PERMITTIVITY CREATES DARK MATTER AND AN OLDER UNIVERSE WITH ACCELERATING EXPANSION. By Morton F. Spears

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1 8 July 1998 PERMITTIVITY CREATES DARK MATTER AND AN OLDER UNIVERSE WITH ACCELERATING EXPANSION By Morton F. Spars Abstract: Th purpos of this rport is to provid simpl answrs to th following thr qustions by considring th ffcts of what has bn happning ovr tim to on singl proprty of opn spac; namly, th prmittivity of that spac: What is dark mattr and why dos it xist? Why do so many distant stars appar to b oldr than th xpanding "Big Bang" Univrs of which thos sam stars ar a part? Why is our Univrs xpanding at a gratr vlocity now than it did many millions of yars ago? Introduction Thr ar many puzzling things happning in our hug spac-tim hom which, so far, cannot b xplaind by modrn physics in a mannr accptabl to a majority of thos xploring th Univrs. Thr spcific unanswrd qustions ar: 1.) What is dark mattr and why dos it xist?.) Why do so many far-away stars appar to b oldr than th xpanding Big-Bang Univrs of which thos sam stars ar a part? 3.) Why is our Univrs xpanding at a gratr vlocity now than it did many millions of yars ago? Th purpos of this papr is to submit simpl answrs to th thr qustions abov by just considring th ffcts of what has bn happning ovr tim to on singl proprty of opn spac; namly th prmittivity of that spac. Prmittivity is on of th proprtis of an absolut vacuum spac that dtrmins th vlocity of light and th sam vlocity for othr lctromagntic wav nrgis which happn to propagat through th spac. It is also a factor that dtrmins a diffrnt vlocity of light through othr mdia such as glass or watr. Howvr, th usual maning for th spd of light is thought of as a light wav travling through vacuum spac (or through air which lowrs th vlocity by an insignificant amount for most purposs). Th othr important proprty which dtrmins th vlocity of light, and th vlocitis of othr lctromagntic wav nrgis propagating through a mdium, is calld prmability. For this papr, th prmability of opn spac is assumd to always hav th sam valu, although opn spac in arly tims, shortly aftr th big bang for 1

2 xampl, may hav containd nough disbursd magntic matrials to incras th spac ffctiv prmability valu. Dark Mattr To bgin th analysis of th Univrs prtinnt to this rport, start with th famous Einstin xprssion, E = Mc, [1] whr E is th nrgy and M is th mass of a slctd portion of mattr at rst, and c is th vlocity of light. From this, on knows th total nrgy E that thortically can b xtractd from a particular blob of anything whn all of its mass M is convrtd to nrgy. Thr ar additional intrnal nrgis such as motional ons producd by individual particls within th mass at high tmpraturs. Also, if th ntir blob is st in motion at a vlocity v, th blob of mass has xtra kintic nrgy so that th Einstin nrgy-mass rlation bcoms E = Mc + Mv /. Nxt, in this rport, howvr, only masss at rst and at a constant tmpratur ar considrd. Th vlocity c in th xprssions mans a vlocity of light of approximatly mtrs pr scond, which is th uniqu spd of light masurd through vacuum spac and not through any othr mdium. But whn on dfins our prsnt vacuum spac th implid maning is a mdium with a prmittivity ε of 1 approximatly farads pr mtr and a prmability μ of approximatly hnrys pr mtr. Th subscript zro is usd to dnot particular constant valus for both ε and μ that apply to opn vacuum spac. It follows that c should b usd instad of just c in th Einstin xprssions sinc c also applis to a uniqu vlocity of light in th sam vacuum spac; thus E = Mc. [] Thr is a dirct rlationship btwn c, ε, and μ givn by th quation: c = 1/ ε μ, or = 1/ ε μ c. [3] Thrfor, for this rport thr is no rason that Einstin s nrgy quation cannot b shown in anothr and mor usful form: E = M / ε μ. [4] Thr ar normous consquncs that ffct radical changs to th modl of th Univrs if th prmittivity of opn spac somhow varis with tim. It is th spcific purpos of th matrial that follows to show that not only dos th prmittivity of opn

3 spac lssn with tim in an xpanding univrs, but also to dmonstrat just how this happns. First in an xprimntal laboratory, two mtal plats with paralll surfacs spacd at a rasonabl distanc in a vacuum can b usd as trminals of a capacitor across th tund circuit of a high frquncy oscillator. Th frquncy of th oscillator is rcordd. Whn a quantity of sparatd solid particls, vaporizd liquids or gass ar insrtd in th capacitor spac (as long as a conductiv short circuit is not mad btwn th plats), th nw frquncy gnratd by th oscillator is rducd. Th capacitanc of th capacitor has thrfor incrasd, which rally mans th ffctiv prmittivity of th spac btwn th plats has incrasd. Using this kind of incras in prmittivity, applid to arlir tims in our compactd young xpanding Univrs, rsults in visualizing a gratr prmittivity for spac as on looks back in tim at th distant galaxis. A givn larg volum of spac, for xampl, containd many mor solid particls (th stuff galaxis and stars ar mad of) and thr wr many mor clouds of various gass and vaporizd liquids pr a larg volum of spac. Consquntly, th ovrall ffctiv prmittivity of opn spac was gratr thn than it is now thr shouldn t b much doubt about that. Scond, howvr, thr is anothr complling rason to projct a spac prmittivity that lssns with tim in our xpanding Univrs, vn for th smallst of spac volums. To visualiz this happning, assum that a vacuum pump has vacuatd a bll jar volum down to absolut zro prssur with nothing but pur vacuum in th jar (possibl only as a thought xprimnt). Th valu of ε for th pur vacuum spac in 1 th bll jar is th sam as mntiond arlir, and masurs about farads/mtr. Th bll jar volum can b xpandd or contractd with no chang in th prmittivity valu for th spac insid. Eithr thr is nothing in th bll jar, or whatvr is in it passs frly through th walls with no friction or any othr known ffct. Although th trm athr (or thr) has gon out of vogu for dsignating th mdium of pur vacuum spac, many modrn physicists bliv that vacuum spac is composd of somthing(s). Othrwis how can lctric and magntic filds b maintaind propagating through nothing, or how dos a magnt attract a pic of iron through nothing? And, vn mor puzzling, how can proprtis lik prmittivity and prmability xist in nothing? If vacuum spac consists of somthing(s), howvr, what dos it consist of? On of th popular thoris visualizs vacuum spac packd with many nutrinos, thos illusiv vry small particls that carry no lctrical charg. Th String Thory advancs th concpt of our Univrs filld with vn smallr minut strings and trousrshapd particls that ar prsnt vrywhr dominating spac. Still anothr thory contnds that vacuum spac consists of protons and lctrons without lctrical chargs, rady to form hydrogn whn lctrical dischargs through spac nrgiz many of th protons and lctrons to ffct an thr to mass transformation. It dos not mak any diffrnc for purposs of this rport which thory (or non of thm) is corrct, bcaus in an xpanding univrs th dnsity of whatvr on blivs xists in vacuum spac is lssning. For dtaild calculations, who knows, or can vn guss, what th prmittivity is of a nutrino, or a string, or an lctron, or a proton or any othr sub-atomic particl. But, as long as th particls individually hav a 3

4 gratr prmittivity than th spac around thm, th ovrall spac prmittivity will dcras with xpansion. This ffct cannot b vrifid by xprimnts with prsnt stat-of-th-art tchniqus, bcaus in a laboratory a portion of vacuum spac can not b forcd to contract or xpand by comprssion or dcomprssion. Nxt, considr that vry blob of mass M is an quivalnt bit of nrgy E that cannot b incrasd without som work don on th mass, nor can th quivalnt nrgy b dcrasd unlss som work is don by th mass on somthing ls. Assuming no work is don on or by th mass, th nrgy E will hav a constant valu ovr any tim priod (from a past tim at t, through th prsnt tim at, to a futur tim at +t). Thus: E t + t ( = + t + t + t = E = E = M / ε μ ) = ( M / ε μ ) ( M / ε μ ). [5] But how can Exprssion [5] b tru whn th valu of prmittivity ovr tim is changing? It has just bn shown how opn vacuum spac prmittivity ε in an xpanding univrs must dcras with tim so that: ε. [6] t > ε > ε +t And, in th Exprssion [5], if th prmability μ stays at th sam constant magnitud ovr tim (as assumd in this rport), thr is only on othr paramtr lft which has to chang to kp E from changing too; that is, th ffctiv mass of M must b dcrasing with tim! This dcras in mass is thn at th idntical rat as th dcras in prmittivity with tim. (If on wr to assum also a lssning of prmability with tim in our xpanding Univrs, thr would b an vn fastr rat of ffctiv mass lssning with tim, proportional to th εμ product). Th ε, M dpndncy rlationship lads to th rquird conclusion that: M t M > M + t >. [7] Th ffct of mass rduction with tim applis to not just a singl portion of mass undr scrutiny, but to all masss. This mans that at a givn tim in th distant past, for xampl, that th gravity forc btwn two masss, GM 1 ( t) M ( ) / r, was incrasd rlativ to today s mass ffcts by th squar of th M t / M (or ε t / ε ) ratio, as dducd from Exprssions [5], [6] and [7]. Suppos Profssor A, a lading astronomrcosmologist-physicist, looks with his powrful tlscop far away and back to a tim whn ε = 3ε. H carfully obsrvs that all havnly bodis that h watchs ar bing pulld nin tims as much as thy ought to b, so h naturally concluds that thr ar mystrious unsn bodis of mass ight tims as prvalnt as th dtctabl bodis. H prsnts his rsults to th scintific community, concluding that th mass w ar familiar with is only about 11% of th total, whil narly 89% of th mass in our Univrs is dark mass (or dark mattr) that has not bn obsrvd. Profssor B, on th othr hand, thn looks back to a tim whn ε = 4ε. Sh prsnts hr qually convincing rcordd data that shows a fiftn-to-on ratio of dark mattr to normal mattr, or dark mass consists of 4

5 about 94% of th total. And so it will go until prmittivity is rcognizd as a truly important proprty of spac, affcting and ffcting many othr phnomna. To quantify dark mass in an xprssion, lt ( ε t / ε ) = k t, whr k t rprsnts th dilctric constant of vacuum spac at som tim long ago. Also, lt M d rprsnt a hypothtical quantity of dark mass and M n rprsnt a hypothtical quantity of normal mass. Thn: M M ( k 1). [8] d ( ) = n( ) Th Ag of th Univrs On of th untouchabls of scinc, considrd sacrd and invariabl, has bn c, th spd of light through opn vacuum spac. But, whn prmittivity lssns with tim, it s a whol nw ball gam. Whn w look through our tlscops at galaxis and stars as thy wr aons ago, bcaus of a gratr ε prmittivity thn, light was travling at a slowr vlocity. It follows that th light w s has travld part of its distanc through a mdium that slowd it down. This mans that th light has takn a longr tim to gt hr than prviously supposd; and th Univrs, and vrything in it, is thrfor oldr than w hav hrtofor rcognizd. Acclrating Expansion of th Univrs Earlir in this rport it was mntiond that a quantity of mass dos not chang its nrgy unlss som work is prformd by th mass for a loss of nrgy, or som work is prformd on th mass for a gain in nrgy. Tak th cas of a mass lik our Earth moving radially outward ovr tim from th cntr whr th big bang initially ruptd, and assum no nrgy has bn addd or takn away, as far as xpansion is concrnd. Th mass of th Earth M has a constant nrgy E associatd with its radial xpansion vlocity v so that: E ) = ( M () v() / ) = E( t) = ( M ( ) v( ) / ) = E( + t ) = ( M ( + t) v( + ( t ) / ). [9] Eons ago, according to Exprssion [7], th ffctiv mass of Earth M was gratr than it is now bcaus of th gratr prmittivity of opn vacuum spac, which in turn mans that th vlocity of Earth during xpansion had to b lss at th sam tim to conform to Exprssion [9]. Much latr on, th ffctiv mass of th Earth will b lss than it is now, causing a gratr xpansion vlocity. From Exprssions [6], [7] and [9] it can b shown that th radial xpansion vlocity of th Univrs v r is continuously incrasing with 5

6 tim, and that th rat is proportional to th squar root invrs of prmittivity. Th mathmatical rprsntation for this is: 1/ v r [1] ε To provid a somwhat applicabl analogy to this, think of a prson holding a pair of dumbblls rotating on a frictionlss platform. Whn th two wights ar hld in two hands at full arm s lngth, rotation occurs at a slowr rat than whn th dumbblls ar pulld in closr to th body. Th nrgy has not changd in th systm as a whol, but th rotation rat changs to prsrv th Mv / nrgy of th two wights (plus th two arms). Similarly, th nrgy of an objct moving with xpansion stays constant, but whn th ffctiv mass is rducd, th xpansion vlocity must incras to kp th nrgy constant. Conclusions In accordanc with th statd purpos of this papr, answrs to th thr qustions posd in th opning paragraph ar givn blow. Now that it is rcognizd that th proprtis of opn vacuum spac can chang with tim, howvr, a numbr of nw unanswrd qustions aris, not discussd hrin. On such qustion concrns th ffct of changs in vacuum spac with tim in rlation to lctrical charg forcs. 1. Dark mattr, as a sparat ntity, dos not xist. Instad, dark mattr is an illusion arising from gratr gravitational forcs for normal masss as thy xistd a long tim ago. Th ffctiv masss thn for th sam bodis today wr gratr, but wr, and still ar, lssning with tim. Th rat of dcras in mass is xtrmly slow, only significant ovr tim priods of many millions of yars. Th mass dcras is proportional to th prmittivity dcras of opn vacuum spac with tim. Th prmittivity dcras is th rsult of xpansion of our Univrs, which provids ovr tim a lowring population of particls of whatvr natur for any volum of spac. Whn th individual particls ar assumd to hav gratr prmittivitis than thir surrounding spac, a lowr particl count rsults in a lowr ffctiv prmittivity for that spac. Thn, by nrgy consrvation, a lssning ffctiv prmittivity in th xpanding volum of our Univrs dictats a lssning of ffctiv mass as dtrmind by Exprssions [4] and [5]. Finally, looking back in tim from th prsnt, on ss gratr mass ffcts than xpctd, lading to th postulation of additional dark mass (or dark mattr).. Th ag of our xpanding Univrs from th initial big-bang until now is a lot oldr than th 1-15 billion yars as hypothsizd in all th scintific litratur. Th mthods of acquiring information from dp spac to formulat th ag hav always dpndd upon th vlocity of light, assumd to b consistntly about mtrs pr scond. Howvr, as brought out in this papr, th prmittivity of spac in th distant past was highr than it is now which dcrasd th spd of light passing through th spac. Consquntly, th information rcivd by light has takn a longr tim to gt to us than cosmologists hav postulatd, making th Univrs significantly oldr. For xampl, th ag may b as much as -3 billion yars or mor, 6

7 which provids ampl tim for th formation of vn th oldst stars in accordanc with accptd thory. 3. Our Univrs is xpanding at an vr-incrasing vlocity. Th acclrations of th bodis in spac moving radially away from th Univrs cntr ar not nough to hav bn dtctd until rcntly. Postulations of th caus so far hav not bn convincing. Th tru rason for th incrasd rat of xpansion with tim still rmains a mystry. Howvr in this papr, th combination of th consrvation of nrgy plus th lssning of ffctiv mass with tim, srvs to provid th answr. Th kintic nrgy E = Mv r / of a radially moving body with mass M and radial vlocity v r is constant; yt th mass is dcrasing with tim (as dvlopd for Exprssion [7] in th txt). To consrv th nrgy of th body, th squar of th vlocity of th body has to incras with tim to just compnsat for th dcras in mass. 7