Wave Particle Duality & Interference Explained

Transcription

1 Journal of Modern Physics, 016, 7, Published Online February 016 in SciRes. hp:// hp://dx.doi.org/10.436/jmp Wave Paricle Dualiy & Inerference Explained Narendra Swarup Agarwal 704 HUDA CGHS Limied, Gurgaon, India Received 17 December 015; acceped 1 February 016; published 5 February 016 Copyrigh 016 by auhor and Scienific Research Publishing Inc. This work is licensed under he Creaive Commons Aribuion Inernaional License (CC BY). hp://creaivecommons.org/licenses/by/4.0/ Absrac Phoons and elemenary paricles display he properies of paricle as well as of wave known as Wave Paricle Dualiy. Quanum Theory could no explain Wave Paricle Dualiy only due o he belief ha phoon has no mass and acceped Wave Paricle Dualiy as realiy of quanum scale paricles. Experimenal Proof of Mass in Phoon [1] discovered Inerial Force developed by he phoons on Reflecion. This Inerial Force is developed in he spinning phoon from inside due o he mass of phoon. These experimens also discovered ha he cenre of mass of phoon was differen from he cenre of phoon. Such presence of mass in a phoon developing Inerial Force from wihin he phoon gifs special properies o display Wave Paricle Dualiy, Inerference and Polarizaion ec. These phenomena are explained in his work which could no be explained by he Quanum Theory earlier. This work also confirms mass in phoon based on boh Newonian and Special Theory of Relaiviy. New equaions of rue mass of phoon are also derived. Keywords Phoon, Cenre of Mass, True Mass of Phoon, Angular Momenum, Resulan Momenum, Wave Paricle Dualiy 1. Inroducion Elecromagneic Waves are acually he radiaions of Phoon paricles which always move in he pah of wave. Phoons are paricles bu display behavior of boh paricle as well as wave. The Wave Paricle Dualiy is explained in his work. How acually he phenomena of Inerference & Polarizaion ake place are also explained? The mass of phoon is confirmed by boh Newonian heory as well as special heory of relaiviy. New equaions for rue mass of phoon according o special relaiviy are also derived. Mos of he paricles of he size of quana, micro & macro levels display Wave Paricle Dualiy. Any paricle How o cie his paper: Agarwal, N.S. (016) Wave Paricle Dualiy & Inerference Explained. Journal of Modern Physics, 7, hp://dx.doi.org/10.436/jmp

2 can display Wave Paricle Dualiy phenomenon and move in he form of a wave if i mees he following crieria: - The paricle has mass; - The cenre of mass of paricle is differen from he cenre of he paricle; - The paricle is spinning and moving. Mass is a primary crierion for a paricle o exhibi Wave Paricle Dualiy. Wihou mass in he paricle, i can neiher display Wave Paricle Dualiy nor any oher phenomena like Inerference & Polarizaion ec.. Discussion PROVES OF MASS IN PHOTON Phoon is one of he inies paricles in he universe. Being very small he mass of phoons could no be measured or calculaed direcly. Phoon has mass is proved by he properies and characerisics of mass exhibied by he phoon. Mass of phoon produces inerial force, graviaional force, angular momenum and linear momenum ec. (a) Inerial Force Due o he Mass in Phoon Conrary o he known rule of Reflecion Angle of Reflecion and he Angle of Incidence are no same bu slighly differen, his difference in angle of reflecion is due o he Inerial Force developed by he mass of spinning phoon from wihin he phoon. Phoons deviae from heir sraigh line pah on reflecion by plain surface coaed mirror due o he inerial force developed from wihin he phoon. This inerial force increases wih he increase in he angle of polarizaion concluding ha he cenre of mass and cenre of phoon are differen. Experimenal Proof of Mass in Phoon [1] describes he deails of he experimens and discovers he presence of mass in phoon. This also discovers ha he cenre of mass of phoon is differen from he cenre of phoon. The observaions of he experimens are given below: 1. The phoons of polarized laser ligh on reflecion deviae from heir sraigh line pah afer reflecion.. The angle of deviaion of phoons on reflecion depends on he angle of plane of polarizaion of laser ligh wih respec o he plane of reflecing mirror. 3. The angle of deviaion increases by increasing he frequency of laser ligh. 4. The angle of reflecion and he angle of incidence of phoons are no same. The above experimens conclude: - Phoon deviaes from is sraigh line pah due o he inerial force developed by is mass. - Higher he angle of polarizaion, higher is he inerial force and higher he deviaion. - Higher he frequency, higher is he inerial force and higher he deviaion. The deviaion of phoons on reflecion proves he followings: 1. Phoon has mass.. The cenre of mass of phoon is differen from he cenre of phoon. Based on he Experimenal Proof of Mass in Phoon [1], he srucure of a phoon is conceived as shown in Figure 1. The cenre of mass of spinning phoon locaed a disance r from he cenre of phoon generaes Angular Momenum which is a vecor wih direcion changing wihin 360 wih he spin of phoon. The combined effec of he angular momenum and he linear momenum creaes Resulan Momenum. The phoon always moves in he direcion of Resulan Momenum which is also a vecor wih direcion changing wihin 360 wih he spin of phoon. The Resulan Momenum wih coninuously changing direcion and magniude impars peculiar characerisics o phoon o exhibi Wave Paricle Dualiy, Inerference and Polarizaion ec. The experimens are based on New Quanum Theory [] developed in he year 01 hypohesizing ha phoon has mass and he cenre of mass is locaed away from he cenre of phoon. (b) Graviaional Force due o Mass of Phoon I is known ha he phoons from he differen sars bend while passing near he Sun by he graviaional force beween he mass of phoon and he mass of he Sun. This bending of phoons proves he presence of mass in phoon. (c) Inerference 68

3 Figure 1. Phoon is shown in yellow circle wih is cenre of mass as red circle. The cenre of mass of phoon is locaed a disance r from he cenre of phoon. The direcion of angular momenum is a angle θ from Horizonal Axis. Phoon is moving in horizonal direcion and spinning clockwise in verical plane X-Z. The direcion of linear momenum is consan and is in horizonal direcion X-axis. The angular momenum is vecor and is direcion keeps on changing coninuously wih he spin of phoon wihin 360. The direcion of Resulan Momenum is ϕ from he horizonal direcion X-axis and also keeps on changing coninuously wih spin of phoon wihin Consrucive Inerference In consrucive inerference wo monochromaic elecromagneic waves are eiher in same phase or in muliple phase of π. The phoons of boh waves superpose and behave as one due o coalescing effec. The superposed phoons wih heir cenre of mass and angular momenums are shown in Figure. Since boh he phoons are in he same phase, heir angular momenums are added o double. This resuls in double ampliude a he cress and roughs wih maximum brighness.. Desrucive Inerference In desrucive inerference he wo monochromaic elecromagneic waves are in phase difference of odd muliple of π. The phoons of boh waves superpose and behave as one due o coalescing effec. The superposed phoons wih heir cenre of mass and angular momenums are shown in Figure 3. Since boh he phoons are in he opposie phases, boh he cenre of mass are locaed a 180 from each oher. The angular momenums of boh phoons are always in he opposie direcions. Boh he coalesced phoons hough keep on spinning bu canno go up & down o form wave and move only in he sraigh line. This resuls in desrucive inerference wih minimum brighness. 3. Inerference wih Oher Phase Differences When wo monochromaic elecromagneic waves, wih phase difference oher han 0 or muliple of π inersec, he phoons of boh superpose each oher wih coalescing effec. Depending on phase difference of he wo phoons, boh he cenre of mass are locaed a differen posiions wih angular momenums in differen direcions as shown in Figure 4(a) & Figure 4(b). The angular momenums of boh he phoons are in differen direcions and he vecor sum of boh he angular momenums is he resulan angular momenum. Such inerference resuls in inermediae brighness beween minimum o maximum. The Inerference phenomenon can only ake place if he phoons have mass and he cenre of mass is differen from he cenre of phoon. The Inerference phenomenon is no possible wihou he mass in phoon. The phenomenon of inerference proves ha phoon has mass and he cenre of mass is differen from he cenre of phoon. (d) Polarizaion On polarizaion of elecromagneic radiaions, he phoons form wave in one plane only known as he plane of polarizaion. The phoons spin and move in he plane of polarizaion only. Figure 5 shows a polarized phoon wih is cenre of mass and he circular pah of movemen of cenre mass wih he spin of phoon. 69

4 Figure. The angular momenums of boh phoons are in he same phase and added o double. Figure 3. Boh he phoons in phase difference of π have cenre of mass locaed a 180 apar. The direcions of angular momenums of boh are opposie o each oher. (a) Figure 4. (a) Wih phase difference closer o 0, boh he cenres of mass are close o each oher wih heir angular momenums. Therefore he vecor sum of boh angular momenums is more and he brighness is on higher side; (b) Wih phase difference closer o π, boh he cenres of mass are away wih angular momenums closer o opposie direcion. Therefore he vecor sum of boh angular momenums is less and he brighness is on lower side. The direcion of angular momenum originaing from he cenre of mass of phoon keeps on roaing wih he cenre of mass and changes is direcion wihin 360 wihin he plane of polarizaion only. The direcion of resulan momenum which is he vecor sum of angular momenum and he linear momenum also changes is direcion wihin 360 in he same plane. The resulan momenum moves he phoon up and down in he plane of polarizaion and limis he phoon movemens forming he wave in one plane only. The polarizaion phenomenon can only ake place if phoon has mass and he cenre of mass is differen from he cenre of phoon. The polarizaion phenomenon is no possible wihou he mass in phoon. (b) 70

5 Figure 5. Cenre of Mass of phoon roaes in circular pah wih he spin of phoon in he plane of polarizaion. This changes he direcion of angular momenum coninuously wihin 360 angle. The resulan momenum due o angular momenum & linear momenum moves he phoon up & down in X Z plane of polarizaion o form he wave. The phenomenon of polarizaion proves ha a phoon has mass and he cenre of mass is differen from he cenre of phoon. 3. Mass of Phoon by Special Relaiviy The special heory of relaiviy correlaes energy, mass, momenum, velociy from he observer s frame of reference. Since a phoon is never a res, he mass of phoon (he maer in he phoon) can be called True Mass of phoon (m ) insead of res mass (m 0 ). True mass of a phoon is always consan irrespecive of he posiion of he observer. For a single phoon paricle, he res mass and he invarian mass are he same. A. True Mass of Phoon from Toal Energy of Phoon The equaion E = mrelc of special relaiviy is used o derive new equaion for he True Mass of phoon (m ) as under: The E of he above equaion specifies he Toal Energy (E) of Phoon. This includes he energy in all he physical forms possessed by he phoon plus he energy produced when he mass of phoon is also convered o he energy. Phoon is always spinning and moving wih velociy of ligh. A phoon as per Figure 1 is considered o calculae he oal energy and True mass of he phoon. Toal Energy of Phoon ( E) = Linear Kineic Energy + Roaional Kineic Energy - + True Mass of Phoon ( c) 1 - Kineic Energy of phoon: mc 1 - Roaional Kineic Energy of phoon: Iω - Energy by conversion of Mass of phoon: mc Toal Energy of phoon E= mc + Iω + mc 3 1 E= mc ( π ) + mr f 1 E = m 3c + 4π r f Or True Mass of Phoon ( ) E m = 3c + 4π r f (1) 71

6 B. True Mass of Phoon from he Momenum of Phoon According o he special relaiviy, he oal energy of phoon is specified by he following equaion: ( ) ( ) E = pc + m c (True mass m is used insead of m 0 ) For a phoon, rue mass (m ) and linear velociy (c) are always consan. Bu in he erm (pc) boh he momenum (p) and he insananeous angenial velociy of phoon in he curve pah of wave are vecors and variable in one cycle of wave. Considering he direcion of Resulan Momenum is (ϕ) from he X-axis, he resulan momenum of phoon is denoed as (p ϕ ) and he velociy of phoon (c ϕ ) in he curve pah of wave. The above equaion is rewrien as under: ( ) ( ) φ φ E= p c + mc From Figure 1, he cenre of mass of phoon is a a disance (r) from he cenre of phoon. The phoon is always spinning and moving in he pah of wave. The equaion for True mass of phoon (m ) can be derived by calculaing he Resulan Momenum (p ϕ ) of phoon a any spin posiion/posiion of curve pah of wave as under: Angular momenum a angle θ from X-axis = Iω = mr πf - ( )( ) - - Angular momenum in X-axis = πfm r cos Angular momenum in Z-axis = πfm r sin - Linear momenum in X-axis = mc - Toal momenum in X-axis = + π cos θ θ m c fm r θ - Magniude of Resulan Momenum of phoon (p ϕ ) (when he direcion of angular momenum is (θ) from horizonal axis) Or Or ( π cos + ) + ( π sin ) pφ = fm r θ m c fm r θ ( π cos ) ( π sin ) φ = θ + + θ p m fr c fr p = m 4π f r + 4πfr c cosθ + c φ 4 The direcion of resulan momenum (ϕ) from horizonal X-axis is given below: πfm r sinθ anφ = m c + πfm r cosθ Subsiuing he value of resulan momenum (p ϕ ) in he oal energy equaion: True mass of phoon ( 4π 4π cosθ ) E = m f r + fr c + c c + m c m = 4 4 φ E { c ( 4π 4 4π cos ) 4 φ f r + fr c θ + c + c } Boh he linear momenum and he angular momenum accoun for he True mass of phoon and he momenum can be used o calculae he rue mass of phoon. Above menioned wo new equaions provide new ools o calculae rue mass of phoon if some more informaion of he phoon can be explored. C. Relaion beween Mass & Momenum of Phoon Momenum can exis wihou mass in phoon is a misconcepion and explained here. () 7

7 Whereas The oal energy (E) of phoon (paricle) includes all physical forms of energy possessed by he phoon plus he energy produced by he rue mass of phoon by he equaion E = mc, he energy (e), according o he Planck-Einsein equaion e = hf specifies only all he physical forms of energy possessed by he phoon. This (e) does no include he energy produced if he rue mass of phoon is convered o energy. The special heory of relaiviy specifies he oal energy of phoon by he following equaion: ( ) ( ) E = pc + m c (True mass m is considered insead of m 0 ) In he above equaion he erm (pc) relaes o he average values of momenum & velociy of phoon in one complee cycle of wave. When he mass of phoon (m ) is assumed o be zero in he above equaion, he (E) of he above equaion changes o (e) as under: e = pc The Planck-Einsein equaion specifies he energy (e), all physical forms of energy possessed by he phoon only wihou he energy produced by he conversion of rue mass of phoon o energy. Or e = pc = hf e = hf hf Or momenum p = c In boh he above menioned equaions (Planck-Einsein equaion and Special Relaiviy), he rue mass (m ) of he phoon has been oally ignored. The relaion beween momenum and frequency is derived wihou considering he mass of phoon. I is presumed ha he momenum can exis wihou he mass in phoon, which is no correc. Only he mass/maer produces momenum in a paricle. Energy canno exis in isolaion wihou mass. There has o be mass (maer) o possess any form of energy. Boh Newonian heory as well as special heory of relaiviy confirms ha phoon has mass. where - m : True Mass of phoon; - c: Linear velociy of phoon in X-direcion; - c ϕ : Tangenial velociy of phoon in curve pah of wave when he direcion of resulan momenum is a angle ϕ from X-axis; - I: Momen of Ineria of phoon; - ω: Angular velociy of phoon; - ƒ: frequency of phoon; - r: Disance of cenre of mass of phoon from he cenre of phoon; - p: Average resulan momenum of phoon in one cycle of wave; - p ϕ : Resulan momenum of phoon when he direcion of resulan momenum is a angle ϕ from X-axis; - h: Planck s consan; - θ: Angle of Angular Momenum from X-axis; - ϕ: Angle of Resulan Momenum from X-axis; - E: Toal energy possessed by phoon including energy by conversion of mass of phoon o energy; - e: Energy possessed by phoon excluding he energy by conversion of mass of phoon o energy. 4. Example of Mass of Phoon An example of Phooelecric effec conserving he mass of phoon is given below: A phoon his a free elecron in PV cell and combines wih elecron. The phoon ransfers is energy (e = hf) o he elecron. The combined energy of phoon and elecron ejecs he elecron (along wih phoon). The mass of phoon is no convered o energy and remains as such since here is no reacion o conver mass ino energy. This elecron ravels o a LED bulb which emis ou a new phoon wih is mass (frequency of phoon depends on ype of LED). From LED bulb he elecron reurns o PV cell. In he above example he mass of phoon remains as such and only he ransfer of energy akes place. 73

8 5. Wave Formaion by Phoon Experimenal Proof of Mass in Phoon [1] discovers ha phoon has mass and is cenre of mass is differen from he cenre of phoon. This discovery of mass is furher suppored by he various facs, he Newonian heory and special heory of relaiviy. How a paricle of phoon forms wave by virue of is mass is explained here? A moving phoon spins around is own cenre. The cenre of mass of phoon, locaed a a disance r from he cenre of phoon, roaes in a circular pah of radius r wihin he phoon. The mass of phoon develops angular momenum originaing from he cenre of mass in direcion perpendicular o he radial line from cenre of phoon o he cenre of mass. Wih he spin of phoon, he direcion of angular momenum keeps on changing coninuously from 0 o 360. The direcion of linear momenum of phoon is always consan. Figure 6 shows he direcions of angular momenums a inervals of 45 in one revoluion of phoon. The mass of a spinning phoon develops angular momenum from wihin he phoon of coninuously changing direcion. This angular momenum and linear momenum develops resulan momenum of coninuously changing direcion wihin 360 also from wihin he phoon. Resulan Momenum is he vecor sum of boh he linear momenum and he angular momenum. The magniude (p ϕ ) and he direcion (c ϕ ) of he resulan momenum a any posiion of curve pah of wave have been already calculaed above. The direcion of resulan momenum (ϕ) changes wihin 360 wih he spin of phoon and is also he direcion of he phoon in he curve pah of wave. The formaion of wave is explained below sep by sep: - The phoon moves coninuously in X-direcion (direcion of ravel) due o he linear momenum (m c) which always remains in X-direcion. - During he 1 s quarer of wave formaion (posiion 1 o 3) as he phoon spins, he cenre of mass roaes and he direcion of resulan momenum keeps on changing coninuously from posiion 1 o posiion 3 (horizonal X-direcion) as shown in Figure 7. During his 1 s quarer movemen, he phoon moves in X-Z direcion upward o he cres posiion of he wave by is resulan momenum. The upward movemen of phoon boh in X & Z direcions simulaneously forms he wave of he 1 s quarer as shown in Figure 7. - During he nd quarer of wave formaion (posiion 3 o 5) as he phoon spins, he cenre of mass roaes and he direcion of resulan momenum keeps on changing coninuously from posiion 3 o posiion 5 as shown in Figure 7. During his nd quarer movemen, he phoon moves in X-Z direcion downward o he posiion 5 of he wave by is resulan momenum. The downward movemen of phoon boh in X & Z direcions simulaneously forms he wave of he nd quarer as shown in Figure 7. Figure 6. The direcion of linear momenum is consan, whereas he direcion of angular momenum keeps on changing coninuously wih he roaion of phoon along wih is cenre of mass. The direcions of angular momenums saring from 0 are shown a inervals of 45. The angular momenum/resulan momenum moves he phoon up and down coninuously o form wave. 74

9 Figure 7. As he phoon spins he cenre of mass roaes. The direcion of he resulan momenum changes coninuously o move he phoon up & down o form wave. - During he 3 rd quarer of wave formaion (posiion 5 o 7) as he phoon spins, he cenre of mass roaes and he direcion of resulan momenum keeps on changing coninuously from posiion 5 o posiion 7 (horizonal X-direcion) as shown in Figure 7. During his 3 rd quarer movemen, he phoon moves in X-Z direcion downward o he rough posiion of he wave by is resulan momenum. The downward movemen of phoon boh in X & Z direcions simulaneously forms he wave of he 3 rd quarer as shown in Figure 7. - During he 4 h quarer of wave formaion (posiion 7 o 1 of he nex wave cycle) as he phoon spins, he cenre of mass roaes and he direcion of resulan momenum keeps on changing coninuously from posiion 7 o posiion 1 of he nex wave cycle as shown in Figure 7. During his 4 h quarer movemen, he phoon moves in X-Z direcion upward o he posiion 1 of he nex wave cycle by is resulan momenum. The upward movemen of phoon boh in X & Z direcions simulaneously forms he wave of he 4 h quarer as shown in Figure 7. - Wih every cycle or spin of phoon he above process is repeaed o form elecromagneic wave by he paricle of phoon. All elemenary paricles display Wave Paricle Dualiy as explained above. This also explains how any spinning paricle wih cenre of mass being differen from he cenre of paricle always moves in he pah of wave. A spinning spherical paricle of uniformly disribued mass moves in sraigh line. Similarly a spinning spherical paricle having mass locaed in he cenre of he paricle also moves in he sraigh line. Whereas spinning spherical paricle wih cenre of mass which is no in he cenre of paricle moves in he pah of wave. If he plane of spin of cenre of mass of phoon is differen from he direcion of ravel of phoon, wave in all 3 dimensional is formed. 6. Conclusions A spinning phoon develops resulan momenum from inside due o he mass of phoon wih cenre of mass differen from he cenre of phoon. The resulan momenum moves he phoon paricle in he pah of a wave and explains Wave Paricle Dualiy. The angular momenum of phoon due o he mass of phoon explains all differen ypes of Inerference phenomena and also he Polarizaion phenomena. The phenomena like Wave Paricle Dualiy, Inerference and Polarizaion displayed by he elemenary paricles including phoons are only possible wih he presence of mass in he paricles wih cenre of mass differen from he cenre of he paricles. The mass of phoon explains Wave Paricle Dualiy, Inerference and Polarizaion phenomena o supplemen he Quanum Theory. 75

10 References [1] Agarwal, N.S. (015) Journal of Modern Physics, 6, hp://dx.doi.org/10.436/jmp [] Agarwal, N.S. (01) Indian Journal of Science and Technology, 5,