Wave Particle Dualism for Both Matter and Wave and Non-Einsteinian View of Relativity

Transcription

1 Talukder and Aad: Wave Partle Dual for Bot Matter and Wave and Non-Entenan Vew of Relatvty (8-91) Wave Partle Dual for Bot Matter and Wave and Non-Entenan Vew of Relatvty M.O.G. Talukder 1, Mufq Aad 1 Varendra Unverty, Raja 64, BANGLADESH Departent of Py, Raja Unverty, Raja-65, BANGLADESH Abtrat In t paper, we deontrate te gnfane of Non-Entenan vew of relatvty n relaton to wave odel of partle and partle odel of wave. To aoodate wave-partle dual, we ave ondered de-brogle atter wave onept and Copton Effet. Te kneat of te poton and te poton etter partle (poton-gun) are taken nto onderaton. Ten, we ave orrelated te oton related paraeter of te gun wt te aratert of te poton. T provde a orrelaton between wave apet of partle (atter wave) and partle apet of wave. Keyword: Wave, partle, atter wave, poton, wavelengt, oentu and Copton wave. INTRODUCTION Te wave partle dualty a fundaental property of bot atter and wave. In 194, de-brogle propoed a odel, w an be regarded a te wave odel of atter, to explan te wavelengt of atter wave. In odel, t wa aued tat wavelengt for u a wave aoated wt a ovng partle proportonal to t oentu wt te Plank ontant a te proportonalty ontant 1,. Sybolally, t an be wrtten a were 3,4, v d 1 (1) p v v () v 1 In te above equaton, λd = de Brogle wavelengt = Plank ontant v = veloty of te partle p = v = oentu of te partle = ret a of te partle Page 8 Copyrgt CC-BY-NC, Aan Bune Conortu AJASE

2 Aan Journal of Appled Sene and Engneerng, Volue, No 1/13 ISSN X(p); (e) = relatvt a of te partle Moreover, te veloty (w) of te atter wave gven by w v vw (3) In te above equaton, v te peed of te partle and te peed of lgt. On te oter and, te partle nature of wave wa frt ntrodued by Enten. He propoed a partle or poton odel, w alo known a te quantu odel, of lgt. In tat odel, e vewed lgt a ontng of trea of partle, alled poton, rater tan of wave nature. Te energy ontent of ea poton equal to te produt of Plank ontant and te frequeny of lgt 5. Tat E (4) were, E = energy of poton = Plank ontant ν = frequeny of lgt It ould be ponted out ere tat te ret a of a poton zero. However, t a oentu w an be obtaned fro te relaton p (5) E p (6) were, p te oentu of te poton and te peed of lgt. In te tudy, preented ere, onderng a poton-gun yte ettng a poton, we ave deontrated te wave partle dualty for bot partle and wave. Preuably, te Copton Effet 6 te ot obvou and onvnng aong all te penoena pontng to te partle properte of poton. It derbe te ollon of a poton and an eletron a own n Fg. (1) below. Copyrgt CC-BY-NC, Aan Bune Conortu AJASE Page 81

3 Talukder and Aad: Wave Partle Dual for Bot Matter and Wave and Non-Entenan Vew of Relatvty (8-91) Fg. 1: Copton Satterng: φ angle between ndent poton and reol eletron and θ angle between ndent and attered poton. Te Copton Effet derbe te ollon of a poton and an eletron. It expreed n ter of te wavelengt by te followng equaton: 1o (7) were, λ = wavelengt of te ndent poton λ = wavelengt of te attered poton = ret a of an eletron = peed of lgt = Plank ontant θ = angle between ndent and attered poton It ould be ponted out ere tat te quantty / alled te Copton wavelengt of te attered eletron. In t paper, we preent a opreenve explanaton of te Copton Effet and of Copton wave troug ung te onept of non-entenan relatvty. Page 8 Copyrgt CC-BY-NC, Aan Bune Conortu AJASE

4 Aan Journal of Appled Sene and Engneerng, Volue, No 1/13 ISSN X(p); (e) RESULTS AND DISCUSSIONS (a) Matter Wave In a prevou paper 7, onderng a poton-gun ettng a poton, we ave own fro te oentu onervaton law: 1 v v 1 NL v (8) Te LHS ndate te oentu of te poton and RHS repreent te oentu of te gun. Te RHS te longtudnal oentu of te gun; terefore, te LHS te longtudnal oentu of te poton. Terefore, te latter ndate tat ν of te poton te relatve longtudnal energy. Tat 1 v NL 1 (9) Now, onderng = νλ (ν and λ are te frequeny and wavelengt, repetvely, of te etted poton), Eq. (8) take te for were, NT NLv NLv (1) NT (11) NT 1 v 1 (1) Equaton (8) learly ndate te oentu onervaton n te longtudnal dreton. Hene, te oentu wll alo onerve n te tranvere dreton a follow: were, NT NT v NT v (13) NL (14) 1 v NL 1 (15) Copyrgt CC-BY-NC, Aan Bune Conortu AJASE Page 83

5 Talukder and Aad: Wave Partle Dual for Bot Matter and Wave and Non-Entenan Vew of Relatvty (8-91) and 1 v 1 NT (16) Hene, fro Eq. (1) and (14), we get v NLNT (17) Now, f we onder tat te energy of te etted poton u tat te reol gun ove at te peed of lgt (.e. v = ), ten fro te above equaton, we get C v (18) were, λc=/ te Copton wavelengt. Hene, we an onlude tat te wavelengt of te etted poton beoe equal to te Copton wavelengt for v =. Terefore, puttng λc = /νc (νc te Copton frequeny) n te above equaton, we get C (19) Tat for v =, te poton energy or te Copton wave energy beoe equal to te ret a energy of te gun. Now, let u expre λnl and λnt n ter of λc. In order to do o, we expre te veloty of te gun a te fraton of (.e. v = (v/)). Ten Eq. (14) take te for, were, 1 v NL 1 CL () v v 1 v CL 1 (1) te longtudnal Copton wavelengt. Slarly, Eq. (1) take te for NT CT () 1 v v v 1 Page 84 Copyrgt CC-BY-NC, Aan Bune Conortu AJASE

6 Aan Journal of Appled Sene and Engneerng, Volue, No 1/13 ISSN X(p); (e) were, (3) CT 1 v 1 te tranvere Copton wavelengt. It ould be ponted out ere tat (4) CL CT C and NL CL (5) NT CT Nevertele, n order to ave better undertandng, let u onder te energy onervaton law a gven n te prevou paper, 1 v 1 (6) 1 v Followng te above equaton, let u draw an energy trangle a follow: A p 1 v 1 B 1 v θ C Fg.: ABC a trangle baed on energy onervaton law (Eq. 6) and o 1 v. Copyrgt CC-BY-NC, Aan Bune Conortu AJASE Page 85

7 Talukder and Aad: Wave Partle Dual for Bot Matter and Wave and Non-Entenan Vew of Relatvty (8-91) Fro te above trangle, NL 1 v Sn 1 (7) 1 v n o (8) Hene, ung Eq. (8) n Eq. () and (), repetvely, we get and NL v 1 o (9) NT 1 o v (3) Furter, ung Eq. (8) n Eq. (1) and (3), repetvely, we get and 1 o CL (31) 1o CT (3) Coparng wt Eq. (1), we an onlude tat λnl gven by Eq. (14) repreent te atter wave n non-entenan relatvt ae. It ould be ponted out ere tat λnl te wavelengt of te etted poton n te longtudnal dreton. Hene, we an onlude tat te atter wave aoated wt a ovng body an be repreented by a poton, of w te longtudnal oponent te onventonal de-brogle or atter wave. Tu, te above duon gve a lear and opreenve explanaton of te atter wave revealed troug non-entenan relatvty. It ould be entoned ere tat te atter wave a been derbed elewere 8 n a dfferent perpetve (ee Appendx-A). In te followng duon, we deontrate te gnfane of u relatvty n relaton to Copton Effet. (b) Copton Effet For θ = 18, Eq. (7) take te for Page 86 Copyrgt CC-BY-NC, Aan Bune Conortu AJASE

8 Aan Journal of Appled Sene and Engneerng, Volue, No 1/13 ISSN X(p); (e) (33) Te orrepondng pyal tuaton an be derbed a follow. Te ndent poton trke an eletron at ret n u a way tat te attered poton ove n te oppote dreton, but te eletron ove n te dreton of te ndent poton. Te above reult an alo be obtaned troug derbng te Copton atterng by a poton-gun yte a follow. Let u onder tat te attered eletron a gun and t et a poton of energy equal to te energy dfferene between te ndent and te attered poton. Tat (34) (35) were, ν, ν and ν are frequene of te etted poton, te ndent and attered wave repetvely. Equaton (35) an alo be wrtten a (36) (37) Te above equaton repreent te wavelengt of te poton n ter of te wavelengt of te ndent and attered poton. In order to ave better undertandng, let u take te oentu onervaton law (Eq. (8)) nto onderaton, tu, we an wrte NL v (38) were, NL te relatve a n te longtudnal dreton. For v =, NL 1 v 1 v 1 (39) v Terefore, fro te above two equaton, we get 1 (4) (41) Hene, fro Eq. (33) and (41), we obtan Copyrgt CC-BY-NC, Aan Bune Conortu AJASE Page 87

9 Talukder and Aad: Wave Partle Dual for Bot Matter and Wave and Non-Entenan Vew of Relatvty (8-91) (4) (43) It ould be ponted out ere tat te above equaton a been derved for v =. Now, for v =, Eq. (37) take te for v (44) Terefore, ung Eq. (43) n te above equaton and oparng te reult wt Eq. (33), we an wrte v C (45) were, C (46) te Copton wavelengt of te attered eletron. Now, fro Eq. (), for v =, we get NT v CT v (47) It ould be ponted out ere tat Eq. () repreent te tranvere wavelengt of te etted poton fro a poton-gun yte. Hene, oparng Eq. () wt (47), we an onlude tat λ n Eq. (45) alo repreent tranvere wavelengt (λ NT) of te poton-gun yte n relaton wt Copton atterng derbed above. Now, λ NT related to λ CT gven by Eq. () and te expreon for λ CT gven n Eq. (3) w CT 1 v 1 p (48) CL were, (49) CT p CL p CL 1v (5) te Copton oentu n te tranvere dreton. Te LHS of te above equaton te produt of wavelengt and oentu bot of w are relatvt. Page 88 Copyrgt CC-BY-NC, Aan Bune Conortu AJASE

10 Aan Journal of Appled Sene and Engneerng, Volue, No 1/13 ISSN X(p); (e) In te produt for, bot te quantte annot be relatvt beaue n tat ae t wll be non-relatvt (for furter detal ee appendx A). Hene, onderng te wavelengt a relatvt and oentu a non-relatvt, te above equaton an be wrtten a 1 v 1 (51) Ung te value of λ fro Eq. (46) n te above equaton, we get 1 v 1 (5) Furter, ung Eq. (8) n te above equaton, we obtan 1 o (53) Te above equaton an repreent te Copton atterng expreon gven by Eq. (7) f we replae te angle θ by θ. It ould be entoned ere tat te angle o 1 v and θ te angle between ndent and attered poton. Tu, te paper preented ere, deontrate a opreenve explanaton of te Copton Effet and te expreon gven by Eq. (53) gve u a deeper undertandng of te effet revealed troug a dfferent perpetve. It alo explan te relevane of te non-entenan relatvt ae for te orrepondene between laal and quantu ean. Furter, Eq. (5) an alo be expreed a (54) p CT p CT (55) Now, t lear fro Eq. (5): and p CT v (56) v p (57) CT Copyrgt CC-BY-NC, Aan Bune Conortu AJASE Page 89

11 Talukder and Aad: Wave Partle Dual for Bot Matter and Wave and Non-Entenan Vew of Relatvty (8-91) Terefore, fro te above two equaton, we an wrte for v, pct (58) Tat te produt of te ange of wavelengt and te relatve oentu n te tranvere dreton le between and. Furter, puttng λ =t (t te te perod) n te above equaton, we get were, and t ECT (59) t t t (6) ECT p CT (followng Eq. (6)) (61) In te above equaton, t and t are te te perod of te attered and ndent poton repetvely and E CT te Copton wave energy n te tranvere dreton. It rearkable tat te above reult are te onequene of ung te Non- Entenan relatvt ae for v. Tee reult annot be obtaned ung Enten teory of peal relatvty a obvou fro Eq. (1) tat λ d a v. CONCLUSIONS Conderng a poton-gun yte ettng a poton and orrelatng te wave paraeter of te poton wt te oton related paraeter of te gun troug non- Entenan relatvty, we ave found: (a) Te aratert of te etted poton are lke toe of atter wave aoated wt a ovng partle. Tat te atter wave an be derbed by a poton avng relatve energe n bot te longtudnal and tranvere dreton. Te longtudnal wave orrepond to te onventonal de-brogle atter wave. Wen te gun ove at v =, te wavelengt of te etted poton or of te atter wave beoe equal to te Copton wavelengt. It ean te energy of te atter wave beoe equal to te Copton energy or ret a energy of te gun. Furter, onderng te attered eletron n Copton atterng a a gun ettng a poton avng energy equal to te energy dfferene between te ndent and attered poton, we ave found: (b) A lear and opreenve undertandng of te Copton wavelengt and oter paraeter (e.g. frequeny, energy and veloty) of te Copton wave. () Te relatvt kneat of a partle ovng at v = owng te relevane of Non-Entenan relatvty to explan te quantu eanal penoenon lke Copton atterng w annot be done ung Enten teory of relatvty. (d) In te produt of two dfferent pyal entte (e.g. lengt-oentu, teenergy et.), bot annot be relatvt at te ae ntant of te. Page 9 Copyrgt CC-BY-NC, Aan Bune Conortu AJASE

12 Aan Journal of Appled Sene and Engneerng, Volue, No 1/13 ISSN X(p); (e) REFERENCES 1. L. de Brogle, Nature, 11, 54 (193).. L. de Brogle, Ann. Py. (Par) 3, (195). Reprnted n Ann. Found. Lou de Brogle 17 (199) p.. 3. A. Enten, Annalen der Pyk, 17, 891 (195). 4. A. Enten, Annalen der Pyk,, 67 (196). 5. A. Enten, Annalen der Pyk, 17, 13 (195). 6. A. H. Copton, Py. Rev.,, 49 (193). 7. M.O.G. Talukder, Proeedng, ISSR-1, Raj. Unv. J. of S., 38, (1). 8. M.O.G. Talukder (1), An Alternatve Approa to te Relatvty, Granta Proaton, Raj. Banglade, p.11. Copyrgt CC-BY-NC, Aan Bune Conortu AJASE Page 91