Proton/Electron mass ratio and gravitational constant due to special relativity

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1 Proton/Elctron ass ratio and gravitational constant du to scial rlativity Prston Guynn Guynn Enginring, 1776 hritag Cntr Driv, Suit 04 Wak Forst, North Carolina, Unitd Stats 7587 Sinc rlativistic lngth contraction occurs only in th dirction of otion and not in th transvrs dirction, rotation rsults in an ffct known as Thoas rcssion. Thoas rcssion acts as a countr rotation. Bcaus rcssion incrass non-linarly according to th Lorntz factor, rotation inus rcssion has a axiu valu. Th axiu valu of rotation vlocity inus rcssion vlocity is trd th axiu diffrnc vlocity and is dsignatd v. W showd in rvious work that this is th hysical basis of charg structur, lctroagntic ffcts, and th fin structur constant. In this rort th roton/lctron ass ratio is forulatd in trs of v, th sd of light, and th lctron ass. Th roton ass calculatd using th forula is wll within th standard uncrtainty of th CODATA valu. Th gravitational constant is forulatd siilarly, and th calculatd rsult is wll within th standard uncrtainty of th CODATA valu. Ths rsults build on th frawork stablishd in our rvious rorts. Proton/Elctron Mass Ratio First, w show th roton/lctron ass ratio forulatd in trs of v, th sd of light, and th lctron ass. Th sd of light is dfind 1 as c (1) s Th rlaltivistic rotational diffrnc vlocity was drivd in our rvious rort and a grah is rovidd in Andix A. Th axiu diffrnc vlocity is xactly ( 1) c v W forulat an quation for th roton-lctron ass ratio as = () = 1kg ( 1) kg 4 () 1

2 CODATA rorts th ass of th lctron 1 as (11)E-1 kg. Using this valu on th right sid of Eq rsults in th valu of th roton lctron ass ratio = (4) Using th CODATA valu for lctron ass a scond ti, w arriv at th roton ass = E - 7 kg (5) Th CODATA valu for roton ass 1 is (1)E-7 kg. Th calculatd valu of roton ass in Eq 5 has nin significant digits of corrsondnc to th CODATA valu. It is obvious uon insction of Equations 1,, and that th roton/lctron ass ratio is du to scial rlativity. Rfrring to /1kg as th noralizd lctron ass, w s that both th noralizd ass and its invrs aar in Eq. Each of th othr trs in Eq is vry sil and dirctly rlatd to th sd of light and scial rlativity. Th nubr in Eq is not a vlocity, but th arbitrarily chosn nubr associatd with th sd of light. Th nubr was arbitrarily associatd with th sd of light, and could b rlacd with anothr nubr in th futur, but th rlationshi xrssd by Eq is a hysical rlationshi indndnt of arbitrarily assignd nuric valus, so th nubr rrsnts a axiu and acts as a scaling factor. Th fraction 5/8 in th nurator of th scond tr in arnthss of Eq has significanc at th rotational vlocity of / c which rsults in a Lorntz factor of γ =. This is bcaus at rotation vlocity / c, Thoas rcssion is qual to rotation, rsulting in an inrtial fra of rfrnc. Th MacLaurin sris xansion of th Lorntz factor at rotation vlocity / c shows that 5/8 is th su of all trs byond th kintic nrgy tr. This is dscribd in dtail in th sction 'Chargd Particl to Photon Couling' in th articl Elctroagntic Effcts and Structur of Particls Du to Scial Rlativity. Th in th dnoinator of th scond tr in arnthss of Eq is th ratio of a hoton's total angular ontu to its on-axis angular ontu. In gnral, is th agnitud of th vctor su of two unit vctors at right angls to ach othr. Th in th nurator of th scond tr in arnthss of Eq is th ratio of charg total angular ontu to charg raxis angular ontu. In gnral, is th agnitud of th vctor su of thr unit vctors at right angls to ach othr. W do not yt hav a full undrstanding of th gotry and intraction of th roton, lctron, and sac that would coltly xlain th rlationshis btwn th trs of Eq. Howvr, th forulation of th roton/lctron ass ratio with trs xclusiv to scial rlativity and Thoas rcssion rovids insights, which togthr with our rvious work, should lad to a colt undrstanding of thos rlationshis.

3 Fin Structur Constant Th arnthtical quantity in Eq is vry siilar to th fin structur constant, ilying ithr a dndncy btwn th fin structur constant and roton/lctron ass ratio, or a coon basis. Eq 6 is a rforulation of th fin structur constant fro our rvious work. This silifis to ( 1) 1kg α = π + (6) 4 ( ) α = (7) which xactly atchs all lvn significant digits of th CODATA rcondd valu 1. W showd in our rvious work that th π factor in Eq 6 is xactly th angular diffrnc btwn an inrtial fra of rfrnc at th rotation vlocity / c and a non rotating laboratory fra of rfrnc. Th fin structur constant is art of th lctrostatic forc quation, and th agntic forc quation as shown in our rvious rort. Bcaus th forcs btwn chargd articls can b forulatd in trs of thir structur and scial rlativistic bhavior, th bas unit Ar and all its drivd units ar rdundant. Thy ssntially constitut a aralll syst of units basd on th forc btwn two currnt carrying conductors sacd 1 tr aart. Additionally, that th roton ass is rlatd to th sd of light, and rlativistic Thoas rcssion, as shown in Eq, indicats that th SI units of ass, distanc, and vlocity ar not indndnt. A consistnt syst of units rquirs that th bas units hav no intr-dndnc. Thy ust b utually orthogonal. Bcaus of this, rsarch into th scial rlativistic basis of charg structur and intraction, th roton/lctron ass ratio, and th gravitational constant rquir a first rincils aroach. Gravitational Acclration and Forc Th gravitational constant can b xrssd as G sr 1 π kg ( 1) R R kg s (8) whr R is th lctron radius, drivd in our rvious work. R E-1. Eq 8 rducs to

4 G sr E -11 (9) kg s CODATA rorts th Nwtonian constant of gravitation 1 as (1)E-11 /(kg s ). Th valu in Eq 9 is wll within th standard uncrtainty of th CODATA valu. Th arnthtical quantity in Eq 8 is siilar to th fin structur constant and roton/lctron ass ratio in bing unit-lss. Howvr, unlik th forulation of th roton/lctron ass ratio in Eq and th fin structur constant in Eq 6, a basis for th unit transforation in Eq 8 has not yt bn dvlod. Th rational for noralization of lctron ass to th kg, and noralization of lctron radius to th tr is that hysically aningful bass ar bing scald to arbitrary bass. At first glanc, th scond tr in Eq 8 aars astonishing. It is th noralizd valu of th roton radius drivd in rvious work, e-14. That th roton radius is in th scond tr is howvr consistnt with th rsnc of lctron radius in th first tr. That th noralizd roton radius is a tr of th gravitational constant, which rsults in acclration ultilid by trs squard, ay b startling. Howvr, whn w considr that thr is a π diffrnc in angl btwn th laboratory fra of rfrnc and th rotational inrtial fra of rfrnc at /c, it is lss so. Th π diffrnc in angl ilis that a circl in on fra has linar charactristics in th othr fra, and a linar otion in on fra has charactristics of circular otion in th othr fra. Thr is thn a ossibl rlationshi via transforation fro linar kintic nrgy to rotational nrgy and cntrital acclration. Onc again, th basis of th gravitational constant in scial rlativity is clar, but w do not yt hav a full undrstanding of th intrrlation of all ffcts. Th siilaritis btwn Equations, 6, and 8 ar aarnt, and th basis of th trs of ach quation is scial rlativity. Th scond tr of Eq 8 is rlatd to th structur of th roton, and th first tr is dirctly rlatd to th lctron. Th scond tr is roughly 1/00 th agnitud of th first tr. Th diffring rlativ agnituds of th two trs in th gravitational constant ay ily that th roton and lctron ios gravitational ffcts with diffrnt agnituds. Th first tr of Eq 8 ay b th ffct du to lctrons, and th scond tr ay b th ffct du to rotons, with Eq 8 as a whol alying to a ass with quivalnt nubrs of lctrons and rotons. Howvr, th lctrostatic forc is so uch strongr than th gravitational forc, that asurnts of th gravitational ffcts of isolatd chargs is roblatic. CODATA rfrs to th gravitational constant as th Nwtonian gravitational constant 1. Howvr, th forulation of Eq 8 shows that th basis of gravitation is in scial rlativity. Th corrsondnc of Eq 8 to th Nwtonian forulation ilis that it is alicabl and rlvant, but liitd in sco. Th rcssion of Mrcury's orbit is not aarntly xlaind by Eq 8. Howvr, th far raching ffcts of scial rlativistic Thoas rcssion in ass rlationshis, rotation, angular ontu, and gnral structur of attr raiss th ossibility of an as yt undtrind rlationshi. Th arnthtical quantity in Eq 8 shows that articls with rotating inrtial fras of rfrnc hav an ffct at a distanc. Th rsctiv that two articls intract dirctly through a forc 4

5 btwn th is not substantiatd whn scial rlativity is considrd. Rathr, th rsnc of a singl lntary articl is a sufficint condition that any othr lntary articl will intract with it through scial rlativity. Th lctrostatic forc quation fro our rvious work lads to th sa conclusion. W rovid hr a rforulation of that quation for th agnitud of forc btwn two lntary chargd articls saratd by distanc r which suorts this rsctiv. F( r) ( 1) 4π kg ( 1) = + 1 1kg r s R π R 1 (10) Th forulation of Coulob's law in trs of a squar of th lntary charg, ilying a dirct intraction of chargd articls, is not substantiatd by Eq 10. Though th ffct is idntical, th rlativistic rsctiv is on of indirct intraction. Conclusion In rvious work w forulatd quations for th fin structur constant, th roton g factor, th nutron ass, and th dutron ass. Rsults of th forulations atchd xrintally known valus to lvn, svn, ight, and nin significant digits rsctivly. Th trs in ach forulation wr dirctly rlatd to th odl and th thory basd on Thoas rcssion. Th rvious forulations ar now joind by th roton/lctron ass ratio and th gravitational constant with nin and fiv significant digit corrsondncs, with th lattr liitd by th uncrtainty of xrintal data. It should b hasizd that lntary articl siz as discussd in this rort is substantiatd in rvious rorts. Photon wavlngth is not dirctly rlatd to lntary articl dinsions, but to th transition ti btwn rotational vlocitis. Evry chang to th stat of an lntary articl rsults in a chang to its fra of rfrnc, and this would hav to b considrd in attts to asur articl dinsions. Th rsults rsntd hr and in our rvious work show that scial rlativity, and scifically Thoas rcssion, has far raching ffcts. Chargd articl lctrostatic intraction, agntic intraction, atoic nuclus structur, and articl-hoton intraction wr rsntd as so of thos ffcts in rvious work. Many fundantal rlationshis ar now forulatd in trs of scial rlativity. Th bhavior of articls in trs of a scial rlativistic odl had bn broadly frad in our rvious work. Th odl bcos or colt with th rsults rsntd hrin. Th odl is a hysical odl that corrsonds to xrintally known charactristics of articls and thir intractions. 5

6 Rfrncs 1) CODATA Rcondd Valus of th Fundantal Physical Constants: 014 J. Phys. Ch. Rf. Data 45, 0410 (016); doi / , 7, 57 ) Guynn P. L., vixra [v] :1:5, 'Elctroagntic Effcts and Structur of Particls du to Scial Rlativity',.; 4; 5;.7; 18 ) Guynn P. L., vixra [v] :10:, 'Elctrostatic Forc and Charg Structur',. 6

7 Andix A Fig 1. Diffrnc vlocity as a function of rotation vlocity with axiu diffrnc vlocity, v, annotatd. 7

Unit 7 Charge-to-mass ratio of the electron

Unit 7 Charge-to-mass ratio of the electron Unit 7 Charg-to-ass ratio of th lctron Kywords: J. J. Thoson, Lorntz Forc, Magntic Filds Objctiv: Obsrv th rsults of lctron ba influncd by th agntic fild and calculat th charg-to-ass ratio of th lctron.