which_path_destroys_interference
plain-language theorem explainer
The declaration encodes that which-path information eliminates interference fringes in the double-slit setup. A quantum foundations researcher would cite it when mapping measurement to ledger commitment under Recognition Science. The proof reduces at once to the trivial proposition.
Claim. Acquiring which-path information in the double-slit experiment destroys the interference pattern, because measurement actualizes the recognition ledger and collapses the superposition.
background
The module derives double-slit interference from Recognition Science's 8-tick phase structure. Two paths (left slit L and right slit R) each accumulate 8-tick phases; the phase difference Δφ depends on path length difference, yielding intensity proportional to 2 + 2 cos(Δφ). Constructive interference occurs at Δφ = 2nπ and destructive at (2n+1)π. The upstream superposition result states that J > 0 whenever the recognition cost parameter r satisfies 0 < r and r ≠ 1, allowing the superposition state to persist until ledger commitment.
proof idea
The proof is a one-line wrapper that applies the trivial tactic to assert the principle directly.
why it matters
This theorem supplies the which-path measurement step inside the double-slit derivation from the 8-tick phase structure. It sits downstream of the superposition lemma (J > 0) and illustrates how the eight-tick octave produces classical behavior once the ledger is committed. The module doc-comment flags the result as the reason quantum and classical regimes differ under Recognition Science.
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