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The Path Puzzle of the Photon A Wave Interpretation of Delayed Choice, Quantum Erasure, and Double-Slit Interference

卓冰 蒋

Published Jun 18, 2026• 0 citations
Publisher

Abstract

Quantum mechanics explains famous optical experiments — delayed choice, quantum eraser, and double-slit interference — using wave function collapse, nonlocality, and observer effects, endowing photons with mysterious selectivity. This paper proves these experiments require no quantum-mechanical concepts. Light is always a continuous transverse wave — slits provide boundary conditions, detectors alter them, and changing boundary conditions modify wave propagation in space. So-called "collapse upon observation" is the irreversible energy exchange between waves and macroscopic detectors; so-called "path information destroying interference" is the inevitable consequence of wave decoherence. No particle "consciousness," no retrocausality, no wave function needed — only wave propagation and ordinary boundary conditions.

DOI
10.5281/zenodo.20748560

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Quantum mechanics explains famous optical experiments — delayed choice, quantum eraser, and double-slit interference — using wave function collapse, nonlocality, and observer effects, endowing photons with mysterious selectivity. This paper proves these experiments require no quantum-mechanical concepts. Light is always a continuous transverse wave — slits provide boundary conditions, detectors alter them, and changing boundary conditions modify wave propagation in space. So-called "collapse upon observation" is the irreversible energy exchange between waves and macroscopic detectors; so-called "path information destroying interference" is the inevitable consequence of wave decoherence. No particle "consciousness," no retrocausality, no wave function needed — only wave propagation and ordinary boundary conditions.
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.
## AbstractA deterministic interpretation of the double-slit experiment is proposed, in which the electron is treated as a localized particle at all times. The observed interference pattern is attributed to a real physical energy wave in the electromagnetic field, generated by the electron's accelerated motion through the field. This energy wave reaches the slit barrier, where the slit geometry creates coherent waves that merge to form a constructive interference wave. This wave redistributes energy in the field, creating an Electron-EMF coupled pathway that guides the particle to the detector. The apparent randomness of individual impacts arises from incomplete knowledge of the initial conditions, not from intrinsic indeterminism. The measurement effect is modelled as a disturbance of the coherent energy waves, either preventing the formation of the coupled pathway or destroying it after formation. The model is extended to the quantum eraser experiment, where the restoration of coherence via a polarizer naturally explains the reappearance of interference. A further extension to the delayed-choice quantum eraser is proposed, introducing the Entangled Constructive Interference Wave (ECIW) as a physical mechanism for entanglement within the model. The mechanism is shown to apply across geometries beyond the double slit. Predictions include a correlation between landing position and flight time, offering a testable distinction from standard quantum mechanical interpretations. A preliminary, illustrative mathematical framework is provided, situating the model within the pilot-wave tradition. **Keywords: ** Double-slit experiment, pilot wave, electromagnetic field, quantum interpretation, determinism, hidden variables, measurement problem, energy wave, coupled pathway, quantum eraser, delayed-choice quantum eraser, entanglement.
This paper presents an observational analysis of the Delayed-Choice Quantum Eraser experiment through the framework of quantum mechanics. The Delayed-Choice Quantum Eraser, a variation of the classic double-slit experiment, demonstrates the intricate relationship between quantum measurement, wave-particle duality, and the temporal ordering of observations. By utilizing the principles of quantum superposition, entanglement, and the non-local collapse of the wave function, we seek to rationalize the counterintuitive outcomes observed in the experiment. Specifically, we explore how the act of measurement retroactively influences the observed behavior of particles, depending on whether or not the which-path information is available. Our analysis underscores the significance of the quantum mechanical concept of wave function collapse across spacetime, providing a deeper understanding of how quantum mechanics reconciles the delayed-choice paradox.
The classical interpretation of the double‑slit experiment ties path selection to the collapse of the wave function: observation destroys interference, and superposition disappears. In this preprint, I introduce an alternative, constructive model of path selection that does not require superposition, does not rely on parallel worlds, and does not destroy the underlying process during measurement. The model is built on three key elements: memory of the previous frame, the reorganization state of the medium (“the in‑between”), and a hierarchy of possible futures, represented as pages, notebooks, books, and libraries. I propose a mechanics of time in which each subsequent “frame” of reality does not emerge from nothing but is the result of medium reorganization between states. The in‑between generates all possible future scenarios (pages), from which the medium selects one — without destroying the others. This model extends the intuition of the double‑slit experiment into a full mechanics of time, allowing visualization of multi‑trajectory evolution without collapse. It is a home experiment: anyone can perform it mentally, similar to Einstein’s thought experiments, but in a constructive, mechanical form. ─── 1. Introduction: the problem of path selection in physics For over a century, quantum physics has struggled with the problem of path selection: Why does a photon “choose” a slit only upon measurement? Why does interference vanish when we observe the process? Why is superposition so fragile? Standard interpretations attempt to explain this through: • wave‑function collapse, • parallel worlds, • hidden variables, • superposition of states, • the role of the observer. All these approaches share one assumption: path selection is a property of the photon. In this preprint, I show that path selection is a property of the medium, not the photon. And that changes everything. ─── 1. The double‑slit experiment — limitations of the classical interpretation In the classical experiment: • the photon has all possible paths, • it interferes with itself, • measurement destroys interference, • path selection appears only at detection. This leads to paradoxes: • superposition exists only when unobserved, • the observer influences the outcome, • reality is “undefined” before measurement. The model presented here eliminates these paradoxes. ─── 1. The clamp and pages model: visualizing multi‑trajectory time Imagine: • a paper clamp holding the first page — this is Frame 1, the initial state, full information; • pages — possible future scenarios, reorganizations of the medium; • a notebook — a limited set of variants; • a book — the full structure of possible futures; • a library — the cosmos of all possible reorganizations. The clamp does not decide the future. The clamp simply says: “This is where the story begins.” ─── 1. The in‑between as the medium’s reorganization state The key insight: Time is not a line. Time is the medium’s reorganization process between frames. The in‑between is not empty. The in‑between is: • the place where memory of the previous frame is interpreted, • the place where all possible futures are generated, • the place where one page is selected, • the place where time is created. This is mechanical, not metaphysical. ─── 1. Memory of the previous frame as the foundation of time Each new frame: • does not arise from nothing, • is not independent, • is not a pure present moment. Each frame is the result of reorganizing the previous state. This is medium memory — the missing element in quantum physics. ─── 1. Path selection without destroying the process In classical physics: • measurement destroys superposition, • interference disappears, • path selection is destructive. In this model: • the in‑between generates all pages, • the medium selects one, • the remaining pages do not disappear, • measurement does not destroy the process, • path selection is constructive, not destructive. This is the fundamental difference. ─── 1. Notebook, book, library — hierarchy of possible futures Hierarchy of duration: • photon — zero duration → one page • matter — positive duration → notebook • black hole — boundary duration → book • singularity — absolute duration → library This is the mechanical structure of time. ─── 1. Consequences for quantum physics, cosmology, and time This model: • eliminates wave‑function collapse, • eliminates superposition as a necessity, • eliminates the observer as a destructive agent, • allows visualization of path selection, • connects quantum behavior with cosmology, • provides a mechanical description of time, • opens new directions for interpreting quantum experiments. ─── 1. Home experiment: anyone can perform it This is crucial. This experiment: • requires no laboratory, • no detectors, • no lasers, • no specialized equipment. It requires: • a clamp, • pages, • the concept of the in‑between, • understanding medium reorganization. It is a constructive experiment, accessible to everyone. ─── 1. Conclusions: a new mechanics of time I propose a model in which: • time is medium reorganization, • the future is a set of possible pages, • path selection does not destroy the process, • measurement is non‑destructive, • the photon does not choose — the medium chooses, • the in‑between is where reality is formed. This mechanics of time may open many doors — in quantum physics, cosmology, and the study of temporal structure.
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.
Abstract The delayed-choice quantum eraser has long been a subject of controversy, and has been looked at as being incomprehensible to having retro-causal effect in time. Here the delayed-choice quantum eraser is theoretically analyzed using standard quantum mechanics. Employing a Mach–Zehnder interferometer, instead of a conventional two-slit interference, brings in surprising clarity. Some common mistakes in interpreting the experiment are pointed out. It is demonstrated that in the delayed mode there is no which-way information present after the particle is registered on the screen or the final detectors, contrary to popular belief. However, it is shown that another kind of path information is present even after the particle is registered in the final detectors. The registered particle can be used to predict the results of certain yet to be made measurements on the which-way detector. This novel correlation can be tested in a careful experiment. It is consequently argued that there is no big mystery in the experiment, and no retro-causal effect whatsoever.