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Preliminary Summary of Acceleration-Basis and Localization Exchange in Exchange-Interference Scattering-Matrix Fermion-Like Collisions

Noriaki Kihara

Published Jul 13, 2026• 1 citation
Publisher

Abstract

This preliminary summary reports exchange-interference scattering-matrix experiments in a closed phase system. It evaluates whether an acceleration-like AB two-body readout is preserved while low odd-harmonic bottoms, one-sided high-harmonic conditions, recursive scattering, and reflection-rate sweeps are recorded as localization-index exchange in the outgoing channels.

DOI
10.5281/zenodo.21333766

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This preliminary summary reports exchange-interference scattering-matrix experiments in a closed phase system. It evaluates whether an acceleration-like AB two-body readout is preserved while low odd-harmonic bottoms, one-sided high-harmonic conditions, recursive scattering, and reflection-rate sweeps are recorded as localization-index exchange in the outgoing channels.
Observational note (thought-experiment style; not a proof or claim paper). A sequel to the preceding note, which defined a single particle-like state as a phase-bearing local mode on the subjective geometry S^4(R_U) with spread W_a = 2 R_a and deferred the multi-particle case. Here we treat the minimal case: two particle-like states with the same spread phase, on a closed one-dimensional relational setting (period-1 phase line, a single great circle of S^4). Representing each particle as a rectangular standing wave (odd harmonics only), the n-th harmonic amplitude of the superposition is A_n = (2/n) cos(n pi f), where f is the relative position in fundamental wavelengths, and the total squared norm (energy-like quantity) is the triangle wave E(f) = (pi^2/4)(1-2f) for 0 <= f <= 1/2 (the autocorrelation of a square wave). Within the continuous f, discrete feature points appear: fusion (f=0), orthogonality / independent coexistence (f=1/4), and complete cancellation (f=1/2). Depending on whether the superposition is symmetrized or antisymmetrized, complete overlap (f=0) is allowed (boson-like) or makes the field vanish, i.e. exclusive (fermion-like). For unequal frequencies, interference arises only from shared odd harmonics (the irreducible ratio r/s with both r,s odd, i.e. matching 2-adic valuation); without sharing, interference vanishes and placement is free. All results are presented as observations of structural correspondence (with standing-wave quantization and the exchange symmetry of quantum statistics); no derivation of quantum statistics or the spin-statistics theorem is claimed. Notably the existence of the three feature points is universal to any half-wave-antisymmetric (odd-harmonic) profile, while only the linear (triangle-wave) envelope is specific to the square-wave (1/n) choice. This record contains Japanese and English versions (Markdown, LaTeX, PDF) and one figure.
This technical report packages a set of hardware component-witness experiments run on IBM superconducting quantum processors. The experiments test whether a hidden auxiliary phase can affect a later system-qubit measurement, whether that phase can be recovered from basis-resolved readout, and whether two auxiliary registers can produce a nonadditive response rather than a simple sum of their individual effects. The package includes the report draft, figures, raw hardware result JSONs, raw-count appendix, and scripts for regenerating the figures and count tables. The central result chain is: echo/phase response on real hardware, basis-resolved phase readout without density-matrix tomography, and a two-register Y-basis nonadditivity test where the first run remains a frozen FAIL and an independent higher-shot replication reaches STRONG_PASS. The longer-term motivation is to develop small, testable quantum hardware primitives for systems that can preserve, read out, and combine latent histories or unchosen alternatives, instead of reducing every intermediate state to a single classical output immediately. In that sense, these experiments are intended as early building blocks for future quantum-assisted sequence or language-model architectures. This work does not claim a completed quantum language model, natural-language processing on a quantum computer, consciousness, selfhood, classical impossibility, or quantum advantage. It reports only hardware component witnesses on specific IBM backends, edges, and calibration windows, with the possibility of richer classical explanations left open.
This thought experiment begins with a naive question about classifying wave-packet collapse and decoherence as separate phenomena. Using experience with laser holography as a guide, it asks whether coherence is not an absolute attribute of a single wave but depends on the partner wave, the harmonic structures of both, their phases and the readout conditions. A localized wave built from aligned high harmonics forms a sharp peak, but its spatiotemporal alignment with another localized wave is extremely restrictive. When a localized wave scatters on a monochromatic background wave, its high harmonics can be redistributed to the background. If a particle acquires a mass-like response through interaction with the background, why does it not keep losing harmonics and dissipate? Re-examining the author's earlier closed two-wave scattering experiment shows that localization is not lost in one direction but is redistributed back and forth between the two waves. The original program was re-run as a byte-identical copy (all data and figures identical to the original output): the two channels are orthogonal, so the per-collision normalization is a no-op and the update is the pure exchange operator U_R; no dissipation occurs, each wave keeps unit power while its peak height changes by a factor of about 30, and the effective harmonic orders satisfy N_A = 1 + 31 sin^2(k omega/2) with N_A + N_B = 33 exactly. If such circulation closes stably, finite periodicity U^n = I may be observed as a result, not imposed as a rule. The paper asks whether periodic closure, phase locking, quasi-stationarity and lifetimes appear as results, and whether the temporal and spatial readouts of the circulation correspond to internal clock delay and Lorentz contraction. The 'background' is treated not as a container with places, times and a number of waves, but as the anonymous part of the total state not yet distinguished by interaction readouts; the paper ends by asking whether particle species are names for conserved quantities of the interaction. This is a thought experiment that formulates verification tasks arising from the reinterpretation of existing numerical experiments; it does not complete derivations of mass, the Lorentz metric, quantum energy levels or real particle lifetimes. Main text in Japanese with an English translation; the verification package of the re-run is included as a zip archive.