The Gauge Transformation of Matter Wave in the Dual 4-Dimensional Complex Space-Time and the New Internal Relation between Quantum Mechanics and the Theory of Relativity
物质波是物理波，不是概率波。自由微观客体从整体规范变换过渡到局域规范变换，通过协变导数引进规范场，尽管体现了场与微观客体的相互作用，但那是让微观客体恢复自由状态，实现规范不变性引进的抵消作用。定态波函数Ψ(x)可以分解成微观客体的各种自由运动状态——本征态(平面波)Ψn(x)的叠加。建在本征态上的坐标系是惯性系，由本征态之间的关系，将引导出惯性系之间的关系。由此，我们可以从惯性系到非惯性系的转变，为相对论与量子力学的统一找到一条可能的新的认识通道。 The matter-wave is a physical wave rather than a probability wave. Free micro object transforms from the whole gauge to the local gauge, and then brings in specification field by covariant deriva-tive, reflects interaction between field and micro object, but it has counteract effect of realizing gauge invariance in order to restore the free state of the micro object. The steady state wave func-tion Ψ(x) can be decomposed into the superstition of all kinds states of free movement of the micro object, namely, the eigen state Ψn(x) (plane wave). The system building for eigen state is inertial system. By analyzing the relationship between each eigen state, we can get the new relation between each inertial system thus we may get the transformation from inertial system to noninertial system. This work would pave a new understanding way for unifying the Quantum Mechanism and the Theory of relativity.
物质波是物理波，不是概率波。自由微观客体从整体规范变换过渡到局域规范变换，通过协变导数引进规范场，尽管体现了场与微观客体的相互作用，但那是让微观客体恢复自由状态，实现规范不变性引进的抵消作用。定态波函数Ψ(x)可以分解成微观客体的各种自由运动状态——本征态(平面波)Ψn(x)的叠加。建在本征态上的坐标系是惯性系，由本征态之间的关系，将引导出惯性系之间的关系。由此，我们可以从惯性系到非惯性系的转变，为相对论与量子力学的统一找到一条可能的新的认识通道。 The matter-wave is a physical wave rather than a probability wave. Free micro object transforms from the whole gauge to the local gauge, and then brings in specification field by covariant deriva-tive, reflects interaction between field and micro object, but it has counteract effect of realizing gauge invariance in order to restore the free state of the micro object. The steady state wave func-tion Ψ(x) can be decomposed into the superstition of all kinds states of free movement of the micro object, namely, the eigen state Ψn(x) (plane wave). The system building for eigen state is inertial system. By analyzing the relationship between each eigen state, we can get the new relation between each inertial system thus we may get the transformation from inertial system to noninertial system. This work would pave a new understanding way for unifying the Quantum Mechanism and the Theory of relativity.
The matter-wave is a physical wave rather than a probability wave. Free micro object transforms from the whole gauge to the local gauge, and then brings in specification field by covariant derivative, reflects interaction between field and micro object, but it has counteract effect of realizing gauge invariance in order to restore the free state of the micro object. The steady state wave function ( ) ψ x can be decomposed into the superstition of all kinds states of free movement of the micro object, namely, the eigen state ( ) ψ n x (plane wave). The system building for eigen state is inertial system. By analyzing the relationship between each eigen state, we can get the new relation between each inertial system thus we may get the transformation from inertial system to noninertial system. This work would pave a new understanding way for unifying the Quantum Mechanism and the Theory of relativity.
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.
Microscopic objects have some spatial distribution, which influences quantum phenomena. The particle model does not apply to the microworld. In this work, we use a rotating field matter sphere model. The size of the sphere change along with the movement state, harmonized with special relativity. Thus, we independently construct a dual 4-dimensional space-time to describe the microscopic quantum phenomenon and established the objective reality of plural description, which has obvious theoretical advantages. In the dual 4-dimensional space-time, the wave function describes matter waves as physical waves. Which is the physical basis of quantum communication. Quantum probability originates from the tangible structure and matter density distribution of the microscopic objects and is reflected in the transformation of space-time. Matter waves and probability waves can be transformed by using Fourier transformation. Keywords: field matter sphere; model; matter wave; quantum probability; origin; transformation
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.
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.
This book “Foundation of quantum mechanics in Dual 4-dimension space-time——The spacetime origin of quantum probability,” is a new exploration discussing the physical foundations of quantum mechanics. It contains two parts. One is the interactive realism, the other is the quantum mechanical description of the dual-4 dimensional spacetime. The first one is the philosophical basis of the second. The author thought that the conventional mass-point model is no long proper for the microscopic quantum world. The author used the movement of the rotating matter wave sphere in complex space to deduce the de Broglie matter-wave formula, and pulled the metaphysical hypothesis of the wave function back into the real physical realism. A matte wave is the physical wave, and it has potential applications. The matter wave transfers in the dual-4 dimensional complex space-time, and the complex number enters the cognition domain of space-time intrinsically. The author pointed out that, the state of a moving microscopic object is the combination of its eigen-states from quantum slicing, coherent hence; after quantum measurement, projected into the real 4-dimensional space-time and showing a probability distribution of point particles. Before and after the quantum measurement, the object is not in the same cognition level, nor the same physical space-time, and the Hilbert space is just their common math application space. The quantum measurement induces the transition of the microscopic object in space-time, manifestation, physical model, and theoretical structure, and the quantum probability comes from the space distribution of the field matter sphere, representing the transition from dual-4 complex to real 4-dimensional space-time, and the sphere to the point model. Physical phenomena, phenomenal entity, physical space-time, physical model, and theoretical structure all must consist intrinsically in logic. These are changing with the change of human cognition, embodying the unity of the human being and the nature. Dual-4 dimensional space-time quantum mechanics gives the wave function the physical realism. So, the concepts of the quantum entanglement, quantum communication and quantum teleportation all may be clarified and understood physically. The book is self-consistent with detailed justification, wherein the interactive realism concept is a new innovation.