3 Experiment 2: Boson Structure

Python: boson_structure.py

Rather than measuring ∥B∥ alone, we analyse the structure of B:

• Symmetry: is B symmetric (spin-0 candidate) or antisymmetric (spin-1 candidate)?
• Propagation: does the dominant eigenvector of B resemble a plane wave?
• Quantisation: is ∥B∥ a simple rational multiple of 2^−C_s?

Results

For the video (1,2) — a single fermion hopping from site 0 to site 1 — the boson matrix is purely antisymmetric, not approximately but exactly. Its eigenvalues are ±1∕2, symmetric about zero. The forward hop (1,2) and reverse hop (2,1) produce identical boson structure with opposite momenta k = ±0.157, exactly as expected from a particle–antiparticle pair.

For the block hop (3,12) — two fermions moving together,

the boson has a longer wavelength and lower effective momentum, consistent with a heavier or composite mediator.

Conclusion: The compression residual of a single fermion hop is purely antisymmetric, has definite momentum, and pairs with its time-reverse into a particle–antiparticle pair. No interaction term was introduced; these properties follow from the codec structure alone.