The theory is based on a new hypothesis on the nature of matter. This hypothesis is that the elementary particles, atoms, and molecules we have found in nature are not part of the real world, but constitute information about the real world. They are the wave components of a generalized Fourier analysis of our observations (which in the final analysis are always space-time distributions of photon- or particle-counter clicks). This Fourier analysis should be so general that every observation can be expressed in its terms; it thereby becomes axiomatic. Physicists of past generations, with their sound instincts, were intuitively approaching this most general and most powerful possible analysis of our observations. With the discovery of quantum mechanics, this development had advanced so far that the precise formulation of this ultimate analysis could be guessed. The model which can guide us to this mathematical formulation is that of an ideal optical observation on a physical object. This observation is made by illuminating the object with a finite number of laser beams of known amplitude and phase, and observing the amplitude and phase of the finite number of light beams emerging from the object space. The assumption that this is all the information we can ever obtain about the object leads to a wave function of the object which consists of light waves, extrapolated from the photon detectors back to the object space. It is suggested that these light waves should be presented as a product of amplitudes in a $4n$-dimensional space, where $n$ is the number of light quanta in the signal. Most important, force, or interaction, can then be described as a linear transformation in this space. The actual mathematical formalism proposed on the basis of that model is $Xf=\frac{\mathrm{it}df}{\mathrm{dt}}$. $X$ is the Hamiltonian of the whole universe with ${n}_{0}\ensuremath{\cong}{10}^{80}$ particles. It is a $4{n}_{0}\ifmmode\times\else\texttimes\fi{}4{n}_{0}$ linear matrix operator. $f$ is a $4{n}_{0}$-component vector wave function representing waves traveling at the speed of light. The coordinates are the homogeneous coordinates (${x}_{j}, {y}_{j}, {z}_{j}, {u}_{j}$) of the ${n}_{0}$ particles in the closed universe. The eigenvalue $\ensuremath{\omega}$, in $Xf=\ensuremath{\omega}f$, is a $4{n}_{0}\ifmmode\times\else\texttimes\fi{}4{n}_{0}$ Hermitian matrix. It can be divided into ${n}_{0}\ifmmode\times\else\texttimes\fi{}{n}_{0}$, 4 \ifmmode\times\else\texttimes\fi{} 4 submatrices, each representing a complete set of dynamic and inertial quantities of elementary particles, or interaction quanta between particles. $\frac{\mathrm{it}df}{\mathrm{dt}}=\ensuremath{\omega}f$ is therefore a complete expression of the dynamic conservation laws. A special orthogonal transformation ${\ensuremath{\alpha}}_{0}$ transforms the solution into a standard solution with eigenvalue ${\ensuremath{\omega}}_{0}$, representing ${n}_{0}$ identical elementary particles. The assumption that the universe is of maximum probability then leads to simple explicit expressions for all matrix elements of ${\ensuremath{\omega}}_{0}$. This means that the energy levels of all $n$-particle systems (atoms or molecules) of the theory can be directly calculated. The equations demand relations between cosmological constants and atomic constants. In a universe of the size and mass of our observed universe, the elementary particle would have to be the size of the proton.
The theory is based on a new hypothesis on the nature of matter. This hypothesis is that the elementary particles, atoms, and molecules we have found in nature are not part of the real world, but constitute information about the real world. They are the wave components of a generalized Fourier analysis of our observations (which in the final analysis are always space-time distributions of photon- or particle-counter clicks). This Fourier analysis should be so general that every observation can be expressed in its terms; it thereby becomes axiomatic. Physicists of past generations, with their sound instincts, were intuitively approaching this most general and most powerful possible analysis of our observations. With the discovery of quantum mechanics, this development had advanced so far that the precise formulation of this ultimate analysis could be guessed. The model which can guide us to this mathematical formulation is that of an ideal optical observation on a physical object. This observation is made by illuminating the object with a finite number of laser beams of known amplitude and phase, and observing the amplitude and phase of the finite number of light beams emerging from the object space. The assumption that this is all the information we can ever obtain about the object leads to a wave function of the object which consists of light waves, extrapolated from the photon detectors back to the object space. It is suggested that these light waves should be presented as a product of amplitudes in a 4n-dimensional space, where n is the number of light quanta in the signal. Most important, force, or interaction, can then be described as a linear transformation in this space. The actual mathematical formalism proposed on the basis of that model is Xf=dtitdf. X is the Hamiltonian of the whole universe with n0\ensuremath≅1080 particles. It is a 4n0\ifmmode×\else\texttimes\fi4n0 linear matrix operator. f is a 4n0-component vector wave function representing waves traveling at the speed of light. The coordinates are the homogeneous coordinates (xj,yj,zj,uj) of the n0 particles in the closed universe. The eigenvalue \ensuremathω, in Xf=\ensuremathωf, is a 4n0\ifmmode×\else\texttimes\fi4n0 Hermitian matrix. It can be divided into n0\ifmmode×\else\texttimes\fin0, 4 \ifmmode\times\else\texttimes\fi{} 4 submatrices, each representing a complete set of dynamic and inertial quantities of elementary particles, or interaction quanta between particles. dtitdf=\ensuremathωf is therefore a complete expression of the dynamic conservation laws. A special orthogonal transformation \ensuremathα0 transforms the solution into a standard solution with eigenvalue \ensuremathω0, representing n0 identical elementary particles. The assumption that the universe is of maximum probability then leads to simple explicit expressions for all matrix elements of \ensuremathω0. This means that the energy levels of all n-particle systems (atoms or molecules) of the theory can be directly calculated. The equations demand relations between cosmological constants and atomic constants. In a universe of the size and mass of our observed universe, the elementary particle would have to be the size of the proton.
Those defile the purity of mathematical and philosophical truthy who confound real quantities with their relations and sensible measures. —ISAAC NEWTON, Principia Before we say anything about quantum mechanics, let us take a quick look at the Newtonian (or ‘classical’) view of the physical universe. According to that view, nature consists of an enormous number of particles. When Newtonian physics is combined with the theory of the electromagnetic field, it becomes convenient to think of these particles as dimensionless (even if there is a kind of conceptual strain involved in trying to think of something as having a mass but not any size ), and as possessing electrical properties – negative charge, or positive charge, or neutrality. This leads to the well-known ‘solar system’ view of the atom – with the electrons whirling around the nucleons (neutrons and protons) just as the planets whirl around the sun. Out of atoms are built molecules; out of molecules, macroscopic objects, scaling from dust motes to whole planets and stars. These latter also fall into larger groupings – solar systems and galaxies – but these larger structures differ from the ones previously mentioned in being held together exclusively by gravitational forces. At every level, however, one has trajectories (ultimately that means the possibility of continuously tracing the movements of the elementary particles) and one has causality (ultimately that means the possibility of extrapolating from the history of the universe up to a given time to its whole sequence of future states).
Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the whole framework is built. In quantum physics, first in non-relativistic mechanics and later in quantum field theories, even familiar concepts of position, momentum, wave or particle, are derived constructs from the classical limit in which we live but not intrinsic to the underlying physics. Most crucially, the very idea of the individual, whether an object or an event, distinguished only in a mere label of identity from others identical to it in all the physics, exists only as an approximation, not an element of underlying reality. Failure to recognize this and seeking alternative explanations in many worlds or multiverses leads only to incoherent logic and incorrect physics. As an example, in a physical system such as an atom in a particular state, physics deals with the universal system of all such atoms but makes no meaningful prediction of the position of an electron or the time of decay of any specific atom. Those are incidental, entirely random among all possible positions and times, even while physics makes very precise predictions for the distribution of the outcomes in measurements on atoms in that state. Physics deals with the universal, not the individual.
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.
Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the whole framework is built. In quantum physics, first in nonrelativistic mechanics and later in quantum field theories, even familiar concepts of position, momentum, wave, or particle, are derived constructs from the classical limit in which we live but not intrinsic to the underlying physics. Most crucially, the very idea of the individual, whether an object or an event, distinguished only in a mere label of identity from others identical to it in all the physics, exists only as an approximation, not an element of underlying reality. It is not an element of physics. Failure to recognize this and seeking alternative explanations in many worlds or multiverses leads only to incoherent logic and incorrect physics. As an example, for an atom in a particular state, physics deals with the universal system of all such atoms but makes no meaningful prediction of the position of an electron or the time of decay of any specific atom. Those are incidental, entirely random among all possible positions and times, even while physics makes very precise predictions for the distribution of the outcomes in measurements on atoms in that state. Physics deals with the universal, not the individual.
Aiming at the quantum mechanics wave function description probability feature, statistical interpretation, randomicity, uncertainty, nonlocality and agnosticism etc fundamental principles and concepts, based on the mass-space interaction, mass-space space-time view, microscopic mass-energy systems correlating with space-time model etc principles and theories, and the quantum entanglement particle experiments etc facts, present the matter-ordering-energy conservation laws and the Dong Pei innovating group interpretation of quantum mechanics. Simultaneously indicate: In the universe there exists the ordering- and disordering-energy matter, together known as matter. Existing the absolute space and absolute time. The absolute space-time is continuous. Matter and the absolute space-time together create and compose the objective world. The objective world is a harmonious and unified whole. Physical laws are completely unified. The objective world and matter are all finite. Matter exists, evolves and moves in the absolute space-time. Interactions are the most essential and most root basic attribute of matter. The interaction among matter is the mass-space interaction. The mass-space interaction is continuous and stable, is not random and intermittent. Macroscopic and microscopic regions all observe the identical physical laws. Elementary particles and they compose the microscopic mass-energy systems are all the ordering-energy matter, their mass-energy space-time is a interdependent whole, their feature, state, structure and motion laws are all entirely determined by the mass-space interaction, correspond with the determinism and causality, the motion state and feature, motion orbitals, position and speed of particles in the absolute space-time are all absolutely determined and could be measured exactly, their quantum states could be approximately described by the wave function of quantum mechanics. The wave functions are the simplified mathematical function approximate expression of quantum system states of adopted interaction, can be used to calculate the correlative physical quantities. The wave functions could approximately describe the state of the mass-energy space-time whole of a microscopic mass-energy system with the mass-space interaction acting and continuously moving. An eigenstate just is the state making the system energy minimum and in rather stable existence. Scientific theories are the abstract simplified approximate expression for the essential of natural phenomena. Physical theory is the abstract simplified approximate representation for the matter structure and its motion laws. Whereas the mathematical formulation then is the further simplified approximate representation for physical contents. All of theories, include quantum mechanics and relativity, only when the assumed approximate condition is satisfied, just are the applied correct scientific theory, could describe the objective world good enough but not exactly. Develop scientific theory, correctly cognize and reasonably interpret the objective world, without the end.