Configuration-Dependent Complex Time in Delayed-Choice Interferometry

Abstract

We introduce a configuration-dependent parametrisation of coherence in Wheeler’s delayed-choice experiment based on the complex quantity T = t ? i τ . The real component t retains its usual causal role, while the imaginary component τ encodes the attenuation of coherence without representing a physical time coordinate or an additional degree of freedom. Different interferometric configurations correspond to different decompositions of T , effectively acting as an internal rotation that modifies the imaginary-time difference between paths and therefore the visibility. This mechanism alters coherence without affecting causal evolution and does not require retrocausality. The construction is fully compatible with standard quantum mechanics: it preserves unitary evolution, the Born rule, and the structure of completely positive trace-preserving (CP-TP) maps, and is equivalent to a standard dephasing channel written in a compact parametrised form. The framework yields experimentally testable predictions for visibility modulation and temporal correlations, including a temporal CHSH protocol that departs from classical bounds through the configuration dependence of Δ τ rather than through any modification of the underlying dynamics.