Afshar's double-slit experiment probes wave--particle complementarity by placing a wire grid at the dark fringes of a downstream interference pattern while retaining an imaging basis that appears to preserve which-path information. Here we propose and analyze a time-reversed Young--Afshar configuration in which the corresponding null test is transferred from the downstream field plane to the source-label plane of a time-reversed Young interferometer. In this reciprocal geometry, a point-addressable source illuminates a double slit, while the detector remains fixed. The observed fringe is therefore not a single-shot spatial intensity pattern, but a detector-conditioned response reconstructed by scanning the source coordinate. Consequently, a null in this pattern is not a node of a freely propagating field; it is a source label for which the coherent two-slit transfer amplitude to the selected detector vanishes. A mask placed at such source-plane labels is invisible to that detector when both slits are open, yet becomes visible when either slit is opened alone. We develop the scalar Fresnel model, derive the source-space null condition, introduce a detector-conditioned null-mask loss, and examine how this loss evolves under a tunable which-path marker. The source-space visibility and path distinguishability satisfy the standard duality relation, so no violation of complementarity is implied. The essential new feature is instead a reciprocal, detector-conditioned form of complementarity: Afshar's field-space transparency is replaced by response-function transparency in a reconstructed source basis.
Afshar's double-slit experiment probes wave--particle complementarity by placing a wire grid at the dark fringes of a downstream interference pattern while retaining an imaging basis that appears to preserve which-path information. Here we propose and analyze a time-reversed Young--Afshar configuration in which the corresponding null test is transferred from the downstream field plane to the source-label plane of a time-reversed Young interferometer. In this reciprocal geometry, a point-addressable source illuminates a double slit, while the detector remains fixed. The observed fringe is therefore not a single-shot spatial intensity pattern, but a detector-conditioned response reconstructed by scanning the source coordinate. Consequently, a null in this pattern is not a node of a freely propagating field; it is a source label for which the coherent two-slit transfer amplitude to the selected detector vanishes. A mask placed at such source-plane labels is invisible to that detector when both slits are open, yet becomes visible when either slit is opened alone. We develop the scalar Fresnel model, derive the source-space null condition, introduce a detector-conditioned null-mask loss, and examine how this loss evolves under a tunable which-path marker. The source-space visibility and path distinguishability satisfy the standard duality relation, so no violation of complementarity is implied. The essential new feature is instead a reciprocal, detector-conditioned form of complementarity: Afshar's field-space transparency is replaced by response-function transparency in a reconstructed source basis.
Time-reversed Young (TRY) interferometry holds a detector channel fixed while a source coordinate is scanned or programmed. We describe this measurement through a single accepted source-detector probability law obtained from scalar Fresnel propagation, the programmed source prior, and detector acceptance. The conventional fixed-source Young distribution, the source and detector marginals, and the fixed-detector TRY distribution are then different reductions of that common record. Standard information measures can therefore be assigned without ambiguity to the probability law actually measured. For a symmetric double-slit response with matched source and detector windows, the fixed-source and fixed-detector conditional distributions have the same entropy; the physically useful information from detector conditioning is instead expressed by grid-stable entropy deficits and Kullback-Leibler information gains. The canonical example gives a modest prior-to-posterior information gain and establishes a transparent baseline for more selective source programming, detector modes, or operating points. Finite slit width, finite-source element width, finite detector pixels, and finite-count entropy estimation are included to connect the ideal model with experiments. A phase scan then shows that conditional entropy and Fisher information characterize different properties of the same likelihood, while a two-mode coherence model separates record entropy from optical coherence entropy and distinguishes coherent superposition from incoherent mixture. The framework gives a unified statistical interpretation of fixed-detector, source-programmed Young interferometry while keeping optical reciprocity, Bayesian conditioning, local parameter sensitivity, and quantum state disturbance conceptually distinct.
We develop a general theory of null-constrained parameter estimation in a time-reversed Young (TRY) interferometer, where measurement is performed through programmable source-basis encoding with a fixed detector. We address the fundamental question of how to design source patterns that enforce a true metrological null -- vanishing nominal response at the operating point -- while preserving finite first-order sensitivity to the parameter. Under a general shot-noise-limited channel model, we show that the optimal null-constrained receiver is obtained by projecting the derivative response onto the subspace orthogonal to the nominal background in the inverse-noise metric. This yields a constructive solution in which the optimal source-basis code is given by the inverse-noise-weighted derivative response with its background-parallel component removed. We further derive an exact and universal information-retention law: the locally accessible Fisher information is reduced by a factor 1−χ2, where χ quantifies the inverse-noise overlap between the nominal and derivative response vectors. This result establishes a precise geometric interpretation of the cost of null enforcement. Numerical examples demonstrate the null-coded TRY receivers can retain nearly the full local information and can be accurately implemented using binary and positive-only source patterns. These findings identify source-basis null engineering as a distinct and practically viable modality for derivative-mode sensing, with implications for superresolution metrology and programmable optical measurement architectures.
We show that time-reversed Young interferometry reorganizes, rather than reverses, optical entropy. A fixed detector conditions the reciprocal source--detector Green function and produces a source-label probability distribution. Marginal entropies in the standard and time-reversed geometries are generally unequal; the reciprocal invariant is instead the mutual information between source and detector coordinates. Near a destructive response, the conditioned source-label entropy can decrease while Fisher information for small phase, tilt, or defocus perturbations increases. The result identifies time-reversed Young interferometry as a source-space information processor with no analogue in ordinary detector-plane fringe readout.
Time-reversed Young (TRY) interferometry reconstructs interference from a fixed detector by reading out a programmable source-label distribution. This work formulates the architecture as a source-coded Bayesian response sensor. For a perturbation parameter θ, the detected source-label histogram is a posterior distribution determined by a programmed source prior, an optical likelihood for a fixed-detector click, and an evidence factor equal to the click probability. The key point is not the Bayesian identity itself, but its physical implementation: in TRY the prior is imposed before propagation and can therefore reshape the response ensemble actually sampled by the detector. The normalized posterior is shown to respond through a centered likelihood score, and the detected-event Fisher information is the posterior variance of this score. This identifies posterior-weighted score contrast, rather than local response magnitude alone, as the relevant sensing resource. The framework separates posterior-shape information from evidence information, giving a resource-aware way to judge near-null response enhancement. It also yields practical design rules: a two-label source code converts a weak perturbation into a fixed-detector label imbalance, while the multiparameter score covariance provides a route to nuisance rejection and gives a minimal-label rank condition for sensing multiple perturbations. A passive double-slit implementation with weak one-slit phase and loss perturbations is proposed, requiring only fixed-detector source scans before and after calibrated perturbations. Practical tolerances associated with source-programming error, drift, background, imperfect coherence, and polarization mismatch are analyzed, and extensions to multi-aperture and integrated photonic systems are formulated. The results position TRY as a source-programmable Bayesian sensing architecture complementary to conventional detector-plane Young interferometry.
Standard double-slit and interferometer experiments treat apparatus geometry, boundary conditions, coherence, detector response, and which-path distinguishability as sufficient variables for predicting interference visibility. This paper preserves that standard quantum-optical null model as the baseline and asks a narrower residual question: whether a dynamically reconfigured two-path apparatus can show visibility dependence on the time at which the relevant apparatus context becomes locally available. The proposed apparatus-context hypothesis is intentionally carrier-neutral. It may be represented inside the broader space-cell program either by deformation-like geometry, stress, shear, or topology variables, or by an extrinsic scalar χ-like compression/event-density coordinate. The first experimental question is not which internal carrier is correct. It is whether any additional finite-speed apparatus-context variable is required after ordinary quantum-optical effects are modeled and controlled. The primary observable is residual visibility as a function of reconstructed apparatus-context delay, Δ_ctx = τ_interaction − τ_context available. Under this sign convention, Δ_ctx < 0 means the photon-apparatus interaction occurs before the relevant two-path context has become available, while Δ_ctx > 0 means the context is available before interaction. The proposed support signature is a reproducible negative residual in the negative-Δ_ctx timing window, absent in sham-switch, one-path, decoherence, detector-angle, path-phase, material, and deformation-only controls. The proposed experiment reflects findings from toy-model interaction/accounting tests and design-translation results. These simulations sharpen criteria for a falsifiable experiment, define controls, and translate the timing variable into implementable design constraints.
We develop a differential source-encoding protocol for local parameter estimation in a time-reversed Young interferometer, where the source plane is used not merely as a scan coordinate but as a programmable measurement basis. Two sequential positive-only source patterns implement an antisymmetric differential probe about a chosen operating point, converting the deterministicc source-coordinate response into a derivative-gradient sensing channel. In the local regime, the differential signal separates naturally into an envelope-gradient term, which is also present in noninterferometric differential sensing, and an interference-gradient term, which is specific to the time-reversed Young fringe law. This decomposition identifies the physical origin of the interferometric advantage and clarifies why it is regime dependent rather than universal. Using a shot-noise-limited Poisson model, we derive the corresponding Fisher information and Cramér--Rao bounds and compare the protocol with raster sampling in the same geometry and with a matched noninterferometric differential baseline. Representative numerical examples show a strong and robust gain over raster sampling, while the additional improvement from the time-reversed Young interference is parameter dependent but can be substantial in favorable regimes. The results establish the time-reversed Young geometry as a practically simple platform for programmable differential interferometric metrology.