The photon model and equatons are derved through tmedoman mutual energy current Shuang-ren Zhao, Kevn Yang, Kang Yang, Xngang Yang, (Imrecons Inc, London Ontaro, Canada) Xnte Yang (Avaton Academy, Northwestern Polytechncal Unversty, X an, Chna) Abstract: In ths artcle we wll buld the model of photon n tme-doman. Study photon n the tme doman s because the photon s a short tme wave. In our photon model, there s an emtter and an absorber. The emtter sends the retarded wave. The absorber sends advanced wave. Between the emtter and the absorber the mutual energy current s bult through together wth retarded wave and the advanced wave. The mutual energy current can transfer the photon energy from the emtter to the absorber and hence photon s nothng else but the mutual energy current. Ths energy transfer s bult n 3D space, ths allow the wave to go through any 3D structure for example the double slts. But we have proven that n the empty space the wave can been seen approxmately as 1D wave wthout any wave functon collapse. That s why the lght can be seen as lght lne. That s why a photon can go through double slts to have the nterference. The dualty of photon s explanted. We studed the phenomenon of the wave functon collapse. The total energy transfer can be dvded as self-energy transfer and the mutual energy transfer. In our photon model the wave carres the mutual energy current s never collapse. The part of self-energy part has no contrbuton to the energy transferrng. Furthermore, we found the equaton of photon should satsfy whch s a modfed from Maxwell equaton. From ths photon equaton a soluton of photon s found, n ths soluton the electrc felds of emtter or absorber must parallel to the magnetc feld. The current of absorber must perpendcular to the emtter. Ths way all self-energy tems dsappear. Energy s transferred only by the mutual energy current. In ths soluton, the two tems n the mutual energy current can just nterpret the lne or crcle polarzaton or spn of the photon. The concept of wave functon collapse s avoded n our photon model. Keyword: Photon, Quantum, Advanced wave, Retarded wave, Poyntng theorem, mutual energy 1. Introducton The Maxwell equatons have two solutons one s retarded wave, another s advanced wave. Tradtonal electromagnetc theory thnks there s only retarded waves. The absorber theory of Wheeler and Feynman n 1945 offers a photon model whch contans an emtter and an absorber. Both the emtter and the absorber sends half retarded and half advanced wave [1,2]. J. Crammer bult the transactonal nterpretaton for quantum mechancs by appled the absorber theory [3,4,5] n 1986. In 1978 Wheeler ntroduced the delayed choce experment, whch strongly mples the exstence of the advanced wave [6]. The delayed choce experment s further developed to the delayed choce quantum eraser experment [7], and quantum entanglement ghost mage and the ghost mage clearly offers the advanced wave pcture [8]. The author has ntroduced the mutual energy theory n 1987 [9-11]. Later the author notced that n the mutual energy theory the receve antenna sends advanced wave [12] and
begn to apply t to the study of the photon and other quantum partcles [13,14]. The above studes are n Fourer doman whch s more sutable to the case of the contnual waves. The authors know photon s very short tme waves, hence decded to study t n the tme-doman. The goal of ths artcle s to buld a model for photon, found the equatons of the photon. Some one perhaps wll argue that photon s electromagnetc feld t should satsfy Maxwell equatons, or photo s a partcle t should satsfy Schrodnger equatons, why to fnd other equatons? Frst we are lookng vector equatons whch photon should satsfy. These equatons cannot be Schrodnger equaton. Second we say nfnte photon become lght or electromagnetc feld whch should satsfy Maxwell equatons. Hence Maxwell equatons are a macrocosm feld. In mcrocosm, only photon we are very dffcult to thnk t stll satsfes the Maxwell equatons. We try to fnd the equatons for photon to satsfy, from whch, f we add all equatons for a lot of photons, we should obtan Maxwell equatons. 2. The photon model of Wheeler and Feynman In the photon model of Wheeler and Feynman there s the emtter and absorber whch sends all a half retarded wave and half advanced wave. The wave s 1-D wave whch s plane wave send along x drecton. Lke wave transferred n a wave gude. For bother emtter and the absorber, the retarded wave s sent to the postve drecton along the x. The advanced wave s sent to the negatve drecton along x. We take color red to draw the retarded waves. We take color blue to draw the advanced wave, see the Fgure 0. For the retarded wave the arrow s drawn nto the same drecton of the wave. For the advanced wave the arrow n the opposte drecton of the wave (snce the energy transfers n the opposte drecton for the advanced wave). For the absorber, Wheeler and Feynman assume the retarded wave send by absorber s just negatve (or 180 degree of phase dfference) compare to the retarded wave send from the emtter. The advanced wave sent from the emtter s just negatve (or 180 degree of phase dfference) of the advanced wave sent by the absorber. See Fgure 1. Hence, In the regons I and III, all the waves are canceled. In the regon II the retarded wave from emtter and the advanced wave from absorber renforced. Fgure 0. The Wheeler and Feynman model. The emtter sends retarded wave to rght show as red arrow. The emtter sends advanced wave to the left whch s blue. We have drawn the arrow n the opposte drecton to the advanced wave. Ths s same to the absorber. However the retarded wave of the absorber s just the negatve value of the retarded wave (or t has 180 degree phase dfference). The advanced wave sent by the emtter s also wth negatve value of that of the absorber (or has 180 degree
phase dfference). Hence the n the regon I and III the waves cancel and n the regon II the waves renforce. All ths model looks very good and t s very success n cosmography, but t s dffcult to be beleve. Frst (a) Why retarded wave s sent by the emtter to the postve drecton and the advanced wave s sent to the negatve drecton? As I understand the wave should send to all drectons, n 1- dmenson stuaton should send to the postve drecton and send to the negatve drecton. (b) Why the absorber sends retarded wave just wth a mnus sgn so t can cancel the retarded wave of the emtter? It s same to the Emtter, why t can send an advanced wave wth mnus sgn so t just can cancel the advanced wave of the absorber? (c) 1-D model s too smple. The wave s actually send to all drecton and should check whether ths model can be used also n 3D stuaton. What happens f ths model for 3D? These questons perhaps are the real reasons that Wheeler and Feynman theory and all the followng theory for example the transactonal nterpretaton of J. Crammer cannot be accept as a manstream of photon model or the theory for nterpretaton of the quantum mechancs. We endorse the absorber theory of Wheeler and Feynman. In ths artcle we wll ntroduce a 3D tmedoman electromagnetc theory whch suted the advanced wave and retarded wave to replace the 1-D photon model of Wheeler and Feynman. In ths new theory the mutual energy current wll play an mportant role. 3. Poyntng theorem For a photon, all the energy has been receved by one absorber, t s clear the feld of the photon cannot fully satsfy the Maxwell equatons. Because accordng Maxwell equaton the emtter wll send ther energy to whole space nstead to only one pont. However we beleve the equatons of photon should be very close to Maxwell equatons, that means even n the mcrocosm the Maxwell equaton s not satsfed but, for the total feld that means the feld of nfnte photons should stll satsfy the Maxwell equatons. The next step we begn to fnd the equatons of the photon. We started from Maxwell equatons, whch mples that Poyntng theorem s establshed. Hence we started from Poyntng theorem to fnd the theory sut to photon. (1) (E H) n d = (J E + u)d Where E s the electrc feld. H s the magnetc H-feld. J s the current ntensty. s the boundary surface of volume. u s energy saved on the volume. n s unt norm vector of the surface. u s the electromagnetc feld energy ntensty. u s defned as (2) u = t u = E t D + H t B D = εe s the electrc dsplacement, B = μb s magnetc B-feld. u s the ncrease of the energy ntensty. The above equaton s Poyntng theorem, whch tell us the energy come through the surface to
the nsde the regon (E H) n d s equal to the loss of energy (J E)d n the volume and ncrease of the energy nsde the volume ( u) d. We assume the feld as ζ = [E, H] s electromagnetc feld can be a supermposed feld wth retarded wave and advanced wave. Ths means we assume the advanced wave and retarded wave can be supermposed. Ths s not self-explanatory, f we consder many people even do not accept advanced wave. We have known form Poyntng theorem we can derve all recprocty theorems. We also know the Green functon soluton of Maxwell equatons can be derved from recprocty theorems. If we obtan all the soluton of Maxwell equatons, from prncple we should be possble do obtaned Maxwell equatons by nducton. Hence even we cannot derve Maxwell equaton from Poyntng theorem but we stll can say the Poyntng theorem contans nearly all nformaton of the Maxwell equatons. We can say that f some feld satsfes Poyntng theorem, t also satsfes Maxwell equatons. Ths pont of vew wll be appled n the followng secton. 4. 3D photon model n the tme-doman wth mutual energy current Assume the -th photon s sent by an emtter and receved by an absorber. The current n the emtter can be wrtten as J 1, the current n the absorber can be wrtten as J 2. In the absorber theory of Wheeler and Feynman, the current s assocated half retarded wave and half advanced wave. We don t take ther choce, but take a very smlar proposal. We assume the emtter J 1 s assocated only to a retarded wave and the absorber J 2 s assocated only to an advanced wave. The photon should be the energy current sends from emtter to the absorber. Ths proposal, s same as the pcture of the bottom of Fgure 0. It should be notce that n the followng artcle there two knds of fled, one t the photon s feld whch wll have subscrpt, and ths s mcrocosm feld for example J 1, E 1. Another s the feld wthout the subscrpt whch s the macrocosm feld, for example J 1, E 1. Assume the advanced wave s exstent same as retarded wave. Assume the current can produced advanced wave and also retarded wave. In ths case we always possble to dvde the current as two parts, one part created advanced feld and the other part created retarded wave. Assume J 1 produces retarded wave ξ 1. J 2 produces advanced wave ξ 2. Assume the total feld s a supermposed feld ξ = ξ 1 + ξ 2, ξ 1 s retarded wave and ξ 2 s advanced wave. ξ 1 = [E 1, H 1 ] whch s produced by J 1 and ξ 2 = [E 2, H 2 ] whch s produced by J 2. Substtute ξ = ξ 1 + ξ 2 and J = J 1 + J 2 to Eq.(1). From Eq.(1) subtract the followng self-energy tems, (3) (4) (E 1 H 1 ) n d = (J 1 E 1 + u 1 )d whch becomes (E 2 H 2 ) n d = (J 2 E 2 + u 2 )d
(5) (E 1 H 2 + E 2 H 1 ) n d = (J 1 E 2 + J 2 E 1 )d + (E 1 D 2 + E 2 D 1 + H 2 B 1 + H 2 B 1 )d If we call Eq.(3 and 4) as self-energy tems of Poyntng theorem, the Poyntng theorem Eq.(1) wth ξ = ξ 1 + ξ 2 are total feld of the Poyntng theorem. Then the above formula Eq.(5) can be seen as mutual energy tems of Poyntng theorem. It also can be referred as mutual energy theorem because t s so mportant whch wll be seen n the followng sectons. Fgure 1. Photon model. There s an emtter and an absorber, emtter send retarded wave. The absorber sends advanced wave. The photon s sent out n t = 0, n short tme Δt, hence photon s sent out from t = 0 to Δt, the photon has speed c. After a tme T t travels to dstance R = ct, where has an absorber. The fgure shows n the tme t = 1 T, the photon s at the mddle between the emtter and 2 the absorber. The length of the photon s Δt c. The photon s showed wth the yellow regon. Eq.(5) can be seen as the tme doman mutual energy theorem. For photon, t s very small. The selfenergy part of Poyntng theorem Eq.(3-4) perhaps s no sense. Ths s because that the frst part of selfenergy t cannot be receved by any other substance. It can ht some atom, but the atom has a very small secton area, so the energy receved by the atom s so small hence cannot produce a partcle lke a photon even wth very long tme. Because photon s a partcle, all ts energy should eventually be receved by the absorber. Ths part energy current s dverged and sends to nfnte empty space. Hence t ether does not exstent or need to be collapsed n some tme. Ths two possblty wll be dscussed later n ths artcle. For the moment we just gnore these two self-energy tems of Poyntng energy current tems. Assume all energy s transferred through the mutual energy current tems. We know that ξ 1 = [E 1, H 1 ] s retarded wave, ξ 2 = [E 2, H 2 ] s advanced wave. On the bg sphere surface, ξ 1 s no zero at a future tme T to T + Δt. T = R/c, where c s lght speed, R s the
dstance from the emtter to the bg sphere surface. Δt s the lfe tme of the photon (from t begn to emt to t stop to emt, n whch J 1 0). Assume the dstance between the emtter and the absorber s d wth d R. J 2 0, Is at tme T to T + Δt, T T. ξ 2 s an advanced wave and t s no zero at T to (T + Δt) on the surface Hence the followng ntegral vanshes (ξ 1 and ξ 2 are not nonzero n the same tme, on the surface ). In the above calculaton we have assume T s very small compared wth T, hence we can wrte T 0. Hence we have, (6) (E 1 H 2 + E 2 H 1 ) n d = 0 We notce that the above formula s very mportant, that means the mutual energy cannot send energy to the outsde of our cosmos. The above formula s only establshed when the ξ 1 and ξ 2 are one s retarded wave and another s advanced wave. If they are same wave for example both are retarded waves the above formula s not establshed. Ths s also the reason we have to choose for our photon model as one s retarded wave and the other s advanced wave. Hence from Eq.(5) and (6) we have (7) (J 1 E 2 )d = (J 2 E 1 )d + (E 1 D 2 + E 2 D 1 + H 2 B 1 + H 2 B 1 )d The left sde of Eq.(7) s the sucked energy by advanced wave E 2 from J 1, whch s the emtted energy of the emtter. (J 2 E 1 )d s the retarded wave E 1 act on the current J 2. It s the receved energy of J 2. (E 1 D 2 + E 2 D 1 + H 2 B 1 + H 2 B 1 )d s the ncreased energy nsde the volume. In the tme t = 0 to the end t = T + Δt, ths energy s begn wth 0 and n the end tme s also 0. Ths part can show the energy move from emtter to the absorber and n a partcle tme the energy stay at the place n the space between the emtter and the absorber. Consder our readers perhaps are not electrc engneer, we make clear here why we say the left of the Eq.(7) s the emtted energy. In electrcs, If there s an electrc element wth voltage U and current I, and they have same drecton, we obtaned power IU. Ths power s loss energy of ths electrc element. If U has the dfferent drecton wth current I or t has 180 degree phase dfference. Ths power s an output power to the system,.e. ths element actually s a power supply. In the power supply stuaton the suppled power s IU = IU. Hence IU express a power supply to the system. Smlarly (J 2 E 1 )d s the loss power of absorber J 2. (J 1 E 2 )d s the energy supply of J 1. Assume 1 s a volume contans only the emtter J 1. In ths case snce there s a part of advanced wave and retarded wave and the retarded wave close the lne lnked the emtter and absorber are synchronous, the other part of energy are dfferent phase dfference and perhaps cancel each other. Hence ths part of energy current should not as 0,.e., (8)
(E 1 H 2 + 1 E 2 H 1 ) n d 0 Fgure 2., Red arrow s retarded wave, blue lne s advanced wave. The arrow drecton shows the drecton of the energy current. The emtter contans nsde the volume 1. 1 s the boundary surface of 1. The energy current consst of the retarded wave and the advanced wave. Eq.(5) can be rewrtten as, (9) (J 1 E 2 )d = (E 1 H 2 + E 2 H 1 ) n d 1 1 + (E 1 D 2 + E 2 D 1 + H 2 B 1 + H 2 B 1 )d 1 In ths formula, (J 1 E 1 2 )d s the emtted energy. (E 1 H 2 + E 2 H 1 ) n d s the energy current from the emtter to the absorber. (E 1 D 2 + E 2 D 1 + H 2 B 1 + 1 H 2 B 1 )d s the ncrease of the energy nsde volume 1. Fgure 2 shows the pcture of ths stuaton. The red arrow s retarded wave. The blue arrow s the advanced wave. For retarded wave, the arrow drecton s same as the wave drecton. For the advanced wave the arrow drecton s n the opposte drecton of the wave. In the Fgure 2, we always draw the arrow n the energy current drectons. Assume 2 s the volume whch contans only the absorber J 2, Eq.(5) can be wrtten as (10) (E 1 H 2 + 2 E 2 H 1 ) n d = (J 2 E 1 )d 2 1 + (E 1 D 2 + E 2 D 1 + H 2 B 1 + H 2 B 1 )d 2
Fgure 3. Choose the volume 2 s close to the absorber. Red arrows are retarded wave, blue arrows are advanced wave. The drecton of retarded wave s same as the drecton of red arrow. The drecton of advanced wave s at the opposte drecton of the blue arrow. The arrow drecton (red or blue) s always at the energy transfer drecton. From the above dscusson t s clear that, I. (E 1 H 2 + E 2 H 1 ) n d can be seen as energy current on the surface (or energy flux). II. u 12 = (E 1 D 2 + E 2 D 1 + H 2 B 1 + H 2 B 1 ) s the ncrease of the photon energy dstrbuton. III. u 12 d s the energy ncrease n the volume. I. 2 (J 2 E 1 )d s the absorbed energy of the absorber.. (J 1 E 1 2 )d s the emtted energy whch can be seen as the sucked energy by the advanced wave E 2 on the current J 1. Consderng, (11) (E 1 D 2 + E 2 D 1 + H 2 B 1 + H 2 B 1 ) = E 1 εe 2 + E 2 εe 1 + H 2 μh 1 + H 2 μh 1 = (εe 1 E 2 + μh 1 H 2 ) = u 12 Where u 12 = εe 1 E 2 + μh 1 H 2. We have assume ε and μ are constant. We know u 12 0 take place at t = 0 to t = T + Δt. We can assume that u 12 (t = ) = u 12 (t = + ) = constant (12)
dt u 12 d = u 12 (t = + ) u 12 (t = ) Ths means after the photon s go through from emtter to the absorber the energy n the space should recover to the orgnal amount. Consderng the above formula, from Eq.(7) we can obtan, (13) dt (J 1 E 2 )d = dt = 0 (J 2 E 1 )d Ths means all energy emtter from the current J 1 whch s the left of the above formula s receved by absorber J 2 whch s the rght of the above formula. Consderng Eq.(9,10 and 12,13) we have (14) = dt dt (E 1 H 2 + E 2 H 1 ) n d 1 (E 1 H 2 + E 2 H 1 ) ( n )d 2 The above formula tell us the all energy send out from 1 are flow nto (please notce the mnus sgn n the rght) the surface 2. Consder the surface 1 and 2 s arbtrarly, that means n any surface between the emtter and the absorber has the same ntegral wth same amount of the mutual energy current. Defne Q m = (E 1 H 2 + E m 2 H 1 ) n d, here we change the drecton of n always from the emtter to the absorber, then we can get the followng, see Fgure 4. (15) dt Q m = dt Q 1 = 1,2,3,4,5
Fgure 4. 5 surface s shown, the mutual energy current through each surface ntegral wth tme should be equal to each other. From Fgure 4 we can see that the tme ntegral of the mutual energy current on an arbtrary surface are are all the same, whch are the energy transfer of the photon. In the place close to the emtter or absorber, the surface can be very small close to the sze of the electron or atom. When energy s concentred to a small regon the moment should also concentred to that small regon. In ths case the energy of ths mutual energy current wll behaved lke a partcle. However t s stll mutual energy current. Fgure 4 and Eq.(15) tell us the energy transfer wth the mutual energy current can be approxmately seen as a 1-D plane wave.e. a wave n wave gude. But the wave s actually as 3D wave, ths allow the wave can go through the space other than empty space, for example double stlts. The mutual energy current has no any problem to go through the double slts and produce nterference n the screen after the slts. Ths offers a clear nterpretaton for partcle and wave dualty of the photon. Fgure 5. Photon n empty space, photon s just the mutual energy current. In a tme photon s stayed at a place. Ths shows there s nothng about the concept of the wave functon collapse.
5. The equaton Photo should satsfy Whch equatons photon should satsfy? Frst we thnk Maxwell equatons. But t s clear Maxwell equatons can only obtan the contnual soluton. But Photon s a partcle, ts energy s sent to an absorber drecton nstead sent to the whole drectons. Ths tell us we cannot smply ask photo to satsfy Maxwell equatons. Does photon satsfy Schrodnger wave equaton? Schrodnger wave equaton s scale equaton, when there are many photons, the supermposed felds should satsfy Maxwell equatons whch s vector equatons. Hence photon cannot satsfy Schrodnger wave equaton. We are nterestng to know whch equatons photon should satsfy. when the number of photon become nfnte, from these equatons the Maxwell equatons should be obtaned. In the photon model of last secton, f only consders the mutual energy current, there s no thng call wave functon collapse. Everythng s fne. However, n the Poyntng theorem there are self-energy tems, ths secton we need gve a detals of dscusson about the self-energy tems. In ths secton we need to consder the self-energy tems Eq.(3 and 4). The advanced wave and retarded wave all send to all drectons nstead send to only along the lne lnked the emtter and absorber. In ths model the absorber doesn t absorb all retarded wave of the emtter. The emtter doesn t absorb all advanced wave from absorber. The self-energy part of wave n Eq.(3 and 4) s sent to nfnte. However, we can assume (a) The self-energy tems vansh. Ths s because ths energy cannot be absorbed by any thngs f t doesn t collapse. It need to collapse to a pont to be absorbed. When mutual energy current can transfer energy, there s no any requrement for the wave to collapse. We can just throw ths part of energy away. (b) These tems are exstent, thy just send to nfnte. Because for the whole system wth an emtter and an absorber there are one advanced wave and a retarded wave both send to nfnte the pure total energy dd not loss. The retarded wave loss some energy, but the advanced wave gans the same amount of energy. Ths part of energy can be seen as t s transferred from the emtter to the nfnte and reflect back to become advanced wave of the absorber and receved by the absorber. The dea of (b) has been appled to any current dstrbuton ether an emtter or an absorber n whch t sends a half retarded wave and a half retarded wave n Wheeler and Feynman. Hence no pure loss of energy for ths knd of emtter or absorber. Now we apply t to the system wth an emtter and an absorber, t should also be acceptable. The retarded wave send from emtter s reflect from nfnte become advanced wave of the absorber. Ths concept has the same effect as the wave s collapses to the absorber but t s more easly to be acceptable. We can also say the self-energy parts of wave are collapsed through nfnte far away. The only dffcult for ths knd of energy transfer s that f there s metal contaner, and the emtter and the absorber are all nsde the contaner, how the self-energy current send to nfnte? We can thnk the retarded self-energy current send the surface of metal contaner become advanced wave of the absorber. But snce the postons of emtter and absorber are n any places nsde the contaner and the contaner can be any shape, there s no any electromagnetc theory can support ths concept. Hence for ths dea of (b) there s stll some problem. We can prove that from the dea (b) the Poyntng theorem s satsfed n macrocosm.
For dea (a) we can show even we throw away the self-energy tems, t doesn t volate the Maxwell equatons. After we throw away Eq.(3 and 4), there s only equaton Eq.(5) left. We start from Eq.(5) to prove the Poyntng theorem n macrocosm. Fgure 5. Ths shows emtters all at the center of the sphere. The absorbers are dstrbuted at the surface of the sphere. The absorber s the envronment. We assume the absorbers are surrounded the emtter. Ths s our smplfed macrocosm model. Assume the emtters send retarded wave randomly wth tme. In the envronment there are many absorbers n all drectons whch can absorb ths waves. Ths s our smplfed macrocosm model see Fgure 5. (1) Assume self-energy doesn t vansh correspondng to the dea (b) We actually endorse the dea (a), but frst we check the dea (b), see f we don t worry about the stuaton n whch the emtter and the absorber are all nsde a metal contaner. We need to show that for (b) Maxwell equatons are stll satsfy for the macrocosm. Assume for the -th photon the tems of self-energy doesn t vansh,.e., (16) (17) (E 1 H 1 ) n d = (J 1 E 1 + u 1 )d (E 2 H 2 ) n d = (J 2 E 2 + u 2 )d Assume for the -th photon there s mutual energy current whch satsfy: (18) (E 1 H 2 + E 2 H 1 ) n d = (J 1 E 2 + J 2 E 1 )d
+ (E 1 D 2 + E 2 D 1 + H 2 B 1 + H 2 B 1 )d These 3 formulas actually tell us the photon should satsfy Poyntng theorem, from the above equatons can derve the Poyntng theorem for the photon, (19) (E 1 + E 2 ) (H 1 + H 2 ) n d = (J 1 + J 2 ) (E 2 + E 1 )d + (E 1 + E 2 ) (D 1 + D 2 ) + (H 1 + H 2 ) (B 1 + B 2 )d Or we can take sum to the above formula t becomes, (20) (E 1 + E 2 ) (H 1 + H 2 ) n d = (J 1 + J 2 ) (E 2 + E 1 )d + (E 1 + E 2 ) (D 1 + D 2 ) + (H 1 + H 2 ) (B 1 + B 2 )d In another sde, assume J 1 = J 1 and J 2 = J 2, E 1 = E 1, E 2 = E 2, and so on. Hence there s, (21) (E 1 + E 2 ) (H 1 + H 2 ) = ( E 1 + E 2j ) ( H 1m + H 2n ) j m n = E 1 H 1m + E 1 H 2n + E 2j H 1m + E 2j H 2n m n j m j n We have known photon s a partcle that means all energy of photon sends out from an emtter has to be receved by only one absorber. Hence only the tems wth = j doesn t vansh. Hence we have (22) E 1 H 1m = E 1 H 1m = E 1 H 1 m In the above, consderng E 1 H 1m = 0, f m. Ths means that the feld of -th absorber only acton to -th emtter. Smlar to other tems, hence we have m
(23) (E 1 + E 2 ) (H 1 + H 2 ) = = (E 1 H 1 + E 1 H 2 + E 2 H 1 + E 2 H 2 ) And smlarly we have, = (E 1 + E 2 ) (H 1 + H 2 ) (J 1 + J 2 ) (E 1 + E 2 ) = (J 1 + J 2 ) (E 1 + E 2 ) (E 1 + E 2 ) (D 1 + D 2 ) = (E 1 + E 2 ) (D 1 + D 2 ) (H 1 + H 2 ) (B 1 + B 2 ) = (H 1 + H 2 ) (B 1 + B 2 ) Consderng Eq.(23), Eq.(20) can be wrtten as, (24) (E 1 + E 2 ) (H 1 + H 2 ) n d = (J 1 + J 2 ) (E 2 + E 1 )d + (E 1 + E 2 ) (D 1 + D 2 ) + (H 1 + H 2 ) (B 1 + B 2 )d If we take = 1 whch only contans the current of J 1 that means the current of envronment J 2 s put out sde of the volume 1, we have, (25) (E 1 + E 2 ) (H 1 + H 2 ) n d = J 1 (E 2 + E 1 )d 1 1 + (E 1 + E 2 ) (D 1 + D 2 ) + (H 1 + H 2 ) (B 1 + B 2 )d 1 Consderng the total felds can be seen as the sum of the retarded wave and advanced wave. In the macrocosm we don not know whether the feld s produced by the retarded feld of the emtter current J 1 or produced by the advanced wave of the absorber n the envronment. We can thnk all the feld s produced by the source current J 1, hence we have E = E 1 + E 2, D = D 1 + D 2, H = H 1 + H 2, B = B 1 + B 2. Here the feld E, H are total electromagnetc feld whch are thought produced by emtter J 1, hence we have
(26) E H 1 n d = J 1 Ed 1 + (E D + H B)d 1 Ths s the Poyntng theorem n macrocosm. In ths formula there s only emtter current J 1. The feld E, H can be seen as retarded wave but t s actually consst of both retarded wave and advanced wave. We have started wth assume mcrocosm photon model where the feld s produced from the advanced wave of the absorber and the retarded wave of the emtter. We assume that the self-energy tems doesn t vansh, we obtaned the macrocosm Poyntng theorem, n whch the feld s assumed that the feld s produced only by the emtters. We know that Poyntng theorem s nearly equvalent to Maxwell equatons. Although from Poyntng theorem we cannot deduce Maxwell equatons, but Poyntng theorem can derve all recprocty theorem, from recprocty theorem we can obtaned the green functon soluton of Maxwell equatons. From all soluton of Maxwell equatons, the Maxwell equatons should be possble to be nduced from ther all solutons. The above proof s not trval. We have shown that f photon consst of self-energy and mutual energy tems of an advanced wave and a retarded wave, the electromagnetc feld whch s sum of all felds of the emtters and absorbers stll satsfy Poyntng theorem and hence also Maxwell equatons. In our macrocosm model, the emtters are at one pont and all the absorbers are at a sphere. However, ths can be easly wdened to more generalzed stuaton n whch the emtters are not only stay at one pont and the absorbers are not only on a sphere surface. (2) Assume self energy vanshes In ths stuaton all self-energy tems vansh. If self-energy current s exstent, we have to assume t sends to nfnty and reflect at nfnty and become advanced wave of the absorber. If the energy of photon s transferred through ths wave, when the emtter and the absorber stayed nsde a metal contaner, the self-energy becomes dffcult to transfer. Hence n ths secton we contnue to study when the selfenergy s not exstent. We wll study that f there s only mutual energy current what wll happen. Assume one of the current of emtters s J 1, whch s at the orgn and the current of the correspondng absorber s J 2, whch s at the sphere, see Fgure 5, here = 0,1, N. We can apply mutual energy theorem to ths par of emtter and absorber, we obtan, Eq.(5) can be wrtten as, (27) (E 1 H 2 + E 2 H 1 ) n d = (J 1 E 2 )d + (J 2 E 1 )d
+ (E 1 D 2 + E 2 D 1 + H 2 B 1 + H 2 B 1 ) d We assume the feld of emtter J 1 can only be receved by the absorber J 2, here = 1,, N. Ths requrement s asked because that the photon s a partcle and all ts energy must be receved by only one absorber. The whole package of energy should be receved by only one absorber. That means for example, consderng (28) E 1 H 2j = 0 f j (29) E 2 H 1j = 0 f j (30) J 1 E 2j = 0 f j Hence, there s (31) E 1 H 2 = E 1 H 2j = E 1 H 2 j Assume J 1 = J 1 and J 2 = j J 2j, E 1 = E 1, E 2 = E 2, consder Eq.(31) the Eq.(27) becomes (32) (E 1 H 2 + E 2 H 1 ) n d = (J 1 E 2 )d + (J 2 E 1 )d + (E 1 D 2 + E 2 D 1 + H 2 B 1 + H 2 B 1 )d We assume all the advanced waves average should close to the retarded wave that s, (32) E 1 = E 2 1 2 E H 1 = H 2 1 2 H The above formula tell us that the total retarded wave feld H 1 s half of the macrocosm feld. The total advanced waves from all photons E 2 s the half of the macrocosm feld. Where means s defned as. Consderng the above formula, we obtan, (33) 1 (E H) n d = 1 4 2 (J 1 E)d + 1 2 (J 2 E)d
+ 1 (E D + H B)d 4 We can choose as 1 whch s very small volume close to emtter, n that case, J 2 s at outsde of 1 and the mddle tem n the rght of the above formula vanshes, and hence we obtan, (34) (J 1 E)d = 1 [ (E H) n d + (E D + H B)d] 1 2 1 1 Comparng to Poyntng theorem Eq.(26), the above formula equal sgn actually dd not establshed. The rght sde s only has half value of the left sde. The reason of the above formula s clear, we have thrown away the self-energy tems, (J 1 E 1 )d and (J 2 E 2 )d and so on. (E H) n d s energy current. 1 [ (E H) n d means the we only obtaned half the mutual energy current t 2 1 should be. J 1 = J 1, s the current of the emtter, we actually do not know t s exactly value. We can make the replacement, J 1 1 J 2 1. Ths means that we have used 1 J 2 1 to replace J 1. Actually ths s also because the energy transferred by self-energy part Eq.(3 and 4) must be replaced by the transfer of the mutual energy current. We can say the energy transfer wth mutual energy has taken over the transfer of the self-energy. We can also say transfer wth the self-energy collapse to the transfer wth mutual energy. Any way we can say to the photon the mutual energy theorem can be establshed whch consder the fact 2, Eq.(3-5) becomes, (35) 1 (36) (37) (E 1 H 1 ) n d = (J 1 E 1 + u 1 )d = 0 (E 2 H 2 ) n d = (J 2 E 2 + u 2 )d = 0 2 (E 1 H 2 + E 2 H 1 ) n d = (J 1 E 2 + J 2 E 1 )d +2 (E 1 D 2 + E 2 D 1 + H 2 B 1 + H 2 B 1 )d Accordng above dscusson, f we assume the above formula establshed, Eq.(34) can be replaced as (38) 1 (J 1 E)d = [ (E H) n d + (E D + H B)d 1 1 ]
Ths means even we assume the energy transfer of photon s only through mutual energy current, the self-energy doesn t have any contrbutons, we stll can obtan Poyntng theorem n macrocosm. Eq.(35-36) are the self-energy tems, f these tems are vanshed, as compensaton we have to double the mutual energy current n mcrocosm. Ths way we can stll keep the Poyntng theorem s establshed n macrocosm. We have proven that all recprocty theorem can be proven from Poyntng theorem [12], we also know the Green functon soluton of Maxwell equaton can also be obtaned from Lorentz recprocty theorem. Maxwell equaton cannot be derved from ther soluton, but Maxwell equatons should be possble to be obtaned from ther soluton by nducton. Hence we can say for photon (for mcrocosm) there s only the mutual energy theorem to be establshed. In mcrocosm the all self-energy tems are all vansh. The Poyntng theorem correspondng to the self-energy tems are all vansh n both sde of Poyntng theorem. However, the adjusted mutual energy theorem (please notce the factor 2 n the formula) stll establshed. The above dervaton tells us that the macrocosm the Poyntng theorem s establshed and hence the Maxwell equatons can also be establshed. Ths means n mcrocosm the mutual energy theorem s more fundamental than Poyntng theorem. Hence we can thnk t s a prncple: the mutual energy prncple. We can start from the Mutual energy prncple n mcrocosm to obtan the Poyntng theorem and hence also the Maxwell equatons of macrocosm. We can further assume that the mutual energy prncple s establshed also for all other partcles of the whole quantum mechancs. (3) Summary In ths secton we have ntroduced two methods to deal wth the self-energy tems of the transfer of the energy. One s that ths knd transfer of self-energy exstent. The self-energy current of the retarded wave of the emtter sends to nfnty and reflected at the end of the cosmos, becomes the advanced wave of the absorber, hence ths energy s send from the emtter to the absorber. The self-energy tems transferred half total energy, the other half part of energy s transferred by the mutual energy current. The only problem of ths assumpton s that f the emtter and the absorber s not at nfnte empty space but nsde a metal contaner, we stll have to assume the self-energy tems can send to nfnty, ths seems doesn t possble. Hence we make another assumpton. Another s that the transfer of self-energy doesn t exstent or self-energy tems are taken over by the transfer of the mutual energy current. We also can say that the self-energy tems collapse to the mutual energy current. The mutual energy current s the only one whch can transfer the energy n mcrocosm. In ths case the mutual energy current has to be adjusted by a fact 2. Both vew of ponts are very good and could be acceptable. And we trend to the concept that the self-energy doesn t transfer any energy and hence the mutual energy current s the only one whch can transfer the energy. The above both vew of ponts are much better than assume there s no advanced wave, n whch f the absorber need to receve energy, the only possblty s all the energy s collapse to the absorber. We can also not derve macrocosm Poyntng theorem from mcrocosm photon model.
J. Crammer ntroduced the concept of contnually collapse that means 3D wave contnually collapse to a 1-D wave [3-5]. In our mutual energy current theory, the energy transfer s also very close to a 1-D wave. The transferred energy current n any surface s same. The self-energy current collapse to the mutual energy current that s also very easy to be understand. If we assume the energy of photon are composed by small parts, t s clear there should be some bndng force between them, we do not know ths force. But ths force makes the energy current transferred from emtter to the absorber nstead send energy to the whole space. That s reason we assume the self-energy tems collapse to the mutual energy current. Hence there s only mutual energy current for photon. The mutual energy current s composed wth the advanced wave of absorber and the retarded wave of the emtter. For the mutual energy current, the energy transfer s centered at the lne lnked the emtter and the absorber. However, we derved t from a 3D radaton pcture. The mutual energy current can go any other lght road, for example the double slts. The wave functon collapse n quantum physcs actually comes from the msunderstandngs that the wave energy s transferred by Poyntng energy current or self-energy current. In ths case the retarded energy transferred from emtter must collapse to the absorber. The advanced wave transfer negatve energy from absorber to the emtter has to collapse to the emtter. However, we have proven that the mutual energy current can transfer the energy too, n ths case we can easly throw away the self-energy current tems, let the mutual energy current to take over the task orgnally should be done by selfenergy current. The concept of the wave functon collapse of quantum physcs does not need any more n our photon model. Ths secton tells us, f photon are composed as an emtter and an absorber, and the emtter send retarded wave and the absorber send advanced wave, and photo satsfy mutual energy theorem (adjusted by a factor 2 for the mutual energy current), then the system wth nfnte photons should satsfy Poyntng theorem n macrocosm, whch make t n turn satsfy Maxwell equatons (Poyntng theorem s equvalent to Maxwell equatons n practcal). 6. The photon equatons In the above we obtan the concluson that photon should satsfy the mutual energy theorem formula, and self-energy tems vanshes. Ths secton let us found the equaton photon should satsfy. For the emtter and the absorber of the photon, we assume the feld of absorber and emtter together satsfy some equatons, whch can derve the above mutual energy prncple. (39) ζ = ζ 1 + ζ 2 where ζ 1 = [E 1, H 1 ], whch s produced by the emtter where ζ 2 = [E 2, H 2 ], where ζ 1 = [E 1, H 1 ], the above supermposton s (40) (41) (E 1 + E 2 ) = (B 1 + B 2 ) (H 1 + H 2 ) = 1 2 (J 1 + J 2 ) + (D 1 + D 2 )
(42) J 1 E 1 = 0 J 2 E 2 = 0 E 1 H 1 = 0 E 2 H 2 = 0 We can derve Eq.(37) from above group equatons. The above equaton can be seen as photon s equatons, whch s very close to Maxwell equatons, but the feld of photon must put the feld of emtter and absorber together. All self-feld tems are assumed to be vanshed. There are a factor 2 (or 1 2 ) whch s appled to compensate the vanshed tems of all the self-energy tems. In quantum physcs, there s also the renormalzaton and Regularzaton process to deal wth the nfnty. Here we throw away the self-energy tem perhaps because the same reason. Snce there s mutual energy current, that allow us to throw away the self-energy tems wthout bg nfluence to the feld or equatons of macrocosm. Proof: Frst from self-energy Poyntng theorem Eq.(16,17) and consderng Eq(42) we obtan, (43) Assume that (44) We have the followng equatons, (45) E 1 D 1 = 0 E 2 D 2 = 0 E = E 1 + E 2 H = H 1 + H 2 J = J 1 + J 2 D = D 1 + D 2 B = B 1 + B 2 E = B Hence, we have H = 1 2 J + D
(46) (E H ) = ( E H E H ) = ( B H E ( 1 2 J + D )) = H B + E D + 1 2 J E Thant s we have, (47) (E H ) = H B + E D + 1 2 J E Or consderng Eq.(44) we have (48) ((E 1 + E 2 ) (H 1 + H 2 )) = (H 1 + H 2 ) (B 1 + B 2 ) + (E 1 + E 2 ) (D 1 + D 2 ) + 1 2 (J 1 + J 2 ) (E 1 + E 2 ) Or consderng Eq.(42,43) we obtan, (49) (E 1 H 2 + E 2 H 1 ) = H 1 B 2 + H 2 B 1 + E 1 D 2 + E 2 D 1 Or make an ntegral to the above equaton we have, (50) + 1 2 J 1 E 2 + 1 2 J 2 E 1 2 (E 1 H 2 + E 2 H 1 ) n d = (J 1 E 2 + J 2 E 1 )d +2 (E 1 D 2 + E 2 D 1 + H 2 B 1 + H 2 B 1 )d Ths s the Eq.(37). We have obtaned the adjusted mutual energy theorem from the equaton photon should satsfy.
Here we have not assume that the wave of emtter and the wave of absorber satsfy Maxwell equatons separately. The reason of that s n that case Maxwell equaton has the soluton, when we add the condton of the self-energy tems vansh, perhaps can produce a zero soluton whch s not we want. 7. Fnd a soluton to the above photon equatons In ths secton we wll try to fnd a specal soluton whch satsfes the above equatons. We do not try to fnd all solutons and we only show one soluton n whch can be the photon model. From E 1 H 1 = 0, We know that the fled, E 1 H 1, here means parallel to, we can assume (51) E 1 = K 1 H 1 E 2 = K 2 H 2 K 1, K 2 are constants and can have postve value and negatve values. We assume the current of the absorber s perpendcular to the current of the emtter for example, (52) J 1 = δ(x)δ(y)δ(z)z J 2 = δ(x d)δ(y)δ(z)y z s unt vector n z axs drecton. y s unt vector n z axs drecton. d s the dstance between the emtter and the absorber. δ( ) s delta functon. We assume the magnetc feld stll can be obtaned wth the rght hand rule. We can assume for the emtter the constant K 1 s postve, for smple we can just take K 1 = 1 (here we omt the scale value and the unt), hence the electrc feld E 1 = H 1 s n the same drecton of magnetc feld. We assume, for the absorber we assume that E 2 = H 2. In the last few secton we have shown that the energy current of the photon s close to a one dmensonal wave, even t actually a 3D wave. The most energy current s go through along the lne from the emtter to the absorber. Hence here we only study the stuaton of the felds n whch the energy current go along the lne lked the absorber to the emtter. We can see n the Fgure 6. In ths stuaton the drecton of E 1 H 2 and E 2 H 1 are all n the drecton of x whch s just the drecton from emtter to the absorber. Fgure 6. The current of the emtter s perpendcular to the current of the absorber. The fled of E 1 H 2 and E 2 H 1 has the same drecton as the radaton drecton whch s from the emtter to the absorber. We have assume E 1 = H 1, E 2 = H 2.
Snce we have assume the E 1 H 1, ths also guarantee that J 1 E 1 = 0. E 2 H 2, ths also guarantee that J 2 E 2 = 0. E 1 H 1 = 0, J 1 E 1 = 0, further guarantees E 1 D 1 through the Poyntng theorem Eq.(3). Smlarly E 2 H 2 = 0, J 2 E 2 = 0 further guarantees E 2 D 2 through the Poyntng theorem Eq.(4). Hence n the above example all self-energy tems all vanshed. To the absorber s also same all self energy tems are all vansh. Electrc feld of emtter s parallel to ther magnetc feld. The Electrc feld of the absorber s also parallel to ther magnetc feld, whch wll make the self-energy tems all vansh, hence there are only mutual energy tems left. Ths wll guarantee the mutual current s the only one can transfer energy. 8. Polarzaton and spn of the photon In the mutual energy current (53) Q 12 = (E 1 H 2 + E 2 H 1 ) n d there are two tems, E 1 H 2 and E 2 H 1, From Fgure 6 we know along the lne of from emtter to the absorber, E 1 just perpendcular to E 2, ths made them perfectly to buld a polarzed feld. If E 1 H 2 has the same phase wth the tem E 2 H 1, we obtan a lnear polarzed feld. If the two tems has 90 degree n phase dfference, we wll obtan a crcular polarzed feld. Orgnally n the tme the author wrte other artcle [15,16], he has thought that the crcle polarzaton or spn s because of the two waves retarded wave and the advanced waves that have a phase dfference and hence produces the polarzaton. If t s crcle polarzaton, then t can be seen as spn. E 1 H 1 and E 2 H 2 to produce the polarzaton. However, to produce polarzaton there need the two electrc felds E 1 and E 2 must be perpendcular. He can not fnd a correct reason that the two electrc felds E 1 and E 2 are perpendcular n that tme. Now the above model tells us the two electrc felds E 1 and E 2 are perpendcular by concdence. It s nterestng to notce ths two tems E 1 H 2 and E 2 H 1 are both wth the retarded feld and the advanced wave. If the electrc feld s retarded wave of the emtter, then the correspondng magnetc feld s advanced wave of the absorber and vce versa. Up to now, the photon model s very clear. The current of the absorber must perpendcular to the current of the emtter. The electrc feld of the absorber and emtter mast parallel to ther magnetc feld and ths guarantee the self-energy tems dsappear. The mutual energy current offer two tems whch can nterpret the photon polarzaton or photon spn. From ths photon model, the spn and polarzaton of photon s not only related to the emtter but also the absorber, ths can offer a good nterpretaton to the delayed choce experment of J. A. Wheeler [6]. 9. The feld equaton of the feld agan
Eq.(42) E 1 H 1 = 0 actually tell us E 1 cannot be produced by H 1 and H 1 cannot be produced by E 1. E 2 H 2 = 0 actually tell us E 2 cannot be produced by H 2 and H 2 cannot be produced by E 2. Hence we can smply the equatons Eq.(41,42) as (54) E 1 = B 2 E 2 = B 1 H 1 = 1 2 J 1 + D 2 H 2 = 1 2 J 2 + D 1 Consderng Eq.(54) can derve the Eq.(40,41), but t stll cannot derve the Eq.(42), Eq.(42) should be nclude as photon equatons. Hence we rewrte t here, (55) J 1 E 1 = 0 J 2 E 2 = 0 E 1 H 1 = 0 E 2 H 2 = 0 (E 1 H 1 ) = 0 (E 1 H 1 ) = E 1 H 1 H 1 E 1 = B 2 H 1 ( 1 2 J 1 + D 2 ) E 1 = B 2 H 1 D 2 E 1 1 2 J 1 E 1 Eq.(54,55) can be seen as photon equatons. All feld of the photon should be possble to be solved from them. From these equatons we known that the felds of absorber and emtter are not ndependent to each other. Ther felds communcate to each other. These communcated feld can be referred as coupled felds. The photon energy s also transferred by mutual energy current. The mutual energy current to the emtter t s retarded wave. The mutual energy current to the absorber t s advanced feld. But mutual energy current tself s actually not only retarded wave and also not only advanced wave. It just a wave transferred from emtter to the absorber. Ths energy doesn t go to nfnte empty space. The feld only transfer the energy from emtter to the absorber. Ths energy transfer looks smlar to the water go through a ppe. The wave doesn t collapse.
10. Derve the macrocosm Maxwell equatons from the mcrocosm photon equatons In last secton we have obtan the Photon equatons. Now we try to obtan the Maxwell equatons. From Equaton Eq.(44) we can obtan Eq.(40,41). The summaton of all felds of the photon becomes, (56) (E 1 + E 2 ) = (B 1 + B 2 ) (H 1 + H 2 ) = 1 2 (J 1 + J 2 ) + (D 1 + D 2 ) Consder that the retarded macrocosm felds of all emtters can be obtan by (57) J 1 = J 1 E 1 = E 1 H 1 = E 1 D 1 = D 1 B 1 = B 1 And the advanced feld of the absorber can be obtaned, (58) J 2 = J 2 E 2 = E 2
H 2 = E 2 D 2 = D 2 B 2 = B 2 We obtan, (59) (E 1 + E 2 ) = (B 1 + B 2 ) (H 1 + H 2 ) = 1 2 (J 1 + J 2 ) + (D 1 + D 2 ) Or (60) (E 1 + E 2 ) = (B 1 + B 2 ) (H 1 + H 2 ) = 1 2 (J 1 + J 2 ) + (D 1 + D 2 ) For the macrocosm feld we can not dstngush the feld s advanced feld or t s retarded feld hence there s the We obtan, (61) E = E 1 + E 2 H = H 1 + H 2 D = D 1 + D 2 B = B 1 + B 2 (62) E = B H = 1 2 (J 1 + J 2 ) + D (63) E I = B I
H I = 1 2 J 1 + D I (64) E II = B II H II = 1 2 J 2 + D II The soluton of Eq.(63) s wrtten as E I, H I, D I, B I, assume E I, H I, D I, B I ths s retarded wave. Eq.(64) can be wrtten as E II, H II, D II, B II. Assume E II, H II, D II, B II s advanced feld. We must notce that E I s not same as E 1 and E II s not same as E 2. E 1 and E 2 are sum of mcrocosm felds. Whch are fled coupled felds. E 2. E 1 are all produced by current J 1 and J 2 together. E I and E II are uncoupled felds. E I only relate to J 1. E II s only relate to J 2. (65) E I = E II = 1 2 E H I = H II = 1 2 H D I = D II = 1 2 D Substtutng Eq.(65) to Eq.(63), we obtan, B I = B II = 1 2 B (66) E = B H = J 1 + D Or (67) E = B H = J 2 + D Eq.(66) s the Maxwell equatons. Eq.(67) s redundant to the macrocosm and hence can be omtted. Ths proves our mcrocosm photon equatons con derve the macrocosm Maxwell equatons. Concluson The photon model s bult. Photon s composed as an emtter and an absorber. The emtter sends the retarded wave and the absorber sends the advanced wave. The retarded wave and the advanced wave
together produced the mutual energy current. In mcrocosm the energy s only transferred by mutual energy current. The self-energy current n mcrocosm doesn t exstent. The pontng theorem s not satsfed for the absorber or emtter n the photon model. However, we have proven f the mutual energy theorem establshed n mcrocosm for photon, the Poyntng theorem s establshed also to macrocosm. We also obtan the equatons photon should satsfy whch s a modfed equaton from Maxwell equatons. In ths equaton all self-energy tems are all vanshes. From ths equaton we can fnd a soluton n whch the absorber s perpendcular to the emtter. The mutual energy current has two tems whch can be nterpreted as lne polarzaton / crcle polarzaton and hence nterprets the concept of spn of the photon. The above photon model s derved from electromagnetc feld wth Maxwell theory, but t very lkely also sut the wave of other partcles, for example electrons. [1] J. A. Wheeler and R. P. Feynman, Interacton wth the absorber as the mechansm of radaton, Rev. Mod. Phys., vol. 17, p. 157, Aprl 1945. [2] J. A. Wheeler and R. P. Feynman, Classcal electrodynamcs n terms of drect nterpartcle acton, Rev. Mod. Phys., vol. 21, p. 425, July 1949. [3] J. Cramer, The transactonal nterpretaton of quantum mechancs, Revews of Modern Physcs, vol. 58, pp. 647 688, 1986. [4] J. Cramer, An overvew of the transactonal nterpretaton, Internatonal Journal of Theoretcal Physcs, vol. 27, p. 227, 1988. [5] J. Cramer, The transactonal nterpretaton of quantum mechancs and quantum nonlocalty, https://arxv.org/abs/1503.00039, 2015. [6] Mathematcal Foundatons of Quantum Theory, edted by A.R. Marlow, Academc Press, 1978. P, 39 lsts seven experments: double slt, mcroscope, splt beam, tlt-teeth, radaton pattern, one-photon polarzaton, and polarzaton of pared photons. [7] Walborn, S. P.; et al. (2002). "Double-Slt Quantum Eraser". Phys. Rev. A. 65 (3): 033818. arxv:quant-ph/0106078freely accessble. Bbcode:2002PhRvA..65c3818W. do:10.1103/physreva.65.033818. [8] Yaron Bromberg, Or Katz, Yaron Slberberg, Ghost magng wth a sngle detector, https://arxv.org/abs/0812.2633, 2008 [9] S. ren Zhao, The applcaton of mutual energy theorem n expanson of radaton felds n sphercal waves, ACTA Electronca Snca, P.R. of Chna, vol. 15, no. 3, pp. 88 93, 1987. [10] S. Zhao, The smplfcaton of formulas of electromagnetc felds by usng mutual energy formula, Journal of Electroncs, P.R. of Chna, vol. 11, no. 1, pp. 73 77, January 1989. [11] S. Zhao, The applcaton of mutual energy formula n expanson of plane waves, Journal of Electroncs, P. R. Chna, vol. 11, no. 2, pp. 204 208, March 1989. [12] S. ren Zhao, K. Yang, K. Yang, X. Yang, and X. Yang. (2015) The modfed poyntng theorem and the concept of mutual energy. [Onlne]. Avalable: http://arxv.org/abs/1503.02006 [15]Shuang-ren Zhao, Kevn Yang, Kang Yang, Xngang Yang, Xnte Yang, The prncple of the mutual energy, arxv:1606.08710, 2016 [16]Shuang-ren Zhao, Kevn Yang, Kang Yang, Xngang Yang, Xnte Yang, The mutual energy current nterpretaton for quantum mechancs, arxv:1608.08055, 2016