Structural BCT Letter 2: Maxwell, Dirac, and Einstein from a Single Quantum Fluid — Emergent Field Equations of the BCT Superfluid Vacuum

The three pillars of modern physics—Maxwell's electromagnetism, Dirac's relativistic quantum mechanics, and Einstein's general relativity—have historically been formulated as independent theories with separate axioms and distinct mathematical structures. We show that all three emerge as low-energy effective descriptions of a single quantum fluid: a body-centred tetragonal (BCT) superfluid lattice with axial ratio c/a = √ 2. Maxwell's equations arise as the long-wavelength dynamics of the irrotational phonon mode in the octahedral void condensate, with the electromagnetic field tensor identified as the curl of the superfluid velocity field. The Dirac equation emerges as the effective equation of motion for quantised vortex excitations propagating through the lattice, with the four-component spinor structure arising from two void types times two chiralities, and Fermi statistics from the topological π-phase under 2π vortex rotation. The linearised Einstein equations follow from the Unruh–Visser acoustic metric theorem applied to the BCT superfluid, with Newton's gravitational constant G determined by the lattice bulk modulus and the cosmological constant Λ = 0 at the classical ground state. The speed of light, Planck's constant, and Newton's constant are all expressible in terms of the BCT condensate parameters. This unification requires no additional postulates beyond the existence of a BCT superfluid ground state—the three sets of field equations are three aspects of the same medium's dynamics.