理论力学的底层逻辑之三

1、43光子构成万事万物理论力学的底层逻辑之三胡良，Hu Liang摘要：理论力学包括静力学(静力学公理，物体的受力分析，平面力，空间力系及摩擦等)，运动学(点的运动学，刚体的简单运动，点的合成运动及刚体的平面运动等)和动力学(含质点动力学的基本方程，动量定理，动量矩定理，动能定理，达朗贝尔原理及虚位移原理等)。宇宙天体的质量是一个重要的物理学量，当小质量天体遇到大质量天体的时，就只能处于从属地位。麦克斯韦方程组在洛伦兹变换之下，是保持协变的。但是，麦克斯韦方程组在伽利略变换之下，却是非协变的。万有引力常数是万有引力的核心逻辑；最大的信号速度（真空中的光速）是相对论的核心逻辑；而普朗克常数则是量子

2、力学的核心逻辑。关键词：动量定理，动量矩定理，动能定理，天体，质量，万有引力，协变性原理，坐标变换，波粒二象性，万有引力常数，卡文迪许扭秤，测量，光子，电子，质量，能量，动量，相对论，量子力学，电磁学，普朗克常数第八部分内容，量子化及连续化本质1波函数的内涵光子的波函数可表达为：1 The connotation of wave functionThe wave function of a photon can be expressed as: (x,y,z,t)=1VpC3=1Vp1C3=1Vp1fC2=1Vp1fC21 ；自由电子的波函数可表达为：The wave function of

3、free electrons can be expressed as: （xe,ye,ze,t)=1(Vpfp)1C2p= 1Ve1Ve3 ;内禀自旋电子的波函数可表达为：The wave function of the intrinsic spin electron can be expressed as: （xer,yer,zer,t)=1(Vpfp)fp1Cp2 ;由一个自由电子及一个光子构成的复合态电子可表达为：A composite electron composed of a free electron and a photon can be expressed as: （xe1,

4、ye1,ze1,t)=1(Vpfp)1C2p+1Vp1fC2=1Ve11Ve13 .（xe1,ye1,ze1,t)=C1ei(x,y,z,t)+C2ej（xe,ye,ze,t);其中，Vp，普朗克空间（最小的空间荷），量纲，<L(3)T(0)>；(Vpfp)，电子单元电荷，量纲，<-L(3)T(-1)>；Ve，电子的内禀空间（电子的空间荷），量纲，<L(3)T(0)>；Ve3 ，电子的能量动量张量（场），量纲，>L(3)T(-3)<；C2p，电子的电场（通量），量纲，>L(3)T(-2)<；(Vpfp)fp，内禀自旋电子的磁荷，量纲，

5、<-L(3)T(-2)>；in,Vp， Planck space (the smallest space charge), dimension, <L(3)T(0)>(Vpfp)， electron unit charge, dimension, <-L(3)T(-1)>Ve， the intrinsic space of the electron (the space charge of the electron), dimension, <L(3)T(0)>Ve3 ， electron's energy-momentum tensor

6、 (field), dimension, >L(3)T(-3)<C2p， the electric field (flux) of electrons, dimension, >L(3)T(-2)<(Vpfp)fp， the magnetic charge of the intrinsic spin electron, dimension, <-L(3)T(-2)>Cp2，内禀自旋电子的磁场（通量），量纲，>L(3)T(-1)<；C，最大的信号速度，量纲，>L(1)T(-1)<；C1,系数，量纲，L(0)T(0)；C2,系数，量纲，L

7、(0)T(0)；ei，相位，L(0)T(0)；ej，相位，L(0)T(0)。Cp2， the magnetic field (flux) of intrinsic spin electrons, dimension, >L(3)T(-1)<C， the maximum signal speed, dimension, >L(1)T(-1)<C1, coefficient, dimension, L(0)T(0);C2, coefficient, dimension, L(0)T(0);ei， phase, L(0)T(0);ej， Phase, L(0)T(0).从量子

8、力学来看，量纲完全相同的物理学量之间的运算可用线性代数方程表达；换句话说，线性代数方程可揭示量纲完全相同的物理学量之间的联系。根据量子三维常数理论，x（物理学量）与y（物理学量）的量纲必须完全相同;x（物理学量）的相位与y（物理学量）的相位可以不同.From the perspective of quantum mechanics, operations between physical quantities with identical dimensions can be expressed by linear algebraic equations; in other words, lin

9、ear algebraic equations can reveal the connections between physical quantities with identical dimensions.According to the quantum three-dimensional constant theory, the dimensions of (physical quantity) and (physical quantity) must be exactly the same; the phase of (physical quantity) and the phase

10、of (physical quantity) can be different.2相对论的基本假设相对论的基本假设是相对性原理（物理定律与参照系的选择无关）。狭义相对论的推论是质能公式，体现了质量随能量的增加而增加。相对论的动量能量表达式，The basic assumption of relativity is the principle of relativity (the laws of physics have nothing to do with the choice of frame of reference). The corollary of special relativit

11、y is the mass-energy formula, which shows that mass increases with energy.Relativistic momentum energy expression, E2=p2C2+m02C4；其中，E,表达物体运动时的总能量（内禀能量与相对动能之和），量纲，<L(3)T(-1)>*>L(2)T(-2)<；p，表达物体运动时的动量，量纲，<L(3)T(-1)>*>L(1)T(-1)<；C, 最大的信号速度（真空中的光速），量纲，>L(1)T(-1)<；m0，表达物体静止时

12、的质量，量纲，<L(3)T(-1)>。in,E, expresses the total energy of the object in motion (the sum of intrinsic energy and relative kinetic energy),Dimension, <L(3)T(-1)>*>L(2)T(-2)<p， expressing the momentum and dimension of the object in motion, <L(3)T(-1)>*>L(1)T(-1)<C, the maximu

13、m signal speed (the speed of light in a vacuum), dimension, >L(1)T(-1)<m0， express the mass of the object at rest, dimension, <L(3)T(-1)>.值得注意的是，运动能量（PC）与静止能量（m0C2）的相互垂直（相位）。It is worth noting that the motion energy （PC） and the rest energy （m0C2）are perpendicular (phase) to each other.3

14、固体中的电子运动在固体金属内部是由金属原子（或正离子）构成其晶格结点上的粒子；由于金属原子的价电子的电离能较低，在一定边界条件（外界环境）下，价电子可脱离原子，并且不固定在某一原子（或正离子）子的附近，而能够在晶格中自由运动，可称为自由电子。正是这些自由电子将金属原子（或离子）联系在一起，构成了金属整体。该作用力又称为金属键。显然，金属中为数不多的价电子并不足以形成如此多的共价键；这意味着，这些价电子只能为整个金属晶格所共有。金属键属于一种特殊的离域键（共享电子分布在多个原子间的一类键，既无方向性，也无饱和性）；值得注意的是，金属键不同于共享电子局限在两个原子间的那种共价键。3 Electro

15、n motion in solidsInside a solid metal, the particles on the lattice nodes are composed of metal atoms (or positive ions); due to the low ionization energy of the valence electrons of the metal atoms, under certain boundary conditions (external environment), the valence electrons can be separated fr

16、om the atoms , and is not fixed in the vicinity of an atom (or positive ion), but can move freely in the lattice, which can be called free electrons. It is these free electrons that link the metal atoms (or ions) together and make up the metal as a whole. This force is also known as a metallic bond.

17、 Obviously, the few valence electrons in a metal are not enough to form so many covalent bonds; this means that these valence electrons can only be shared by the entire metal lattice. Metallic bonds belong to a special kind of delocalized bonds (a type of bond in which shared electrons are distribut

18、ed among multiple atoms, with neither direction nor saturation); it is worth noting that metallic bonds are different from shared electrons that are confined to two The kind of covalent bond between atoms.从广义的角度来看，材料中原子（或分子，离子）的不同排列方式，导致材料内部具有不同的势场；电子在不同的材料中体现出不同的运动方式。基于晶体结构的平移对称性，考虑离子实际势场对电子的影响，才能解

19、读电子实际的运动方式。在固体中，存在有大量的电子，这些电子的运动都是相互联系的；而将每一个电子（采用单电子近似的方式）视为独立的在一个有效势场的运动，可让问题变得简约。在固体中，原子内层的电子变化较小，变化最大的是价电子；因此，可将原子核及内层电子看成为一个离子实（固定有瞬间位置）与价电子构成的等效势场。这意味着，可将电子的运动与离子实分开。晶体中的原子排列具有周期性，因此，晶体中的势场也具有周期性（周期性势场）。晶体周期性的势场，可表达为：From a broad perspective, the different arrangements of atoms (or molecules,

20、ions) in the material lead to different potential fields inside the material; electrons show different movement patterns in different materials. Based on the translational symmetry of the crystal structure, the actual movement mode of the electrons can be interpreted only by considering the influenc

21、e of the actual potential field of the ions on the electrons.In solids, there are a large number of electrons, and the motions of these electrons are related to each other; and treating each electron (using the one-electron approximation) as an independent motion in an effective potential field make

22、s the problem Minimalistic.In a solid, the electrons in the inner layer of the atom change little, and the valence electrons change the most; therefore, the nucleus and the inner electrons can be regarded as an equivalent potential field composed of an ionic real (fixed instantaneous position) and v

23、alence electrons. This means that the movement of the electrons can be separated from the ions.The arrangement of atoms in a crystal is periodic, so the potential field in the crystal is also periodic (periodic potential field).The periodic potential field of a crystal can be expressed as: U(r+Rn)=U

24、(r);其中，Rn，表达正格矢（任意晶格矢量），量纲，>L(1)T(0)<；U(r)，势能场，量纲，L(3)T(-1)*>L(2)T(2)<；in,Rn，express the positive lattice vector (arbitrary lattice vector), dimension, >L(1)T(0)<U(r)， potential energy field, dimension, <L(3)T(-1)>*>L(2)T(2)<晶体中的电子并不束缚于个别的原子，而是在整个晶体中运动，体现为共有化电子属性。假设原子实处

25、于平衡位置，而原子实偏离平衡位置的影响可视为微扰。由于晶格的离子对价电子影响较小，因此，可将该势场对电子的影响视为微扰。晶体中的电子是在整个晶体内运动的共有化电子，而共有化电子是在晶体周期性的势场中运动；共有化电子的本征态波函数是Bloch函数形式；这意味着，能量是由准连续能级构成的许多能带。能带理论解释了导体，绝缘体及半导体的区别；解释了晶体中电子的平场自由程的问题；借助单电子近似的假设，将晶体中每个电子的运动视为独立的在一个等效势场中的运动。值得注意的是，电子的运动受到晶格中原子（或离子）周期势的影响。晶体中的电子平均自由程远大于原子（或离子）的间距。能带理论是单电子的近似理论，电子的能量

26、状态是由能量的充带及能量的禁带相间隔组成的。The electrons in the crystal are not bound to individual atoms, but move in the whole crystal, which is reflected in the shared electronic properties.It is assumed that the atomic real is in the equilibrium position, and the effect of the atomic real deviation from the equilibr

27、ium position can be regarded as a perturbation.Since the ions of the lattice have little effect on the valence electrons, the effect of the potential field on the electrons can be regarded as a perturbation.The electrons in the crystal are shared electrons that move throughout the crystal, and the s

28、hared electrons move in the periodic potential field of the crystal; the eigenstate wave function of the shared electrons is in the form of the Bloch function; this means that the energy is Many energy bands composed of quasi-continuous energy levels.The energy band theory explains the difference be

29、tween conductors, insulators and semiconductors; explains the problem of the flat field free path of electrons in crystals; with the assumption of the one-electron approximation, the motion of each electron in the crystal is regarded as independent in an equivalent potential sports in the field.It i

30、s worth noting that the movement of electrons is affected by the periodic potential of atoms (or ions) in the lattice. The mean free path of electrons in a crystal is much larger than the spacing of atoms (or ions).The energy band theory is an approximate theory of a single electron, and the energy

31、state of the electron is composed of the energy charge band and the energy band gap interval.根据，According to, 2m2+U(r)(r)=E(r); then there is, 则有，2m2+U(r+Rn)(r+Rn)=E(r+Rn)。固体有很多原子（很多个原子核），原子核外面有许多层薄薄的内层能级，更远的外面则有许多层薄薄的外层能级。设想，很多个原子核是集中在这块固体的正中央，从而形成一个中心（大原子核）； 而很多层薄薄的内层能级集合起来就会形成一层有厚度的能带（称为价带），价带填满了

32、电子；很多层薄薄的外层能级集合起来就会形成一层有厚度的能带（称为导带），导带没有电子。导带与价带之间是禁带宽度。围绕原子核运行的区域就称为能带；例如，半导体的能带可进一步分为价带(由内层能级集合起来形成)及导带(由外层能级集合起来形成)在没有外加能量（光子）时，原子核外所有的电子都在价带围绕着原子核运行，价带的电子能量较低（比较稳定）。在有外加能量(光子)时，则有电子会从价带跳跃到导带；导带的电子能量较高（不稳定）。禁带宽度就是价带与导带之间没有电子存在的区域。具体来说，在价带及导带之间的区域是没有电子存在的；电子原来在价带，当对外施加能量（光子）时，电子并不是慢慢地爬到导带，而是电子吸收这个

33、能量（光子）后，直接跃迁到导带。而禁带宽度大小就是价带与导带之间的能量差(位能差)。反过来，电子（复合态电子）可辐射光子，从导带跃迁到价带。值得注意是，绝缘体（非导体）：电子填满价带，禁带宽度很大；因此，电子不能够轻易跃迁导电带，所以导电属性差。半导体：电子填满价带，而，禁带宽度中等；因此，电子可跃迁到导带自由移动。导体：电子填到导电带，没有禁带宽度；因此，电子可自由移动，所以导电属性好。Solids have many atoms (many nuclei), with many thin layers of inner energy levels outside the nucleus,

34、and many thin layers of outer energy levels farther out.Suppose that many atomic nuclei are concentrated in the center of the solid to form a center (large nucleus); and many thin inner layers of energy levels gather to form a layer of thick energy bands (called valences) band), the valence band is

35、filled with electrons; many thin outer energy levels combine to form a thick band (called the conduction band), which is devoid of electrons. Between the conduction band and the valence band is the forbidden band width.The region that runs around the nucleus is called the energy band; for example, t

36、he energy band of a semiconductor can be further divided into the valence band (formed by the collection of inner energy levels) and the conduction band (formed by the collection of outer energy levels)In the absence of external energy (photons), all the electrons outside the nucleus run around the

37、nucleus in the valence band, and the electrons in the valence band have lower energy (more stable).In the presence of applied energy (photons), electrons jump from the valence band to the conduction band; electrons in the conduction band have higher energy (unstable).The band gap is the area between

38、 the valence and conduction bands where no electrons exist. Specifically, there are no electrons in the region between the valence band and the conduction band; the electrons are originally in the valence band, and when energy (photons) is applied to the outside, the electrons do not slowly climb to

39、 the conduction band, but the electrons absorb After this energy (photon), it jumps directly to the conduction band. The forbidden band width is the energy difference (potential energy difference) between the valence band and the conduction band.In turn, electrons (recombination electrons) can radia

40、te photons, transitioning from the conduction band to the valence band.It is worth noting that,Insulator (non-conductor): The electrons fill the valence band, and the forbidden band width is large; therefore, the electrons cannot easily transition the conduction band, so the conductive properties ar

41、e poor.Semiconductors: Electrons fill the valence band, while the forbidden band width is moderate; therefore, electrons can transition to the conduction band and move freely.Conductor: The electrons fill the conductive band, and there is no band gap; therefore, the electrons can move freely, so the

42、 conductivity is good.4物质的量纲电场是存在于电荷周围，能够传递电荷与电荷之间相互作用。换句话说，电荷的周围存在着由电荷形成的电场；而电场对场中其他电荷可产生力的作用。观察者相对于电荷静止时所观察到的场就称为静电场。如果电荷相对于观察者运动，则除静电场外，还可形成磁场。此外，变化的磁场也可以引起电场（涡旋电场或感应电场）。任何一个物理学量都必须用一个专用的字符（或字符组合）表达。任何专用的字符（或字符组合）都必须有明确的物量学含义。根据量子三维常数理论，物质的量纲可表达为:4 Dimensions of matterAn electric field exists aro

43、und an electric charge and is able to transfer the electric charge and interact with the electric charge. In other words, there is an electric field around the electric charge; the electric field acts as a force on the other electric charges in the field.The field observed by the observer at rest re

44、lative to the charge is called the electrostatic field. If the charge moves relative to the observer, a magnetic field can form in addition to the electrostatic field.In addition, changing magnetic fields can also induce electric fields (vortex or induced electric fields).Any physical quantity must

45、be expressed in a special character (or combination of characters). Any special character (or combination of characters) must have a clear physical meaning.According to the quantum three-dimensional constant theory, the dimension of matter can be expressed as: <LnT(m)>>L(6n)T(3+m)>；其中，&l

46、t;LnT(m)>，表达物质的荷，定域性，信号速度；>L(6n)T(3+m)>，表达物质的场，非定域性，超距。这意味着，物质的荷与物质的场具有量子力学的互补性。in,<LnT(m)>， the charge of the expressed substance, the locality, the signal speed;>L(6n)T(3+m)>， Fields expressing matter, nonlocality, hyperdistance.This means that the charge of matter and the fie

47、ld of matter have the complementarity of quantum mechanics.对于一个由N个基本粒子组成的孤立量子体系来说，可表达为：For an isolated quantum system consisting of N elementary particles,It can be expressed as: VnVn(3)=(Vnfnp)Vn(2)np=mnpVn(2)/bn(npbn) =NVPC3 ；对于一个由M个基本粒子组成的孤立量子体系来说，可表达为：For an isolated quantum system composed of M

48、 elementary particles,It can be expressed as: VmVm(3)=(Vmfmp)Vm(2)mp=mmpVm(2)/bm(mpbm) =MVPC3；如果，if,mnpVn(2)/bn=mmpVm(2)/bm；then there are，在广义拉格朗日点，受到的万有引力完全相同，但力的方向相反。At the generalized Lagrangian point, the gravitational force is exactly the same, but the direction of the force is opposite.即，That

49、is, VnVn(3)/(npbn)=VmVm(3)/(mpbm);或，NVPC3/(npbn)=MVPC3/(mpbm)；显然，Obviously, Nmpbm=Mnpbn；或or，bm/bn=Mnp/Nmp；其中，bm ，孤立量子体系（由M个基本粒子组成的）离广义拉格朗日点（受到的所有力之和等于零的点）的距离,量纲，>L(1)T(0)<；bn ；孤立量子体系（由N个基本粒子组成的）离广义拉格朗日点（受到的所有力之和等于零的点）的距离；量纲，>L(1)T(0)<。in,bm ， the distance of the isolated quantum system (

50、composed of M elementary particles) from the generalized Lagrangian point (the point where the sum of all applied forces equals zero),dimension, >L(1)T(0)<bn ； the distance of the isolated quantum system (composed of N elementary particles) from the generalized Lagrangian point (the point wher

51、e the sum of all the applied forces is equal to zero);Dimension, >L(1)T(0)<.5等效原理比萨斜塔试验的观测精度不够。比萨斜塔试验并不能证明等效原理成立。It is worth mentioning that, theoretically, the Leaning Tower of Pisa test is completely due to insufficient observation accuracy. The Leaning Tower of Pisa test does not prove the

52、principle of equivalence.虽然，引力质量等价惯性质量； 但是，严格来说，等效原理并不成立； 只有在对质量较小的物体（小铁球）进行实验时，它才能近似正确。Although, the gravitational mass is equal to the inertial mass; however, strictly speaking, the equivalence principle does not hold; rather, it can only be approximately true when experiments are performed on obj

53、ects with small masses (small iron balls).由于铁球的质量比地球的质量小很多；因此，铁球对地球的影响极小，而地球对铁球的影响极大。Since the mass of the iron ball is much smaller than that of the earth; therefore, the iron ball has very little influence on the earth, and the earth has a great influence on the iron ball.这意味着，铁球的运动状态几乎完全由地球的属性来决定

54、。具体来说，地球在比萨斜塔位置的质量场大小是决定铁球运动状态的主要原因。This means that the state of motion of the iron ball is almost entirely determined by the properties of the earth. Specifically, the size of the mass field of the earth at the position of the Leaning Tower of Pisa is the main reason for determining the motion stat

55、e of the iron ball.从广义的角度来看，如果两个铁球完全相同，根据不确定性原理，这两个铁球也不能完全同时落地。From a broad point of view, if two iron balls are exactly the same, according to the uncertainty principle, the two iron balls cannot land at the same time.更进一步来看，相对于地球来说，大小铁球的质量不同，将会影响铁球的落地速度。Looking further, compared to the earth, the

56、different masses of large and small iron balls will affect the landing speed of the iron balls.因为，虽然，地球（质量场 ）对大小铁球的影响相同，但是大小铁球（质量场）对地球的影响不同。Because, though, the Earth (mass field) has the same effect on the big and small iron balls, but the big and small iron balls (mass field) affect the Earth diff

57、erently.此外，虽然，地球（质量场 ）对铁球及木球的影响相同；但是铁球及木球（质量场）对地球的影响不同。In addition, although, the earth (mass field) has the same effect on the iron ball and the wooden ball; but the iron ball and the wooden ball (mass field) have different effects on the earth.值得注意的是，大铁球及小铁球合在一起，则铁球（大铁球及小铁球之和）的总质量更大。因此，铁球（大铁球及小铁球之

58、和）对地球的万有引力更大。这意味着，铁球（大铁球及小铁球之和）落向地球的速度更快。Notably,When the large iron ball and the small iron ball are combined, the total mass of the iron ball (the sum of the large iron ball and the small iron ball) is greater.Therefore, the iron ball (the sum of the large iron ball and the small iron ball) has a greater gravitational force on the earth.This mean