The Cross Radial Force*

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1 College Pak, MD PROCEEDINGS of he NPA The Coss Radial Foe* Sanka Haja Calua Philosophial Foum, Sal Lake, AC -54, Seo-, Calua 7 64 INDIA sankahaja@yahoo.om Elei hages, elei & magnei fields and eleomagnei enegy ae eal physial eniies (objes). Beause, hese eniies possess momenum and enegy and we ould epeiene hese eniies wih ou sense ogans. Now, all physial objes ae subje o gaviaion. Theefoe, eleomagnei eniies should similaly be subje o gaviaion. In his lee, we have shown ha lassial physis wih his simple onsideaion ould eplain a lo of hiheo uneplained puzzling physial phenomena.. Inoduion In lassial physis, oss adial foe aing on a plane in a enal foe field is always as given in he sandad e book d m d, (i) whee m is he mass of he plane. When a plane onains hages whih have masses, he oss adial foe should be wien as pe ou analysis given in his lee in he seion 4 as wih d 3 m mp, (ii) d /, k. k u whee m p is he non-eleomagnei mass and 3 m is he longiudinal eleomagnei mass of hages assoiaed wih he plane. Now he adial foe aing on he plane as pe sandad lassial e book GM s, (iii) whee M s (eleomagnei as well as non eleomagnei) is he mass of he sun. 3 u When u and m mp, Eq. (ii) will ombine wih Eq. (iii) o give du GMs 3GMs U d H U,, (iv) whih eplains he advane of he peihelion of he Meuy. We ae pesening hee a gis of ou wok. We eques ou NPA olleagues o send hei ommens on ou lassial deduions of he ansvese Dopple s effe, inemen of life spans of adioaive pailes, Fizeau Epeimen, Mihelson-Gale Epeimen, Sagna Epeimen and he eplanaion of he null esul of he M-M ype epeimen as given in his lee. Ou appoah will a one eplain planeay moion, gaviaional ed shif, he bending of ligh ays gazing he sufae of he sun and why all eleodynami phenomena (like efleion, efaion, diffaion, inefeene e.) as obseved on he sufae of he moving eah ae independen of he movemen of he eah, obsevaions of Badley, Aiy and Zapffe on abeaion of ligh - lassially.. Classial Physis Heaviside (888) [, ] fis dedued he E field and of a seadily moving poin hage as Qk u sin 3 4 e 3/ * B field E, () * u E B, () whee is he angle beween and u. Now, if a dipole and he soue of he field whih eies he dipole move ogehe wih a veloiy u in he fee spae in any dieion pependiula o is dieion of osillaions, he elei foe and he magnei foe aing on he poin osillaing hage in he dipole will be espeively fom Eqs. () and () (when 9 ), F and - u F whee F is he foe aing on he osillaing hage by he soue field when he dipole is a es in he fee spae. Theefoe, he oal eleomagnei foe aing on he osillaing poin hage inside he dipole moving pependiulaly o is is dieion of osillaion is u F F F F k. (3) Eleomagnei momenum P and he magnei enegy T of a seadily moving poin hage ould be wien fom he onsideaion of lassial eleodynamis as * d all spae P D B, * T B d, all spae whee D and B * ae he elei induion veo and he indued magnei field veo espeively, and d is he infiniesimal volume elemen in he fee spae. Using Eq. () we have Tu P. u

2 Haja: The Coss Radial Foe Vol. 8 Seale in 897 [3] followed Heaviside and alulaed qu a l al a T ln 6l l a l l fo a moving haged ellipsoid wih he aes a: b: b, when a kb, whee l a k b. Puing al S 3 a S S, we have qus T S... S qu... 3 qu 6 a 3S kb when S. This oesponds o he Heaviside s Ellipsoid (i.e. a poin hage as pe an eellen analysis of Heaviside) fo when S, a k b. Replaing b wih R, we ge qu T. kr Fom hese equaions, we have in veo noaion q u P mu, (4) 6 k R q m whee m ons, m m,. 6e R k k We may find he alenaive lassial deduion of P in [4].. When he hage moves seadily in a dieion paallel o he dieion of he unifom elei field opeaing in fee spae d P m 3 F f f m 3 f du k, (5) whee f is he aeleaion of he poin hage in he dieion paallel o u.. When he hage is moving a a dieion pependiula o he dieion of he unifom elei field opeaing in fee spae P m F f f m f, (6) u k whee f is he aeleaion of he poin hage in he dieion pependiula o u. Fom Eqs. (5) and (6), we have longiudinal eleomagnei mass of a seadily moving poin hage 3 m. (7) And ansvese eleomagnei mass of a seadily moving poin hage m. (8) 3. Appliaions of Classial Physis 3.. Tansvese Dopple Effe As pe lassial eleodynamis, an elasi eleomagnei foe aing on poin hages inside mae auses eleomagnei adiaion. Now if he mae moves, he dipole moves wih i. Theeby he eleomagnei foe inside mae hanges and onsequenly, fequeny and ime- peiod of osillaion of he dipole hange as pe he following lassial equaions. Le an elei foe F (oiginaing fom a small hage inside a dipole) dive a poin hage bak and foh fom one end o he ohe end of a adiaing dipole saionay in fee spae. Then, as pe lassial equaion m F S, (9) he veloiy of osillaion being small, whee m is he eleomagnei mass of he hage in he saionay dipole, is he adian fequeny of osillaion of he hage, S is he sepaaing disane of he dipole. Now, when he above dipole moves pependiulaly o is dieion of osillaion and adiaes, we have F m S, () whee m m is he ansvese eleomagnei mass of he hage in he moving dipole as defined by he equaion (8), is he fequeny of osillaion of he hage whih is moving wih a veloiy u in fee spae wih he dipole and F is he eleomagnei foe aing on he moving hage. Compaing Eqs. (9) and () and using Eq. (3) fo he dipole moving wih an unifom veloiy in any dieion pependiula o is dieion of osillaion we have k. () The equaion eplains ansvese Dopple s effe lassially. 3.. So-alled Time Dilaion Now if he fequeny hanges, ime peiod oo hanges. Fo a adiaing dipole saionay in fee spae, () whee is he osillaion peiod and is he adian fequeny. If he same adiaing dipole moves wih a veloiy u in fee spae in a dieion pependiula o is dieion of osillaion, hen fo he moving dipole he osillaion peiod and adian fequeny saisfy. (3) Compaing Eqs. () wih (3 ), using eq. () we have, (4) o he peiod of osillaion of he above moving dipole ineases wih is veloiy in fee spae Lifespan Inemens of Moving Radioaive Pailes A adioaive paile deays when elei and magnei foes inside he paile a o disinegae he paile. When he adioaive paile moves, he elei and magnei foes aing inside he paile hange. And onsequenly, he disinegaion poess in he moving adioaive paile hanges as pe he following lassial equaions: The equaion of deay of he saionay adioaive pailes, (5) N N e F

3 College Pak, MD PROCEEDINGS of he NPA 3 whee is he popoionaliy onsan, F is foe aing inside a adioaive paile o disinegae a paile N and N eain usual meanings. Now if he adioaive pailes move wih a veloiy u in fee spae in any dieion pependiula o hei dieion of aing disinegaing foe, afe a ime we will find N unansfomed pailes suh ha N N e F, (6) whee F is he magniude of foe aing on he hage o be deahed in he moving paile. Compaing Eqs. (5) wih (6) using Eq. (3), we have. (7) This analysis a one desoys hee is one ime, hee is anohe ime -onep as well as he win paado of elaiviy. Now, if he soue be saionay in he fee spae and he obseve moves, fom he onsideaion of Mawell, hee should be no ansvese Dopple effe and no ime inemen. If ansvese Dopple effe and ime inemen ae onfimed epeimenally in suh ases, only hen some speial heoies ould be held supeio in his egad Fizeau Epeimen The esul of Fizeau epeimen has aleady been eplained by Loenz [5, 6] by he appliaion of lassial eleodynamis whih is given below. The equaion of Polaizaion P fo a dielei moving wih veloiy v in he fee spae ould be wien in ems of he elei field veo E and magnei field veo B as follows [7]: n P E, (8) E EvB, (9) whee is he absolue pemiiviy of he fee spae and n K, whee K is he dielei onsan of he medium. Now le he ais of z be aken paallel o he dieion of moion of he dielei, whih is supposed o be dieion of popagaion ligh. Conside a plane polaized wave. Le he ais of paallel o he Elei field so ha magnei field paallel o he ais of y. Now he fundamenal equaions in his sysem will ake he following foms: D H => B E => H y D P v z z () E B y () z D E P () Theefoe P n E vby Eliminaing D, P, E E vby (3). (4) H y and negleing E E E n v n z z v, we have (5) Subsiuing E n z/ V e, (6) whee V denoes he veloiy of ligh in he moving dielei wih espe o he fee spae. Theefoe Negleing v, we ge n V v n V. (7) V n n v. (8) The fao assoiaed wih v in he igh hand pa of he equaion is Fesnel dag oeffiien veified by Fizeau Epeimen. We may find he alenaive lassial deduion in [8]. 4. Ineaion of Eleomagnei Eniies wih Gaviaion: We know ha elei hages possess momenum and enegy jus like all ohe physial objes and we ould epeiene momenum and enegy of hages wih ou sense ogans. Theefoe, hages ae eal physial eniies (objes). All objes ae subje o gaviaion and hey have he same aeleaion owads he ene of gaviy in he same gaviaing field. Theefoe, hages should similaly be subje o gaviaion and he aeleaion of a poin hage should be he same as he aeleaion of a poin obje and ha should be dieed owads he ineaing gaviaing field (unlike is aeleaion duing is ineaion wih he elei field). This implies ha he gaviaing mass of a poin hage is popoional o is longiudinal eleomagnei mass. Tansvese eleomagnei mass should have no ole in his ineaion. If i had any ole in he ineaion, hages should no have he same aeleaion owads he ineaing gaviaing field as hose of he maeial bodies in he same gaviaing fields. Thus, in a gaviaing field, a poin hage as a mass poin; mass of he mass poin is popoional o he longiudinal eleomagnei mass of he poin hage. 4.. Ea Equaion of Planeay Moion Thus, when a plane moves in a gaviaing field, by din of ou above analysis, we have fo he Radial foe: GM s, (9) whee G is he gaviaional onsan, M s is he oal mass (noneleomagnei mass & mass oiginaing fom hages in he gaviaing body) of he gaviaing body onenaed a he oigin and he plane passes he poin, in he plane of moion in he pola oodinae. Now, as pe he old physis, Coss-adial Foe, in a enal foe field is always. Theefoe fo he plane wih hages, Coss Radial Foe d 3 m mp, (3) d o p 3 A m m ons. (3)

4 4 Haja: The Coss Radial Foe Vol. 8 In ase he plane of non-eleomagnei mass m p onains Q amoun of posiive and negaive hages in oal (ignoing he sign of he hages) and fo simple alulaion le us assume ha he posiive and negaive hages ae onenaed sepaaely nea he ene of he plane. Le M s be he oal mass (noneleomagnei mass and mass oiginaing fom he hages assoiaed wih he sun). 3 u When u and m mp, o A u / p 3/ m m 3 H ons. (3) Theefoe, he equaion of moion of a plane in he sun s gaviaing field should be (noing ha fo iula moion) u du GM U s 3GMs d H U (33) This eplains he advane of he peihelion of Meuy. 4.. Equaion of Moion of Ligh Rays in he Gaviaing Field of he Sun Ligh-ays possess eleomagnei momenum and eleomagnei enegy. Many people believe ha an eleon and a posion oming ogehe, ould annihilae eah ohe wih he emission of ligh o gamma ays [9] and ligh also as like eleons []. If ha be so, a poin ligh will similaly be subje o gaviaion as in he ase of a poin hage. Now, he equaion of moion of a poin hage in a gaviaing field ould be alulaed fom he Eqs. (3) and (3) puing mp. The esulan equaion will be he same as given in he Eq. (33). Bu in his ase, m fo a poin ligh being, H fo he poin ligh will be infiniy, and he equaion of moion of a poin ligh in a gaviaing field is du 3GMs U d, (34) whih will a one eplain he bending of ligh ays gazing he sufae of he sun Gaviaional Red Shif Suppose ha a ay wih he adian fequeny is oming fom he sufae of a sa of adius R and of mass M o he sufae of he eah whih is disane away fom he ene of a sa. As pe ou pevious disussion, eleomagnei enegy has he same aeleaion as ha of maeial bodies as well as poin hages in he same gaviaional field. Le f R be he gaviaional aeleaion of a ay on he sufae of a sa and f be he gaviaional aeleaion of he same ay when i is on he sufae of he eah. Then, we have fom he law of gaviaion [] f f R and emembeing f R g GM, R R, (35) GM whene f. (36) Now, fo he eilinea moion of he ay owads OX dieion we have dv dv d dv f v. (37) d d d d Theefoe, he diffeenial equaion fo he veloiy of he ay should ead, fom Eqs. (36) and (37) v d vdv GM, (38) R whee is he veloiy of he ay on he sufae of he sa and v is he veloiy of he same ay on he sufae of he eah. Fom whih we have / GM R v. (39) R GM Theefoe v, (4) R when is lage. Fom whih we have GM (4) R ( is he adian fequeny of he same ligh ay a he sufae of he eah) as he numbe of omplee waves passing hough a poin (i.e. fequeny) mus be popoional o he veloiy of he waves. 5. Puzzling Eleodynami Phenomena Mawell s equaions of eleomagnei fields ae appliable only in fee spae and inside sysems saionay in fee spae. One would hen epe some oeions/ modifiaions of Mawell s equaions when he eleomagnei phenomena ae sudied on he sufae of he eah whih is moving wih a high veloiy in he fee spae. Bu hose oeions ae no needed! All eleodynami phenomena like efleion, efaion, diffaion, inefeene e., as obseved on he sufae of he eah, eihe wih sa ligh o wih eah ligh ae independen of he movemen of his plane. Tha is, he eah s sufae is ealy equivalen o fee spae fo ou desipion of eleomagnei phenomena on i. 5.. Mihelson-Moley Type Epeimens in Ai & Wae Jus like elei hages and eleomagnei enegy, eleomagnei fields possess momenum and enegy whih we ould epeiene wih ou sense ogans. Theefoe, eleomagnei fields, oo, ae eal physial eniies (objes). All physial objes

5 College Pak, MD PROCEEDINGS of he NPA 5 a he suoundings of he eah ae aied wih he eah. Theefoe, he eah should ay elei and magnei fields along wih i a he viiniy of is sufae. This will a one eplain he null esuls of all he Mihelson-Moley ype Epeimens in ai and he Masa-Jamin ype Epeimen in wae a es on he eah s sufae; and may give us some insigh o undesand why all eleomagnei phenomena as obseved on he sufae of he eah ae independen of he moion of his plane. 5.. The Kennedy Thondike Epeimen Eleomagnei adiaion is he popagaion of vibaion of elei and magnei fields. In he Kennedy Thondike epeimen, i is obseved ha he veloiy of ligh on he sufae of he eah is independen of spinning, ona he Mihelson-Gale Epeimen, o anslaion and oaion of he eah in is obi The Tomashek (94) and Mille Epeimens (95) The Mihelson-Moley epeimen has been pefomed wih saligh and sunligh, simila null esuls have been onfimed. This an only happen if he elei and magnei fields oiginaing eihe fom he eah, sas o fom he Sun and eising a he nea viiniy of he eah s sufae, spins, anslaes and oaes wih he eah, ealy in he same way as ohe physial objes on eah do The Touon-Noble Epeimen (94) In a laboaoy, when a haged ondense moves, he elei field aound i hanges and heeby a magnei field is eaed. If he elei field oiginaing fom he ondense would move along wih he ondense, hee would be no hange of elei field aound he ondense and heeby, hee would be no magnei field aound i. Now, a ondense a es on he eah s sufae moves wih he eah. Bu he elei field aound he ondense, oo, moves wih i. And heefoe, he Touon-Noble Epeimen (94) fails o dee any magnei field aound he ondense. This implies ha he eah aies he ondense along wih is elei field Sagna Epeimen As pe lassial eleodynamis, ligh signals, divided in wo pas and sen in opposie dieions aound a fied iui on a spinning disk, should no eun o he poin of division a he same insan. Beause, he speed of ligh on a spinning disk is w when he ligh beam avels owads he dieion of spinning of he disk, and w when he ligh beam avels in he opposie dieion, w being he spinning veloiy of he poin on he disk whee he speed of ligh is being measued. This effe is he pimay effe of spinning. The aual epeimen onfims his. This effe of ligh on a spinning disk was obseved by G. Sagna in an inefeomee fied on he disk in 93, and is known as he Sagna effe. Bu he eah s moion seems o have no effe on he esul. The impliaion is he same as saed in he pevious eamples The Obsevaions of Badley (78), Aiy (87) and Zapffe (99) on Abeaion of Ligh When a ligh beam omes fom a sa and eahes he suoundings of he sun, i is aied wih he sun. Then he ay moves owads eah whih is moving wih espe o he sun wih a veloiy 3 Km/ se. Theefoe, he angle of abeaion of he asal ay is v/ whee v is he veloiy of he eah wih espe o he sun, bu no wih espe o he sa. Bu when he beam eahes he sufae of he eah, is dieion is no moe appaen. I will be he eal dieion of he beam nea he sufae of he eah as he eah aies he beam wih i! Theefoe, hee will be abeaion fo he asal ays elaing o he elaive veloiy of he eah and he sun as obseved by Badley (78), bu hee will be no fuhe abeaion (when he elesope is filled wih wae) as obseved by Aiy (87) and hee will be no abeaion of a ligh beam oming fom a mounain op as epoed by Zapffe (99) [] The Epeimens of Mihelson-Gale and Bilge, e al The eah jus like all ohe physial objes aies ligh wih i a he viiniy of is sufae. Theefoe, Coiolis foe due o he oaion of he eah mus a on he dieion of popagaion of ligh on he sufae of he eah. This will eplain he epeimens of he Mihelson-Gale and he epeimen of Bilge, e al. Le us hoose a poin O on he sufae of he eah a he laiude Noh and onsu a angenial plane a his poin. Now le us fi a Caesian oodinae sysem in he plane suh ha OY epesens he Noh and OX epesens he Eas. Now suppose ha he eah is no oaing and an elemen of ligh beam is aanged o move fom a poin P in he OY ais a he insan in a small iula moion in he lokwise dieion suh ha a he ime i ouhes he poin Q in he OX ais and say OP OQ. Tha is, when,, y and when,, y. Now suppose ha he eah oaes wih an angula veloiy. Then he Coiolis foe due o he oaion of he eah should defle he beam mainly easwadly and he beam will no ouh he poin Q. Insead i will ouh a poin R vey adjaen o he OX ais. Now fo a ough alulaion of he disane OR, le us onside he moion of he beam on he OY ais wih a veloiy fom he poin P o he poin O. In his ase, we may wie F ( )sin sin (4) d sin (43) d d sin C d (44) sin C C (45) Remembeing he iniial ondiion and aking ino aoun, (46) we have sin, (47) whih is he defleion of he beam owads OX ais fo a small ile. Theefoe, in ha ase we have OR sin. (48)

6 6 Haja: The Coss Radial Foe Vol. 8 Fo he beam moving in he anilokwise dieion, his disane will be sin (49) Fom he las wo equaions we have fo one omplee oaion 4A sin (5) whee A is he aea of he ile. The finge shif elevan o seems o be veified by he Epeimens of Mihelson-Gale [3] and Andeson and Bilge, e al. [4]. The esul will emain moe o less he same when he ile is lage. 6. Conlusion The analysis esablishes lassial physis and ovehows he speial and geneal elaiviy fom he domain of physis a a soke. Anybody wahing a physis book o a physis jounal should a one onlude ha he subje he is wahing is he subje of pue meaphysis, no a subje dealing wih aional inepeaion of his physial wold. Bu he sill goes o undesand he subje wih he onviion ha he subje is he epiome of physial knowledge and he nineeenh enuy physis is eihe obsolee o an impefe wold view of he pedeessos. Wha is he ause behind i? This is he age of ehnology. Monopoly and he Sae goven onempoay ehnology ha needs seey fo he susenane and developmen of is govenos. The bes way of mainaining seey is he meaphysial inepeaion fo he poduion and woking of he ehnologial podus. Theefoe monopoly and sae enouage meaphysial inepeaions of he poduion and he woking of hei podus and eend i o he inepeaions of he physial wold. Hee lies he suess of he elaiviy heoy. Any sienifi debae o any ousanding epeimen will hadly be able o demolish he elaivisi meaphysis wihou eposing he soiologial onen of onempoay heoies. * The main poposiion of his lee has been published in GED 6 (5), 4, 63-7; GED 7 (6),, 3-8; GED 8 (7), 3, 73-76; GED 9 (8), 5, Refeenes [ ] O. Heaviside, The Eleomagnei Effe of a Moving Poin Chage, The Eleiian :47-48 (888). [ ] O. Heaviside, On he Eleomagnei Effes due o he Moion of Eleiiy hough a Dielei, Philo. Mag. 7: (889). [ 3 ] G. F. C. Seale, On he Seady Moion of an Eleified Ellipsoid, Philo. Mag. 44: (897). [ 4 ] Sanka Haja, Anina Ghosh, Collapse of SRT: Deivaion of Eleodynami Equaions fom he Mawell Field Equaions, Galilean Eleodynamis 6: 67 (5). [ 5 ] H. A. Loenz, The Theoy of Eleons, p (Dove Publiaions In. New Yok, 95). [ 6 ] E.T. Whiake, Hisoy of he heoies of Aehe and Eleiiy, Vol., pp (Thomas Nelson and Sons Ld., 95). [ 7 ] E.T. Whiake, Hisoy of he heoies of Aehe and Eleiiy, Vol., pp (Thomas Nelson and Sons Ld., 95). [ 8 ] Sanka Haja, Anina Ghosh, Collapse of SRT: Deivaion of Eleodynami Equaions fom he Mawell Field Equaions, Galilean Eleodynamis 6: 69 (5). [ 9 ] R. P. Feynman, R. B. Leighon, M. Sands, The Feynman Leues on Physis, p. 3 (Naosa Publishing House, New Delhi, 998). [ ] R. P. Feynman, R. B. Leighon, M. Sands, The Feynman Leues on Physis, p. 45 (Naosa Publishing House, New Delhi, 998). [ ] V. M. Sazhinskii, An Advaned Couse of Theoeial Mehanis anslaed fom he Russian by V. M. Vosolov, pp (Mi Publishes, Mosow 98). [ ] C. A. Zapffe, Badley Abeaion and Einsein Spae Time, Ind. J. of Theo. Phys. 4: (99). [ 3 ] A. Mihelson, H. G. Gale, The Effe of he Eah s Roaion on he Veloiy of Ligh, Asophys. J. 6: (95). [ 4 ] R. Andeson, H. R. Bilge, G. E. Sedman, A Cenuy of Eah Roaed Inefeomee, Am. J. Phys. 6: (994).

Lecture 9. Transport Properties in Mesoscopic Systems. Over the last 1-2 decades, various techniques have been developed to synthesize

Lecture 9. Transport Properties in Mesoscopic Systems. Over the last 1-2 decades, various techniques have been developed to synthesize eue 9. anspo Popeies in Mesosopi Sysems Ove he las - deades, vaious ehniques have been developed o synhesize nanosuued maeials and o fabiae nanosale devies ha exhibi popeies midway beween he puely quanum