vacuum_8_tick_interference
plain-language theorem explainer
Vacuum fluctuations exhibit an 8-tick phase structure arising from the discreteness of τ₀. The eight phases cancel via destructive interference, which accounts for the small observed vacuum energy. Researchers studying the cosmological constant would reference this cancellation mechanism. The proof is a direct one-line reduction to the sum of phase exponentials equaling zero.
Claim. The sum of the eight phase exponentials vanishes: $∑_{k=0}^{7} phaseExp(k) = 0$. This produces destructive interference among the eight flavors of vacuum fluctuations generated by τ₀ discreteness and suppresses the vacuum energy density.
background
In the QFT.VacuumFluctuations module, vacuum fluctuations are derived from τ₀ discreteness, where the uncertainty principle at the tick scale produces virtual particle pairs and zero-point energy. The 8-tick octave supplies eight phase flavors that interfere. Upstream results include Constants.tick defining τ₀ := 1 and Foundation.EightTick.phaseExp defining the complex exponentials, together with the sum rule that their total vanishes.
proof idea
The proof is a one-line term-mode triviality that directly invokes the imported theorem Foundation.EightTick.sum_8_phases_eq_zero. Its doc-comment records that the sum of the eight phaseExp terms equals zero and thereby produces the required destructive interference.
why it matters
This theorem realizes the core claim of the QFT-010 module by linking the eight-tick octave (T7) to vacuum energy suppression. It connects to downstream work on the cosmological constant problem via sibling declarations such as rs_resolves_cc_problem. The result rests on the proven sum rule from the EightTick foundation layer and explains the small observed vacuum energy through coherent cancellation of the eight phases.
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