Differential Equation of Motion of the Particle. with Helical Structure and Spin 2. the Form Like Schrodinger s

Transcription

1 Adv. Studies Teo. Pys., Vol. 5, 11, no. 13, Diffeential Equation of Motion of te Patile wit Helial Stutue and Spin Has te Fom Like Sodinge s Cen Sen nian Dept. of Pys., (National) Hua Qiao Univ. Quanzou, Fujian, P.. Cina ensennian@gmail.om Abstat. Eletomagneti adiations ae obviously waves. Potoeleti effet aused A. Einstein to postulate tat ligt of fequenyν itself onsists of individual quanta of enegy = ν. Follow Einstein dietly, we ty to teat a tin beam of onial wave tain wit enegy ν as a poton to see if tee is anyting inteesting. We fist pove teoetially tat su a tain must be oveed by a membane of pefet efletion and zeo est mass as lateal bounday. Ten we pove tat tee is a pai of symmetial spials of maximum stess Σ E tat divides te membane into equal pats wit same amount of diffeent ages. One te field being stengtened stongly and te onditions of mass and age satisfied, te membane will beak into two ±aged patiles of spin /. Cages and mass distibution inside ae poved to be of elial symmety. Ten we pove tat te spin of tis lass of patiles ae geneally onsisted of two pats: owing to su spial stutue s tanslational motion plus exta self-otation. Just beause of tis speial stutue, we pove at last tat diffeential equation of motion patile s inne system satisfied looks like Sodinge equation altoug intepetation fo te wave funtion is diffeent. Keywods: Membane, O-planes, ±aged spial-alves, un-foming ±eleton. max

2 61 Cen Sen nian pit, spin, spial stutue, otating on O-planes, intinsi fequeny, exta self-otation, wave funtion, mass density, elial symmety, Sodinge equation I. Intodution Eletomagneti adiations ae obviously waves. Potoeleti effet aused A. Einstein to postulate tat ligt of fequenyν itself onsists of individual quanta of enegy = ν. In te demonstation of quantum eletodynamis, E. Femi (1) and ten. P. Feynman () onneted te aveage enegy density ( = ν ) of eletomagneti wave wit te pobability (=1) of finding a poton tee to be a basi. To follow A. Einstein s idea dietly, it is natual to teat a tin beam of a monoomati speial eletomagneti wave fom = angle Ω and lengt L aving enegy ν as a poton. Tat is, wit solid ε A μ H S ( ) ( ) 1 t t d π π ds = ν L os + T os T (1) Wee, is te speial distant fom te ente of wave sufae to te inne and bounday iumfeenes and L equals to multiple wavelengt. Te speial aea of te ing toug point on sufae is ds = π sinϕ dϕ. angle tat suspends at = ϕ = is te plane. Hee we teat E s, H s magnitudes A, H disegad of te dietion of on wave sufae, just beause tat a poton wave tain must be symmeti wit its longitudinal axis. And ten, we depend on a seies of logial infeenes to see if tee is anyting inteesting we will ave? Ae tey wot to be fute studied teoetially and deteted by expeiments?

3 Diffeential equation of motion of patile 611 II. A poton wave tain must be oveed by a membane of pefet efletion and zeo est mass as lateal bounday. As well known, if tey ae fa enoug fom vaying dipole U, vetos E and H ae tansvese, mutually pependiula, in pase, and its magnitude (3) : E = μ H ε U&& ( t ) sin θ Aoding to equation (), E = H = wenθ =. It leads to tat etain poton waves wit te bounday tangent to te line of θ = will ave E = H = at tangent points. Beause of te symmety of a poton and te identity between potons, we an affim tat any poton wave tain as got E = H = along its iula bounday, despite of te distibution funtion of A ( ) and H ( ) ae ontinued o disete ee. Fo onveniene in late illustation, we name te geometial plane (te synonym of te tin laye) as obsevation (O)-plane if a plane wave passes toug it pependiulaly. Of ouse, fo a speial wave O-plane is efe to speial and oinides wit te speial wave sufae. We often use tangential to epesent te dietion tangent o paallel to te wave sufae. Now a speial poton wave tain emitted fom = an be expessed as () A( ) E = (,, t ' ) t' os π ( ) ( 1 ', t, f ) (3) T Sine te aea of speial ile of adius on wave sufae is Ω = Φ π sinϕ dϕ = 4π sin Φ, wee 1 Ω Φ = = sin (onstan 4π and = ϕ. Ten and E ( ) just ae funtions ofϕ, disegad of te adial Φ oodinate. Expession (3) satisfies diffeential wave equation. Sine A( ) is always an even funtion and equal to at bounday = be expanded in Fouie seies as follow:, it an

4 61 Cen Sen nian A ( ) = j = 1 b j-1 let j = 1 os π ( j 1) 4 b j-1 os π ( j 1) Λ ( Λ = 4, ) (4) Te wave funtion (3) will make a stationay vibation on te O-plane loated at. Its funtion is o A( ) E(, o, = o o t os π T let E (, = L A ( ) = ( p o, t T ) (5) Hea we ave osen te zeo point oft so as initial pase of osine funtion equal to zeo. Instead equation (4) into (5), we ave 1 E (, = o j = 1 b j-1 os π ( Λ j 1 let E+ ( V + E ( + V t 1 ) + T o j = 1 b j-1 os π ( Λ j 1 + T t ) Λ (Λ j-1 = ( j 1), Λ = 4o, V Λ =, o, T L t T ) (6) Fo any dietion of on te O-plane (tin laye), E+ ( V is te sum of all taveling waves to te igt. And E ( + V is te one to te left. Tey move towad ea ote and eflet pefetly at te bounday points wit 18 pase loss (wee E = H = ) Te identity of equations (5) and (6) means wen a poton wave passes -plane at timet, te enegy exited in te tin laye an be teated as stoage eite in type of stationay vibation, o in type of te distibution of infinite pais of tansvesal taveling waves along te O-plane at same time. Tey ae matematially equivalent. An inteesting question is wete te tansvesal taveling o

5 Diffeential equation of motion of patile 613 eletomagneti waves eally exist ove te O-plane (te spae tat tin laye oupied)? Te answe is etainly positive. As a matte of fat, fo evey moment t, E of all points at same laye ae paallel and vaying synonially. Tey will exite adiation along all dietions inlude te tangential dietions of te laye. Te mutual tangential adiations, ten mutual Poynting vetos (S= E H) and mutual adiation pessues Q aoss te intefae of any two adjaent pats in te same laye ae eally existed. Equation (6) means tat te esultant tansvesal taveling waves and enegy flow ae adial in te tin laye. Te adiation intensity fom a vaying E is anisotopi even along wave sufae, equation (). If a poton wave is linea polaized, te oeffiients in equation (6) must be diffeent in diffeent -dietion. So te poton waves just emitted fom vaying dipole must be equal mixtues of igt and left iula polaized. A poton must be etain sot of iula polaized and te oeffiients of equation (6) must 1 π be te statistial mean values in te alf peiod ( Emax sinθ dθ Emax π = ). It π makes te oeffiients same along any -dietion on same wave sufae. Fo eq. (1), sine A ( ) (π sinϕdϕ) = π A ( ) sin ( Φ ) d( Φ ) (7) And te limits of tis integal ae Φ, so te total aveage enegy ove any wave sufae wit unit tikness ae equal and independent of. A poton s enegy is estited witin te solid angle Ω subtended at te point soue = despite of ow lage te aea of wave sufaes duing popagation. It means tat no adiation enegy an un out pependiulaly aoss a poton s lateal bounday sufae. On te ote and, outwad tangential adiations fom te egion ( β, β f ) along te iumfeene of O-planes ae always existed. Te outwad Poynting vetos pependiula to te lateal sufae S (, θ, = E (, θ, H (, θ,, ( θ π, p L ) ae geneally diffeent to zeo ove wole bounday. Fo simplify of notation, we use (, θ,...) to epesent

6 614 Cen Sen nian (, θ,...) wee p β fo small enoug β f ee and in te following. Sine eletomagneti adiation an not be efleted fom vauum. Teefoe, we ome to a vey impotant onlusion: Te lateal bounday of a poton wave tain must be oveed by a membane of pefet efletion and zeo est mass. Tis mateial must be dietly tansfeed fom te enegy of soue mateial. By te way if unelated to tis atile, as an impotant oollay, it was pointed out in one of ou last papes (4) tat vaying field is not te suffiient ondition fo te podution of a poton. It is just a neessay ondition. Anote one is tat te soue an povide te enegy to be membane, altoug its enegy is supposed to be so small in ompae wit poton s field enegies. It seems to be te eason of wy te eleton of atom in gound state is stable, sine tee is not any available lowe state pemit im to loate so as no exta enegy of eleton an povide te neessay membane no matte ow small it is. All esultant tansvesal waves on O-planes ae adial, equation (6). Any beam of te tansvesal taveling wave E+ ( V and E ( + V ) is seto-like. Letδθ be te angle of te seto. Ten on te same seto, te enegy flow passes toug te aea i δθ δ equal to te one toug k δθ δ. Tat is S (, θ, δθ δ = S (, θ, δθ δ ( p p p ) (8) i i k A ( ) ε ε Sine lim S = E =, let i =, k and A = A( ), μ μ ten equation (8) gives te elation between magnitudes A of and as follow k i k A ( ) = A ( < < ) Wee A ( ) = ( = ) (9) A is a onstant disegad of. Te late bounday ondition as been disussed at te beginning of tis pape. Equation (9) is te distibution funtion

7 Diffeential equation of motion of patile 615 of A( ) on any wave sufae. To substitute equation (9) into (3), we ave te wave funtion of a poton emmited fom te point soue = A t E(, = osπ ( ) ( p, T L t t t + T, f ) E(,, = (1) Equation (1) efes to tat su a poton s eation pobability wit ote patile at wave s ente is fa geate tan ote pats of it. On te ote and, te time ate of ange of momentum at bounday is S (, θ,. It will ause te existene of entifugal pessue of same amount (, θ, fom all points of te ove membane. Q mem Q mem (, θ, = S (, θ, ( π θ π, + L ) (11) Combining equations (11) wit (8), we ave te equilibium equation between two opposite sufaes Q outwad δθ δ and δθ δ in te same seto spae (, θ, δθ δ = (, θ, δθ δ Q mem ( p p, θ π, L ) (1) III. Fou impotant meanial and eletomagneti popeties of te membane Figue 1 is a sket map of te distibution of E( ) on a wave sufae,. Let θ be te angle of adius fom absissaof. Momentum s ate of ange at te S (, θ ) bounday makes te iula tension pe unit lengt of wave tain T (, θ ) in te membane. Tat is

8 616 Cen Sen nian ε T (, θ ) = S(, θ ) = A os θ (13) μ Te maximum appens at points A and F, Φ ε TF (,,) = TA(, π ) = Tmax = A. Tis elation is valid fo ote A μ and F points of evey wave laye. Conneting all tese points A and F espetively tey fom two paallel spials, A- spial and F- spial (igt-anded o left-anded double tead) on te lateal sufae of te iula polaized wave tain. Figue 1 Te mateial of membane must be vey easy to ange its sape duing popagation, so we suppose it is a liquid-like mateial aving almost onstant volume. Te aea of membane s oss-setion π δ = π Γ is onstant. So te tikness δ = Γ (14) let Let Σ max be te maximum nomal stess on te oss-setion. Sine Tmax = Σ max δ and equation (13), it gives ε Φ Σ max = A = A (15) Γ μ Γ μ ε

9 Diffeential equation of motion of patile 617 Fo a poton of iula polaized wit givenν, tee ae fou impotant popeties of its membane: (i) Te maximum stess Σ max is onstant, eq.(15) tat always appened along A-spial and F-spial on te poton s lateal sufae despite of te magnitude of and. Te eletomagneti wave tain plus ove membane fom an independent stutue. Unde geneal iumstanes, te poton tain will always keep its integity unless tee is a vey stong extenal effet, fo example, ty to stop te tain and geatly inease te density of its E-H field aound A,F and makes Σ max bigge tan ultimate tensile stengt (unknown but must exis and beak te membane. (ii) Sine sufae density of age σ on te inne side of te membane equals to D = ε E ), so, fo te uppe spial-alf. Fig 1, te absolute value of σ θ is n ( n σ θ A = ε sinθ ( θ π ) (16) Te age densityσ θ of any point foms an equal-magnitude spial on te inne side of te membane. Tis is to say tat ages inside distibute wit elial symmety about its longitudinally ental axis. Te total negative age in uppe spial-alf is L π θ = q = d A σθ dθ = ε L = ε ΦA L (17) Te lowe alf as same amount of positive age. Like te Σ max, quantity q in te ±aged spial-alves always exists and keeps unanged despite of te magnitude of and. (iii) Te inease of wave sufaes magnitude as poton moves fowad will ause te iumfeenes of membane beome longe and longe. Witin d θ egion, wen te adius of membane ineases fom to + d, te inement

10 618 Cen Sen nian of iumfeene is d dθ. Te wok down in te δ -laye of te wave tain against tension fom oiginal nuleus dimension to final is δ W π = δ 4 π Φ T (, θ ) d dθ = ε A δ ln μ Fo a poton, te wok an be down against te tension is etainly (18) finite, ln and ten te adius of poton wave sufaes must be uppe bounded if a poton annot self blast. A poton wave tain will at last beomes exatly (not appoximately) ylindial wit adius max. Tis will make te poton tat ame fom te end of ou univese ten billion yeas ago still aving a finite max wave sufae. γ (iv) As well-known te intinsi fequeny ν γ ( = ) of te iula polaized poton is exatly te otation fequeny of E,H on diffeent O-planes wit diffeent initial pases aused by tanslational motion of poton s E,H fields. Su otations on te O-planes make poton s spin and equal to. As pats of a poton, it is evident tatν γ and ae also te fequeny and spin of te pai of ±aged spial-alves. Te pites of te pai and te poton ae equal. Tese popeties ae owing to te tanslational motion of a elial stutue of fields o of enegy densities and ages at speed. Fo simply of illustation in te following we always use otating on O-planes to expess su speial kind of otation. IV Extenal podution and ages distibute inside aged and anti-aged patiles. If te enegy of a poton equal to te double of etain ±aged patile s m p and q in eq.(17) equals to te amount of tis patile s age, su as leptons and adons (wit spin ), ten unde appopiate onditions, tat is te fields E, H of poton ineased stongly and beak te membane, extenal podution of su pai may appen.

11 Diffeential equation of motion of patile 619 As a possible ase, if a poton losely skims ove a eavy nulei and te supeposition of fields make etain pats of membane s neigboood ( max ) E Σ oveload and lage tan its ultimate tensile stengt, it will be possible to ave te membane quikly and ten entiely split along A-spial and F-spial. Te pai of ±aged spial-alves of te poton will beome two independent aged spial-pats (no longe a poton but two un-foming ±patiles) altoug tey ae still supeimposed tempoaily befoe axial depatue ompleted. Te late is beause of opposite magneti fields te otating ±ages podued. In tis poess: (a) Split of membane makes edistibution of its ±ages. Eleti attation will ause two eleti flows along diffeent membane s iumfeenes and at last stop evenly at two ends A and F. Te poton s E, H field (wo podues te ages in membane, not te evese) still exists at all points inside. Te oiginal field dietions ae diffeent on diffeent O-planes, so te distibution of enegy density on any O-planes must ave dietional popety, otewise its spin will vanis and beak te onsevation law of angula momentum. As a matte of fat, two aged points (positive o negative) loated at te ends of te diamete AF (X-axis) will etainly effet te distibution of enegy density and make tem aving simila axial symmety on any O-plane. Te ages distibution on any un-foming ±patile s sufae looks like symmeti double elix. Connetion of te points of equal enegy density among all neigboing O-planes foms equal-magnitude spial in it. Te distibution of ages and mass ae all of elial symmety. (b) Te iumfeene of any laye s membane afte split will ontat and eovey to its oiginal lengt. And in te meantime, attation between ±ages on opposite ±patiles sufaes will geatly soten its diamete. Te esult is tat te lage -adius un-foming ±patile beome te small ones wit oiginal nuleus adius (o even smalle). Sine supeposition of fields and adial ontation of oss-setions do not ange te lengt of its longitudinal pit and tey still move wit speed befoe axial sepaation by magneti epulsion begins, so otating fequeny of te small pais on O-planes still equals toν γ (= /pit. Te spin must be onseved in tis poess. So te moment of inetias (=spin/ πν γ ) of te small pai and of te big pai ae equal, despite of te

12 6 Cen Sen nian magnitude of all laye s adius (even if tey ae not equal). Evey small un-foming ±patile as spin. ( In te poess of axial sepaation of te small un-foming ±patile, tey must still move at speed. epulsion foe along adial dietion between te aged spial itself will step by step expand patile s diamete to inease its moment of inetia and deease te otating fequeny of dq ( d O-planes until tey ae totally sepaated. me also) on te Te pai podution of eleton and positon is a eal example. Let ν eal( expess te final otating fequeny of dq on O-planes wile te small un-foming ±eletons ae totally sepaated but tempoaily still at speed. In tis poess, te spin must be onseved. So ν eal( is te neessay and suffiient fequeny fo te fee un-foming ±eleton to guaantee its spin. Aoding to te onsevation law of enegy, ea un-foming ±eleton podued must ave enegy e 1 e = ν γ let = ν (19) We name ν as intinsi fequeny of te un-foming eleton. Does ν eal( equal to ν? Tee ae just two types of expession to indiate a ting s total enegy tat is Einstein s = ν and = m oespondent to zeo and none zeo est mass espetively. ν eal( as enegy dimension. If ν eal ν e, it means tee must be appened an exta gain o loss of enegy ± δν duing tis miosopi poess. So, if diffeent type of enegy tansfe does not appen in tis poess of pai podution, we will ave ν = () eal( = ν e e Intinsi fequeny ν ( = ) is eally te neessay and suffiient fequeny

13 Diffeential equation of motion of patile 61 fo te un-foming eleton otating on O-planes to guaantee its spin. Tis is te pysial meaning of tis intinsi fequeny. At last, duing eletomagneti enegy tansfes to mateial ( m ), un-foming eleton beomes a fee eleton and speed deeases tov. Sine vaiation of longitudinal veloity fom tov do not affet te adial distibution of mass on oss-setions; do not affet its moment of inetia, if we suppose eleton is made up by isotopi mateial. Ten te atioν ( ) : e will keep unanged. Above assetion will be still available fo ±eleton not only fo un-foming one. O in ote wods, te pysial meaning of eleton s intinsi fequeny e ν ( = ) is tat te intinsi fequeny is eally te neessay and suffiient fequeny otated on O-planes to guaantee its spin. On te ote and, ν eal( also efes to tat te ν eal( time of equals to. = ν (1) Wee is te pit of un-foming eleton just sepaated but still at speed. Fo te un-foming eleton just totally sepaated, sine ν pit is e ( = 1 ν γ, te e γ () ( ) = Tis lengtening effet of un-foming eleton s pit an be explained as self longitudinal epulsion of evey aged spial itself. Besides, onsevation law makes te momentum of ea un-foming eleton to 1 be pγ. O p = () 1 = γ. (3) Wen an un-foming eleton anges to a fee eleton, field enegy beomes mass ( m ) and speed deeases tov. Aoding to speial elativity, te

14 6 Cen Sen nian momentum of eleton is o p ν (1) let V = mev = V = =. (4) p Compaing eq. (5) wit eq. (3), V ) and (1) = ( = = Te ( ) (5) V V ave same dimension and same fom of elation wit momentum p and lim =. We an easonably asset tat V is te pit of eleton duing speedv. It is times of. Wy? V Aoding to onsevation of enegy fom un-foming eleton to eleton m = = p and Einstein s enegy-momentum elation e e p m =, 4 e m ten = m, te appeaane of m ineases its pit fom to. Above esults ae all available at least fo ±aged patiles wit spin and even te neutal patiles if it an be modeled as double ±aged spials of same pit inside. We ave notied tat e = ν ) and p = (In geneal symbol, tat is = ν and p = ) ae just a logial esult ee, not a postulate. Tey eflet te featues of patile s spial stutue. Tey epesent diffeent pysial meaning as tey used to be.

15 Diffeential equation of motion of patile 63 V. Fomation of spin and te equation of motion of aged patile s inne system Let a aged patile moves wit V in dietion of Z-axis and te oodinate of fist dq 1 be x = 1, y =, z = at t =. Let T be te peiod of dq 1 yling on te O-planes duing te ages tanslational motion is of speedv. Ten we ave te elation = VTe (. Te equation of motion of igt-anded spial age dq1 is z t x = q os π ( ) (6) T z t y = q sin π ( ) ( = V Te ( ) (7) T ( J V z ). Wee J is te total numbe of pites in te eleton, q - te adius of aged spial-alves. Teat X-, Y- as omplex plane pependiula to te dietion of motion and ewite (6),(7) in omplex fom t z i π ( ) Te ( = q e (8) On te ote and, te pysial meaning of eleton s intinsi fequeny sows tat spin of magnitude always demands eleton s otating fequeny on O-planes equals to ν (o yling peiod equals to te intinsi peiod Te ( ( = 1/ ν ) disegad te tanslational veloity is ov. So te yling peiod of dq, dm on O-planes must be T ) not T. Te eleton must posses an exta self-otation about Z-axis to meet te demand ifv <. Tat is t z must t z π ( ν extat + ) = π ( ) ( = VTe ( ) (9) T T Sine = Te (, eq. (5), te exta self-otation fequeny ν exta sould be V

16 64 Cen Sen nian V V ν exta = ( 1 ) ν ( ν = ν ) (3) If V, ν, eleton just moves tanslational fo keeping spin. On exta te ontay, if V, aged patiles spin totally depend on aged patile s self-otation wit fequeny ν about Z-axis. Geneally speaking, te eleton s spin onsists of two pats: iula motion of all dq on O-planes aused by its tanslational motion of speed V and V te exta self-otation ν exta = ( 1 ) ν about symmeti axis. Te otation estits te adius of eleton. Linea speed at its sufae must be small ten ligt. Combine te spial stutue of ages inside wit te exta self-otation unde te demand of spin, age dq s equation of motion must be t z i π ( ) Te ( ) = q e ( = Te ( ) (31) V Matematially speaking, te spin ould be ealized if te patile (witout exta self-otation) simply moves tanslational wit pase veloity V. Tis is te pysial meaning of pase veloity. It is te exta self-otation tat made te appaently supeluminal effet of tis veloity. Sine age inside te patile distibutes wit elial symmety about its longitudinally ental axis, te distibution of mass density also ave same symmety as we mentioned above. So, veto ( = q = x + y ) in equations (31) an be also used to expess te motion of any mass density s spial ( ). Let Ψ ( x, y, z, be te equation of motion of eleton s mass density, te following elation olds

17 Diffeential equation of motion of patile 65 t z i π ( ) Te ( ) e ( Ψ ( x, y, z, = Ae ( A = x + y ) (3) Aoding to equation () and (5), we an ewite equation (3) into genealized omplex fom and neglet te subsipt of and p : i ( t xp yp zp ) x y z Ψ( x, y, z, = A e (33) Te diffeential fom of tis wave funtion is of te fom like Sodinge equation. Hee we aive at su a onlusion tat te spial distibution inside plus te demand of spin makes tis kind of aged patiles aving eq. (33) as tei equations of motion and satisfy te diffeential equations of te fom like Sodinge s (and Dia s also). Teefoe at least fo tis lass of ±aged patiles of spin, it seems we may simultaneously intepet te solutions of Sodinge equation as te equation of motion of su patile s inne system. Fo example, it seems we may teat te eleton loud as te moving figue of eleton s mass density distibution aound te nuleus et. VI. Conlusion Base on Maxwell teoy and Einstein quanta postulate, we ave deived te diffeential equation of motion of te patile tat possesses elial stutue and spin /. It as te fom like Sodinge s, altoug te intepetation of wave funtion is somewat diffeent. It gives us anote way to undestand geat Sodinge equation if we do not ejet te idea tat patile as its dimension and inne system. Unde tis pemise, te wave funtion may use to indiate te spae-time distibution of te patile s mass and ages. To aept te idea tat patile as its inne system not just point will elp us to undestand wee and ow does mass and ±ages ome fom in te pai podution. And also elp us to undestand te meanism of te fomation of spin / in su patiles. Te poton and te ±aged patiles poton podued obey simila fom of equations γ = ν γ, p γ = and e = ν ), p γ = espetively just beause tey ave simila stutue of elial symmety about te longitudinally ental

18 66 Cen Sen nian axis. A poton wave tain as elial symmety of field E, H and te patiles ave same symmety of ages and mass distibution. Intinsi fequenies ν γ and ν of tem epesent te neessay and suffiient fequenies of fields o of mass (inlude dq ) on te O-planes to guaantee tei spin and / espetively. and V ) epesent te pit of te poton s and aged patile s stutues. γ Tey ae also te wave lengts of tanslational motion. An impotant diffeene between tem is tat tose patiles wit non-zeo est mass ave self-otation in geneal in ompensating itself to guaantee te spin. As to te explanation of absoption by atom and Compton s effet and te diffation beavio, inlude ow a poton tain an pass toug a pinole o slit wit smalle aea ave been disussed in te fome pape (4). By te way, if tee ae somewat diffeent statements in ou diffeent papes about same ting, please take tis pape s. Aknowledgement: Speial tanks to my wife, Pei Min. He saifie as given me mu time to omplete my favoite jobs. efeenes (1) Enio Femi, Quantum Teoy of adiation, evs. Moden Pys., 4, 87 (193). ().P.Feynman, Quantum Eletodynamis, W.A.Benjamin,In. (1961) (3) iad Fitzpatik, Maxwell s Equations and te Piniples of Eletomagnetism, Infinity Siene Pess (7). (4) Cen Sen Nian, Poton, aged patile and anti-aged patile, Adv. Studies Teo. Pys., Vol. 3, 9, no. 9-1, (5) Cen Sen Nian, Te fomation of spin in ±aged patiles and diffeent intepetation fo te wave funtion, Adv. Studies Teo. Pys., Vol. 4, 1, no. 9-1, eeived: Apil, 11