Complex Time and Quantum Coherence: a reading of Wheeler's Delayed‑Choice Experiment (v3)

This work proposes a geometric interpretation of Wheeler’s delayed‑choice experiment based on a model in which physical time is represented by a complex variable T=t−iτ. The imaginary component τ, evolving counter to real time, governs quantum coherence and remains adjustable until the final measurement. This structure explains how a late experimental decision can influence interference without invoking retrocausality. We show that the visibility depends on the imaginary‑time difference Δτ between two paths, following V=exp⁡(−Γ∣Δτ∣) with Γ=E/ℏ. An internal dynamics for τ is derived from a variational principle in the two‑dimensional space (t,τ), and the associated non‑unitary evolution is interpreted as a CPTP dephasing channel. We propose an experimental protocol based on a Mach–Zehnder interferometer with two delayed choices, with parameter ranges compatible with current technologies (optical fibers, GHz EOMs). Finally, we introduce a temporal CHSH‑type combination to test the bidimensional structure of time: a violation of the standard bound Sstd≤2 would indicate that coherence cannot be described by a purely real time parameter. This model opens new perspectives for understanding decoherence, enabling quantum‑control strategies, and experimentally probing an internal geometry of time.