sheet rotation \Omega_\text{sheet} = \Omega_F = \kappa_q/(2\xi^2) (Feynman’s relation at one in-plane vortex per coherence cell, n_v^{(2D)} = 1/\xi^2) and the Saffman vortex-line-tension parameter \nu_s = (\kappa_q/4\pi)\ln(\xi/\xi_\text{GP}), the quantum of circulation cancels and the inter-sheet spacing reduces to a purely geometric ratio:
\boxed{\;d_\text{GJO} \;=\; \frac{1}{k_c} \;=\; \xi\sqrt{\frac{\ln(\xi/\xi_\text{GP})}{4\pi}} \;\approx\; 0.166\,\xi\;}
For \xi \approx 100\;\mum this gives d_\text{GJO} \approx 16–19\;\mum — derived from three independent classical-fluid results (GJO Eq. 4, Feynman’s vortex density, Saffman cut-off) with no fitted coefficient. The substrate locks the inter-sheet period to the GJO unstable-mode wavelength because any other spacing would leave the kelvon mode either above or below the natural axial-flow threshold; only at d = 1/k_c does the geometry self-consistently pin the lattice. This is the substrate acting like a self-organizing superfluid (helium-like) rather than an imposed-layer superconductor: the spacing is carved by an instability, not minimized into a pre-existing layer structure — which is why the GJO wavelength sets d in place of the Lawrence-Doniach energy saddle (whose \approx 7\;\mum extremum is an unstable maximum, not a well). That comparison is developed in Substrate Particles § The Vertical Scale; see WIP-15 § 3 for the full derivation and downstream consequences.
What this picture answers. With the LIA bending mode named and d_\text{GJO} now in closed form, four open questions about vertical lattice behavior collapse into a single derivation:
- The vertical mass-motion equation is the LIA bending dispersion \omega^2 \propto k_\perp^4 \ln(1/k_\perp a_c).
- The vertical range of the lattice is d_\text{GJO} = \xi\sqrt{\ln(\xi/\xi_\text{GP})/(4\pi)} — the chirality-coherent stack inherits its period from the GJO Kelvin-wave dispersion at the Feynman vortex density.
- The conditions for vertical motion separate cleanly by frequency: high-frequency modons take the spin-flip channel (above) and decouple from the bending branch; slow lattice deformations couple to the bending branch and feel its k_\perp^4 stiffness. A photon crossing the grain and a planet sitting in a gravitational well belong to different parts of the same dispersion landscape.
The LIA cross-check Evaluating the bending dispersion with the canonical \kappa_q = h/m_\text{eff} = 2.19 \times 10^{-4}\;\text{m}^2/\text{s}, the LIA frequency sits far below every current measurement bound. At 1 cm scale \omega_\text{LIA} \approx 24 rad/s; at 1 m, \approx 4 \times 10^{-3} rad/s; at Earth-Moon, T_\text{LIA} \approx 4 \times 10^{12} yr; at 1 AU, \approx 6 \times 10^{17} yr. The branch carries a hard ceiling — modes exist only for wavelengths above 2\pi a_c \approx 440\;\mum and top out at \approx 340 Hz — so there is no high-frequency LIA. Modes that ring in LIGO’s band have sub-millimeter wavelengths, sub-resolution against the 4 km arms; Eöt-Wash sub-millimeter tests probe scales below the LIA validity floor entirely. Because the inter-sheet spacing d_\text{GJO} \approx 16\;\mum is below the core cutoff a_c \approx 70\;\mum, the dag-pinned lattice is rigid at the inter-sheet scale. See WIP-15 §3.5 for the full cross-check.
Ejection Mechanism
Photons are emitted when an orbital system reorganizes across a boundary layer. During an atomic transition:
- A boundary layer between orbital levels becomes unstable
- One co-rotating and one counter-rotating orbital system are ejected as a pair
- The pair forms a modon that propagates at c through the substrate
- The energy of the pair equals the energy difference between atomic levels
E_\text{photon} = E_{N+1} - E_N = h\nu
The frequency \nu is set by the energy released in the boundary reorganization. The modon’s internal structure — its size, shape, and rotational profile — is determined by the Larichev-Reznik matching condition at the coherence scale \xi. What varies between photons of different energy is the amplitude and tightness of the internal rotation, not the overall soliton envelope.
The atomic transition above is the bound case: a boundary between orbital levels reorganizes and sheds one modon. The same ejection mechanism runs in a free case when an electron is driven to the inner-rim speed v_\text{rot,inner} = 0.776\,c — there the electron’s own counter-rotating boundary can no longer complete its paired handoff inside the light cone, and it sheds a gamma modon. Standard physics calls that free-case emission the (dipole-forbidden, pair-mediated) electron–electron bremsstrahlung channel switching on at the electron rest-mass scale; the substrate reads it as the paired breath beginning to fail. That is the subject of The Inner Rim Spectrum.
Minimum Modon Energy and the Infrared Cutoff
The minimum-energy modon has wavelength equal to the coherence length \xi:
\boxed{E_\text{min} = \frac{hc}{\xi} = 2\pi \cdot m_1 c^2 \approx 13\;\text{meV}}
The minimum modon energy is exactly 2\pi times the dc1 rest energy. Below this energy, modons cannot form — the soliton envelope would be larger than the lattice cell, and the boundary-matching condition has no solution. This creates a natural infrared cutoff at \sim 13 meV, corresponding to a wavelength of \sim 100\;\mum and a frequency of \sim 3 THz — deep in the infrared/terahertz.
For \lambda \gg \xi, excitations are better described as collective lattice modes — phonons of the vortex lattice, which in the substrate framework are gravitational waves. The modon-to-phonon crossover at \lambda \sim \xi may correspond to a detectable feature in the electromagnetic spectrum — a subtle change in propagation character at the boundary between “photon” (solitonic, localized) and “gravitational wave” (collective, delocalized). This is a potentially testable prediction.
The prediction tested from below. If light below the floor rode the substrate’s collective (Bogoliubov) branch, its group velocity would exceed c by 3\nu^2/8\nu_1^2 (\nu_1 = m_1c^2/h = 484 GHz) — a fast radio burst at z \sim 0.5 would arrive roughly 4,500 years early at 600 MHz, with a +\nu^2 spectral signature opposite in both sign and shape to the plasma \nu^{-2} delay (and, unlike a photon mass, degenerate with nothing astrophysical). A refit of the second CHIME/FRB catalog’s full-resolution dynamic spectra — 896 one-off bursts, 425 of them with per-burst scattering marginalized — bounds the soft-branch participation of sub-floor light at \varepsilon < 6.5\times10^{-16} (95%; derivation, pipeline, and robustness battery in sessions/frb-nu2-advance-1.md). So whatever exists below the floor still propagates at c, exactly as the modon does: the naive reading of the crossover — sub-floor electromagnetic energy simply becoming the gravitational-wave phonon, with that branch’s dispersion — is excluded by more than fifteen orders of magnitude. The infrared cutoff is therefore a boundary in the quantization character of light (solitonic and countable above, delocalized and collective below), not a step in its speed. What the delocalized sub-floor mode is microscopically — why it keeps the modon’s exact c — remains an open question (the “radio-photon placement” of sessions/svt-11-gate2.md §5). Observationally, the place the crossover can still show itself is in-band: the $$0.3–10 THz window, which is precisely the terahertz gap no time-domain instrument has ever watched.
And tested at the crossing, by the CMB. Because the floor sits at a fixed local frequency \nu_\text{floor} = 2\pi\nu_1 \approx 3 THz, and a photon’s local frequency was higher in the past (\nu_\text{local} = \nu_\text{obs}(1+z)), every cosmic-microwave-background photon we see today below 3 THz was a modon at recombination and crossed the floor in flight, at 1+z_\text{cross} = \nu_\text{floor}/\nu_\text{obs}. The COBE/FIRAS frequency axis is thus secretly a crossing-epoch map: 600 GHz photons crossed at z\approx4, 60 GHz photons at z\approx50 — the whole crossing band falls in the clean, late, matter-dominated universe. If the soliton-to-collective conversion at the floor were non-adiabatic it would shake energy loose and scar the blackbody, with an imprint that grows toward low frequency (those photons crossed when the universe expanded faster). But the crossing is adiabatic by an enormous margin: the dispersion relation changes by order unity over a Hubble time while the mode oscillates at the cell scale, giving an adiabaticity \mathcal{A} = \nu_\text{floor}/H(z_\text{cross}) \sim 10^{28}. The resulting fractional distortion is \sim 1/\mathcal{A} \sim 10^{-28}, with the predicted shape \propto \nu^{-3/2} (steepest in FIRAS’s cleanest Rayleigh–Jeans channel) — twenty-three orders of magnitude below FIRAS’s spectral-distortion limits (|\mu| < 9\times10^{-5}, |y| < 1.5\times10^{-5}). So FIRAS’s 50-ppm blackbody, read across crossing-epochs z = 4–50, confirms the band edge is non-dissipative for redshifting light: the floor is transparent both below it (the FRB bound) and at the crossing (this one), from two orthogonal observables. A laboratory probe — crystal-optics band edges, terahertz time-domain spectroscopy — would see the same 3 THz edge as a sharp feature at fixed local frequency; the cosmological redshift smears that sharp edge into the smooth \nu^{-3/2} distortion, which is why a broadband CMB instrument, not a line search, is the right place to look from the sky (calculation in scripts/firas_crossover_adiabaticity.py, sessions/firas-crossover-1.md).
What Carries Light Below the Floor
Both confrontations above leave one question open: if a localized modon needs \lambda \le \xi, what is a radio photon, whose wavelength is meters and whose single-quantum energy h\nu is millions of times below E_\text{min}? It cannot be one modon — it lacks the energy for a single breath. Yet the FRB refit shows it travels at c to a few parts in 10^{16}. The resolution sharpens the modon picture into a falsifiable, mechanism-level statement.
Three excitations meet at the floor. Start from the framework’s own modon dispersion, U_{LR} = -\beta/(p^2 + \kappa_\text{ext}^2) with ground state p = j_{11}/\xi, \kappa_\text{ext} = 1/\xi (Emergent Speed of Light). The exterior decays over the healing length \kappa_\text{ext}^{-1} = \xi — a property of the medium — while the interior oscillates on the core scale a. A localized object needs its core to fit inside its own decay length, a \le \xi; the marginal, largest, lowest-energy modon is a = \xi, which is exactly the floor. There is no localized solution for a > \xi — not by fiat, but because the core and healing scales have collided and scale separation is gone. So below the floor, three things are possible, and the data choose between them:
- A localized modon — ruled out, as just shown: it cannot exist for \lambda > \xi.
- The collective Bogoliubov (sound / gravitational-wave) mode — its group velocity runs above c as a power law, \delta_g = \tfrac{3\pi^2}{2}(\nu/\nu_\text{floor})^2. This is the “+\nu^2” branch the FRB refit was built to detect, and excluded as the carrier of light: at 600 MHz it would give \delta_g = 5.8\times10^{-7}, fifteen orders above the FRB sensitivity floor.
- The delocalized winding — the modon’s conserved circulation quantum, spread over \lambda = c/\nu \gg \xi. This is what survives.
The stretched photon. A sub-floor photon is the modon’s winding let loose from its soliton core and smeared across many cells — a stretched photon. Its speed comes from the circulation quantum over the healing length, c = \kappa_1/2\pi\xi = \hbar/m_1\xi, in which the core size a does not appear. Stretching the winding changes nothing about its speed: there is no leading dispersion, and sub-floor light sits at exactly c for the same reason the modon does — the Volovik identity never mentioned the soliton’s size. The winding is topologically quantized and conserved (Kelvin’s theorem; the emergent U(1) of London electrodynamics), and the sound mode carries no circulation, so the two cannot mix — which is precisely why the FRB refit finds no leakage into the collective branch.
The residual is exponential, not power-law — and that is testable. The winding can disperse or dissipate only by a core-scale reconnection that locally unwinds it, an event costing the full gap energy E_\text{min}. A sub-floor photon carries less than that (h\nu < E_\text{min}), so it can reach the core scale only by tunneling, and the residual deviation is suppressed as \delta_g(\nu) \sim \exp\!\big(-E_\text{min}/h\nu\big) = \exp\!\big(-\nu_\text{floor}/\nu\big). This is the substrate’s exact analogue of BCS / Mattis–Bardeen sub-gap absorption: a photon below the superconducting gap cannot break a Cooper pair, and its residual response is exponentially — not power-law — suppressed. Here E_\text{min} is the gap and a modon-core reconnection is the pair-breaking event. The mathematical payoff is decisive: \exp(-\nu_\text{floor}/\nu) is non-analytic at \nu = 0, so it has no \nu^2 term at all. The collective branch has one; the protected winding does not. Since the FRB observable is the coefficient of \nu^2, the null result does more than confirm “c” — it selects topological protection over a generic emergent photon. A photon that were merely the Goldstone/gauge mode of the condensate would still permit a dimension-six (k\xi)^2 = \nu^2 Lorentz-violating term at order unity; FRB bounds that coefficient at \alpha_6 < 2.4\times10^{-16}, excluding it by fifteen orders. Only a topologically protected winding forbids the term outright.
This closes the “radio-photon placement” question with a mechanism, not just a bound: below the floor, light is the modon’s winding stretched thin, held at c by the same topological conservation that quantizes circulation, with anomalous dispersion exponentially locked away until one reaches the floor itself. The three floor probes are then one phenomenon seen three ways — FRB from below (excludes the power law), FIRAS at the crossing (the adiabatic suppression is this protection, caught in flight), and a laboratory terahertz band-edge measurement at the floor. What remains for theory is to compute the modon-core reconnection action that fixes the exponential’s coefficient (derivation and verification in scripts/below_floor_dispersion.py, sessions/below-floor-dispersion-1.md).
Planck’s Constant from Substrate Properties
The quantum of circulation in the substrate is:
\kappa_q = \frac{h}{m_\text{eff}} = \frac{2\pi\hbar}{m_\text{eff}}
where m_\text{eff} = m_e / \alpha_{mf} \approx 1.70 MeV/c^2 is the effective quantum mass — a substrate property, not a particle property. Combined with the Volovik relation c = \hbar/(m_1 \xi) and the condensation number \nu = m_\text{eff}/m_1 \approx 8.3 \times 10^8:
h = m_\text{eff} \cdot \kappa_q = \nu \cdot m_1 \cdot \kappa_q
Planck’s constant is not fundamental — it is the circulation quantum of a superfluid with particle mass m_1 and condensation number \nu. The discreteness of quantum mechanics traces to the discreteness of vortex circulation in the dc1 medium.
The Harmonic Resonance
The two-scale structure produces an exact relationship between the coherence length and the effective Compton wavelength:
\frac{\xi}{\lambda_C(m_\text{eff})} = \frac{\nu}{2\pi}
The coherence length contains exactly \nu/(2\pi) effective Compton wavelengths. This is not a coincidence — it is the resonance condition that allows the outer-scale lattice structure and the inner-scale particle physics to coexist in the same medium. The modon, as the carrier of energy between scales, must satisfy both boundary conditions simultaneously.
The Photon’s Place in the Framework
The photon completes the Foundation section of this framework. Gravity (Gravity as Boundary-Layer Ebbing) is the macroscopic leak current through counter-rotating boundaries. The quantum potential (Two Fluids → Quantum Potential) is the reaction force of those same boundaries on co-rotating flow. And the photon is the solitonic excitation emitted when those boundaries reorganize — a modon that carries energy between orbital systems at the speed set by the medium itself.
All three phenomena arise from the same substrate physics operating at the outer scale \xi \approx 110\;\mum. What happens at the inner scale — where the effective quantum orbits at v_\text{rot,inner} = 0.776\,c with radius r_\text{eff} = 150 fm — is the subject of the next section: how these modons are absorbed and emitted by the layered orbital systems that constitute atoms.