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Wave-Induced Collapse of Quantum and Probabilistic Systems via Observer Interference: A Modified Schrödinger Equation Framework Version 4: Empirical Evidence and Financial Market Applications

Larry Lim

Published Jan 1, 2025• 0 citations
Publisher
DOI
10.2139/ssrn.5283947

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This paper presents an interpretive extension of standard quantum mechanics using the Total Wave Modified Schrödinger Equation (TWMSE), reframing quantum tunneling as a dynamic process of wave interference and stress accumulation rather than a purely probabilistic event. In standard quantum mechanics, tunneling is described by exponentially decaying wavefunctions inside classically forbidden regions, often interpreted as the wave “dying out.” This work argues instead that exponential decay represents blocked propagation and stored evanescent wave deformation. Within the TWMSE framework, continuous wave incidence leads to gradual, logarithmic accumulation of interference (or “wave stress”) until a stability threshold is reached, triggering tunneling or collapse. The paper emphasizes complementarity rather than replacement: standard quantum mechanics correctly describes the spatial shape of the wave, while TWMSE provides a physical narrative for its time-dependent behavior. Analogies such as stiff springs, capacitors, and voltage drops are used to make the interpretation accessible without altering established mathematics. Appendices clarify that the TWMSE interpretation is not a hidden-variable or Bohmian theory, connect the narrative to the formal TWMSE collapse–interference functional, and explore the speculative but testable idea that tunneling rates may be tunable through resonant observer–wave coupling. This contribution is intended as a conceptual and pedagogical bridge between standard quantum tunneling theory and wave-based collapse dynamics, and as a foundation for future quantitative and experimental investigations.

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

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Note added 10 August 2026: The experimental interpretation in this paper has been superseded. See the revised technical account, Zenodo DOI 10.5281/zenodo.21868322, which supersedes the Sorkin parameter, second harmonic, detection time estimates, and history bias claims where those exceed what follows from the minimal written dynamics. This record remains available as part of the development history. 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). Here is the link to the book -https://a.co/d/0hQ0I2i0 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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Schrödinger’s Waves: Propagation and Probability

Arkady Plotnitsky

Springer eBooks•Aug 3, 2009•2 citations
This paper presents an interpretive extension of standard quantum mechanics using the Total Wave Modified Schrödinger Equation (TWMSE), reframing quantum tunneling as a dynamic process of wave interference and stress accumulation rather than a purely probabilistic event. In standard quantum mechanics, tunneling is described by exponentially decaying wavefunctions inside classically forbidden regions, often interpreted as the wave “dying out.” This work argues instead that exponential decay represents blocked propagation and stored evanescent wave deformation. Within the TWMSE framework, continuous wave incidence leads to gradual, logarithmic accumulation of interference (or “wave stress”) until a stability threshold is reached, triggering tunneling or collapse. The paper emphasizes complementarity rather than replacement: standard quantum mechanics correctly describes the spatial shape of the wave, while TWMSE provides a physical narrative for its time-dependent behavior. Analogies such as stiff springs, capacitors, and voltage drops are used to make the interpretation accessible without altering established mathematics. Appendices clarify that the TWMSE interpretation is not a hidden-variable or Bohmian theory, connect the narrative to the formal TWMSE collapse–interference functional, and explore the speculative but testable idea that tunneling rates may be tunable through resonant observer–wave coupling. This contribution is intended as a conceptual and pedagogical bridge between standard quantum tunneling theory and wave-based collapse dynamics, and as a foundation for future quantitative and experimental investigations.
Note added 10 August 2026: The experimental interpretation in this paper has been superseded. See the revised technical account, Zenodo DOI 10.5281/zenodo.21868322, which supersedes the Sorkin parameter, second harmonic, detection time estimates, and history bias claims where those exceed what follows from the minimal written dynamics. This record remains available as part of the development history. 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). Here is the link to the book -https://a.co/d/0hQ0I2i0 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.