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April 14, 20260 citationsOpen Access

From Mathematical Foundation to Experimental Test: A Unified Account of the Total Wave Modified Schrödinger Equation (TWMSE)

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LCLarry Lim Kheng Cheong

Key Points

  • The study aims to provide a comprehensive account of the Total Wave Modified Schrödinger Equation (TWMSE) and its implications for quantum mechanics and computing.
  • Constructs a minimal working model demonstrating pseudo-Hermitian evolution and collapse via interference thresholds.
  • Utilizes Weyl equidistribution and KAM theory to explore phase ergodicity.
  • Introduces the Two-System Falsifiability Argument linking collapse statistics to environmental couplings.
  • Derives experimental signatures from three-slit photon interference and atom interferometry.
  • Demonstrates a quantified deviation ΔP(x) ~ δ²|Ψ|² with δ bounded to 10⁻².
  • Identifies the Sorkin parameter κ ~ δ²/3 in photon interference experiments.
  • Finds a second harmonic fringe component at 2Δφ in Mach-Zehnder interferometry, absent in linear theories.
  • Reports detection of second harmonic requiring approximately 33 minutes at cold-atom count rates.

Abstract

This paper presents the most complete account to date of the Total Wave Modified Schrödinger Equation (TWMSE), a deterministic framework in which quantum wavefunction collapse arises from interference between a system wavefunction and observer fields associated with the four fundamental interactions, rather than from a probabilistic postulate. The paper is organised in two parts with a formal bridge section. Part I constructs the minimal working model demonstrating well-posed pseudo-Hermitian evolution, collapse via interference thresholds, dynamical emergence of phase ergodicity via Weyl equidistribution and KAM theory, statistical recovery of the Born rule, and a quantified deviation ΔP(x) ~ δ²|Ψ|² bounded to δ ≲ 10⁻². The bridge section introduces the Two-System Falsifiability Argument: two identically prepared two-level systems with different environmental coupling histories must produce different collapse statistics under TWMSE and identical statistics under standard quantum mechanics — the conceptually minimal statement of the theory's falsifiability. Part II derives three concrete experimental signatures: the Sorkin parameter κ ~ δ²/3 from three-slit photon interference; a second harmonic fringe component at 2Δφ in Mach-Zehnder atom interferometry, strictly absent in all linear theories; and ILL-type neutron crystal interferometry. Detection of the second harmonic requires approximately 33 minutes at current cold-atom count rates. The architectural implications of TWMSE for quantum computing are developed in Appendix D of the forthcoming book Quantum Computing Is Stalling: A Way Forward (Larry Lim Kheng Cheong, forthcoming). Note: A US non-provisional patent application (Application No. 19/645,198) covering collapse-based quantum computing architectures derived from this framework was filed on 12 April 2026 prior to this upload.

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Cite This Study

Larry Lim Kheng Cheong (2026) studied this question.

synapsesocial.com/papers/69ddd9b1e195c95cdefd70cahttps://doi.org/10.5281/zenodo.19537024
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