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 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.
The framework of classical physics includes the well-established Helmholtz wave equation, which accurately describes the propagation, interference, and diffraction behaviors of steady-state time-harmonic waves such as acoustic and electromagnetic waves at the macroscopic level. Verified by centuries of experiments, it is a universally recognized deterministic formula in fundamental physics. However, traditional physics has long operated within fixed boundaries: academia has always matched the Helmholtz equation with one-dimensional real scalar coordinates, applying it only to macroscopic matter wave fields, and never attempting to use it to describe the microscopic quantum world or the underlying ontology of the universe. Meanwhile, Heisenberg’s matrix mechanics, starting from the microscopic mathematical properties, derived the uncertainty principle based on the non-commutation relations of matrices, directly proving that microscopic mechanical quantities cannot be completely represented by real scalars. The microscopic universe is inherently adapted to matrix-dimensional structures, which is the fundamental cause of the proliferation of paradoxes in quantum mechanics under the real-coordinate framework.Addressing these dual shortcomings of the existing physical system, this paper presents original research: it fully retains the differential operators, wave constraints, and steady-state solution rules of the classical Helmholtz equation, introduces no new physical constants or artificial ad-hoc assumptions, and only replaces the real-space coordinates X and Y within the equation with second-order two-dimensional linear matrix coordinates, independently constructing a theoretical system of two-dimensional linear two-dimensional waves adapted to the microscopic ontology of the universe. It must be clearly defined: classical physics only has real-coordinate Helmholtz waves, used to explain macroscopic waves; the Helmholtz wave model based on two-dimensional linear matrix coordinates is an exclusive original theory of this paper, forming a dedicated new classical system to describe the true microscopic ontology of the universe.Drawing on rigorously verified traditional mathematical and physical tools such as the classical Helmholtz wave principle, Heisenberg’s matrix mechanics, the uncertainty principle, the linear projection theorem, and the principle of wave field superposition, this paper systematically elaborates the mathematical structure, dimensional characteristics, and evolutionary laws of two-dimensional linear two-dimensional waves, and reveals the ultimate physical nature of quantum observation collapse: all material entities in the microscopic world are two-dimensional linear two-dimensional Helmholtz waves, while the human macroscopic perceptual world and detection devices can only carry one-dimensional real information. The essence of the observation process is not the random collapse of the wavefunction as defined by quantum mechanics, but rather the observation system actively extracting one degree of freedom from the two-dimensional matrix wave, with the remaining single dimension completing dimensionality-reduction projection and mapping into the one-dimensional real physical space, ultimately forming the observational illusion of localized particles.This original theory can explain the two core experimental puzzles that have plagued quantum physics for a century without contradictions or ad-hoc patches: First, when observing the interference pattern throughout the double-slit experiment, this observation mode collects the steady-state information of the global superposition of two-dimensional waves without performing dimensional extraction, and thus does not trigger collapse; Second, when a single photon enters the human eye’s retina or a single-point detector completes fixed-point detection, the observation system imposes localized boundary conditions to force the extraction of the wave field dimension, realizing the "screen projection" imaging of two-dimensional waves onto one-dimensional reality, which macroscopically manifests as wavefunction collapse. This study breaks down the barriers between macroscopic classical waves and microscopic quantum phenomena, providing a unified explanation for microscopic phenomena such as wave-particle duality and quantum observation collapse with an original classical model, and offering a new underlying perspective for the grand unification research in fundamental physics.
The framework of classical physics encompasses the well-established and complete Helmholtz wave equation. Capable of accurately describing the propagation, interference and diffraction of steady-state harmonic waves such as acoustic and electromagnetic waves at the macroscopic scale, this equation has been validated by centuries of experiments and is widely recognized as a definitive formula in fundamental physics. Nevertheless, conventional physics has long imposed a rigid scope of application. The academic community has always adopted one-dimensional real scalar coordinates for the Helmholtz equation, limiting its use to macroscopic material wave fields, while never attempting to apply it to the microscopic quantum realm or the underlying ontological structure of the universe. Meanwhile, starting from the microscopic mathematical characteristics, Heisenberg’s matrix mechanics derives the uncertainty principle based on the non-commutation relation of matrices. It directly proves that microscopic mechanical quantities cannot be fully represented by real scalars, and that the microscopic universe is inherently governed by matrix-dimensional structures. This is the fundamental reason why numerous paradoxes persist within quantum mechanics under the framework of real coordinates. Addressing the dual limitations of existing physical theories, this paper presents original research. While fully retaining the differential operators, wave constraints and steady-state solution rules of the classical Helmholtz equation, and introducing no new physical constants or artificial auxiliary hypotheses, this work merely replaces the real spatial coordinates X and Y in the equation with second-order two-dimensional linear matrix coordinates. On this basis, a novel theoretical system of two-dimensional linear waves tailored for the microscopic ontology of the universe is independently established. To clarify: classical physics only adopts the Helmholtz wave with real coordinates to interpret macroscopic wave motions. By contrast, the Helmholtz wave model built upon two-dimensional linear matrix coordinates is an exclusive original theory proposed in this paper. It forms a brand-new independent classical system for depicting the true microscopic essence of the universe. Employing rigorously verified classical mathematical and physical tools, including the classical Helmholtz wave principle, Heisenberg’s matrix mechanics, the uncertainty principle, the linear projection theorem and the wave field superposition principle, this paper systematically elaborates the mathematical structure, dimensional properties and evolutionary laws of two-dimensional linear waves. It further reveals the ultimate physical nature of quantum measurement collapse. All substances in the microscopic world exist inherently as two-dimensional linear Helmholtz waves. Human macroscopic perception and detection devices can only process one-dimensional real-valued information. Essentially, the act of observation is not the random collapse of the wave function as defined in standard quantum mechanics. Instead, the observing system actively extracts one degree of freedom from the two-dimensional matrix wave. The remaining single dimension undergoes dimensionality reduction and projection onto the one-dimensional real physical space, giving rise to the apparent phenomenon of localized particles. This original theory explains two core experimental puzzles that have perplexed quantum physics for a century, without logical contradictions or ad hoc supplements. First, continuous observation of the interference pattern in the double-slit experiment collects global steady-state information of the superimposed two-dimensional waves, and no dimensional extraction occurs, so no collapse takes place. Second, when a single photon reaches the human retina or a single-point detector conducts fixed-position detection, the observing system imposes localized boundary conditions to forcibly extract dimensions from the wave field. This projects the two-dimensional wave onto the one-dimensional physical space, which manifests macroscopically as wave function collapse. This research breaks down the barrier between macroscopic classical waves and microscopic quantum phenomena. The proposed original classical model provides a unified interpretation of microscopic effects including wave-particle duality and quantum measurement collapse, offering a new fundamental perspective for the research on the grand unification of fundamental physics.
For over a century, the Copenhagen interpretation of modern quantum mechanics has been plagued by idealistic tendencies, inconsistent fundamental logic, and the division between the microscopic and macroscopic realms. This paper proposes an original Hypothesis of Two-Dimensional Linear Equation. Grounded on all completed experiments in quantum physics, this hypothesis summarizes objective laws via inductive reasoning, without introducing unknown physical constants or unfalsifiable assumptions. Its core argument is as follows: the objective eigenstates of all material units in the universe stably reside in a two-dimensional orthogonal real linear space, and waves described by two-dimensional constant real vector functions constitute the sole ontological form. Human sensory organs and all physical detection devices are essentially one-dimensional observation systems. Constrained by dimensional barriers, they cannot fully capture two-dimensional ontological vectors and only acquire data through dimensionality reduction projection. A series of counterintuitive experimental phenomena in quantum mechanics, including the illusory wave function collapse, Schrödinger’s cat paradox, anomalous observations in double-slit interference, and abnormal correlations in Bell’s inequality, do not stem from intrinsic uncertainty of microscopic matter, nor do they involve any mechanism whereby consciousness interferes with objective physical laws. All quantum anomalies are essentially projection illusions arising when constant two-dimensional objective vector waves undergo linear dimensionality reduction in one-dimensional observation systems. This paper further clarifies that Heisenberg’s matrix mechanics is not an independent fundamental ontological theory. Its entire matrix operation structure is essentially the practical physical manifestation of the Hypothesis of Two-Dimensional Linear Equation. All observational data adopted by Heisenberg to develop matrix mechanics were wave signals generated by the free evolution of microscopic particles, with no point measurements that could trigger state collapse. From its inception, this theoretical system defined matter based on the manifestation of two-dimensional linear waves, and its mathematical expressions are formulated for one-dimensional observation. Heisenberg summarized observational data and mistook the wave manifestation of free evolution for the intrinsic properties of microscopic particles, failing to recognize that it is merely the natural presentation of two-dimensional vectors within a one-dimensional observation framework. Matrix mechanics was thereby established, laying the groundwork for the subsequent idealistic probabilistic interpretation of the Copenhagen school. This hypothesis redefines the nature of observation: any information collection inevitably leads to energy coupling. Such coupling locks the projection matrix and enforces linear dimensionality reduction from two dimensions to one dimension, which is the physical origin of the so-called "wave function collapse" in academia. Discarding redundant constructs such as Hilbert space, complex wave functions, probability waves, hidden variables and the many-worlds interpretation, this hypothesis completes all derivations solely with elementary real linear algebra and provides unified explanations for all classic quantum paradoxes. It reshapes the worldview of quantum mechanics at the fundamental level, anchors microscopic physics within the framework of objective materialism, and realizes the unification of physical laws governing microscopic particles and macroscopic entities.
For over a century, the Copenhagen interpretation of modern quantum mechanics has been plagued by idealistic tendencies, inconsistent fundamental logic, and the division between the microscopic and macroscopic realms. This paper proposes an original Hypothesis of Two-Dimensional Linear Equation. Grounded on all completed experiments in quantum physics, this hypothesis summarizes objective laws via inductive reasoning, without introducing unknown physical constants or unfalsifiable assumptions. Its core argument is as follows: the objective eigenstates of all material units in the universe stably reside in a two-dimensional orthogonal real linear space, and waves described by two-dimensional constant real vector functions constitute the sole ontological configuration. Human sensory organs and all physical detection devices are essentially one-dimensional observation systems. Constrained by dimensional barriers, they cannot fully capture two-dimensional ontological vectors and only acquire data through dimensionality reduction projection.A series of counterintuitive experimental phenomena in quantum mechanics, including the illusory wave function collapse, Schrödinger’s cat paradox, anomalous observations in double-slit interference, and abnormal correlations in Bell’s inequality, do not stem from intrinsic uncertainty of microscopic matter, nor do they involve any mechanism whereby consciousness interferes with objective physical laws. All quantum anomalies are essentially projection illusions arising when constant two-dimensional objective vector waves undergo linear dimensionality reduction in one-dimensional observation systems.This paper further clarifies that Heisenberg’s matrix mechanics is not an independent fundamental ontological theory. Its entire matrix operation structure is essentially the practical physical manifestation of the Hypothesis of Two-Dimensional Linear Equation. All observational data adopted by Heisenberg to develop matrix mechanics were wave signals generated by the unconstrained evolution of microscopic particles, with no point measurements that could trigger state collapse. From its inception, this theoretical system defined matter based on the manifestation of two-dimensional linear waves, and its mathematical expressions are formulated for one-dimensional observation. Heisenberg summarized observational data and mistook the wave manifestation of unconstrained evolution for the intrinsic properties of microscopic particles, failing to recognize that it is merely the natural presentation of two-dimensional vectors within a one-dimensional observation framework. Matrix mechanics was thereby established, laying the groundwork for the subsequent idealistic probabilistic interpretation of the Copenhagen school.This hypothesis redefines the nature of observation: any information collection inevitably leads to energy coupling. Such coupling locks the projection matrix and enforces linear dimensionality reduction from two dimensions to one dimension, which is the physical origin of the so-called "wave function collapse" in academia.Discarding redundant constructs such as Hilbert space, complex wave functions, probability waves, hidden variables and the many-worlds interpretation, this hypothesis completes all derivations solely with elementary real linear algebra and provides unified explanations for all classic quantum paradoxes. It reshapes the worldview of quantum mechanics at the fundamental level, anchors microscopic physics within the framework of objective materialism, and realizes the unification of physical laws governing microscopic particles and macroscopic entities.
Modern physics is built upon a fragmented set of independent postulates across quantum mechanics, relativity and cosmology. We demonstrate that all established physical laws can be derived from a single fundamental postulate: all objective physical reality consists of two-dimensional (2D) linear travelling and standing waves. Observable 3D space, massive particles, time and gravity emerge as natural consequences of 2D wave dynamics projected onto a 1D observer manifold. This framework eliminates the need for multiple independent axioms, provides a conceptually unified description of all fundamental phenomena, and is in perfect agreement with all existing experimental and observational results.