The Cosserat Supersolid: Deriving the Constants of Nature from Vacuum Lattice Mechanics

Abstract

Modern physics quietly treats the vacuum as a material. It has a permittivity and a permeability. It fixes a wave speed, c = 1/√(μ₀ε₀). It carries zero-point fluctuations, condensates, and an equation of state. The luminiferous aether was discarded after Michelson and Morley, yet its replacement kept every property of a medium and dropped only the name. This monograph asks what happens if the vacuum is taken to be exactly that: a material, and specifically a crystal that is also a superfluid. Such a medium is called a supersolid, and it was first seen in the laboratory in 2019. Its dual character is what lets it pass the test that killed the aether. The crystal carries a transverse shear wave, which is light. The superfluid lets matter drift through without drag, so there is no aether wind for an interferometer to catch. What follows from the hypothesis is unexpectedly specific. One mechanism does most of the work: the probability for a defect in the crystal to tunnel through the lattice's own periodic potential, the Peierls–Nabarro amplitude. That single mechanism produces the fine structure constant, α⁻¹ = 137.035999177, matching CODATA 2022 to 0.003 parts per billion, with nothing measured put in by hand. The same mechanism, applied to a nineteen-node cluster rather than one node, gives Newton's constant to two parts per million. The 10³⁸ gap between electromagnetism and gravity is then not a mystery but a count: one-node tunnelling set against nineteen-node tunnelling. The framework rests on a single axiom. The vacuum is a dense Cosserat medium whose ground state is a crystal. A Cosserat medium is one whose constituents carry a rotation as well as a position. That rotation supplies half-integer spin, and with it the fermion statistics and the short-range repulsion that drive a fluid to freeze. Quantum mechanics is not assumed on top of this. The Schrödinger equation and the Born rule emerge from the crystal's own elastic motion, and ħ is a derived quantity. The crystal is selected, not fitted, and what selects it is a measured fact. Lorentz invariance holds to about one part in 10²¹, and a crystalline vacuum can match that only if its elastic response is perfectly isotropic. No three-dimensional crystal manages this. The four-dimensional lattice D₄ does, and its triality, a symmetry unique to four dimensions, both pins the dimension at four and delivers the three fermion generations. The lattice spacing is the classical electron radius, ℓ = r_e = 2.82 femtometres, fixed by a single identification rather than chosen. The same crystal gives the forces and the particles. The four fundamental forces are four ways the one crystal can deform, recovered as eigenvalues of a single Peierls–Nabarro transfer matrix, with a fifth, massive channel supplying the nuclear tensor force. Five of the ten symmetry channels give exactly zero, so the framework predicts no further force. Particles are defects in the lattice. A screw dislocation is an electron, a partial dislocation is a quark with its colour from the same triality, an edge dislocation is a neutrino, and a missing node is dark matter. Hadron masses then follow from one formula, m = N·m₀ − N(4 − λ_Γ)·m_e, in which N counts the disturbed nodes and λ_Γ is an elastic eigenvalue read from the cluster's geometry. The formula closes roughly thirty hadron masses to within the framework's 0.7% resolution, several of them far closer. It also settles two old puzzles in one stroke. MacGregor noticed long ago that hadron masses fall on a ladder spaced by m_e/α ≈ 70 MeV, and never learned why. Lattice QCD later showed that ninety-nine percent of the proton's mass is binding energy, carried by a field with no rest mass of its own. The lattice supplies the missing unit and the missing carrier with one object: the node, whose rest energy is m₀ = m_e/α = 70 MeV. The reach extends across the rest of the Standard Model. From m_e and α alone the framework gives the electroweak observables, the quark and charged-lepton masses, the CKM mixing angles, and the neutrino oscillation parameters. A single geometric angle, θ_ch = α²/(2π), ties together three numbers the Standard Model treats as unrelated: the neutrino mass sum of 65.5 meV, the matter-antimatter asymmetry, and the cosmic birefringence angle. Twenty-nine decay rates, spanning twenty-four orders of magnitude in lifetime, follow from the elastic mechanics of a defect rearranging itself. The cosmological constant comes out zero. Dark energy is the stored elastic energy of fossil domain walls in the crystal, pinned in place since the universe's first 10⁻⁵ seconds, with an equation of state of exactly −1 at every epoch. The accounting is honest about what it does and does not deliver. There are no free law parameters, so every result above is overconstrained, a prediction rather than a fit. Most retrodictions land within the 0.7% resolution, and many land well inside it. A minority do not. Isospin and hyperfine splittings within hadron multiplets sit at the one to five percent level and are partly open. The framework names their scale, one electron mass per charge-active bond, and the structure they act on, the defect's bond graph. The bilinear, isotensor part of the rule is now a derived bond count, three links per junction pair, verified by the Σ curvature at 0.13%, and the linear base is a territory count of four; the strange-ladder step remains open. On the other side of the ledger, several results reproduce constructions already known under other names: the exponential metric of Yilmaz for gravity, and the fracton elasticity-to-gauge duality. Those coincidences are independent checks, not inputs. The predictions are falsifiable in every sector. The neutrino mass sum is 65.5 ± 1.4 meV, within reach of the Simons Observatory and Euclid this decade. Neutrinoless double beta decay should return a null, which LEGEND-1000 can test. The dark energy equation of state is exactly −1 with Λ = 0: background-degenerate with ΛCDM, so any robust detection of dynamical dark energy by DESI, Euclid, or Rubin falsifies it. New strange dibaryons should appear at the LHC. Gravitational waves should show a birefringence 2/π times that of light, a zero-parameter ratio LISA can test and no other theory predicts. Whether this level of agreement is evidence or coincidence is for the reader to judge.