Boundary Interface Theory: Electron Transition from the Perspective of Spacetime Membrane Standing Waves —— Wave Superposition Mechanism and Membrane-Pressure Orbital Constraints
This paper, under the core framework of Boundary Interface Theory (BIT), takes the intrinsic property of electrons as standing waves on the spacetime membrane and the quantized orbital constraints induced by proton membrane pressure as the theoretical basis, to conduct an in-depth and systematic study on the physical mechanism and mathematical expression of electron transition, a core dynamic phenomenon of micro quantum systems. Different from traditional quantum mechanics theories that only describe electron transition from the perspective of quantum state superposition and fail to link it with the intrinsic spacetime geometric nature, this study defines electron transition as the modal reconstruction and dynamic evolution of discrete steady-state standing wave eigenmodes on the spacetime membrane, and completes the quantitative derivation and qualitative analysis of electron transition through the phase matching of standing wave superposition, the law of energy conservation and the constraints of geometric potential wells. It further reveals the geometric dynamic origins of the non-intermediate state characteristic and proton membrane-pressure orbital constraint of electron transition: the non-intermediate state is due to the fact that the spacetime geometric potential well formed by proton membrane pressure only supports discrete steady-state standing wave eigenmodes satisfying the phase matching condition, and non-eigenmode standing waves cannot stably exist due to rapid interference cancellation; the orbital constraint results from the fact that electron transition is only the coherent superposition of standing wave eigenmodes within the proton membrane-pressure orbit, and the superposed wave function always satisfies the geometric constraints and boundary conditions of proton membrane pressure with no mathematical possibility of out-of-orbital transition. In addition, the paper derives the quantitative expression of the electron transition energy difference composed of basic physical constants and the characteristic physical quantities of protons and electrons, without introducing any new adjustable parameters or experimental inputs. The derivation is highly self-consistent with the previous research conclusions of Boundary Interface Theory, and is consistent with the experimental observational facts of micro quantum mechanics such as the discreteness of atomic spectra and the shell transition rules of atoms. This research realizes the theoretical closed loop of Boundary Interface Theory from the "intrinsic static existence" of electrons to the "dynamic transition laws", reduces quantum transition phenomena to the geometric dynamic effects of the spacetime membrane, and provides a brand-new theoretical path for exploring the classical geometric origin of quantum phenomena. Finally, the paper prospects the future research directions of Boundary Interface Theory, including extending the research to multi-electron atomic systems, constructing an electron-photon interaction model based on spacetime membrane dynamics, exploring the electron transition characteristics of molecular systems, and studying the spacetime membrane origin of quantum entanglement, which points out the way for the further expansion of the theory and the in-depth integration of quantum mechanics and general relativity.
This paper, under the core framework of Boundary Interface Theory (BIT), takes the intrinsic property of electrons as standing waves on the spacetime membrane and the quantized orbital constraints induced by proton membrane pressure as the theoretical basis, to conduct an in-depth and systematic study on the physical mechanism and mathematical expression of electron transition, a core dynamic phenomenon of micro quantum systems. Different from traditional quantum mechanics theories that only describe electron transition from the perspective of quantum state superposition and fail to link it with the intrinsic spacetime geometric nature, this study defines electron transition as the modal reconstruction and dynamic evolution of discrete steady-state standing wave eigenmodes on the spacetime membrane, and completes the quantitative derivation and qualitative analysis of electron transition through the phase matching of standing wave superposition, the law of energy conservation and the constraints of geometric potential wells. It further reveals the geometric dynamic origins of the non-intermediate state characteristic and proton membrane-pressure orbital constraint of electron transition: the non-intermediate state is due to the fact that the spacetime geometric potential well formed by proton membrane pressure only supports discrete steady-state standing wave eigenmodes satisfying the phase matching condition, and non-eigenmode standing waves cannot stably exist due to rapid interference cancellation; the orbital constraint results from the fact that electron transition is only the coherent superposition of standing wave eigenmodes within the proton membrane-pressure orbit, and the superposed wave function always satisfies the geometric constraints and boundary conditions of proton membrane pressure with no mathematical possibility of out-of-orbital transition. In addition, the paper derives the quantitative expression of the electron transition energy difference composed of basic physical constants and the characteristic physical quantities of protons and electrons, without introducing any new adjustable parameters or experimental inputs. The derivation is highly self-consistent with the previous research conclusions of Boundary Interface Theory, and is consistent with the experimental observational facts of micro quantum mechanics such as the discreteness of atomic spectra and the shell transition rules of atoms. This research realizes the theoretical closed loop of Boundary Interface Theory from the "intrinsic static existence" of electrons to the "dynamic transition laws", reduces quantum transition phenomena to the geometric dynamic effects of the spacetime membrane, and provides a brand-new theoretical path for exploring the classical geometric origin of quantum phenomena. Finally, the paper prospects the future research directions of Boundary Interface Theory, including extending the research to multi-electron atomic systems, constructing an electron-photon interaction model based on spacetime membrane dynamics, exploring the electron transition characteristics of molecular systems, and studying the spacetime membrane origin of quantum entanglement, which points out the way for the further expansion of the theory and the in-depth integration of quantum mechanics and general relativity.
This paper fully recognizes repeatable experimental facts related to atomic spectral observations electron shell arrangement and energy level transitions and respects all observed phenomena. It does not deny the statistical laws corresponding to energy level effects and the Pauli exclusion effect. The core purpose of this paper is to correct the long standing model inversion misunderstanding in quantum theory that is treating artificial definitions and mathematical approximation diagrams used by humans to simplify calculation and facilitate academic communication directly as physical reality in the microscopic world. This paper clearly distinguishes practical calculation rules from underlying physical mechanisms. Induced laws for human deduction and analysis cannot replace the true interaction nature of particles. This paper constructs a microscopic atomic picture based purely on mechanical balance with the core conclusions as follows. Atomic energy levels are not discrete geometric thin lines but continuous spherical potential energy intervals centered on atomic nuclei. The steady state of electron orbits arises from the combined balance of Coulomb repulsion and nuclear attraction instead of being preset in advance. The textbook diagrams showing intersecting orbits and dynamic avoidance of electrons are only effects of planar simplified drawing and do not represent the true microscopic state. Electrons in the same layer maintain stable equal spacing by Coulomb repulsion but spherical surfaces of inner and outer layers have different potential energy gradients leading to obvious differences in energy level gaps and finally differentiated transition spectra. Segmentation of visible light spectra originates from the difference in photoreception of cone cells in human eyes. Man is the measure of all things. Classification of spectra and energy levels by discrete criteria comes from human observational induction while natural ontology remains continuous. The Pauli exclusion effect is not an innate axiom of the universe but a natural mechanical result formed jointly by three dimensional space Coulomb repulsion and potential energy balance. This paper takes mechanical causality as the only main line to uniformly explain atomic energy levels spectral features and electron arrangement rules. All inferences strictly rely on experimental observations.
This work presents a systematic study on the dual nature of quantum tunneling within the self-consistent axiomatic framework of Boundary Interface Theory (BIT). It strictly distinguishes two fundamentally distinct quantum tunneling mechanisms: nuclear fusion tunneling, which arises from 4D normal‑direction yielding of the boundary membrane and the unraveling of rigid topological knots; and electron tunneling, which corresponds to direct 4D normal‑direction penetration of membrane standing waves. The theory provides a unified microscopic geometric and mechanical origin for quantum tunneling and the strong interaction without introducing new particles, free parameters, or extra dimensions. Both Chinese and English full texts are included for open access and cross‑lingual academic reference.
To date in the development of modern physics, relativity and quantum mechanics can precisely agree with experimental observations within their respective scopes of application. However, the underlying logics of the two theoretical systems remain incompatible, giving rise to a host of intractable paradoxes and puzzles. This paper investigates nine representative problems: the quantum grandfather paradox, Hawking's chronology protection conjecture, the causality paradox of quantum fluctuations, the black hole information loss paradox, the quantum Maxwell's demon, the Boltzmann brain paradox, the ultraviolet catastrophe, the quantum tunnelling paradox, and the quantum no-cloning and identical particle paradox. This research is built upon the original Two-Dimensional Linear Matrix Wave Theory. It holds that the objective ontology of the universe consists of a one-dimensional propagation substrate and a global two-dimensional linear matrix wave field. A free two-dimensional linear matrix wave is defined as a travelling wave, while stable structures formed by constrained superposition of energy are standing waves. Electrons, protons and neutrons are the only three fundamental primitive standing waves in the universe, and all macroscopic matter in nature is composed of their combinations. Time is not an independent spacetime dimension; essentially, it refers to the intrinsic oscillation frequency inside fundamental standing waves. The basic equations and theorems of the Two-Dimensional Linear Matrix Wave Theory are not rederived herein, and are directly adopted as an established original theoretical framework. The research reveals that all the aforementioned paradoxes stem from cognitive biases in conventional physics: regarding the three-dimensional space perceived by humans as the primordial structure of the universe, treating time as an independently flowing dimension, and misinterpreting microscopic wave phenomena as random particle behaviours. Within the framework of the Two-Dimensional Linear Matrix Wave Theory, all these paradoxes can be fundamentally resolved based on the fundamental laws of wave propagation, standing wave evolution and wave field superposition, without introducing additional hypotheses or ad hoc theories. This paper focuses on constructing a complete physical interpretation system, and relevant detailed mathematical formulas can be supplemented and refined by subsequent researchers. The original intellectual property rights of the core theory are clearly defined. This study provides a new perspective for fundamental physics to break through existing theoretical constraints.
To this day, relativity and quantum mechanics can accurately match experimental observations within their respective scope of application in modern physics. Nevertheless, the underlying logics of the two theoretical systems are incompatible, giving rise to a series of intractable paradoxes and sophisms. This paper investigates nine representative puzzles: the quantum grandfather paradox, Hawking's chronology protection conjecture, the causality paradox of quantum fluctuation, the black hole information loss paradox, the quantum Maxwell's demon, the Boltzmann brain paradox, the ultraviolet catastrophe paradox, the quantum tunneling paradox, and the quantum no-cloning and identical particles paradox.Based on the original Two-dimensional linear 2D wave theory, this paper holds that the objective ontology of the universe consists of a one-dimensional propagation substrate and a global two-dimensional linear 2D wave field. A free two-dimensional linear 2D wave is defined as a traveling wave, while stable structures formed by constrained superposition of energy are standing waves. Electrons, protons and neutrons are the only three types of primitive fundamental standing waves in the universe, and all macroscopic matter in nature is composed of their combinations. Time is not an independent spacetime dimension; its essence is the intrinsic oscillation frequency inside fundamental standing waves. This paper does not re-derive the basic equations and theorems of the Two-dimensional linear 2D wave, and directly adopts them as an established original theoretical framework.The research reveals that all the above paradoxes stem from cognitive biases in conventional physics: regarding the three-dimensional space perceived by humans as the primordial structure of the universe, treating time as an independently flowing dimension, and misinterpreting microscopic wave phenomena as random particle behaviors. Within the framework of the Two-dimensional linear 2D wave theory, all paradoxes can be fundamentally resolved following the basic laws of wave propagation, standing wave evolution and wave field superposition, without introducing additional assumptions or ad hoc theories. This paper focuses on constructing a complete physical interpretation system. Relevant refined mathematical formulas can be supplemented and improved by subsequent researchers, and the original authorship of the core theory is clearly confirmed. This study provides a new perspective for fundamental physics to break through existing constraints.
We propose that wave-particle duality is not a fundamental physical phenomenon but a linguistic paradox arising from projecting three-dimensional quantum objects onto incompatible low-dimensional mental models. We propose that the electron in any quantum state is a spherical membrane: the unique SO(3)-invariant surface in three-dimensional space, whose vibration modes are the spherical harmonics. For bound states, the membrane is a standing-wave shell with discrete modes; for free states, it is a propagating wave packet with all modes continuously excited; for scattering states, each mode acquires a phase shift. A single unified definition covers all three cases, with the external potential as the sole distinguishing parameter. This identification is mathematically equivalent to standard quantum mechanics but provides a unified geometric picture that dissolves the particle-wave dichotomy. We extend the framework to multi-electron atoms as nested charged membranes and demonstrate compatibility with sixteen fundamental quantum phenomena. This work is a reinterpretation of quantum mechanics, not a new theory.
Mainstream quantum mechanics and atomic physics have long relied on the Schrödinger equation, spherical harmonics, and probabilistic cloud assumptions to precisely fit atomic orbital morphology, energy level distributions, and spectral data, achieving remarkable computational effectiveness. However, they have consistently lacked an ontological morphogenetic mechanism. For over a century, the quantum framework has been able to answer “what is the distribution of orbitals,” but has never been able to answer: why must orbitals exhibit their specific geometric forms? Where do the structural constraints originate? How are wave-particle modalities ontologically generated? Grounded in the PFUSRC axiomatic system of the 45° triple coaxial bicone as the unique steady-state geometry of the cosmos, this paper completes a topological ontological reconstruction of microscopic atomic structure. It rigorously demonstrates that the atom is not a spherically symmetric stochastic probability system, but rather a microscopically solidified 45° triple coaxial biconical interlayer oscillation steady-state structure. All s/p/d/f orbital petal morphologies, spatial nodal surfaces, energy level splittings, and symmetry breakings are not solutions of equations, but geometric necessities generated by biconical nested topology, interlayer angle constraints, and the 12/11 boundary gauge ratio. This paper rigorously distinguishes between two cognitive levels: quantum mechanics belongs to the observational fitting, statistical representation, and mathematical approximation system; PFUSRC atomic topological morphogenesis belongs to the structural origin, topological generation, and ontological mechanism system. The two are fully data-compatible, completely nested in hierarchy, and entirely non-isomorphic in ontology—there is no conflict, only a paradigmatic gap between “representational fitting” and “ontological generation.” This paper further clarifies: the electron is neither a classical particle nor a mechanical wave, but a steady-state node of the four-dimensional flowvariable field topologically latched at the three-dimensional interface. Wave-particle duality is a projective observational effect, not an intrinsic property of the electron. The spherical symmetry of the s-orbital is a time-averaged observational illusion; the instantaneous intrinsic structure of the atom is always a directional biconical configuration. The atom possesses an inherent topological density gradient: dense along the conical axis, sparse in lateral regions the projective distribution is inherently non-uniform. The uniform orbital image in mainstream textbooks is the result of long-term integration smoothing. This paper introduces the 2021 Science σ-hole subatomic direct imaging experiment and the homonuclear diatomic laser-induced dissociation electron localization experiment, demonstrating from real-space observation that the atom exhibits asymmetric conical charge distribution and axial–lateral density magnitude differences, in full agreement with the topological projection predictions of the triple biconical model—piercing through the theoretical blind zone of mainstream symmetric assumptions. This paper redefines the essence of chemical bonding: chemical bonds are not electron orbital overlap couplings, but topological alignment, anchor interlocking, and steady-state co-construction between atomic biconical interlayers. The electron serves only as an interfacial marker node of the latched structure. Four experimentally falsifiable unique topological predictions are proposed, completing the full paradigmatic transition from mathematical fitting and phenomenological description to geometric generation and experimental verification in microscopic atomic systems.