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Modern Physics

The Electron Spin and Spin Magnetic Moment in Dual-Four-Dimensional Quantum Mechanism

国求 赵

Published Jan 1, 2016• 0 citations
Publisher

Abstract

双4维时空量子力学描述中，微观客体的自旋是场物质球自身的转动。在自身参考系，场物质球的半径由静态康普顿动量m0c定义：R0=ħ/m0c，转动频率为：E0= hν0；在运动参考系，场物质球的半径由动态康普顿动量mc定义：R1= ħ/mc，转动频率为：E1= hν1。m，m0是微观客体的动、静质量。电子自旋S及自旋磁矩μs都可以通过场物质球模型来计算。若自身参考系就在复数空间，在闵氏4维时空观察转动场物质球的运动，生成双4维复数时空，形成场物质的波动运动，它就是德布罗意物质波。 In dual-four-dimensional quantum mechanism, the spin of micro object is caused by the rotation of field matter sphere itself. In its own frame of reference, the radius is defined as the static Compton momentum R0=ħ/m0c, and frequency is ν0= E0/h. In the Dynamic frame of reference, the radius is defined as the dynamic Compton momentum R1= ħ/mc, and frequency is ν1= E1/h. m0 and m are the static and dynamic mass of a micro matter sphere, respectively. The electron spin s and spin magnetic moment μs both can be calculated by the field matter sphere model. If the frame of reference is in the complex space-time, and we observe the motion in a Minkowshi Space, then there will be a dual four-dimensional complex space-time. The fluctuation motion of field matter is De Broglie matter wave.

DOI
10.12677/mp.2016.61001

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双4维时空量子力学描述中，微观客体的自旋是场物质球自身的转动。在自身参考系，场物质球的半径由静态康普顿动量m0c定义：R0=ħ/m0c，转动频率为：E0= hν0；在运动参考系，场物质球的半径由动态康普顿动量mc定义：R1= ħ/mc，转动频率为：E1= hν1。m，m0是微观客体的动、静质量。电子自旋S及自旋磁矩μs都可以通过场物质球模型来计算。若自身参考系就在复数空间，在闵氏4维时空观察转动场物质球的运动，生成双4维复数时空，形成场物质的波动运动，它就是德布罗意物质波。 In dual-four-dimensional quantum mechanism, the spin of micro object is caused by the rotation of field matter sphere itself. In its own frame of reference, the radius is defined as the static Compton momentum R0=ħ/m0c, and frequency is ν0= E0/h. In the Dynamic frame of reference, the radius is defined as the dynamic Compton momentum R1= ħ/mc, and frequency is ν1= E1/h. m0 and m are the static and dynamic mass of a micro matter sphere, respectively. The electron spin s and spin magnetic moment μs both can be calculated by the field matter sphere model. If the frame of reference is in the complex space-time, and we observe the motion in a Minkowshi Space, then there will be a dual four-dimensional complex space-time. The fluctuation motion of field matter is De Broglie matter wave.
In dual-four-dimensional quantum mechanism, the spin of micro object is caused by the rotation of field matter sphere itself. In its own frame of reference, the radius is defined as the static Compton momentum R0 = ħ/m0c, and frequency is ν0 = E0/h. In the Dynamic frame of reference, the radius is defined as the dynamic Compton momentum R1 = ħ/mc, and frequency is ν1 = E1/h. m0 and m are the static and dynamic mass of a micro matter sphere, respectively. The electron spin s and spin magnetic moment µs both can be calculated by the field matter sphere model. If the frame of reference is in the complex space-time, and we observe the motion in a Minkowshi Space, then there will be a dual four-dimensional complex space-time. The fluctuation motion of field matter is De Broglie matter wave.
In dual-four-dimensional space-time quantum mechanics, the spin of micro object is caused by the rotation of field matter sphere itself. In its own frame of reference, the radius is defined as the static Compton momentum R0=ħ/m0c，and frequency is ν0=E0/h. In the Dynamic frame of reference, the radius is defined as the dynamic Compton momentum R1=ħ/mc，and frequency is ν1=E1/h. m0 and m is the static and dynamic mass of a micro matter sphere, respectively. The electron spin s and spin magnetic moment both can be calculated by the field matter sphere model. If the frame of reference is in the complex space-time, and we observe the motion in a Minkowshi Space, then there will be a dual four dimensional complex space-time. The fluctuation motion of field matter is De Broglie matter wave.
Spin is the inherent attribute of the micro-object. Micro-object can be understood as a rotating matter ball which is limited in a certain spatial distribution that can not be appropriately abstracted as a particle in the mi- cro-environment. The rotation frequency is defined by Eh   , radius of curvature is defined by R   p . Mi- cro-object exists in the dual 4-dimensional complex space-time. The rotation and movement of the micro-object gener- ate matter waves. Information of space structure and matter field density distribution of the micro-object can be propa- gated by matter waves. The establishment of complex space-time curvature coordinate is a geometric matter of mi- cro-object itself (geometry of matter). Matter waves are real. Matter field density distribution and probability distribu- tion of micro-object can be mutual mapped, micro-object can not be appropriately abstracted as a particle and its rotat- ing and vibration are the physical source of micro-object probability event in quantum measurement.
Micro-object is both particle and wave, so the traditional Particle Model (mass point model) is actually not applicable for it. Here to describe its motion, we expand the definition of time and space and pick up the spatial degrees of freedom hidden by particle model. We say that micro-object is like a rolling field-matter-ball, which has four degrees of freedom including one surface curvature degree and three mapping degrees in the three-dimensional phenomenal space. All the degrees are described by four curvature coordinate components, namely “k1, k2, k3, k4”, which form the imaginary part of a complex phase space, respectively. While as to the real part, we use “x1, x2, x3, x4” to describe the micro object’s position in our real space. Consequently, we build a Dual 4-dimensional complex phase space whose imaginary part is 4-dimension k space and real part is 4-dimension x space to describe the micro-object’s motion. Furthermore, we say that wave function can describe the information of a field-matter-ball’s rotation & motion and also matter-wave can spread the information of micro-object’s spatial structure & density distribution. Matter-wave and probability-wave can transform to each other though matter-wave is a physical wave. The non-point property is the foundational source of the probability in Quantum Mechanics.
A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects such as electrons. A superfluid vacuum formed the base to describe the basic vortex structure and properties of the electron, whereas various formulations derived from hydrodynamic laws described the electron vortex circumference, radius, angular velocity and angular frequency, angular momentum (spin) and magnetic momentum. A vortex electron fully explained the associations between momentum and wave, and hydrodynamic laws were essential in deriving the energy and angular frequency of the electron. In general, an electron traveling in space possesses internal and external motions. To derive the angular frequency of its internal motion, the Compton wavelength was used to represent the length of one cycle of the internal motion that is equal to the circumference of the electron vortex. The angular frequency of the electron vortex was calculated to obtain the same value according to Planck’s theory. A traveling vortex electron has internal and external motions that create a three-dimensional helix trajectory. The magnitude of the instantaneous velocity of the electron is the resultant of its internal and external velocities, being equal to the internal velocity reduced by the Lorentz factor (whose essence is presented in a detailed formulation). The wavelength of the helix trajectory represents the distance traveled by a particle along its axis during one period of revolution around the axis, resulting in the same de Broglie wavelength that corresponds to the helix pitch of the helix. Mathematical formulations were presented to demonstrate the relation between the energy of the vortex and its angular frequency and de Broglie’s wavelength; furthermore, Compton’s and de Broglie’s wavelengths were also differentiated.