Topological Fracture and Massless Discrete Wave Packets: A Discrete Network Mechanism for Wave–Particle Duality and Measurement Collapse(Distance, Measurement, and the Ontological Reconstruction of Light (Final Version))
Year: 2026
Type: preprint
Abstract: n standard quantum mechanics, wave–particle duality and wavefunction collapse lack an intuitive physical mechanism, and across astronomical distances they easily lead to an energy-dilution paradox. Within the framework of a discrete asynchronous Poisson (DAP) network, we reconstruct the dynamics of the continuum background and the probability-wave hypothesis. We explicitly give the underlying discrete action for a massless photon (in the scalar limit, a pure wave equation), modeling the photon as a massless localized wave packet on the DAP network. Since the photon rest mass is zero, the dispersion correction in the long-wavelength limit is extremely small (); within observable precision the packet does not undergo longitudinal dispersion, and its front advances locally at the base speed , consistent with relativistic causality at current experimental precision. We clarify an ontological misunderstanding concerning energy and probability amplitude: at the single-photon level, the field is a probability-amplitude field; at the multi-photon ensemble level, it is a photon-number-density field. The total energy of a single photon is a global Noether charge and is conserved as a whole; the local decay describes the geometric projection ratio between the detector cross-section and the total spherical shell area, not the decay form of the wavefunction itself. By strictly distinguishing global conservation from local probability distribution, we derive a probability distribution consistent with the Born rule of standard quantum mechanics. On this basis, we introduce a “topological fracture mechanism”: when the wavefront sweeps across a detector, macroscopic coherent cumulative response occurs inside the detector; when the volume-integrated absolute probability amplitude exceeds the network percolation critical threshold, non-unitary boundary conditions trigger a local cutoff. Wavefunction collapse is understood as single-photon-state localization completed within the detector’s local refresh window ()—the energy as a whole acquires a definite spatial position at the fracture point, rather than collapsing over a distance. This mechanism is consistent with double-slit interference and delayed-choice experiments at current experimental precision, and through a topological-fragmentation picture (a nonlinear effect in strong fields) provides a heuristic physical picture connecting the single-photon state () and macroscopic multi-photon states (). This paper proposes an ontological interpretation framework for quantum mechanics whose mathematical predictions coincide with standard quantum mechanics at current experimental precision. Under canonical quantization, ZTD provides a physical picture of based on spatial coupling tension. ZTD’s distinctive predictions (such as extremely high-frequency dispersion corrections of the discrete network and the time scale of topological fracture) belong to Planck-scale physics and are currently inaccessible. This paper does not claim to give new experimentally testable physical predictions. Keywords: wave–particle duality; measurement collapse; DAP network; massless wave packet; topological fracture; localization; probability amplitude; field hidden variables; category mistake.
Author: Zhuang, Yan
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225823643
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