本文以双波包双原点微观粒子模型和全时间D、全动量G及微观粒子运动全速度c等新概念为基础，在三维x空间和三维E空间范围内，对电子、质子及光子等进行了讨论。从而明确了微观粒子波–粒二象性即双波包Ψ(x,t)和φ(E,p)与惯性系的内在关系；通过分析澄清了单个粒子态叠加原理的概念并进一步确认其不应是源于粒子之间的相互作用；认为电子、质子是在三维x空间和三维E空间存在大对称关系的一对粒子，并由此推导计算出了原子核半径X0的数值，还建立了电子、质子各自新的波动方程；通过对光子双波包Ψ(x,t)和φ(E,p) 的分析,推断三维 空间存在有“时空子”。 Based on the double-wave packet double-origin particle model, quaternion full time D, quaternion full momentum G and quaternion full speed c and other new concepts, in three-dimensional x space and three-dimensional E space, the electrons, protons and photons are discussed. Thus the micro particle wave-particle duality—double-wave packet Ψ(x,t) and φ(E,p) ’s internal relationship with the inertial system is confirmed. Through the analysis, this paper clarifies the concept of single particle state superposition principle and further confirms that it is not originated from the interaction between particles. It is pointed out that the electrons and protons in three- dimensional x space and three-dimensional E space are a pair of particles having a big symmetrical relationship, hence calculating the numerical value of radius of the nucleus X0 , and establishing new wave equation for electrons and protons respectively. Through the analysis of the photon of double-wave packet Ψ(x,t) and φ(E,p) , it can be concluded that there are “space particles” existing in three-dimensional E space.
本文以双波包双原点微观粒子模型和全时间D、全动量G及微观粒子运动全速度c等新概念为基础，在三维x空间和三维E空间范围内，对电子、质子及光子等进行了讨论。从而明确了微观粒子波–粒二象性即双波包Ψ(x,t)和φ(E,p)与惯性系的内在关系；通过分析澄清了单个粒子态叠加原理的概念并进一步确认其不应是源于粒子之间的相互作用；认为电子、质子是在三维x空间和三维E空间存在大对称关系的一对粒子，并由此推导计算出了原子核半径X0的数值，还建立了电子、质子各自新的波动方程；通过对光子双波包Ψ(x,t)和φ(E,p) 的分析,推断三维 空间存在有“时空子”。 Based on the double-wave packet double-origin particle model, quaternion full time D, quaternion full momentum G and quaternion full speed c and other new concepts, in three-dimensional x space and three-dimensional E space, the electrons, protons and photons are discussed. Thus the micro particle wave-particle duality—double-wave packet Ψ(x,t) and φ(E,p) ’s internal relationship with the inertial system is confirmed. Through the analysis, this paper clarifies the concept of single particle state superposition principle and further confirms that it is not originated from the interaction between particles. It is pointed out that the electrons and protons in three- dimensional x space and three-dimensional E space are a pair of particles having a big symmetrical relationship, hence calculating the numerical value of radius of the nucleus X0 , and establishing new wave equation for electrons and protons respectively. Through the analysis of the photon of double-wave packet Ψ(x,t) and φ(E,p) , it can be concluded that there are “space particles” existing in three-dimensional E space.
Dispersion dynamics applies wave-particle duality, together with Maxwell’s electromagnetism, and with quantization E = hν = ħω (symbol definitions in footnote) and p = h/λ = ħk, to special relativity E2 = p2c2 + m2c4. Calculations on a wave-packet, that is symmetric about the normal distribution, are partly conservative and partly responsive. The complex electron wave function is chiefly modelled on the real wave function of an electromagnetic photon; while the former concept of a “point particle” is downgraded to mathematical abstraction. The computations yield conclusions for phase and group velocities, vp⋅vg = c2 with vp ≥ c because vg ≤ c, as in relativity. The condition on the phase velocity is most noticeable when p≪mc. Further consequences in dispersion dynamics are: derivations for ν and λ that are consistently established by one hundred years of experience in electron microscopy and particle accelerators. Values for vp = νλ = ω/k are therefore systematically verified by the products of known multiplicands or divisions by known divisors, even if vp is not independently measured. These consequences are significant in reduction of the wave-packet by resonant response during interactions between photons and electrons, for example, or between particles and particles. Thus the logic of mathematical quantum mechanics is distinguished from experiential physics that is continuous in time, and consistent with uncertainty principles. [Footnote: symbol E = energy; h = Planck’s constant; ν = frequency; ω = angular momentum; p = momentum; λ = wavelength; k = wave vector; c = speed of light; m = particle rest mass; vp = phase velocity; vg = group velocity].
提出微观粒子双波包双原点(双弦双原点)模型，新模型使微观粒子波–粒二象性不再费解。提出w-p空间和s-t空间概念，在此基础上定义了全时间 和全动量 并明确了它们之间的关系。建立微观粒子运动新方程。以粒子新模型为基础对诸如自旋、电子、质子、中子、反粒子和微观粒子相互作用力等经典概念的物理内涵进行了讨论。进而对自然界最简单的宏观粒子氢原子的结构和运动作了定性描述。The micro-particle wave-particle duality would be easy to understand through the new conception of microscopic particles double-wave packet double-origin (two-string dual-origin) model. The concept of w-p space and s-t space were proposed, then concepts of full-time and all-momen- tum were defined and the relationship between them was illustrated. A new equation of mi-croscopic particles motion was established. Based on a new particle model, the classical concepts’ physical meanings of the spin, electrons, protons, neutrons, interaction force of antiparticles and micro-particle were discussed. Then the structure and motion of the simplest hydrogen atoms were qualitatively described.
原有量子力学的由Schrodinger方程不能很好地描述微观粒子的局域特性和波-粒二象性，因此，量子力学必须改进和发展。在非线性系统中我们考虑了粒子之间或它与背景场之间的非线性相互作用，于是必须用非线性Schrodinger方程去描述的微观粒子的状态。至此，微观粒子的状态和特征相对于线性系统发生了根本性的变化。在这种情况下不论外势场如何变化，但非线性Schrodinger方程都能给出具有波-粒二象特性的解，它由包络孤子和一个载波组成，有一个具有确定的位置的质心；同时，微观粒子此时也具有一个确定的质量，能量和动量，和它们遵守的质量，能量和动量守恒定律，在外场作用时粒子是稳定的，并满足经典运动方程和遵守哈密顿方程和拉格朗日方程。于是用非线性Schrodinger方程去描述的微观粒子具有一个明显的的局域特性和波-粒二象性， 从而彻底消除了原有量子力学存在近一个世纪的困难和问题。基于这些新的结果我们可建立起完整和系统的非线性量子力学理论体系，推动量子力学的发展。因此这一研究具有重要意义。 In original quantum mechanics the Schrodinger equation is, in essence, a wave equation, wherein the microscopic particles depicted have only a wave feature, and not a corpuscle nature. These descriptors do not agree only with the Broglie relation of wave-corpuscle duality, but also with experimental results and the traditional knowledge of particle concept. Meanwhile, the theory gives only some approximate solutions. Thus a series of contradictory representations and problems occur in quantum mechanics, which have re-sulted in durative disputations focused on the area of physics and have not led to any united conclusions until now. The only way to solve these problems and difficulties is to develop the quantum mechanics. We inves-tigate in detail wave-corpuscle duality of microscopic particles described by a nonlinear Schrodinger equa-tion in nonlinear quantum systems. Concretely speaking, we here study the properties of the solution of the nonlinear Schrodinger equation, the stability of microscopic particles, invariance and conservation laws of motion of particles, the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations, the classical rule of microscopic particle motion, and so on. Studied results show that the solution of the nonlinear Schrodinger equation depicting microscopic particles is a soliton and have a wave-corpuscle duality, microscopic particles have always a mass center and possess determinant positions, sizes, mass, mo-mentum, energy and form, their mass, momentum and energy satisfy corresponding conservation laws, their dynamic states can be described by both nonlinear Schrodinger equation and classical Lagrangian and Ham-ilton equations, their motions obey the classical Newton-type law of motion. These properties indicate that the microscopic particles described by a nonlinear Schrodinger equation have a corpuscle nature. However, the solutions of dynamic equation are some solitary waves which are accompanied by a carrier wave to propagate in space-time, and possess certain frequency and wave speed. Thus microscopic particles described by nonlinear quantum mechanics have also wave feature. Thus we can affirm that the microscopic particles depicted by a nonlinear Schrodinger equation have a perfect wave-corpuscle duality, which are in essence different from those in linear quantum mechanics. Based on these results we can establish a new nonlinear quantum mechanics, which can solve these difficulties and problems disputed for about a century in linear quantum mechanics.
本文以双波包双原点粒子模型和四元数全时间D、四元数全动量G和四元数全速度C等新概念为基础，对电子进行了分析研究，通过推断粒子存在波–粒二象性的原因，对自由电子形象有了新的理解，因此得出全新的结论：一是不确定范围Δt是粒子具有波动性质的根本原因；二是象电子存在静止能量Eo ,它也还存在参数Xo；三是海森堡不确定性原理存在的原因是Eo的不确定量ΔEo和Xo的不确定量ΔXo。还对电子为什么带电作了定性的猜想。 Based on the double wave packet double origin particle model and quaternion full time D , qua-ternion full momentum G and quaternion full speed C and other new concepts, the electronic research was analyzed. By inferring the reason why there are wave-particle duality particles, a new understanding of free electron image was occurred, thus new conclusions were obtained: First the uncertainty range Δt is the root cause of the particles that have wave properties; Second, like electronic is static energy Eo , it still exists parameters Xo ; Third, the reason for the existence of the Heisenberg uncertainty principle is the Eo uncertainty ΔEo and Xo uncertainty ΔXo . We also made a qualitative guess why there was charge to electronic.
The behavior of classical macroscopic particles – from baseballs to planets – is governed by Newtonian mechanics as we have described in the first chapters of this book. The behavior of very small particles, on the other hand, is governed by an entirely different collection of equations and rules that go under the name of “quantum mechanics” and these particles are referred to as quantum particles. These rules have analogies to classical mechanics, but are fundamentally different and somewhat mysterious as we discussed in Chapter 8. The fundamental principles of quantum mechanics cannot be proven to be correct. They were developed based on the results of experimental observation, by analogy with classical mechanics, and through the consideration of logical implications of the formalisms used. There is no way to derive the fundamental elements of quantum mechanics, any more than one could predict from first principles that Newtonian forces should add as vectors. On the other hand, quantum mechanics is among the most rigorously tested theories in science, and the predictions of quantum mechanics have, so far, always been in agreement with experiment. In this chapter, we will present quantum mechanics as a series of postulates and examine their implications in application to simple one-dimensional systems. In the next chapter we will examine quantum effects in real systems including atoms, molecules, crystals, and artificially engineered nano-structures. Postulates of quantum mechanics QM Postulate 1: A quantum particle is described by a wave function Ψ( x , y , z , t ) which is a function of spatial coordinates and time. All physically determinable quantities can be derived from the wave function Ψ( x , y , z , t ) ; quantities which cannot be found from the wave function are not physically meaningful. Note that some things that one could ask about a quantum particle, for example the exact position and simultaneous exact momentum of a particle, are not derivable from the wave function and are therefore considered indeterminate (or uncertain ). These are things which cannot ever be known about a particle, and, as such, they are meaningless to contemplate.
The classical electrodynamic conclusion that an accelerating point charge mustradiate has long been regarded as an iron law, yet the electron in the hydrogen atom does notradiate and fall into the nucleus. This paper points out that the root of this contradiction is not inclassical electromagnetic theory itself, but in the untested hidden assumption that “the electronis a point particle”. Compton scattering experiments have already shown that the electron, whencolliding with a photon, behaves as a particle with a finite size, and its intrinsic geometric radius isgiven by the reduced Compton wavelength: re = ℏ/(mec) . Based on this physical fact, andconsidering that while the electron revolves around the nucleus (orbital motion) it also has anintrinsic spin, the electron itself generates two homologous electromagnetic radiation fields:orbital radiation and spin radiation. These two real electromagnetic waves always superpose andinterfere in space. Under specific conditions (frequencies forming an integer ratio, oppositephases, and matching amplitudes), the two waves completely interfere destructively, resulting inzero net external radiation and forming a stable standing wave inside the system– this is thestationary state of the hydrogen atom. The destructive interference condition naturally leads toωs = nΩ (n integer) and re/R = α/n2 , where α is the fine-structure constant. Combined withthe Coulomb force (centripetal force) equation, one uniquely obtains the quantized orbital radiiRn = n2a0 (a0 is the Bohr radius) and the angular momentum quantization Ln = nℏ . Thefine-structure constant thus acquires a geometric meaning: α = re/a0 .This paper further reveals the classical nature of wave-particle duality: the electron is always aparticle (with a definite trajectory), and its wave-like behavior comes from the superposition andinterference of the electromagnetic waves of spin and orbital radiation. The “particle-like”behavior observed in experiments is essentially the point-like signal produced when the photonradiated by the electron is absorbed, while the wave-particle duality of the photon itself is an1intrinsic property of it being an electromagnetic wave packet. Based on this picture, the paperprovides a classical causal explanation for the electron double-slit experiment– the electron asa particle barely passes through the slits; the interference fringes originate from theself-interference of the radiation wave packet (photon) generated by the electron interactingwith the slit plate, and the bright spots on the screen come from the discrete absorption eventsof photons, with the accumulation of many events forming the fringes. Observation inevitablydisturbs the electron because any measurement disrupts the destructive interference condition,thereby eliminating the mystery of “wavefunction collapse”.The paper also systematically expounds the electromagnetic nature of the photon: the photon isan electromagnetic wave packet radiated when the electron transitions between stationarystates due to the imbalance of interference; its energy E = hλ is determined solely by thefrequency, with constant amplitude; the photon is born at the speed of light because it originatesfrom a pre-existing electromagnetic wave. Finally, the paper discusses the essence of theelectromagnetic field: the electromagnetic field is not matter but energy; the vacuum is theground state electromagnetic field (filled with photons), and the cosmic microwave backgroundradiation is its observational evidence. Macroscopic electromagnetic fields (such as radio waves,visible light) are perturbations superimposed on the ground state field, acting as carriers ofenergy and information. The paper also links the background photon field to the cosmicmicrowave background radiation, providing a new causal picture for the interaction mechanismof charged particles and the inverse-square law of forces.This model is completely based on classical electromagnetism and the physical fact that theelectron has a finite size, providing a causally clear and physically intuitive unified picture for thestability of the hydrogen atom, quantized orbits, wave-particle duality, the nature of the photon,the double-slit experiment, the measurement problem, and the energy origin of theelectromagnetic field.The model further suggests that the proton may also be a similar self-sustaining electromagneticbound state, and the origin of cosmic matter can be attributed to the process of energy lockingby the condensation of electrons and positrons, offering a unified perspective for physicalphenomena from the atom tothe cosmos.