The dipole radiates along θ, not φ.
Zero field along the dipole axis.
Maximum at θ = 90° — the equatorial
plane of the torus. This is not a
vector cancellation. It is scalar
density equilibrium: the field seeks
the path of least scalar resistance.
Matter seeks scalar density equilibrium, not force balance.
Quaternionic Dipole
q = w + xi + yj + zk
‖q‖² = w² + x² + y² + z²
ℒ = ‖Ψ‖² − 𝔐·∇·Ψ + Φ·Ψ
The radiation pattern is a quaternionic
magnitude surface: ‖E(θ,φ)‖² mapped
onto the unit sphere, then extruded
by the scalar magnitude ρ(θ).
Ψ(x,y,z,t) = ρ + u + p + T + e
The dipole axis is the imaginary
quaternion axis. The radiation torus
is the real scalar magnitude shell.
No vectors. Only scalar density.
Direction is an emergent property
of density differential, not a force.
Olinto De Pretto · 1903 · "Ipotesi dell'Etere"
"Aether is not a medium. It is the scalar substrate from which all density differentials emerge.
E = mc² is not a conversion. It is a scalar density equilibrium statement." MGDH: Macachor · Gauss · De Pretto · Hamilton
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RADIATION PHASE
◈ 4D Scalar Field · De Pretto's Aether · Ω-Gateway