Delayed Choice Quantum Eraser and Wheeler's Participatory Universe in the ENTROPIX MESA Framework

We interpret the delayed choice quantum eraser (DCQE) experiment within the EN
TROPIX MESA research program, where physical states emerge holographically from a fi
nite capacity Quantum Information Network (QIN) of N = 64 Majorana fermions governed
by SYK interactions exhibiting maximal chaos (Lyapunov exponent λL ≈ 0.85±0.12 at low
reduced temperature T/J ≈ 0.01–0.1). Path states are encoded non locally across bound
ary entanglement wedges. Measurement entangles the path with macroscopic substrate
modes, inducing localization through Gaussian regulated von Neumann entropy growth
(Sreg(ϵ) = S0 + bϵ2 + O(ϵ4), |b| ≈ 0.5–0.75, where ϵ is the correlation length regulator de
rived from finite level spacing ∆ ≈ JN1/2/2N/2). Delayed erasure orthogonal projection
onto the symmetric/antisymmetric substrate basis disentangles the wedges, restoring coher
ence in post selected subsets (visibility 1.0000 per subset, with π phase shift between ±
outcomes; phase aligned coincidence counting reconstructs the full interference pattern).
Proxy simulations (PowerShell density matrix algebra and Python/NumPy/QuTiP im
plementations) reproduce standard quantum mechanical predictions and post selection sub
tleties: visibility 1.0000 (no measurement), 0.0000 (post-measurement), 1.0000 (post-erasure
subsets). Diagrammatic analysis of qubit dephasing coupled to finite-N SYK and spectral
form factor diagnostics motivate visibility correction V (N) ≈ V∞(1 − α/N) from explicit
1/N corrections to SYK dephasing rates (α = ag2t, a subleading coefficient; mechanism:
incomplete scrambling due to finite bandwidth ∼ JN1/2 and suppressed OTOC growth
O(1/N)).
The entropic persistence cost heuristic from spectral form factor dip suppression (dip
time polynomial in N at fixed T) penalizes long lived correlations. The Master Entropy
Selection Algorithm (MESA) variational principle extremizes the proposed informational
action B[ρ] = Tr(ρH)+κ∆Spers[ρ] under the constraint Trρ = 1. Variation yields δB/δρ =
H +κδ∆Spers/δρ + λI = 0. Assuming approximate linearity ∆Spers[ρ] ≈ Tr(ρK) for
effective operator K (mean field from form factor suppression of persistent modes), the
stationary solution is the conjectural effective density ρ ∝ e−β(H+κK), Z = Tre−β(H+κK)
(heuristic; κ phenomenological, setting persistence scale). This self selects low persistence
states, realizing Wheeler’s participatory universe intrinsically via substrate minimization of
informational overhead.
Finite-N SYK exhibits strong Bell inequality violations in appropriate subsystems (max
imal Tsirelson bound in large-N; bounded deviations O(1/N) from finite capacity), consis
tent with non-local holographic encoding and reinforcing the framework’s quantum founda
tional implications. SYK extensions to AdS/CFT (finite-N analogs of JT gravity duality,
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traversable wormholes) remain speculative. Scaling arguments support N = 64 as a work
ing benchmark for near maximal chaos with discrete capacity effects; limitations (heuristic
elements, conjectural corrections) acknowledged.