A Reexamination of the Velocity of Light, Dark Mass, and the Accelerated Expansion and Age of the Universe

Transcription

1 3 Auust 4 A Rxamination of th Vlocity of Liht, Dark Mass, and th Acclratd Expansion and A of th Univrs By Morton F. Spars Abstract: This papr stablishs th amazin ability of spac prmittivity and prmability to dtrmin th vlocity of liht, th xtnt of Dark Mass, and th acclratd xpansion of th univrs. In addition, takin into account th dpndnc of th vlocity of liht on prmittivity and prmability, it is shown that th univrs is sinificantly oldr than is nrally accptd. From Einstin, E=M c, or M=E/ c. (1) From Maxwll, c =1/[εμ ]. () Thus, solvin for M by substitution of () into (1), M=E [εμ ]. (3) Hraftr, quation (1) will b rfrrd to as th Einstin Equation, quation (), as th Maxwll Equation; and quation (3) as th Einwll Equation. In ths quations, ε dnots prmittivity in vacuum spac and μ dnots prmability in vacuum spac. Th subscriptd variabls ε and μ ar usd blow to dnot prsnt stablishd valus for ε and μ. In quations (1) throuh (3), abov, E stands for th nry of a slctd body in spac in units of forc-tims-th-distanc, i.., in nwton-mtrs, or jouls, in th MKS systm of units that will b usd hrin. M stands for th masurd mass of th sam body in units of kilorams. c stands for th vlocity of liht throuh spac in units of mtrs pr scond. Prmittivity ε and prmability μ ar in lss familiar units of farads/mtr and hnrys/mtr, rspctivly, which can b translatd in trms of standard MKS units. For th purposs of this rport, th nry, E, in quations (1) throuh (3) will oby th consrvation of nry law with no work bin don by th slctd body mass, and no work prformd on th slctd body mass. E will thrfor b a constant in all th analyss to follow. Also assumd is an xpandin univrs trird by th Bi Ban. 1

2 Nxt, with th abov assumptions, it will b shown that th Einwll Equation (3) lads to profound solutions to problms ncountrd tryin to undrstand Dark Mattr, th a of th univrs, and th acclratin xpansion of th univrs. As will b clarifid blow, to do all this only rquirs an undrstandin of how th prmittivity ε and th prmability μ in ffct vary systmatically with chans in th condition of th spac that surrounds us. To illustrat how this works, considr th capacitanc of any ivn objct in spac, which includs, alon with many othr thins, th capacitanc to som 4x1 or so stars in th univrs around us. Th currnt capacitanc to spac, C A, of any objct A with an ffctiv radius of r is 4πε r, or C A = 4πε r, (4) whr ε is th prsnt prmittivity of th spac around us. Add on, or a fw million, stars and quation (4) still holds sinc th chan in capacitanc is insinificant. Nxt, howvr, considr th univrs contractd to a smallr siz such as xistd a fw billion yars ao. Thn, alon with all othr thins, vry star is closr to A and th capacitanc of A to ach and all of th 4x1 stars has incrasd considrably. In ordr for quation (4) to accuratly provid th corrct hihr valu of C A, on can simply us a nw valu of ε hihr than ε, callin this hihr ε valu th ffctiv prmittivity of spac for th chosn comprssd univrs xampl. Convrsly, as th univrs continus to xpand in th futur, th valu of ε in quation (4) will nd to b dcrasd to rtain th accuracy of th quation as all th objcts in spac mov farthr from A. It has bn dtrmind xprimntally that, simulatin conditions in spac, and all ls qual, th capacitanc of a ivn objct A in a volum V of spac varis in proportion to 1/V; s rfrnc [1]. It thn follows from th abov discussion that, undr th sam conditions, th ffctiv prmittivity ε varis in proportion to 1/V as wll. Carryin this analysis on stp furthr, similar ffcts ar producd for th prmability μ. Walkin into any frrit makr s stablishmnt, on finds that a ivn volum V of manufacturd frrit is composd of a volum V p of hi- μ particls (usually composd of iron or nickl basd matrials) disprsd throuhout th volum plus a usually larr amount of inrt low- μ (cramic) matrial surroundin th particls. All ls qual, th ffctiv μ of th total volum V of th manufacturd frrit is dtrmind by th ratio of th particl volum V p to th total volum V. Rlatin this to th univrs, th stars, plants and vn alaxis ar rlativly tiny particls with mantic proprtis disprsd in th hu volum of inrt vacuum spac. Considr a tim priod in th distant past whn th arth (in whatvr form) was half as far away from th location of th cntr of th Bi-Ban as it is now. It follows that th volum V of th univrs in this distant past tim priod was on ihth of what it is now (volum proportional to th cub of th radius). Howvr, th volum V p of all th bas matrials with ithr hi-ε or hi- μ in this distant past tim priod was just as it is now.

3 Lt ε and μ dnot th ffctiv prmittivity and ffctiv prmability of th univrs in this distant past tim priod. By prvious discussion, th ratiosε /ε and μ / μ ar ach approximatly 8. Lt M dnot th mass of th arth in this distant past tim priod, and lt M dnot th prsnt mass of th arth. It thn follows by th Einwll Equation (3) that M/M quals ε / ε tims μ / μ, manin M would hav bn larr by a factor of 8 x 8, or by 64! Th sam arumnt applis to show that vry mass in th univrs would hav bn larr by a factor of 64. Morovr, sinc ravity btwn any two masss is proportional to th product of both masss, this implis ravity forcs would hav bn larr by a whoppin factor of 64 =496. This bir valu, causd by no obsrvd nw physical ntitis, is mor than nouh for any Dark Mass nthusiast, spcially if on looks back at a tim whn th arth was only on third or on tnth as far away from th cntr of th Bi Ban as now. In summary, by this analysis, thr is no nd to introduc a concpt such as Dark Mass to xplain hihr mass in th past. Thr is simply th nd to rconiz that prmittivity and prmability in vacuum spac vary systmatically in proportion to V p /V, and that V was smallr in th past. All of th foroin would b lant xcpt for two rasons. First, th lon-ao mass stp-up sms to b xcssiv. Scond, th analysis in rfrnc [1], whil it also concluds by a compltly diffrnt approach that ravity is proportional to ε (prmittivity squard), dos not say anythin about dpndnc upon μ (prmability). Th ralization that thr ar two kinds of masss which hav to b considrd sparatly solvs both dilmmas. Gravitational mass is on kind; inrtial mass is th othr. In rfrnc [1], any ravitational forc is an lctrostatic phnomnon. In this papr, an assrtion is mad that any inrtial forc is a mantic phnomnon. Chars drad throuh spac mak lctric currnts. Elctric currnts ar producd only by applyin forcs to chars in masss. Such currnts ar incrasd or dcrasd only by applyin forcs. With no applid forc a currnt will rmain constant, ithr zro or at a stady valu. Ths inrtial ffcts all happn bcaus lctric currnts produc associatd mantic fild nris which can b stady, built up or collapsd. Positiv currnts ar not sinificantly offst by nativ currnts (callin positiv chars movin thouh spac as positiv currnts; nativ chars movin throuh spac as nativ currnts) bcaus th spacin btwn sparat chars in a mass is vry rat in comparison to th sizs of th chard particls thmslvs. On th basis of ths assumptions and xprimntal vidnc, th Einwll Equation (3) is dividd into two quations on for ravitational masss dpndnt upon ε, and on for inrtial masss dpndnt upon μ as follows: M = k Eε. (5A) M i = ki Eμ. (5B) 3

4 Intrstinly, by all prsnt masurmnts, th ravitational mass M is qual to th inrtial mass M i. Assumin quations (1) and () ar corrct for ε and μ, th prsnt stablishd valus of ε and μ, it thn follows from th drivd quation (3) applid to M and M i that M k Eε = = k i Eμ Consquntly, th constants k and k i must satisfy = M i = Eε μ. (6) k = μ ; k i = ε. (7a) (7b) Equations (5a), (5b), (7a), and (7b), tothr with th Maxwll Equation (), loically imply that th Einstin Equation (1) divids into two quations, on for ravitational masss and th othr for inrtial masss, as follows: E = [μ/μ ] M c ; (8a) E i = [ε/ε ] M i c, (8b) whr it is important to rcall from th Maxwll Equation () that c = 1/εμ. Howvr, an additional critical obsrvation can b mad. Combinin th four quations (5a), (5b), (7a), and (7b), M/Mi = [μ /μ][ε/ε ]. (9) As prviously arud, ε and μ both vary in dirct proportion to 1/V, whr V dnots th volum of th univrs. Lttin V dnot th prsnt volum of th univrs, this implis ε = V ε /V ; (1a) μ = V μ /V. (1b) Consquntly, combinin (9), (1a), and (1b), in all tim priods ε/ε = μ/μ = V /V ; M = M i. (11a) (11b) It follows from (8a), (8b), (11a), and (11b) that th oriinal Einstin Equation (1) must b nralizd to th followin form in ordr to b applicabl for th cas of a univrs undroin chans in volum: 4

5 E = [V /V] Mc. (1) Combinin th Maxwll Equation () with (1), th oriinal Einwll Equation (3) must in turn b nralizd to th form M = [V/V ] Eεμ. (13) Not that th volum ratio V /V in (1) is th invrs of th volum ratio V/V in (13). In summary, assumin th univrs is xpandin ovr tim, quations (1) and (13) imply that th oriinal Einstin Equation (1) and th oriinal Einwll Equation (3) ar valid only for th prsnt tim priod in which th volum V of th univrs is qual to th prsnt (rfrnc) volum V. Th volum ratio V /V in quation (1) is ratr than 1 for distant past tim priods whn th univrs volum V was sinificantly smallr than V and it is smallr than 1 for distant futur tim priods whn V will b sinificantly larr than V. Th rvrs obsrvations hold for th volum ratio V/V in quation (13). With th analyss shown, on is now abl to undrstand som of th rat ffcts of spac prmittivitis and spac prmabilitis. Considr nxt th xpansion of th univrs. Lt th nry of th arth s movmnt away from th Bi-Ban b rprsntd by: E = M v /, (14) whr th subscripts all rlat to th arth s nry, mass and vlocity with th arth movin radially outward. It has bn shown arlir that any mass such as M is rducd with th univrs s xpansion, vn thouh th nry E is constant. Thus, to kp quation (14) valid, v must incras by th sam amount that M has dcrasd. All th parts of th univrs movin outward, thrfor, hav acclratd xpansion! Actually, any dtctabl ffct happns so slowly that no on has bn abl to postulat or masur any acclration until rcntly. An analoy to this ffct may b undrstood usin an ic skatr s rotational spd incrasin with no outsid-addd nry whn th arms of th skatr ar brouht in clos to th body. Th trm I in th constant nry quation, E = Iω /, has bn rducd by brinin th avra mass in closr to th cntr, makin th squar of th rotational spd ω incras to kp th nry E constant. Also, considr th Maxwll Equation () alon. It shows that whn ε and μ wr much ratr than at prsnt, th vlocity of liht was much slowr. Thrfor, th imas from distant spac w s today ar actually from much lonr ao than implid by th convntional assumption that th vlocity of liht is constant. Sinc th as of all thins in th univrs hav bn dtrmind usin th prsnt vlocity of liht and its travl-tim to dtrmin distancs and tims of happnins, th rsultin conclusions ar 5

6 mostly in rror. For xampl, th univrs from th tim of th Bi-Ban is much oldr than th prsntly dtrmind 13 to 14 billion yars. This allows ampl tim for th formation of old stars, a procss that hrtofor has bn mystriously assumd to tak mor than 13 to 14 billion yars, i.., mor than th stimatd a of th univrs. Howvr, th contractd univrs is not th only way to t incrasd ε and μ. In hih- dnsity clustrs of alaxis or stars, hihr prmittivitis and prmabilitis occur with th sam rsultin ffcts as th foroin. That is, liht travls mor slowly throuh th spac in clustrs (dlayin liht sinals arrivin hr on arth passin throuh thm), ravity is mor intns (indicatin incorrctly additional dark masss, black hols or nutron stars) and th xpansion in th confins of th clustr is acclratin. Anothr intrstin thin to not is that lctromantic forcs btwn chars ar invrsly proportional toε ; that is F m = q1q / 4πεr. This mans that, whil ravity forcs ar incrasin proportional to ε lookin back in tim, char lctromantic forcs ar dcrasin proportional to 1 / ε, sustin prhaps that far back in tim thy 39 wr th sam. This sms a littl far-ftchd, howvr, as thr is an approximat 1 amplitud ratio of char-to-ravity forcs to ovrcom. Nothin much has bn said hr about th futur univrs, but usin th Einwll Equation (3), as nralizd in quation (13) for an xpandin univrs, th radr can postulat for himslf what miht b in stor for us. Rfrncs [1] Spars, Morton F., An Elctrostatic Solution for th Gravity Forc and th Valu of G, January 9,