Photon, Charged Particle and Anti-charged Particle

Transcription

1 Adv. Studies Teo. Pys., Vol. 3, 9, no. 11, Poton, Caged Patile and Anti-aged Patile Cen Sen nian Dept. of Pys., (National) Hua Qiao Univ. Quanzou, Fujian, P.. Cina Abstat: Based on Maxwell teoy and quantum teoy, we pove tat te lateal bounday of a poton wave tain must be oveed by a membane of pefet efletion, povided we aept te idea tat a monoomati eletomagneti wave is omposted of ν potons. Depending on te meanial and eletomagneti popeties of te membane, we pove and explain in detail wee and ow does te ±ages ome fom in te pai podution of aged and anti-aged patiles and te age distibuted inside anyone of tem. We also pove and explain in detail ow does an eleton of atom aptues a poton wave tain totally (o satteing a pat of it in addition) and move togete in a ige enegy level. And ontay, ow does it adiate a poton wave tain and bak to te gound state. At last we pove tee is a pysial meanism tat makes te poton wave tain aving te ability to pass toug a pin ole o a slit (slits) natually. Te diffation pattens ae te podution of a poton s self-intefeenes and inoeent supeposition of potons despite of ow mu diffeene and unstable tei initial pases ae. Keywods: poton wave tain, obsevation plane, membane, adiation pessue, aged spial-alves, aged spial, skin, lepton, adon. Content (I). Intodution (II). A poton wave tain must be oveed by a membane of pefet efletion as lateal

2 4 Cen Sen nian bounday. (III). Impotant meani and eletomagneti popeties of te membane (IV). Extenal podution of aged and anti-aged patiles and te ages distibuted inside of tem. (V). How does an eleton of atom absob and adiate a poton. (VI). Eleton-positon anniilation (VII). Wat meanism makes a single poton wave to pass toug a pinole o a slit. (VIII). Conlusion (I). Intodution 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 as a basi. Now, fo a monoomati speial eletomagneti wave fom te point soue at z = : E ( ϑ, ϕ) t' z E( ϑ, ϕ,, t ' ) = os π ( ) ( t ' T, z f ) (1) z T λ λ z, ϑ π, ϕ p π ae adial oodinate, elevation angle and azimut angle espetively. If we aept te idea tat it is omposted of enegy must be inside a tin beam of onial wave tain wit lengt ν potons, ten a poton s = A, Wee η te adiation lifetime (3) 3 3 ε of poton A =, index of efation η = ε π ν and M AB M AB is a quantity just involved wit atomi emission and absoption. et be te distane fom ental axis and te adius of wave sufae all ounted along geat-ile. Te eletomagneti enegy inside tis tain an be expessed as z z t z t z dz 1 εe ( ) os π α μ H ( ) os π α π d + T λ + + T λ () Wee π = Ω z, Ω is te solid angle tat wave sufae suspends at te point soue. If we now ty to teat tis tain aving enegy ν as a poton and totally depend on Maxwell teoy, quantum teoy and a seies of logial infeenes, ae tee any inteesting esults we will ave? Ae tey wot to be fute studied

3 Poton, aged patile and anti-aged patile 43 teoetially and deteted by expeiments? (II). A poton wave tain must be oveed by a membane of pefet efletion 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 (4) : z U&& ( t ) μ H = E sin θ (3) ε z Owing to symmety, a poton must ave iula wave sufaes and te distibution funtions of field magnitude E and H ove tem ae symmetial wit espet to te axis of momentum P= K ( k = 1/ λ ). Aoding to equation (3), 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 E ( ) 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 plane if a plane wave passes toug it pependiulaly. Of ouse, fo a speial wave, te obsevation 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 te point soue at z = wit amplitude E ( ) ( ) popagates along z-axis an be expessed as 1 E ( ) E (, t ' ) = t' z os π ( ) ( 1, z T λ t ' T, z f ) (4) λ 1 Sine = π and Ω z z is an angle suspends at z =, ten and E ( ) ae funtions of ϑ and ϕ, disegad of te adial oodinate z. Expession (4) satisfies diffeential wave equation.

4 44 Cen Sen nian Sine E( ) is always an even funtion and equal to at bounday = expanded in Fouie seies as follow: E ( ) = b j-1 π j = 1 let j = 1 b j-1 os ( j 1) os π ( j 1) 4 Λ, it an be ( Λ = 4, ) (5) Te wave funtion (4) will make a stationay vibation on te obsevation plane loated at z o in te spae oupied by wave tain at tat time. Its funtion is E ( ) o t E(, zo, = os π z T o E, ( o, t T ) (6) λ let ( Hea we ave osen te zeo point of t, so as initial pase of osine funtion equal to zeo at z o -plane. And let (, z, E o = ( E, fo simplify of notation. Instead equation (5) into (6), we ave 1 E (, = z o j = 1 b j-1 os π ( Λ j 1 let E+ ( V + E ( + V t 1 ) + T zo j = 1 b j-1 os π ( Λ j 1 + T t ) Λ (Λ j-1 = ( j 1), Λ = 4o, V Λ =, o, T t T ) (7) λ Fo any dietion of on te obsevation plane (tin laye), E+ ( V is te sum of all taveling waves towad te igt. And E ( + V is te one towad te left. Tey move towad ea ote and eflet pefetly at te bounday points wit 18 pase loss ( E = H = tee). Te identity of equations (6) and (7) means tat te wave enegy of a tin laye wo passes zo -plane at time t 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 obsevation plane at same time. Tey ae matematially equivalent. An inteesting question is wete te tansvesal taveling eletomagneti waves eally

5 Poton, aged patile and anti-aged patile 45 exist ove te obsevation 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 of 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 (5) 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 (3). If a poton wave is linea polaized, te oeffiients in equation (7) 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 (7) must be 1 π te statistial mean values in etain alf peiod ( E sinθ dθ E π = ). It π makes te oeffiients same along any -dietion on same wave sufae. E ( ) Sine π d = E ( ) Ω ( ) d( ) and te limits of tis integal z is 1, so te total enegy ove any wave sufaes ae equal and independent of z. Te invese squae law of enegy adiation is still valid fo tis poton wave tain. A poton s enegy is estited witin te solid angle Ω subtended at te point soue z = 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 ( o β, β f ) along te iumfeene of obsevation planes ae always existed. Te outwad Poynting vetos pependiula to te lateal sufae of te spae tat poton oupied S (, θ, = E (, θ, H (, θ,, ( θ π, z ) ae geneally diffeent to zeo ove wole bounday. Fo simplify of notation, we use (, θ,...) to epesent (, θ,...) wee p β ee and in te following. Sine eletomagneti adiation an not eflet 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 oiginal eleton o nuleus tat tey podue te poton.

6 46 Cen Sen nian Futemoe, we ave anote impotant onlusion. Vaying field is not te suffiient ondition fo te podution of a poton. It is just a neessay ondition. Anote neessay ondition is tat te soue an povide te mateial (enegy) to be membane. It seems tat is te eason of wy te eleton of atom in gound state is stable, sine tee is not any lowe state pemit im to loate so as no exta enegy of eleton an povide te neessay membane. All esultant tansvesal waves on obsevation planes ae adial, equation (7). Te time ate of ange of momentum at bounday is S (, θ,. Wee θ is te angle between te adius and te absissa on te obsevation plane and we omit te suffix of o ea and late. It will ause te existene of entifugal pessue of same amount Q mem (, θ, fom all points of te ove membane. Q mem (, θ, = S (, θ, ( θ π, z ) (8) On te ote and, any beam of te tansvesal taveling wave E+ ( V o E ( + V ) is seto-like. In a seto, te enegy flow passes toug te aea i δθ δ z equal to te one toug δθ δ z k. Tat is S(, θ, δθ δ z S(, θ, δθ δ z ( p p p ) (9) i i k Combining wit equations (8), (9), we ave te equilibium equation between two opposite sufaes δθ δ z and δθ k δ z in te same seto spae Q outwad (, θ, δθ δ z = Q mem (, θ, δθ δ z i k Sine S E ( p p, θ π, z ) (1) ε lim =, let i =, k and E = E( ), ten equation (9) μ k gives te elation between amplitudes E of and as follow E ( ) = E ( < < ) E ( ) = (11)

7 Poton, aged patile and anti-aged patile 47 Te late bounday ondition as been disussed at te beginning of tis pape. Equation (11) is te distibution funtion of E ( ) on te wave sufae. It is disontinued at bounday. Te expansion poess of wave sufaes is quasi-stati, equation (11) is valid duing wole expansion poess of. To substitute equation (11) into (4), we ave te wave funtion of a poton emmited fom te point soue fa enoug. E t z E(, = os π ( ) (, t T, z f ) (1) z T λ λ Te neessay ove membane plus eletomagneti wave tain inside fom an independent stutue. It is easy to imagine tat unless te tension inside te membane is oveloaded by etain stong effet and beak te membane (we will disuss late), te poton wave of su stutue seems to ave no possibility to split into two o moe pats of diffeent beavio. Tis stutue makes te integity of te poton. So, unde geneal ondition, if not being absobed by a media it met, an inident ν -poton wave an only be eite efated o efleted ompletely, neve be bot of tem wit sameν. Equation (1) efes to tat su a poton s eation pobability wit patile at wave s ente is fa geate tan ote pats of it. (III). Impotant meani and eletomagneti popeties of te membane Figue 1 is a sket map of te distibution of E( ) on te wave sufae,. et θ be te angle of adius fom absissa OF. 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 ε T (, θ ) = S(, θ ) = E os θ (13) μ Te imum appens at points A and F, T (,) = TA (, π ) T = F = ε μ. E Tis elation is valid fo ote A and F points of all wave layes. Conneting all tese points A and F espetively, tey fom two paallel teads, A-spial and F-spial

8 48 Cen Sen nian (igt-anded o left-anded) on te lateal sufae of te iula polaized wave tain. Figue 1 Te mateial of membane must be easy to ange its sape duing popagation, so we suppose it is a liquid-like mateial aving almost onstant volume. Te aea of oss-setion π ( out ) π ς and te tiknessς = out, so Γ ς = (14) Γ is a onstant. et Σ be te imum nomal stess on te oss-setion. Sine T = ς Σ and equation (13), it gives ε Σ = E (15) Γ μ et te sum of time aveage of equation () and te enegy of membane equal to ν, ten we ave 3ν 3 λmem η E ( ) d = let f (ν ) (16) π ε A πηε λ mem dz Wee λ mem is te mass of membane pe unit lengt of te poton wave tain. Instead (11) into (16) and letη = 1, te

9 Poton, aged patile and anti-aged patile 49 E = f ( ν ) (17) Equations (15) and (17) efe to tat fo a given ν, Σ is onstant along A-spial and F-spial in fee spae despite of te magnitude of. Fo a poton of iula polaized wit givenν, tee ae fou impotant popeties of its membane: (i) Te imum stess Σ is always appened along A-spial and F-spial on te poton s lateal sufae despite of te magnitude of. So, exept tee is a vey stong extenal effet to make Σ beome bigge tan ultimate tensile stengt (unknown but must exis and ty to beak te membane, te poton will always keep its integity. (ii) Sine sufae density of age σ on inne side of te membane equals to Dn ( = ε En ), so, fo te uppe spial-alf of it. Fig 1, te absolute value of σ θ is σ θ = ε E sinθ ( θ π ) (18) Te total negative age in uppe spial-alf is π θ = q = d z σ dθ θ = ε E 3ε = 4π ν M AB (19) Hee we neglet λmem -tem in equation (16), sine it must be fa smalle tan te fist tem. Te lowe alf as same quantity of positive age. Just like te Σ, fo a given ν, quantity q in te ±aged spial-alves always exists and keeps unanged duing inease in popagation. (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 of iumfeene is d dθ. Te wok down in te δ z -laye of te wave tain against tension fom oiginal nuleus dimension to final is

10 41 Cen Sen nian δ W π = δ z 4 T (, θ ) d dθ = Ψ δ z f ( ν ) ln () Ψ is a onstant. Sine wok down against te tension only spends a small pat of a poton s enegy, so fo any givenν, ln and ten te adius of poton wave sufaes must be uppe bounded. A poton wave tain will at last beomes exatly (not appoximately) ylindial wit adius. Tis will make te poton tat ame fom te end of ou univese ten billion yeas ago still as a finite, not infinite wave sufae. (iv) A iula polaized wave wit vibating fequeny ν will ause a otating E,H fields on te obsevation plane of same fequeny ν. Tis is also te otating fequeny of points A,F and te otating fequeny tat te ±aged spial-alves sow on te same plane despite of te magnitude of wave sufaes. If etain meanism stops te enegy of poton fom ligt speed to zeo o almost zeo, stong ompession of fields will make Σ oveload and lage tan ultimate tensile stengt, ten it will be possible to ave te membane quikly and entiely boken along A-spial and F-spial. Ten (a) te potential enegyδ W in any aged δ z -alf ing of te membane will onvet to kineti enegy and stongly soten its iumfeene into oiginal nuleus dimension and even smalle. Te two symmetial ±aged spial-alves will beome two tinnest symmetial ±aged paallel teads, I-spial and C-spial. (b) Two spial-alves and two-spials ave same adius and same inetia duing tis ontation. So, tese two±aged spials will sow same angula fequeny as two spial-alves on te obsevation plane. Tis is to say tat fo te ente of mass efeene system, ±aged I-spial and C-spial will otate wit te same ν and same dietion of te poton wo podues te fome. Owing to te onsevation of angula momentum, te pai of ±aged spials podued as same angula momentum as te poton. Te dietions of magneti fields podued by tese two ±aged spials espetively ae opposite. It makes tem epel ea ote and ty to sepaate along tei axis. Can tey beak up? It is a miosopi poess and te quantum onditions must be onsideed.

11 Poton, aged patile and anti-aged patile 411 (IV). Extenal podution of aged and anti-aged patiles and te ages distibuted inside of tem. Wen a iula polaized ν poton aives at te egion of a eavy nuleus and begin to be absobed, tee will appen: (i) et be te diamete of te egion. Duing Absoption appens at te fist wave laye, te outwad Poynting veto fom tis egion S (, θ, = E (, θ, H (, θ, and ten Q outwad (, θ, ae all equal to zeo. Equation (1) gives δθ δ z Q outwad (, θ, z, t ) = p δθ δ z Q membane (, θ, (1) Q membane (, θ, will foe te emained enegy of te fist laye to move tansvesely towad aea and ompess te adius of wave sufaes to. Sine evey time of absoption always makesq outwad (, θ, =, so tis equation will old fo wole poess of being ontated. Finally, te membane of te fist laye will wap, te point of absoption. We an imagine tat ote layes will do so in ode of pioity and at last foms two vey sot and small ±spial-alves otated wit fequenyν ; (ii) In te meantime, te layes must be suddenly stopped fom ligt speed. Stongly ompess of te fields will make E,H and Σ inease geatly and beak ±spial-alves into ±spials; (iii) Sine boken of a poton and been split into two independent patiles wit ±aged espetively is a miosopi poess, it an appen only if te following quantum onditions be satisfied (a) Te q in equation (19) equals to j e ( j = 1,,... n). O 3ε ν M AB = ( j = 1,,... n) () 4 jπ e (b) Total enegy of one spial-alf is equivalent to te mass of etain elementay patile m p, su as leptons and adons (wit spin 1 ). Extenal podution of te pai of eleton and positon is an example. Fo a iula polaizedγ -poton, if ν = me and AB M satisfy () fo j = 1, ten tis pai

12 41 Cen Sen nian will be podued. By magneti epel, tey,±spials, move towad opposite side along its axis in te ente of mass efeene system, but otate in same dietion as poton polaized. Te distibution of ages inside eleton s (positon) p 1 15 m egion is a aged otating spial. Tee ae two possible oientations, left-anded and igt-anded fo eleton and positon espetively. Aoding to onsevation law of angula momentum, te spin of ±eleton podued 1 is ea. We ave notied: (a) Tat otating fequeny of ±spials pai equals to its own m matte wave fequeny e ν pai = ; (b) Wile ±spials begin to deta, epulsion foe between te ages in same spial will expand its diamete to inease moment of inetia and te otating fequeny of tem will ten begin to deease until tey ae totally split. We an easonably onside tat te last fequeny must be te fequeny of an eleton s matte wave ν e = m e. As a fute guess, te pit of te spial as etain unknown elation wit its matte wave lengt λ =. Wee p e is te momentum of te eleton. As anote fute imagination: fo a iula polaized γ -poton, if p e ν = ( m + p me ) and AB M satisfy () fo j =, ten two pais of ± spials will podue. Tese ae ±aged eleton and ±aged poton. Consevation of momentum pevents tem to split into fou independent spials wit 1 -spin ea. Pobably tey will eombine into two mixed double spials as following: a pai of poton-spial wit eleton-spial and a pai of antipoton-spial wit positon-spial. Tey ae 1 1 neuton and anti-neuton of spin +. (V). How does an eleton of atom absob and adiate a poton. Fo simpliity, we just disuss te simplest ydogen atom. (i). et a iula polaized

13 Poton, aged patile and anti-aged patile me poton as ν = ( ), wee ydbeg onstant = and intege n is 1 n 8ε given. As well known, wen te poton is absobed by te eleton of ydogen atom in gound state, te eleton jump to a ige state E =. n In tis ase, wat will appen fo te poton and eleton? Sine ν pp m, above two ±aged spials an not split to beome two independent ±aged patiles. Wen te poton at up te eleton and to be absobed, two vey sot and small otating ±aged paallel spials will losely wap te bounday of eleton, keep otating wit oiginal ν and move togete wit te eleton in te exited state E =. n Te bounday of eleton is also te bounday of its inne foe tat oveomes inside eleti epulsion and keeps eleton s integity. Its edge ation an keep ±aged spials moving wit im, but not stong enoug to make it stable. One a distub appens, te otating ±aged spials will be dopped off and te otating field E podued by te two end points of tei spials will exite and beome a poton of 1 1 ν = ( ). At te same time te eleton etuns to te gound state. 1 n (ii) If poton s enegy ν n + α = ( + α), wee p α p if n finite; 1 n n ( n + 1) o α f if n, (3) Tis poess of Compton Effet an be figued in moe detail as follow. et n+ α be te oiginal lengt of ±aged spials. Sine te enegy distibutes unifomly along it. So, if we imaginaily divide te lengt into two pats wit te 1 1 ( elations n : α = ) :α and n+ α = n + α 1 n 1 1 n possess enegy ( ) and α possess 1 n. Ten, ±aged spials of lengt α. Te aate of enegy 1 1 levels makes te eleton an only absob te amount of enegy ( ), te 1 n e

14 414 Cen Sen nian n -pat beomes a new ±aged spials ound te eleton wit new otating 1 1 fequeny ν n = ( ) and jump wit te eleton to te state E n = ; In 1 n n te same time, te est pat α will be ejeted. Tis otating ±aged spials will α exite and beome itself a new poton wit ν = to satte. Geneally speaking, an eleton (positon) is mainly onsisting of a otating spial wit age e, fequeny m ν = e and spin 1. It may be oveed by a skin of otating±aged spials. We name it as skin just beause it losely waps te eleton and te ode of magnitude of its enegy is about 5 1 in ompae wit te inne one. Poton to be absoption and adiation by te eleton all appen at te skin. Tey ae te poesses of polong o ut off te lengt of ±aged spials in te amount of poton s ν. (VI). Eleton-positon anniilation Fo onvenient, we take te system onneted wit te ente of masses as ou fame of efeene. et us selet z-dietion pependiula to te pape and x-axis paallel to veloity V, (Fig.). We onside te plane motion of ±aged patiles and let be te initial pependiula distant between tem. If tey satisfy te following ondition V + Figue V

15 Poton, aged patile and anti-aged patile πε q 4 = 4π m p ν (4) Te aged patiles beome a otating dipole. As an example, if we onside te eleton and positon and let m e ν =, q = e, m p = me, ten ν = Hz, 14 = m. Fo su small otating dipole, only te otating field E between two aged end points an dietly exite a pai of iula polaized eletomagneti waves (one igt-anded and one left-anded) of same fequeny ν wit membane mateial towad ± z-dietions espetively. Unde te above onditions, te quantum popety will ause te anniilation of te pai of eleton and positon. Sine te mass and te age of membane will unifomly distibute along te axis of poton wave tain. So te deease of tei oiginal masses (inluded skin ) and ages wit z time t o wit z = t must be linea. Tat is m = m p (1 ) and z q = q (1 ). In ode to maintain te fequeny ν of two waves unanged, we z q = q (1 ) 1 need te atio z 1 z 3 o = (1 ). Ten 3 3 z (1 ) olds fo 3 = (1 ) z pp. It means tat two wave tains podued is onial altoug te angle of it will gadually ange. (VII). Wat meanism makes a single poton wave to pass toug a pinole o a slit. If tee is a flat seen wit a pinole of widt enteed at z = z and pependiulaly loated aoss z -axis. Aoding to Maxwell teoy, wen a z-dietion plane poton wave eaes z, noting an pevent te vaying E and H in te ental egion of te wave to exite a adiation toug te empty ole. In te mean time, te oute ollow ylindial pat will also oss pependiulaly into te medium of dieleti onstantε. et us disuss wat will appen in te fist δ z laye. Ten we an easily imagine te stoies of te following layes. Te

16 416 Cen Sen nian invade wave keeps oiginal dietion of popagation. Te E, H of it is of ouse still paallel to te sufae of te seen. Sine ε E = μh, wat we need to deide is only one of te E ( ) o H ( ) in te medium (Poton an not be split, te well known bounday onditions is not available ee). Te adius of poton wave sufae as no eason to ange in tis nomal inidene. So, aoding to equation (16), fo a given fequenyν, te onsevation of a poton s enegy makes an invaiant η E ( ), ( p ) between te media and vauum. Tat is η Emedium ( θ, ) = Evauum ( θ, ), ( p ). (5) On te ote and, we ave Eole ( θ, ) = Evauum ( θ, ), ( ) (6) Sine E vauum ( θ, ), ( ) is ontinued along te iumfeene of = on te sufae of seen, so te mutual Poynting vetos fom two sides of te ylindial intefae of te pinole ave te following elation S inwad ( θ,, = ε E μ medium ( θ,, = ε E μ ole ( θ,, = S outwad ( θ,, ( θ π ) (7) Hee we take μ = μ appoximately. Divided by te speed in medium and in ai η espetively, we ave te elation between te inwad and outwad adial adiation pessues along te sufae Q vauum ( θ,, < Q medium ( θ,,, ( θ π ). Combine wit equation (8), along te inne sufae of te ole, we ave δθ δ z Q vauum (, θ, z, t ) p δθ δ z Q membane (, θ, (8) We aive at te following onlusion. Te entifugal pessue fom membane will foe te enegy witin ollow ylindial pat of te fist δ z laye to onentate towad te ente egion. Tis poess of enegy tansfe tansvesely and te ontation of wave sufaes must be also a quasi-stati poess just like te poess of expansion of wave sufaes.

17 Poton, aged patile and anti-aged patile 417 Tis is to say tat te equation (11) must be valid duing te fist wave laye s ontation to te egion ( < < β ), β f. Afte ten, equation (8) appens again and again fo te new suessive egions. Tis is to say tat equation (8) will valid fo all te egions ( < < kβ ), ( k = 1,,3,...) until wole laye onentate into. Tese suessive poesses of ontation and poton moving fowad poeed simultaneously. All ote layes will do so. Te wave funtion of poton witin te pin ole is t z E(, = E os π ( ) (, t T, z f ) (9) T λ λ Te wave funtion fa away te pin ole is equation (1) wit elation E = E. et a slit oinides wit y-axis and a poton wave aims at it. Owing to simila eason of equation (8), te sufaes will be ontated. Membane pessues will oppess te wave sufaes to ontat along x-dietion into te slit to fom a non-unifom line soue. et be te adius of te wave sufae, take its ente as oigin of y-axis and teat E as te enegy pe unit aea on te wave sufae, ten, te enegy at ( y, y + dy) of te slit (onentated tansvesely fom te tin egion of ψ y oodinate y on te iula sufae) is E ln(tan ) dy. Wee ψ = sin 1, π π ( ψ ). Beind te pin-ole and slit, tey will fom tei own diffation pattens on te seen. Te maosopi patten is te inoeent linea supeposition of potons. Te patten of diffation on obsevation plane is one to one oespondent to te distibution of field intensity E on its wave sufaes. Tey ae te distibutions of a poton s pobability of inteation wit patile. One absoption by a patile appens at etain point on te wave font, adiation pessue fom membane will foe te est enegy to tansfe tansvesely towad te point. Ote sufaes will do so and a poton s enegy ν will be totally absobed by te patile. (VIII). Conlusion As long as we aept te idea tat a poton is a tin beam of onial wave tain wit

18 418 Cen Sen nian enegy ν and lengt = A, we ave poved tat tis tain must be oveed by a η membane of pefet efletion wit zeo est mass. Te membane must be tansfeed fom te enegy of eleton o nuleus tat emits te poton. Su stutue of poton guaantees its integity in geneal iumstanes Te neessity of membane efes to tat te vaying fields E,H itself is not a suffiient but a neessay ondition fo exiting a poton wave. Te stability of te eleton of atom in gound state is beause of tee is not any lowe state pemit im to desent, so as no exta enegy of eleton an povide te neessay membane. Te membane is divided by two spial-lines of equal imum nomal stess Σ into two pats. Tey ontain same amount of ages q but in diffeent sign. Fo a given ν, bot Σ and q keep invaiant despite of te magnitude of. One absoption appens, te wave speed is suddenly stopped fom to almost zeo. Stongly inease of field intensity will beak te membane and beome te poton into two sotest and tinnest symmetial ±aged otating spials wit same ν and spin. (i). If quantum onditions (a), (b) in (IV) being satisfied, te two spials will split into two independent aged and anti-aged patiles wit spin 1 and spial-like distibution of otating age inside. (ii). If poton s fequeny ν is smalle tan quantum ondition (b) and satisfies equation (3), ten te pai of otating ±aged spials just an wap te eleton as skin to move togete in a ige enegy level (o satteing te exta-pat to be a new poton wit lowe fequeny in addition). adiation a poton is a evese poess. Te pai of ±aged spials lag beind te eleton by etain distubs and its otating aged end points will exite a otating field and povide te mateial of membane and at last beome itself (o a pat of itself) a poton. Te eleton will bak to lowe state even gound state in te same time. Poton to be absoption and adiation by te eleton ae all appened at te skin. Tey ae te poesses of polong o ut off te lengt of ±aged spials wit te amount of poton s ν. Te poton wave tain of su stutue as te ability to pass toug a pin-ole o a slit(s) and foms its own diffation patten on wave sufaes by self-intefeene. Te distibution funtion of E and H on a poton s wave sufaes unde tese iumstanes ae diffeent to te equation (11) until fa enoug fom te pin-ole o a slit(s). All potons finges beind tem ae tei inoeent supeposition. Su poton wave tain as a dual natue.

19 Poton, aged patile and anti-aged patile 419 Aknowledgement: Deep tanks my wife, Pei Min fo long time pofound suppot and many tanks Ms. i Yan Min (CangAn U., Xian, PC) fo dawing figues. efeenes (1) Enio Femi, Quantum Teoy of adiation, evs. Moden Pys., 4, 87 ( 193 ). ().P.Feynman, Quantum Eletodynamis, W.A.Benjamin,In. (1961) (3) Gant. Fowles, Intodution to Moden Optis, nd ed., Dove Publiation, In, NY (1989) (4) iad Fitzpatik, Maxwell s Equations and te Piniples of Eletomagnetism, Infinity Siene Pess (7). eeived: May, 9