理論力學的底層邏輯之三

1、43光子構成萬事萬物理論力學的底層邏輯之三胡良，Hu Liang摘要：理論力學包括靜力學(靜力學公理，物體的受力分析，平面力，空間力系及摩擦等)，運動學(點的運動學，剛體的簡單運動，點的合成運動及剛體的平面運動等)和動力學(含質(zhì)點動力學的基本方程，動量定理，動量矩定理，動能定理，達朗貝爾原理及虛位移原理等)。宇宙天體的質(zhì)量是一個重要的物理學量，當小質(zhì)量天體遇到大質(zhì)量天體的時，就只能處于從屬地位。麥克斯韋方程組在洛倫茲變換之下，是保持協(xié)變的。但是，麥克斯韋方程組在伽利略變換之下，卻是非協(xié)變的。萬有引力常數(shù)是萬有引力的核心邏輯；最大的信號速度（真空中的光速）是相對論的核心邏輯；而普朗克常數(shù)則是量子

2、力學的核心邏輯。關鍵詞：動量定理，動量矩定理，動能定理，天體，質(zhì)量，萬有引力，協(xié)變性原理，坐標變換，波粒二象性，萬有引力常數(shù)，卡文迪許扭秤，測量，光子，電子，質(zhì)量，能量，動量，相對論，量子力學，電磁學，普朗克常數(shù)第八部分內(nèi)容，量子化及連續(xù)化本質(zhì)1波函數(shù)的內(nèi)涵光子的波函數(shù)可表達為：1 The connotation of wave functionThe wave function of a photon can be expressed as: (x,y,z,t)=1VpC3=1Vp1C3=1Vp1fC2=1Vp1fC21 ；自由電子的波函數(shù)可表達為：The wave function of

3、free electrons can be expressed as: （xe,ye,ze,t)=1(Vpfp)1C2p= 1Ve1Ve3 ;內(nèi)稟自旋電子的波函數(shù)可表達為：The wave function of the intrinsic spin electron can be expressed as: （xer,yer,zer,t)=1(Vpfp)fp1Cp2 ;由一個自由電子及一個光子構成的復合態(tài)電子可表達為：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，普朗克空間（最小的空間荷），量綱，<L(3)T(0)>；(Vpfp)，電子單元電荷，量綱，<-L(3)T(-1)>；Ve，電子的內(nèi)稟空間（電子的空間荷），量綱，<L(3)T(0)>；Ve3 ，電子的能量動量張量（場），量綱，>L(3)T(-3)<；C2p，電子的電場（通量），量綱，>L(3)T(-2)<；(Vpfp)fp，內(nèi)稟自旋電子的磁荷，量綱，

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，內(nèi)稟自旋電子的磁場（通量），量綱，>L(3)T(-1)<；C，最大的信號速度，量綱，>L(1)T(-1)<；C1,系數(shù)，量綱，L(0)T(0)；C2,系數(shù)，量綱，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).從量子

8、力學來看，量綱完全相同的物理學量之間的運算可用線性代數(shù)方程表達；換句話說，線性代數(shù)方程可揭示量綱完全相同的物理學量之間的聯(lián)系。根據(jù)量子三維常數(shù)理論，x（物理學量）與y（物理學量）的量綱必須完全相同;x（物理學量）的相位與y（物理學量）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相對論的基本假設相對論的基本假設是相對性原理（物理定律與參照系的選擇無關）。狹義相對論的推論是質(zhì)能公式，體現(xiàn)了質(zhì)量隨能量的增加而增加。相對論的動量能量表達式，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,表達物體運動時的總能量（內(nèi)稟能量與相對動能之和），量綱，<L(3)T(-1)>*>L(2)T(-2)<；p，表達物體運動時的動量，量綱，<L(3)T(-1)>*>L(1)T(-1)<；C, 最大的信號速度（真空中的光速），量綱，>L(1)T(-1)<；m0，表達物體靜止時

12、的質(zhì)量，量綱，<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，運動能量（PC）與靜止能量（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、固體中的電子運動在固體金屬內(nèi)部是由金屬原子（或正離子）構成其晶格結點上的粒子；由于金屬原子的價電子的電離能較低，在一定邊界條件（外界環(huán)境）下，價電子可脫離原子，并且不固定在某一原子（或正離子）子的附近，而能夠在晶格中自由運動，可稱為自由電子。正是這些自由電子將金屬原子（或離子）聯(lián)系在一起，構成了金屬整體。該作用力又稱為金屬鍵。顯然，金屬中為數(shù)不多的價電子并不足以形成如此多的共價鍵；這意味著，這些價電子只能為整個金屬晶格所共有。金屬鍵屬于一種特殊的離域鍵（共享電子分布在多個原子間的一類鍵，既無方向性，也無飽和性）；值得注意的是，金屬鍵不同于共享電子局限在兩個原子間的那種共價鍵。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.從廣義的角度來看，材料中原子（或分子，離子）的不同排列方式，導致材料內(nèi)部具有不同的勢場；電子在不同的材料中體現(xiàn)出不同的運動方式?；诰w結構的平移對稱性，考慮離子實際勢場對電子的影響，才能解

19、讀電子實際的運動方式。在固體中，存在有大量的電子，這些電子的運動都是相互聯(lián)系的；而將每一個電子（采用單電子近似的方式）視為獨立的在一個有效勢場的運動，可讓問題變得簡約。在固體中，原子內(nèi)層的電子變化較小，變化最大的是價電子；因此，可將原子核及內(nèi)層電子看成為一個離子實（固定有瞬間位置）與價電子構成的等效勢場。這意味著，可將電子的運動與離子實分開。晶體中的原子排列具有周期性，因此，晶體中的勢場也具有周期性（周期性勢場）。晶體周期性的勢場，可表達為：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，表達正格矢（任意晶格矢量），量綱，>L(1)T(0)<；U(r)，勢能場，量綱，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)<晶體中的電子并不束縛于個別的原子，而是在整個晶體中運動，體現(xiàn)為共有化電子屬性。假設原子實處

25、于平衡位置，而原子實偏離平衡位置的影響可視為微擾。由于晶格的離子對價電子影響較小，因此，可將該勢場對電子的影響視為微擾。晶體中的電子是在整個晶體內(nèi)運動的共有化電子，而共有化電子是在晶體周期性的勢場中運動；共有化電子的本征態(tài)波函數(shù)是Bloch函數(shù)形式；這意味著，能量是由準連續(xù)能級構成的許多能帶。能帶理論解釋了導體，絕緣體及半導體的區(qū)別；解釋了晶體中電子的平場自由程的問題；借助單電子近似的假設，將晶體中每個電子的運動視為獨立的在一個等效勢場中的運動。值得注意的是，電子的運動受到晶格中原子（或離子）周期勢的影響。晶體中的電子平均自由程遠大于原子（或離子）的間距。能帶理論是單電子的近似理論，電子的能量

26、狀態(tài)是由能量的充帶及能量的禁帶相間隔組成的。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.根據(jù)，According to, 2m2+U(r)(r)=E(r); then there is, 則有，2m2+U(r+Rn)(r+Rn)=E(r+Rn)。固體有很多原子（很多個原子核），原子核外面有許多層薄薄的內(nèi)層能級，更遠的外面則有許多層薄薄的外層能級。設想，很多個原子核是集中在這塊固體的正中央，從而形成一個中心（大原子核）； 而很多層薄薄的內(nèi)層能級集合起來就會形成一層有厚度的能帶（稱為價帶），價帶填滿了

32、電子；很多層薄薄的外層能級集合起來就會形成一層有厚度的能帶（稱為導帶），導帶沒有電子。導帶與價帶之間是禁帶寬度。圍繞原子核運行的區(qū)域就稱為能帶；例如，半導體的能帶可進一步分為價帶(由內(nèi)層能級集合起來形成)及導帶(由外層能級集合起來形成)在沒有外加能量（光子）時，原子核外所有的電子都在價帶圍繞著原子核運行，價帶的電子能量較低（比較穩(wěn)定）。在有外加能量(光子)時，則有電子會從價帶跳躍到導帶；導帶的電子能量較高（不穩(wěn)定）。禁帶寬度就是價帶與導帶之間沒有電子存在的區(qū)域。具體來說，在價帶及導帶之間的區(qū)域是沒有電子存在的；電子原來在價帶，當對外施加能量（光子）時，電子并不是慢慢地爬到導帶，而是電子吸收這個

33、能量（光子）后，直接躍遷到導帶。而禁帶寬度大小就是價帶與導帶之間的能量差(位能差)。反過來，電子（復合態(tài)電子）可輻射光子，從導帶躍遷到價帶。值得注意是，絕緣體（非導體）：電子填滿價帶，禁帶寬度很大；因此，電子不能夠輕易躍遷導電帶，所以導電屬性差。半導體：電子填滿價帶，而，禁帶寬度中等；因此，電子可躍遷到導帶自由移動。導體：電子填到導電帶，沒有禁帶寬度；因此，電子可自由移動，所以導電屬性好。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物質(zhì)的量綱電場是存在于電荷周圍，能夠傳遞電荷與電荷之間相互作用。換句話說，電荷的周圍存在著由電荷形成的電場；而電場對場中其他電荷可產(chǎn)生力的作用。觀察者相對于電荷靜止時所觀察到的場就稱為靜電場。如果電荷相對于觀察者運動，則除靜電場外，還可形成磁場。此外，變化的磁場也可以引起電場（渦旋電場或感應電場）。任何一個物理學量都必須用一個專用的字符（或字符組合）表達。任何專用的字符（或字符組合）都必須有明確的物量學含義。根據(jù)量子三維常數(shù)理論，物質(zhì)的量綱可表達為: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)>，表達物質(zhì)的荷，定域性，信號速度；>L(6n)T(3+m)>，表達物質(zhì)的場，非定域性，超距。這意味著，物質(zhì)的荷與物質(zhì)的場具有量子力學的互補性。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.對于一個由N個基本粒子組成的孤立量子體系來說，可表達為：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 ；對于一個由M個基本粒子組成的孤立量子體系來說，可表達為：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，在廣義拉格朗日點，受到的萬有引力完全相同，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)；顯然，Obviously, Nmpbm=Mnpbn；或or，bm/bn=Mnp/Nmp；其中，bm ，孤立量子體系（由M個基本粒子組成的）離廣義拉格朗日點（受到的所有力之和等于零的點）的距離,量綱，>L(1)T(0)<；bn ；孤立量子體系（由N個基本粒子組成的）離廣義拉格朗日點（受到的所有力之和等于零的點）的距離；量綱，>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等效原理比薩斜塔試驗的觀測精度不夠。比薩斜塔試驗并不能證明等效原理成立。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.雖然，引力質(zhì)量等價慣性質(zhì)量； 但是，嚴格來說，等效原理并不成立； 只有在對質(zhì)量較小的物體（小鐵球）進行實驗時，它才能近似正確。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).由于鐵球的質(zhì)量比地球的質(zhì)量小很多；因此，鐵球?qū)Φ厍虻挠绊憳O小，而地球?qū)﹁F球的影響極大。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.這意味著，鐵球的運動狀態(tài)幾乎完全由地球的屬性來決定

54、。具體來說，地球在比薩斜塔位置的質(zhì)量場大小是決定鐵球運動狀態(tài)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.從廣義的角度來看，如果兩個鐵球完全相同，根據(jù)不確定性原理，這兩個鐵球也不能完全同時落地。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.更進一步來看，相對于地球來說，大小鐵球的質(zhì)量不同，將會影響鐵球的落地速度。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.因為，雖然，地球（質(zhì)量場 ）對大小鐵球的影響相同，但是大小鐵球（質(zhì)量場）對地球的影響不同。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，雖然，地球（質(zhì)量場 ）對鐵球及木球的影響相同；但是鐵球及木球（質(zhì)量場）對地球的影響不同。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，大鐵球及小鐵球合在一起，則鐵球（大鐵球及小鐵球之和）的總質(zhì)量更大。因此，鐵球（大鐵球及小鐵球之

58、和）對地球的萬有引力更大。這意味著，鐵球（大鐵球及小鐵球之和）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