Research extension · 6 September 2026

Dust simulation lab

Explore what the equations imply, where the approximations fail, and why a local angle change is not a B-mode forecast.

Two emitting clouds

Layer 1: 20 K, β = 1.60, ψ = 0°, amplitude = 1 at 353 GHz. Change layer 2 below.

Angle change from 353 GHz-4.35°Wrapped into −90° to +90°
Polarized-layer coherence C0.485|ΣPᵢ| / Σ|Pᵢ|; not observed p
Local scalar-fit residual2.29%Fraction of local Q²+U²; not BB power
Δψ relative to 353 GHz (degrees)0.5-3.2-7.090405Frequency (GHz)
Rotation slope: 5.40° per ln νCoherence bound: |dψ/d ln ν| ≤ 6.20° per ln ν

The bound limits possible rotation. Strong cancellation alone does not guarantee it. At zero net polarization, the angle is undefined.

Fixed emission angles, positive polarized amplitudes and modified blackbody spectra in specific-intensity units. No grain population or temperature inference is performed. The local fit permits any real scalar, including negative values: an antiparallel vector can have zero fit residual despite a 90° angle change. At 90° layer separation, cancellation or a 90° flip can occur. Large jumps in the sampled curve are left disconnected.