Within the unified time scale and boundary time geometry framework, this paper provides an axiomatizable characterization of ``what world observers see,'' and on this basis gives a single structural interpretation for two key cases of double-slit interference: delayed choice experiments and time-domain (rather than spatial) double-slit interference. First, using the scale identity of scattering phase derivative--relative state density--Wigner--Smith group delay trace as the time scale benchmark,
Within the unified time scale and boundary time geometry framework, this paper provides an axiomatizable characterization of ``what world observers see,'' and on this basis gives a single structural interpretation for two key cases of double-slit interference: delayed choice experiments and time-domain (rather than spatial) double-slit interference. First, using the scale identity of scattering phase derivative--relative state density--Wigner--Smith group delay trace as the time scale benchmark,
Within the unified time scale and boundary time geometry framework, we provide an axiomatizable characterization of ``what world observers see.'' Starting point: given global boundary algebra and quantum state, all ``world sections'' satisfying field equations and causality form a geometric--measure space; concrete observers access only subfamilies compatible with their worldline, resolution, and records, while ``superposition'' is not simultaneous multiple realization of experiential world but
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.
This study reconstructs the causal structure of the double-slit experiment bydistinguishing two particle families: light-family particles (photons) andmatter-family particles (electrons). Their internal time structures differ,with photons exhibiting Δτ = 0 due to directional excitation, while electronsexhibit Δτ ≠ 0 due to three-dimensional orbital emission. Time Density Mechanics (TDM) is introduced as a causal extension of quantummechanics. TDM preserves geometric and observational causal factors—such astrajectory orientation, occlusion, observer direction, viewpoint geometry, andfocal geometry Δf—that standard quantum mechanics does not include in itsstate representation ψ(x,t). This framework provides causal explanations for interference fringes, spinmeasurements, and quantum entanglement. In particular, entanglement correlationsare interpreted as viewpoint-geometry alignment rather than nonlocal action. TDM does not contradict quantum mechanics; instead, it complements it byrestoring causal structures that quantum mechanics abstracts away. This workoffers a unified causal model for optical and matter-wave interference.
Within the unified context of ``universe = Generalized Light Structure (GLS),'' ``observer = filter chain (windowed compression → CP channel → POVM → threshold counting),'' and ``causality = lightlike cone preorder,'' we establish an axiomatic theory with the master scale πφ′(E)=ρrel(E)=2π1trQ(E),Q(E)=−iS(E)†dEdS(E) (phase derivative---relative density of states---Wigner--Smith group delay trace). \textbf{Causal red line:} Windowed group delay readout Tγ[wR,h] serves solely as operational time scale (can be negative in narrowband/resonance, having no universal size comparison with wavefront time t∗); causality determined exclusively by t∗ and lightlike cone partial order. Core results: (i) windowed group delay readout provides operational time scale, proven series-parallel additive and gauge covariant/relatively invariant (invariant when U,V energy-independent or more generally ∂E(argdetU+argdetV)=0); in vacuum links satisfying Nyquist discipline, high-frequency/alias-free limit aligns with wavefront velocity calibrating c; (ii) redshift characterized by spectral scaling with reciprocal time scaling law; (iii) light speed c normed by vacuum wavefront, yielding wavefront lower bound and no-supercone propagation for arbitrary physical channels; (iv) ``GLS ↔ causal manifold'' mutual construction outline with skeleton and consistency conditions---rigorous proof and naturality verification in separate work; (v) wave-particle duality and double-slit windowed complementarity D2+V2≤1 unified in same ledger; (vi) spectral resolution enhancement (bandwidth narrowing) and redshift amplification are dual; conversely, temporal/image resolution enhancement (σT decrease) and blueshift (bandwidth increase) are dual, consistent with σT≳Cw,h/B in \S4.4, yielding Nyquist--Poisson--Euler--Maclaurin (NPE) finite-order error closure and engineering prescription; (vii) high-frequency platform bridge: under \S4 premises, blueshift limit of any fixed-shape normalized window family---single channel limE0→∞Tγ=t∗, multichannel limE0→∞TC=Nefft∗ and per-mode average limE0→∞TC=t∗, treating causal wavefront t∗ as operational limit scale of Tγ and TC. Theory employs operator-measure-function language throughout (Toeplitz/Berezin compression Kw,h, readout = linear functional on spectral measure), unifying all time/density readouts under global unitarity postulate by Q=−iS†S′; experimental non-unitarity traced back to master scale via unitary dilation S.
The delayed-choice experiment and the quantum eraser experiment are two of the most challenging interpretive problems in quantum mechanics. Standard textbook accounts trace the presence or absence of interference to whether the experimenter "knows" the photon's path — a causal framework implying backward-in-time influence. This article offers an intuitive, diagram-rich account grounded in the wave-or-particle geometric framework, revealing that both experiments share a far simpler backbone: interference depends solely on how many waves reach a given detector. One wave → no interference. Two waves → interference. This conclusion alters no mathematical prediction of quantum mechanics; it merely flips the causal arrow from "knowing the path destroys interference" to "the number of waves creates interference." A forthcoming main paper will present the complete three-column correspondence (experimental step → geometry → QFT standard) with full algebraic verification.