We introduce a configuration-dependent parametrisation of coherence in Wheeler’s delayed-choice experiment based on the complex quantity T=t?iτ . 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 Δτ rather than through any modification of the underlying dynamics.
We introduce a configuration-dependent parametrisation of coherence in Wheeler’s delayed-choice experiment based on the complex quantity T=t?iτ . 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 Δτ rather than through any modification of the underlying dynamics.
We introduce a configuration‑dependent parametrisation of coherence in Wheeler’s delayed‑choice experiment based on the complex quantity T=t−iτ. The real component t retains its usual causal role, while the imaginary component τ encodes coherence attenuation 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 remains fully compatible with standard quantum mechanics: it preserves unitary evolution, the Born rule, and the structure of completely positive trace‑preserving 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 in which the departure from classical bounds arises from the configuration dependence of Δτ rather than from any modification of the underlying dynamics.
We develop a geometric framework in which physical time is represented as a complex variable T=t−iτ. The imaginary component τ encodes the attenuation of coherence, while the real component t retains its usual causal role. Motivated by recent delayed-choice implementations [1–4], we show that the experimental configuration acts as an internal rotation θ of the complex time, modifying the imaginary-time difference between interferometric paths and therefore the visibility. This mechanism alters coherence without affecting causal evolution in t and does not require retrocausality. The model remains fully compatible with standard quantum mechanics, preserving unitary evolution, the Born rule, and completely positive trace-preserving maps. It provides a minimal geometric reparametrisation of the dynamical phase and yields experimentally testable predictions for visibility and temporal correlations.
This work presents a unified, interpretive account of quantum interference and delayed-choice experiments that applies equally to photons and massive particles. Rather than invoking spacetime trajectories, wave–particle duality, retrocausality, or collapse postulates, the paper locates quantum interference in the coherent evolution of internal, pre-geometric degrees of freedom defined over classical spacetime. Within this framework, “which-path” questions are not merely unanswered but fundamentally ill-posed: interference arises from global coherence of an internal field subject to experimental boundary conditions, while spacetime itself remains single-valued and classical at laboratory scales. The approach reproduces all standard quantum-mechanical predictions without modification and is explicitly interpretive rather than predictive. A central result is a unified explanation of why interference occurs across disparate physical systems—photons, electrons, atoms, and molecules—while decoherence manifests through system-dependent physical mechanisms. Photons and massive particles differ in how internal coherence is lost (e.g., electromagnetic absorption versus collisional and thermal interactions), but not in the underlying principle. Delayed-choice experiments are reinterpreted without paradox: changes to the apparatus modify boundary conditions for the internal field rather than retroactively altering particle histories. By removing spacetime paths from the fundamental ontology, the framework offers a consistent, path-free account of interference, decoherence, and localized detection that preserves the empirical success of quantum mechanics while clarifying its conceptual foundations.
Interference phenomena are commonly understood as consequences of path indistinguishability and coherence constrained by the availability of which-path information. While delayed-choice and quantum eraser experiments have demonstrated that interference can be restored or suppressed depending on measurement context, such effects are typically implemented through discrete, externally imposed experimental configurations. In this work, propose a delayed-choice interferometric scheme in which interference visibility is regulated adaptively via predictive estimates of informational accessibility. The proposed architecture introduces an operational measure of predictability derived from ensemble-level intensity statistics, which is used to control downstream interferometric elements after the system has traversed the interferometer. This design preserves the delayed-choice character of the experiment while avoiding any modification of standard quantum mechanical formalism or assumptions of retrocausality. Predictability is treated as an informational control parameter rather than as an intrinsic property of the system’s past evolution. The scheme builds upon established complementarity relations and information-theoretic approaches to coherence and decoherence, extending them toward adaptive, feedback-based control of interference. The proposal is experimentally accessible using classical or semi-classical optical components and does not rely on single-particle detection. By reframing interference as a dynamically regulated informational regime, the work provides a bridge between foundational concepts of quantum measurement and practical architectures for coherence control.
We present complex-time (CT) theory, a framework in which the fundamental structures of quantum mechanics are derived from three physical postulates concerning the internal structure of time. The postulates are: (P1) physical time possesses two orthogonal components — past-fixed (pf), representing actualized, irreversible records, and future-pending (fp), representing physically real but undetermined possibilities; (P2) pf and fp are orthogonal (pf fp); and (P3) the total temporal magnitude is conserved (pf + fp = 1). From these three postulates alone, we show that: (i) the state space is the unit circle and the dynamical group is , so that the imaginary unit arises as the unique generator of temporal evolution — not as a mathematical convenience but as a consequence of temporal geometry; (ii) the Schrödinger equation follows from the identification of energy with the rate of phase rotation in the pf–fp plane, with the Planck constant playing the role of a natural constant intrinsic to the pf/fp structure; (iii) the de Broglie–Einstein relation holds universally — for massive and massless particles alike — because the wave structure belongs to time itself, not to any particular particle; (iv) the uncertainty principle is a geometric consequence of the impossibility of fully eliminating fp while preserving ; (v) the complex structure of Hilbert space, the inner product, and the Born rule all follow from the geometry of fp pf projection; and (vi) energy quantization emerges from a “real-axis sampling” rule without imposing discreteness on the underlying dynamics. We further show that the CT framework provides unified descriptions of double-slit interference, quantum tunneling, unstable-state decay widths, and the structural origin of the arrow of time. Preliminary experimental predictions for quantum-circuit observables are stated, and applications to cosmological dark-energy phenomenology, galaxy rotation curves, and Lorentzian path-integral contour selection are outlined with references to dedicated companion papers. The central thesis is that quantum mechanics is not a theory of particles with mysterious wave-like properties, but a consequence of the internal structure of time — time whose wave-like phase (fp) is projected, irreversibly and discretely, onto the real axis (pf) in every act of measurement. Keywords: complex time; temporal structure; imaginary unit; quantum mechanics derivation; past-fixed / future-pending decomposition; Born rule; energy quantization; measurement; irreversibility; arrow of time
Ce travail propose une interprétation géométrique de l’expérience du choix retardé de Wheeler fondée sur un modèle où le temps physique est représenté par une variable complexe T=t−iτ. La composante imaginaire τ, évoluant à contre‑courant du temps réel, contrôle la cohérence quantique et reste ajustable jusqu’à la mesure finale, permettant d’expliquer l’influence d’une décision tardive sans recourir à la rétrocausalité. La visibilité des interférences dépend de la différence Δτ entre deux chemins, selon V=exp(−Γ∣Δτ∣) avec Γ=E/ℏ. Une dynamique interne pour τ est dérivée d’un principe variationnel dans un espace bidimensionnel (t,τ), et l’évolution non unitaire associée s’interprète comme un canal CPTP, en accord avec le formalisme standard. Nous proposons un protocole expérimental basé sur un interféromètre Mach–Zehnder à deux choix retardés, avec des ordres de grandeur compatibles avec les technologies actuelles (fibres optiques, EOM GHz). Enfin, une combinaison CHSH temporelle est introduite pour tester la structure bidimensionnelle du temps : une violation de la borne classique Sstd≤2 indiquerait que la cohérence ne peut être décrite par un temps purement réel. Ce modèle ouvre des perspectives pour la compréhension de la décohérence, le contrôle quantique et la mise en évidence expérimentale d’une géométrie interne du temps.