THECYCLI CUNI VERSE Summar y: Thi spaper i sananal ysi sof howt heUni ver seasawhol eandt her eal m of t hepar t i cl esof anat omar er el at edbymeanof si mpl eequat i ons. I t i sal soan i nt ent t of i ndt henumer i cal r el at i onsamongt hecoupl i ngconst ant sof t hef ourf or cesof Nat ur eandhowt heychangewi t ht i me.CHAPTER1 THELI NKSOFTHEMI CROCOSMSWI THTHEMACROCOSMS Thi spaper i sananal ysi sof howt heUni ver seasawhol eandt her eal mof t he par t i cl esof anat omar er el at edbymeanof si mpl eequat i ons. I t i sal soani nt ent t o f i ndt henumer i cal r el at i onsamongt hecoupl i ngconst ant sof t hef our f or cesofNat ur e.Thepaper i sanabst r act of al ar ger onet hat I wr ot eabout t heset opi cs, andi n manycasesI won' t ext ent ont heexpl anat i onssoI wi l l keepi t shor t .1. - Wi t hout want i ngt odeepi nat opi cof whi chI amnot anexper t , i t i snecessar yt o speakabout somei t emsr el at edwi t ht heQuant umMechani cs.Oneof t hemost i nt er est i ngaspect sof t heQuant umMechani csi swi t hout adoubtt hepr i nci pl eof uncer t ai nt y, whi ch, t el l sust hat i t i snot possi bl et oknowormeasur et heposi t i onandt hespeedof apar t i cl eat t hesamet i me, si ncet het ot alcer t ai nt yi noneof t hosepar amet er ssi mul t aneousl ymeanst het ot al uncer t ai nt yoft heot her . Oneof t hef or msi nwhi cht hi spr i nci pl ecomesi t i st hef ol l owi ng: DE.Dt >hThat meanst hat t hepr oduct i nt heuncer t ai nt y( D) of t heener gyEandt he uncer t ai nt y( D) i nt het i met shoul dbet hesameor bi gger t hant heconst ant "h". hi s t hePl ank' sconst ant , andhasaval ueof 6. 626e- 27er g- seg. Theconcept i snoteasyt ounder st and, i t meanst hat i f ameasur ement of t heener gyof apar t i cl ewi t h anuncer t ai nt yDEi smadezer o, ani nf i ni t et i mewi l l ber equi r edt omeasur ei t , but i tcoul dhappent hat i t i spossi bl eobt ai nener gyout of not hi ngpr ovi dedt hat i tdi sappear at t het i meconsi der edi nt hi spr i nci pl e. Thi si snot j ust at heor y, t heyar e exper i ment al l ypr ovenf act s. Anot her f or mof seei ngt hepr i nci pl ei si nt hi sway;Dl . Dmv>h I t meanst hat t hepr oduct of t heuncer t ai nt yi nt heposi t i onof apar t i cl e( Dl ) andt he uncer t ai nt yont hei mpul seDmvshoul dbebi gger or equal t oh. For exampl e, l et us supposet hat wemakeanexper i ment i nor der t omeasur et heposi t i onof an el ect r oni nasyst emof coor di nat eswi t hacer t ai npr eci si on, t hesi ngl ef act ofmaki ngt hi smeasur ement al t er st hest at eof movement of t heel ect r onmaki ngmor e uncer t ai nt hepr eci si onof t hemeasur ement of t hespeedof i t . Becauseof t hi swe canassoci at eapar t i cl ewi t hcer t ai namount of i mpul se"mv"wi t hal ongi t ude"l " whi chi sknownast hewavel engt hof t hepar t i cl e. I nt hecasei nwhi cht hel ef t si de of t hepr evi ousequat i oni sexact l yequal t ohast hesamepr i nci pl eper mi t s, we evencoul dcont i nueassoci at i ngt hepar t i cl ewi t hapr oper wavel engt hpr ovi dedt hatwet aket hespeedast hespeedof t l i ght C.l =h/ mCwel l - knownasCompt onwavel engt h Consi der t hat i f wedi vi dedbot hmember sof t hi sl ast equat i onbyCwewi l l obt ai n t hat ;l / C=h/ mC^2 but , l / Chasuni t sof t i mei nver se, whi chi st hat of af r equency, andwet her ef or e canassoci at et heener gywi t haf r equencyof suchwayt hat ;mC^2=hfI ngener al , t oeachener get i cal l yphenomenonwecanassoci at eaf r equencyand vi cever sa. For exampl ei f wet ookal umi nouswaveof f r equencyf , t oi tcor r espondsamass;m=hf / C^2 Thi sdoesn' t meant hat l i ght hasmass. What I amsayi ngher ei st hat t hi si san equi val ent masswhi chi snot ar est mass. Thesameconcept canbeappl yt oot herf or msof ener gy, f or exampl et heassoci at emasswi t ht heel ect r ost at i cf i el d pr oducedbyanel ement ar ychar geqat t hedi st ancel i ssucht hat :q^2/ r =hf =mC^2andf =q^2/ hrCont i nui ngwi t ht hi ssameexampl e, wecoul dmaket hef ol l owi ngequal i t yf or t he massof anel ect r onandpr esent t hef ol l owi ngequal i t y;Ast hel ongi t udeof t heassoci at ewavewi t ht heel ect r oni sh/ meCt henweget t hat ;l e=h/ meCandr e=q^2/ meC^2 Amagni t udewi t hout uni t sexi st st hat i t i st her at i obet ween:l e/ r e=A.Thi smagni t ude, r ecei vest henameof i nver seof t hef i nest r uct ur econst ant ( I j ustcal l i t t hef i nest r uct ur econst ant ) andi t hast hesameval uef or t heel ect r onandt he pr ot onsi ncebot hhavet hesameval ueof el ect r i cchar ge.A=hC/ q^2 Andi t sval uei sappr oxi mat el yequal t o861, i nt er pr et edaswehaveseenast he r at i oof t heel ect r onwavel engt h( or of t hepr ot on) t oi t s"r adi us"cal l edcl assi c r adi usof t heel ect r onor of t hepr ot on.Anot her f or mof ener gyt hat wecoul dt r yt omanagei nt hesamef or mt hant he el ect r i cener gyi st hegr avi t at or yener gy. I nt hi scasewewi l l f i r st associ at et he f r equencywi t ht hemassof t hepr ot onandt heel ect r on:f =Gme. mp/ hr g Now, i t i sf act t hat f =mC^2/ honwhi chi nor der t oobt ai nt hegr avi t at or yequi val entwehavet omaket hat t hef ol l owi ngcondi t i oni saccompl i shed:m^2=mexmp Bei ngmet hemassof t heel ect r onandmpt hemassof t hepr ot on. Andt heequal i t y l eadsust o:Gm^2/ hr g=mc^2/ handr g=Gm/ C^2( 1- 1)I shal l i nt r oducet hi s( m) massasaf act or of cal cul at i on, andI wi l l namei t as "masn". Wi t ht hi smasswewi l l get t hef ol l owi ngpar amet er s:l =h/ mcr =q^2/ mC^2 l / r =A=hC/ q^2 I t i seasyt odemonst r at e( i f weusedt hesubi ndexs1f or t hepr ot onand2f or t he el ect r on) t hat :l ^2=l 1xl 2r ^2=r 1xr 2i sal soeasyt opr oof t hat :r / r g=q^2/ Gm^2=( q^2/ l ) / Gm^2 Whi chsayst hat t her at i oof t heset wor adi usi sequal t ot her at i oof t heel ect r i cand gr avi t at or yf or cesbet weenapr ot onandt heel ect r on, t hi sr at i oaswewi l l seei sa ver yi mpor t ant number wi t hout uni t s( S) whoseval uei sappr oxi mat el yequal t o 2. 27e+39 S=q^2/ Gm^2( 1- 2)I t shoul dbemadenot i cet hat ar el at i onshi pf or t hegr avi t at i onsi mi l ar t ot hat of t he f i nest r uct ur econst ant exi st s( t hei r r eci pr ocat es) , al sowi t hout uni t s.B=hC/ Gm^2 not e: somet i mesI wi l l uset hesi gn( ) i nor der t oi ndi cat emul t i pl i cat i on, i nanot hercasesI wi l l uset hexsymbol andi nanot her I wi l l uset hegener al al gebr ai cnot at i on of not wr i t i ngdownt hesi gnwhent heoper at i oni smul t i pl i cat i on, wi t ht hedi vi si on andaccor di ngt ot hecaseI coul dusewhat ever of t hef ol l owi ngsymbol s: /Aswehavef oundt hat r / r g=Swecoul dal sof i ndt hat :R=Sl ( 1- 3)Thi si saver yl ar gel engt hwavet owhi chi t cor r espondst hef r equencyFwher eC= F/ Rt hen: C/ f =Sl but C/ l =el ect r i c f accor di ngt owhat weal r eadysaw, t hen:S=f / F( 1- 4)F=f / s=f . Gm^2/ q^2=( mC^2/ h) Gm^2/ ( mC^2r ) =Gm^2/ hrF=Gm^2/ hr ( 1- 5)Uponmaki ngt hecal cul at i onof t hi sf r equencywef i ndt hef act t hat i t sval uei s 2. 33e- 181/ secThat i samazi ngl ynear t ot heval uemeasur edof t heHubbl e const ant i nsi det her angeof er r or of measur ement of i t andwhi chf ul f i l l st he pr i nci pl eof uncer t ai nt ysi nce:( 1/ F) Gm^2/ r =h Ther ef or e, I consi der t hepr evi ousdi scover ynot asachance, but r at her I wi l lconsi der t hat i ndeed:H=Gm^2/ hr ( 1- 6) i st heHubbl e' sconst antAndsi ncei t i saf r equency, i t hasassoci at ewi t hi t t hel ongi t ude:R=C/ H That i st hesameas( 1- 3) Thi si st hemai nr easont hat i ncl i nedmet obel i evet hatt her adi usof t heUni ver sei smor eassoci at ewi t hawavel engt ht hanwi t har adi us pr oper l yspeaki ng.I must sayt hat I wi l l useher esomebasi cconcept st or el at et hemass - ener gyof t he Uni ver seandi t ssel f gr avi t at i on. Ther ear esomequest i onswhi chsof ar sci ence hasnot beenabl et oanswer .I sgr avi t at i ont hecauseof mass- ener gy?Or mass- ener gyi st hecauseofgr avi t at i on?Whi chonecomesf i r st ?.Usi ngMachbasi ci deas, I coul dsayt hat massor i ner t i ai scausedbygr avi t yof al lt heUni ver sei nsuchawayt hat i f t her ewer eonl yonesi ngl ebodyi nal l of t he Uni ver se, t hent hi sbodywoul dhave"subst ance"but not mass.Thi si sat t hesamet i mei nt r i gui ng, becauseweaskour sel veswhat cause gr avi t y?. So, doweusemasst oexpl ai ngr avi t yor doweusegr avi t yt oexpl a i n mass?.I nt hi spaper , I wi l l t akeasaf act t hat gr avi t yi smassandmassi sgr avi t y, so,t ot al ener gyi sequal t ot ot al gr avi t y, whi chi nmat hemat i cal f or mI r epr esent l i ke t hi sf or al l t heUni ver seasawhol e:MC^2=GM^2/ R Thi sl eadust ocal cul at et hebasi cpar amet er sof t heUni ver sest ar t i ngwi t hhi gh pr eci si onwel l - knownconst ant s. I won' t st opher et ocal cul at et hef ol l owi ng equat i onst hat coul dbedemonst r at edwi t heasewi t hal gebr ai cor di nar y cal cul at i ons. at t heendof t hi sI wi l l pr esent t heval uesobt ai nedf or eachl i t er alexposed:A=hC/ q^2B=hC/ Gm^2r =q^2/ mC^2 r g=Gm/ C^2 f =q^2/ hr S=f / H S=R/ l S=r / r gS=mc^2/ hH S=B/ AS^2=M/ ( Am) gm^2/ l =q^2/ R Gm^2/ r g=q^2/ rSi nceR=GM/ C^2andR=C/ Hi sdeducedt hat :M=C^3/ GHandsi nce:H=Gm^2/ hr andr =q^2/ mC^2 weobt ai nt hat :M=hCq^2/ G^2m^3( 1- 7)t hesameequat i oncoul dbet r ansf or medeasi l yi nt hef ol l owi ng:M=BSmandbecauseS=B/ Awef oundt hat ;M=AS^2mi f N=AS^2t henM=nm( 1- 8)Thenumber "n"i sr el at edwi t ht het ot al number of el ect r onsandpr ot onsi nt he Uni ver sei nt hef ol l owi ngf or m; wewi l l supposet hat pr act i cal l yt hewhol eUni ver se i sf or medwi t hpar t i cl eswhosemassi sequal t ot hat of t hepr ot on, weknowt hat t he el ect r onsexi st , but t hei r cont r i but i ont ot het ot al massi sver yr educedsi ncet hei rmassi s1/ 1836t hemassof t hepr ot onandt hei r number i st hesame. Havi ngt hi s i nmi ndandknowi ngt hat t hemassof t heneut r onsi sal most t hesamet hant he pr ot on, wecoul dsayt hat t henumber of nucl eonsof t heUni ver sei s; nn=M/ mp,nn=Nm/ mpnn=N( mpme) ^1/ 2/ mp nn=N/ D^( 1/ 2)wher eD=1836=mp/ menn=AS^2/ D^( 1/ 2) ( 1- 9)Val ues:mp=1. 6726311e- 24gr amspr ot onmass me=9. 109389754e- 28gr amsel ect r onmass h=6. 62607554e- 27er g- secPl ank' sconst antC=2. 997924562e10cm/ sec. Li ght speed m=3. 903414992e- 26gr amsmasonmass l =5. 662274982e- 12cms. masonwavel enghtq=4. 803206784e- 10euf undament al el ect r i cchar ge G=6. 6725985e- 8er g- cm/ gm^2Newt onconst antA=861. 0225291el ect r omagnet i ccoupl i ngconst antB=1. 953856383e42gr avi t at i onal coupl i ngconst antS=2. 269227943e39el ect r i ct ogr avi t at i onal f or cesr at i o H=2. 333198137e- 18sec^( - 1) Hubbl econst antR=1. 284899261e28cmsUni ver seRadi us M=1. 730674865e56gmsUni ver semass N=1. 034712072e80Ner of Uni ver senucl eons p=1. 947689124e- 29gr ams/ cm^3Uni ver sedensi t y CHAPTER2 THEFOURFORCESOFNATURE( PART1)For ewor d:What I her eexpose, i sj ust ananal ysi sof t hepossi bl er el at i ons hi psbet weent he const ant sof t hef undament al f or cesof Nat ur e. I sr at her anst udyof t henumer i c r el at i onshi psbet weent heseconst ant s. I nt hi sanal ysi s, youcoul dcal cul at ewi t h hi ghaccur acyt her at i oof t hemassesof t hepr ot ont ot hat of t heel ect r on, andt he neut r ont ot hat of t hepr ot onwi t hj ust t heknowl edgeof t hemagni t udeof t he coupl i ngconst ant sof t hef or cesor vi cever sa. Or cal cul at et heval ueof t heNewt on const ant st ar t i ngf r omt heconst ant sof t heWeakf or ce.I t canal sobeensee, t hat t hef undament al f or cescoul dber el at edt oeachot herwi t ht hef our t hpower of t hepr evi ous"i nt ense"f or ce. Thi schar act er i st i cof var yi ng wi t ht hef our t hpower al l owst oseet hepossi bi l i t yt hat f or cesof super i or or i nf er i oror der exi st t ot hest r ongandgr avi t at or yf or cesr espect i vel y. For exampl e, t he gr avi t at i on, t heweakest of t hewel l - knownf or cescoul dgi ver i set ot heexi st enceofanot her f or ceevenweaker wi t hani nt ensi t yof downt o1e- 256weaker t hant he st r ongf or ce. Theobt ai nedequat i onsandt hepost edval uesf or "J"and"D"f orexampl e, ar esopr eci set hat t hi nki ngonachanceI consi der i t hi ghl yunl i kel y. Ir ecogni zet hat t hi sanal ysi st ouchest opi cscompl et el yunknownf or t hegr eatmaj or i t yof t hepeopl e, I r ecommendt her eadi ngof t hebook"TheAcci dent alUni ver se"of Paul Davi esi nor der t ohel punder st andwhat I her et r yt oexpl ai n.Someof t hemagni t udest hat I usear enot convent i onal , f or exampl e: "m"i snot a par t i cl e, but t hesquar er oot of t hepr oduct of t hemassof t hepr ot onandt hemass of t heel ect r on, or Ai snot t hef i nest r uct ur econst ant but t wopi t i mest hei nver se of t hi sconst ant .Thewr i t i ngi snot at heor yof Uni f i edFi el d, t hi sshoul dr emai ncl ear , but someki nd of uni f i cat i onamongt hef our f or cesar r i vesdependi ngwhat I doi st omakeexactt hi sappr oachof equal i t yandseet henwhat happensupondoi ngi t . I f what I obt ai n i sal most quant i t at i vel yexact l yandt heuni t sar ecor r ect , I t henconsi der sat down t hat t he"f orced"equal i t yi st rue.Anyway, t hi shasper mi t t edmet ocal cul at ewi t hhi ghaccur acyconst ant sl i ket hatof t hegr avi t at i onof Newt on. Ani nt er est i ngr esul t of t hi sanal ysi si st heobt ai ni ng of amagni t udewhoseuni t sar et hoseof amassandt hat I i dent i f yas"mi u"wi t ha val ueof t heor der of 1e- 5gm, t hi smasscanbecal cul at edof t wodi f f er ent ways,andt hei nt er est i ngof i t i st hat i t smagni t udei sof t heor der of whi chapar t i cl eofuni f i cat i onof t hef our f or cesshoul dhave, andt hat wewoul dobt ai ni t j ust by maki ngequal t o1t hecoupl i ngconst ant sof t hef our f or ces.Theuni t ssyst emusedi st he"cgs. "Rel at i onshi psBet weent heFour For cesNat ur e 1. - Gener al : Unt i l t hepr esent t i me, t hephysi cal sci enceshavebeendevel oped st ar t i ngf r omdi ver set heor i est hat i noneor anot her wayexpr essesr el at i onshi ps bet weent heconst ant sof Nat ur eandt hebehavi or of t heUni ver seandi t spar t s.Oneof t hemost i nt r i gui ngquest i onsof sci encehasbeent her easonof bei ngofsomephysi csconst ant ssuchas: t hespeedof l i ght , t heel ect r i cchar geof t h e el ect r on, t hemassof t heel ect r on, t hePl ank' sconst ant , t heconst ant ofgr avi t at i on, et c. Themagni t udeof t heseconst ant si sknownaccur at el yupt ot he or der of t hesevent hdeci mal f i gur e, andt hi sknowl edgei sbasedexcl usi vel yi n measur ement seacht i mebet t er of t hem. Theseconst ant sar ecal l ed"f undament al " i nt hesenset hat t heyar enot der i vedf r omanot her , ont heot her handot herconst ant sasf or exampl et hecal l ed"f i nest r uct ur econst ant "( or el ect r omagnet i c coupl i ngconst ant ) i sder i vedf r omot her swhi char ef undament al . Asexampl e, t hi s l ast const ant i sexpr essedso:A=hC/ q^2=861. 0225291 Thi sconst ant i scommonl yexpr essedoni t sr eci pr ocal f or mandi sequal t oA' =2 pi / A Now, al l t hepr ocessesof Nat ur ear ei nanydi r ect or i ndi r ec t way, t hemani f est at i on of anyor someof t hef our f undament al f or ces. Thesef or ces, unt i l t hemoment ar e consi der edi ndependent f or cest oeachot her , t hat i st osay, wedon' t knowi f each ot her ar ei nanywayr el at ed. Al t houghi nt hel ast year st heor i es havear i sent hatseemst ohavebeenabl et odoi t .Thet askof t het heor et i cal physi csi st oexpl ai nt hephysi cal wor l d, andt hebet t erexpl anat i onshoul dbet ogat her i ncoher ent f or mandasnowi ssai d"beaut i f ul " t hesef our f or cesi nj ust one, t hat hasbeenal r eadybapt i zedas:"Super f or ce" TheFour For ces a) Thest r ongf or ce: i t i st hemost i nt enseof t hef our , i t t akescar eamongot hert hi ngsof mai nt ai ni ngt oghet er t hepr ot onsi nt henucl eusdespi t et her ej ect i ont hatt heel ect r ost at i cf i el dgener at esbyt heel ect r omagnet i cf or ceamongt hepr ot onsi n t henucl eusof t heat om. I t expl ai nst hegr eat amount of ener gyt hat i sgener at ed ont hepr ocessesof nucl ear f i ssi on. I t scoupl i ngconst ant wi l l ber epr esent edwi t h t hesymbol "P"b) t heel ect r omagnet i cf or ce: i st henext i ni nt ensi t yt ot hest r ongf or ce, al l t he el ect r i c, magnet i candopt i cphenomenon' sar ei t smani f est at i on, i t i st hef i r st of t he f or cest hat becameuni f y, becauseunt i l not al ongt i meagoi t wasconsi der edt hatmagnet i smf i el dandel ect r ost at i cf i el dwer esepar at ef or ces. Thankst ot hewor ksofJ. C. Maxwel l i t waspr ovent hat t heyar esepar at emani f est at i onsof anonl yone f or ce, t heel ect r omagnet i cf or ce. i t scoupl i ngconst ant wi l l r epr esent edwi t ht he symbol "A" c) t heweakf or ce: i t i snot af or cei nt hesenseof f or cesof at t r act i onor r epul si on bet weenpar t i cl es, i t sr ol l i st hat of t r ansf or mi ngt hei dent i t yof t hesubat omi c par t i cl esdur i ngt her adi oact i vedi si nt egr at i onpr ocesses, f or exampl e: t he t r ansmut at i onof aneut r oni napr ot onpl usanel ect r onandaneut r i no. Thi sl astpar t i cl ewi t hout mass( seemi ngl y) wasdi scover edt hankst ot heconcl usi onst hatgavet heanal ysi sof t heweakpr ocesses. I t scoupl i ngconst ant wi l l bei dent i f yi twi t ht hel et t er "W"d) l ast l y, t heweakest andt hewel l - knownof t hef or ces, t hef or ceof gr avi t y. I t i san accumul at i vef or cewhi chi ncr easewi t ht hemassof t heobj ect s, i sal waysat t r act i ve andi t i st hef or cet hat mai nt ai nsuni t edt hepl anet st ot hesun, t hest ar st ot he gal axi esandt hegal axi est ot hewhol eUni ver se. t hesymbol f or i t scoupl i ng const ant i s"B".2. - Thef act t hat t heel ect r omagnet i ccoupl i ngconst ant "A"wel l - knownast he i nver seof f i nest r uct ur econst ant i scal cul at edas:A=hc/ q^2 l eadt ousexpr esst heot her coupl i ngconst ant si nt hesamef or mt hat i s:A=hC/ q^2( 2- 1)B=hC/ Gm^2( 2- 2)W=hC/ qw^2( 2- 3)P=hC/ qs^2( 2- 4)Her emi st hepr oduct of me( t hemassof t heel ect r on) andmp( t hemassof t he pr ot on. ) . I t shoul dbenot i cet hat i t doesn' t exi s t or at l east accept edt heexi st ence of aweakchar ge( qw) or anast r ongchar ge( qs) , but t hef act t hat onecoul dmake cal cul at i onsbasedont hat l eadt oususet hat concept of "char ge. " I nhi sbook, Davi esi nf or mst hat qs^2=15hC/ 2PI andt hat t heco nst ant Wi s r el at edwi t hot her const ant i dent i f i edasgwwher e:gw=h^3/ Wme^2C=1. 43e- 49gm- cm5/ seg2 I nt hi sanal ysi s, f or r easonsof anot her t yper el at edwi t hCosmol ogy, i nt hepr evi ous equat i onI r epl acemebym. I nt hesecondi t i onst heval uecal c ul at edf or W, and keepi ngt heval ueof gwi s;W=4. 44612e+10 I nt hecaseof t hest r ongf or ce, t hef act or 15of t heexpr essi onf or t hest r ongchar ge t hat Davi esappoi nt s, wi l l becal cul at edwi t hbet t er pr eci si on. For t het i mebei ngIwi l l i dent i f yi t wi t ht heqsl et t er s.3. - Ther el at i onshi ps:What I her est udyi snot t her esul t of acal cul at i on, but asi mpl eanal ysi sof t he numer i cal r el at i onshi psbet weent hecoupl i ngconst ant s. Fr omt heval uesf or "W" and"B"wehavet hat :B=1. 9538657154e+42W=4. 44612e+10 wef i ndt hat al most exact l y:B=W^4/ 2( 3- 1)andal sot hat :B( D/ 4) ^16/ 2 wher e"D"i t i st her el at i onshi pbet weent hemassesof t hepr ot onandt heel ect r on andequal t o:D=1836. 152756F=D/ 4=459. 038189 t her ef or e, i spossi bl et hat asi mi l ar r el at i onshi pexi st sbet weent heot her const ant s becausewecoul dal soobser vet hat :WF^4 Thenar educt i oni nt heexponent i sobser vedi n4t i mesuponpassi ngf r omBt oW,andt her ei scer t ai nsymmet r yont hi s. Then, whynot t ot hi nkt hat i t hap penst he samet hi ngwi t ht heot her const ant sandseewhat cl assof number swoul dbe?. t hi s i swhat wewoul dhave:A=P^4/ x1( 3- 2) W=A^4/ x2( 3- 3) B=W^4/ x3( 3- 4)A=y1( D/ 4) ^1( 3- 5) W=y2( D/ 4) ^4( 3- 6) B=y3( D/ 4) ^16( 3- 7)Thenumber st hat appear t ot her i ght of t heyor t hexar enot mul t i pl i er snei t herexponent s, t heyar esubi ndexes. andt henumber sbet weensuchpar ent hesi sl i ke ( 3- 2) j ust number edt heequat i on.I haveal r eadyment i onedandcal cul at edt heval ueof t heconst ant A, B, W, but n ott oP. I wi l l doi t her ebef or egoon. Fr omt hedef i ni t i onof Davi esof t hest r ong char geandf r omt hef or mof expr essi on( 2- 1) wehavet hat :qs^215hC/ 2pi =hC/ PP2pi / 15, i sr ead"appr oxi mat el yequal "t hen P0. 4188. Let usput nowi nor der t heval uescal cul at edf or t hexandt hey,f r omt heequat i ons( 3- 2) t o( 3- 5) .Andaccept i ng( 3- 1) ascor r ect .x13. 57e- 5y1=1. 875710017 x2=12. 36166254y2=1. 001350011 x3=2. 0y3=0. 5027054946 obser vet hat 8y1=15. 0056815 Al soobser vet hat : y1^4/ yoA/ 2pi wher e"yo"coul ddef i nei t as:yo=P/ ( D/ 4) ^( 1/ 4) =0. 90478 Taki ngP=0. 4188. l et smakebysi mpl i f yi ngt hat F=D/ 4.I f i ndeedyi ^4/ yo=A/ 2pi =137. 0359916andA=y1F, t hen:y1^4/ yo=A/ 2pi =Fyi / 2pi i t i sdeducedt hat :yo=2PI y1^3/ F=0. 09032919484and:P=yoF^( 1/ 4) =0. 4181097966whi chi ssl i ght l ydi f f er ent t ot heconsi der edval ue 0. 4188or r at her but pr eci se. i nconsequence:Q=2pi / P=15. 0275965 y1^4/ yo=A/ 2pi =x2y2/ yo=x2JF^( 1/ 4) / P and: f r omt heequat i ons( 3- 2) t o( 3- 7) wecandemonst r at et hat :y2^4=x3y3y1^4=x2y2x2=A^4/ w=( A/ ( 2( y2F^( 1/ 4) ) wededuce:W=A^3x2pi y2F^( 1/ 4) / P Thi sl ast si mpl eequat i onr el at est hr eeof t heconst ant sof t hef or cest oeachot herwi t ht her at i oof t hemassof t hepr ot ont ot heel ect r on, t hat i swi t h"D", andwi t h "y2. "( al i t t l eaheadI wi l l cl ar i f ywhat i s"y2") . Theot her f or ce, gr avi t ydoesn' tappear her e, but wecoul di nt r oducei t i f wer epl aceWf or i sgr avi t at or yequi val ent ,t hat i s:B=W^4/ 2( 3- 8)t hi swoul dbeshownas;B=A^12Q4y2^4F/ 2( 3- 9)B=( 2pi A^3/ P) ^4Fy2^4/ 2( 3- 10)Obser vet hat of t heequat i on( 3- 1) andof t hedef i ni t i onof Was;W=h^3/ gwm^2C( 3- 11)wededucedt hat :G=2gw^4m^6C^5/ h^11( 3- 12)l et usmakeat t hi spoi nt asummar yof t henumer i cr esul t sunt i l nowobt ai ned:P=0. 4181097966 A=861. 0225291 W=4. 446119969e+10 B=1. 953865716e+42 x1=3. 549333914e- 5y1=1. 875710017 x2=12. 36166254y2=1. 001378374 x3=2. 0y3=0. 5027054946 4. - I f weal somaket heoper at i ony2xDwewi l l obt ai nt hef ol l owi ngnumber :I =y2D=1838. 683661 What i st hemeani ngof t hi snumber ?. I f I cal cul at enowwi t ht hegi venval uesf ort hemassof t heneut r onandt heel ect r ont hei r r at i o, t hat i st osay:mn/ me=1838. 683661 t hat i sexact l yt henumber "Y"! t her ef or e, i t i snot anyt hi ngvent ur oust osayt hat :mn/ me=y2D=I ( 4- 1)asD=mp/ me, t heny2=mn/ me/ D=mn/ me/ mp/ meand:y2=mn/ mp=J( 4- 2)Her e. wecanal sodeducef r omt heequat i ons( 3- 2) t o( 3- 7) andaccor di ngt ot he al r eadyexpl ai nt hat :y2^4=x3y3( 4- 3) y1^4=x2y2( 4- 4)and: y3=( mn/ mp) ^4/ 2andwecoul dal r eadyexpr esst heequat i onsf r om( 3- 5) t o ( 3- 7) i nt hi sot her f or m:A=( y1) ( D/ 4) ( 4- 5) W=( mn/ mp) ( D4) ^4( 4- 6)B=( mn/ mp) ^4( D/ 4) ^16/ 2( 4- 7)5. - Concl usi on: Wehaveseenhowt ocal cul at ei nanext r emel ysi mpl eway, t he coupl i ngconst ant sof t he4f or cesof Nat ur eandhowt heycoul dber el at et oeach ot her . Ever yt hi ngst ar t i ngf r omt heknowl edgeof si mpl eel ement sast hemassesoft hesubat omi cpar t i cl esandof t hef undament al const ant ssuchas"q".andi f wemaket hef ol l owi ngoper at i on:( hC/ G) ^( 1/ 2) =mi u=5. 456576426e- 5gr amst hat i t i sanext r emel yenor mousmass ( f or anat omi cpar t i cl e) . quest i on: what i st hemeani ngof amassof soenor mous val ue?. Thef act t hat t heexponent 4appear swi t hsomuchf r equency, r emember s met heexponent t hat appear si nt heequat i oni nor der t ocal cul at et hedensi t yofr adi ant ener gy.p=8pi ^5( kT) ^4/ ( 15C^3h^3) THEFOURFORCESOFTHENATURE( PART2)ANDTHECOSMI CBACKGROUNDTEMPERATURE 1. - I nt hi ssecondpar t , I wi l l deepi nt her el at i onshi pbet weent hecoupl i ng const ant sof t hef or cesandi nt hei r r el at i onshi pwi t ht heUni ver seandi t shi st or y.Someof t heval uesof t heconst ant st hat I wi l l obt ai nwi l l bemodi f i edwi t ht henew concept s.I haveal r eadyexpl ai nedt hat i nt hi ssi ngl ewr i t i ng, t hepar amet er sof nat ur ear e st udi edl ooki ngf or r el at i onshi psbet weent hemst ar t i ngf r omsi mpl econcept sand t henseei f t heyhaveanysenseor gi veusnewknowl edge. I f uponf i ndi ngt hatt heser el at i onshi pswehavet he"coi nci dence"upt ot hedeci mal f i gur et hat I can cal cul at e, t henI wi l l consi der sat downt hat t hi si st r ue.2. - I nt hepr evi oussect i onI obt ai nedt heel ect r omagnet i candgr avi t at or yconst ant s def i nedby:A=hC/ q^2B=hC/ Gm^2 Theseval uesobt ai nedf or bot hconst ant sar er epr esent at i veof t hepr esent t i me.I wi l l f i r st obt ai naser i esof magni t udescal cul at edst ar t i ngf r omsomeconst ant sofnat ur e. Let ussupposet hat Bi savar i abl eandal sot hemassm, l et usmakeB=1 . f r omt hat wewi l l get al l t hef ol l owi ngmagni t udes:mi u=( hC/ G) ^( 1/ 2) =5. 45657e- 5gr ams( 2- 1)l o=h/ mi uC=( hG/ C^3) ^( 1/ 2) =4. 05062e- 33cm( 2- 2)f o=C/ l o=( C^5/ hG) ^( 1/ 2) =7. 40114e+42cps( 2- 3)t o=1/ f o=( hG/ C^5) ^( 1/ 2) =1. 35114e- 43seg( 2- 4)eo=hf o=( hC^5/ G) ^( / 2) =4. 90412e+16er g( 2- 5)Theset er msar eknownasmass, l ongi t ude, f r equency, t i me, andener gyof Pl ank t hat t hecur r ent Cosmol ogyconsi der saschar act er i st i cof t hef i r st moment sof t he Uni ver se, t hat i s, dur i ngt hebegi nni ngof t heBi g- Bang.Nowweknowt hat at t hemoment of i nt er act i onof t woopposedpar t i cl es, ( mat t erandant i mat t er ) , t heydi sappear l eavi ngr adi at i on, t het emper at ur eof t hepr ocess i s:T=b/ i o( 2- 6)wher ebt hi sdef i nedby: b=hC/ ZK( 2- 7)Zi st hesol ut i onof t heequat i on( 5- z) e^z=5 Z=4. 965114231740001 K=1. 38065812e- 16er g/ Kel vi ni st heBol t zman' sconst anti oi st hel ongi t udeof waveat whi cht heel ect r omagnet i cemi ssi onof r adi at i oni s maxi mi nabl ackbodyat t heTt emper at ur e. f oi st hef r equencycor r espondi ngt o t hat wavel enght andi t i sequal t o:T=hC/ ZKi o=hf o/ ZK Si ncehf oi st hemaxi mumener gygener at edandequal t o:2mi C^2wher emi i st hemassof t hepar t i cl est hat i nt er act , t hen:T=2mi C^2/ ZK( 2- 8)Weknowt hat t hebackgr oundcosmi ct emper at ur eof r adi at i oni sappr oxi mat el y2. 7 Kel vi ns, t henmi i sof appr oxi mat el y:1. 04e- 36gr ams.Let usnowseet hat t her ear eal sor el at i onshi pssi mi l ar t ot hoseof Pl ankbut wi t hot her magni t udes, I her et akel =h/ mC Fx=Gm^2/ hl =Gm^3C/ h^2=2. 7095e- 21cps( 2- 9)Lx=C/ Fx=h^2/ Gm^3=1. 1064e+31cm( 2- 10)Ex=Fxh=Gm^3C/ h=1. 7953e- 47er g( 2- 11)mx=E/ C^2=Gm^3/ hC=1. 997e- 68gr ams( 2- 12)asbef or em^2=meXmp Wel l , i f wet aket hesquar er oot val uesof t hepr oduct of t het woobt ai nedmassesm andmx, weget obt ai nst hef ol l owi ngval ue:massm' =( mXmx) ^( 1/ 2) =1. 044032456e- 36gm:Obser vet heal most exact val ueof t hi sl ast massm' wi t ht heoneI cal l mi f r omt he equat i on( 1- 8) .Her ei smysupposi t i on; t hat bot har et hesamemass, andi nconsequence, I can expr esst het emper at ur eof r adi at i oni nt hef ol l owi ngf or m:T=2( mi Xmx) ^( 1/ 2) C^2/ ZK( 2- 13)mi =( mXmx) ^( 1/ 2) ( 2- 14)mt =2miThi smassmt coul dbei nt er pr et edast hemass- ener gycar r i edbyt hebackgr ound r adi at i on, or wemi ght supposet hat compl ement ar ypar t i cl esexi st t hat i nt er actgener at i ngt hebackgr oundr adi at i oncor r espondi ngt ot het her mal ener gy( ZKT) .Repl aci ngmi f or i t st wof act or sof t heequat i on( 2- 14) andknowi ng t hat B=hC/ Gm^2weget :mi =m^4/ B( 2- 15)mi ^4=Gm^6/ hC( 2- 16)T=2mC^2/ ZKB^( 1/ 4) ( 2- 17)T=2C^2/ ZK( Gm^6/ hC) ^( 1/ 4) ( 2- 18)t hecal cul at i ongi vemeT=2. 737601899Kel vi n 3. - Obser vet hat t heval uesobt ai nedf or someof t hecoupl i ngconst ant scomef r om aver ysi mpl eexpr essi ons, t hoset hat I ment i onnext :Wf =JF^4 Bf =J^4F^16/ 2 Obser vet hat I useWf andBf i nst eadof j ust WandB. t hi si sbecauseunl essIt hi nkt hat t her at i omp/ mechangeswi t ht i me, whi chI don' t , andt hi si st her eason whyI t hi nkt hat t heobt ai nedval uesr epr esent t heval uest hat wi l l r eacht hese "par amet er s"at t heendof t heexpansi onof t heUni ver se, ( i nf act t heseval uesar e al i t t l ebi t hi gher t hant heact ual val ues) andsomehowt hecur r ent measur ed val uesof t hecoupl i ngconst ant sshoul dbeaf unct i onof t heseWf andBf . For t hatr easonI havei dent i f i edt hemwi t ht hesubi ndex( f ) , but I nowhavet of i ndt hose f unct i ons.5. - Thef i r st f unct i ont osol vewi l l bet hat of "B"t hat bydef i ni t i oni s:B=hC/ Gm^2 I amsupposedt oaccept t hat h, C, andGar et i mei ndependent const ant sand t her ef or et hevar i abl et hat af f ect sBi st hemass.I t i snot di f f i cul t t oaccept t hat , si nceweknowt hat t hemassvar i eswi t ht h espeed sot hat :m=mf / ( 1- v^2/ C^2) ^( 1/ 2)I shal l nowi nt r oducet hef unct i on:si ne=( 1- v^2/ C^2) ^( 1/ 2) ( 5- 1)wi t ht hi sdef i ni t i onof t hemasswehavet hat :m=mf / si ne( 5- 2)Wecanseet hat t het wof or msof expr essi ngt hevar i at i onof t hemassi mpl y negat i vemasses, but t hesecondone( t hesi nef or m) i smor ecl ear concer ni ngwhen t hi shappens.Consi der i ngt hi svar i at i on, wecanexpr esst hegr avi t at i oncoupl i ngconst ant ( I wi l lcal l i t nowcoupl i ngpar amet er ) i nt hef ol l owi ngf or m:B=Bf ( si ne) ^2( 5- 3)Bei ng=wt , wi st hef r equencywi t hwhi cht heUni ver se( i nr adi ansper second)osci l l at es.Nowi t i snecessar yt ocl ar i f yt hat mf i snot t her est massof t hemasn, i s accor di ngwi t ht hedescr i pt i ont hat I amgi vi ng, t hef i nal mass, t hemasst hat mwi l lacqui r ewhent heUni ver ser eachesi t smaxi mexpansi onandt hat accor di ngt ot he gi vendef i ni t i oni s:mf =( mef Xmpf ) ^( 1/ 2)mef andmpf ar et hemassest hat wi l l acqui r et heel ect r onandt hepr ot onwhent he Uni ver ser eachest hemaxi mexpansi onandi nt hat moment i t wi l l beonr est , and ont hat moment andj ust ont hat moment wi l l coi nci dewi t ht her est masst hat we wi l l obser ve. t hemmassi st hecur r ent mass. I nsummar y, what I amsayi ngi st hatt her est massmvar i eswi t ht i me.Nowwecanseet hat uponmaki ngB=1, si newi l l acqui r et heval ue: si ne1=1/( Bf ^( 1/ 2) ( 5- 4)whent hi shappened, t hemasst ookt heval ue: m1=( hC/ G) ^( 1/ 2)whi chcor r espondst ot hemassof Pl ankandof cour set ot het i meof Pl anket c.Thenwehaveof t hat : Gm1^2=hC Now, wi t hout st i l l knowi nghowAvar i esi sobvi oust hat whenA1=1al so: q1^2=h C andt her ef oreGm1^2=q1^2t henof course: B1=A1 6. - Nowt het aski st of i ndt hef or mi nwhi chAvar i es, f or t hi s, t hef ol l owi ng condi t i onsmust bef ul f i l l ed:a) A=1whent =t 1=t p( Pl ank' st i me)b) A=Af whensi nef =1 c) A=act ual Awhensi nei st hecur r entSupposet hat t hef or mof var i at i onof Ai sal soi nasi nef or m. but expr essedas:A=Af ( si ne) ^a2( 6- 1)a2wi l l beat i mei ndependent const ant exponent .Wi t ht hi sequat i on, condi t i onsbi seasi l yf ul f i l l edsi ncesi nef =1andA=Af f or any val ueof t heexponent a2at t hemoment of maxi mexpansi on. Thecondi t i on"a"i s compl et eddoi ngt hat si ne1i st heconsi der edt heequat i on( 5- 4) . now, t he exponent i scal cul at edso:A1=Af ( si ne1) ^a2=B1=Bf ( si ne1) ^2wehavet hat :( si ne1) ^( a2- 2) =Bf / Af =SfSf i st her at i oof t het wof or ceswhensi nef =1. easi l ycal cul abl eaccor di ngt ot he f or mul asf or Bf andAf as:( si ne1) =1/ Bf ^( 1/ 2) =1/ Af ^( 1/ a2) ( 6- 2)andt aki ngl ogar i t hmswef i nal l yobt ai nt hat : a2=2l nAf / l nBf ( 6 - 3)but , what i st heval ueof Af anda2? 7. - Thef ol l owi ngi t emi st ot r yt of i ndt her el at i onshi pbet weenAandBi nanyt i me,f or t hi s, wet aket heequat i ons( 6- 1) and( 5- 1) , wesol vet hesi nef or bot handwe equal edt hemt oeachot her :( B/ Bf ) ^( 1/ 2) =( A/ Af ) ^( 1/ a2)andt her ef or ei seasyt oconcl udet hat : A^( 1/ 2) =B^( 1/ a2) and: a2=2l nA/ l nBf oranyepoch.I f weknowt heval uesof BandBf , t heact ual si ne=( B/ Bf ) ^( 1/ 2) andt her ef or e:Af =A/ ( si ne) ^( 1/ a2)8. - Usi ngt hesamepr ocedur et hat weusedi nor der t ocal cul at ea2wear eabl et o cal cul at et heexponent sf or t he, t heweakf or ceandt hest r ongandt henweobt ai n t hat :a1=2l nB/ l nB=2( 8- 1)a2=2l nA/ l nB=0. 1388012563( 8- 2)a3=2l nW/ l nB=0. 503559034( 8- 3)a4=2l nP/ l nB=- 0. 01790974997( negat i ve)( 8- 4)CHAPTER3 THEORI GI NOFMATTERANDTHECOSMI CBACKGROUNDRADI ATI ON Anal ysi sof t her el at i onshi pbet weent hepar amet er sof t hef or cesAandBi n r el at i onwi t ht hehi st or yof t heUni ver se 1. - Wei nt hef i r st pl acewi l l cl ar i f yt hemeani ngof t heconst ant Ht hat at t he begi nni ngI i dent i f yast heHubbl e' sconst ant andt hat I t hought t hat i t r epr esent ed t hef r equencyof t heuni ver sal osci l l at i on. Uponcal cul at i ngt het empor ar yangl e,wer eal i zet hat i scl oset o90degr ees( seet hesheet of cal cul at i ons) . Fr omher eIhavef oundver yeasyt hi nkt hat Hf r epr esent st hei nver seof t henecessar yt i mef ort heUni ver set or eachesi t smaxi mexpansi onandt her ef or ei t r epr esent st het i meof1/ 4of cycl e, t hef r equencyi ncpsi s. w' , andt hef r equencywi st hef r equencyi n r adi ansper second. Not i cet hat t heuni t sof Hf ar ecps. becauseI uset hePl ank' s const ant andnot h/ 2pi t hat woul dgi vet hef r equencyi nr ps.t heFf r equency=1/ Tf bei ngTf t het ot al per i od, wehave:t f =1/ Ht f =Tf / 4=( 1/ 4w) ( Ht f means: f i nal t ot al becausei t i ncl udest heef f ect soft hemassaswel l ast het her mal ener gy)t hen: Ht f =4wHt f =2F/ pi andw=2pi FHt f =Gmf ^2/ hr f ( 1- 1)wher er f =qf ^2/ ( mf C^2) , andwededucedt hat : Ht f =C^3Af / Gmf ^2Bf ^2I fBf ^2/ Af =Nf t hen:Hf =C^3/ Gmf Nf ( 1- 2)Now, weknowasI sol vedi nanot her chapt er , Mt f =C^3/ GHt f ( 1 - 3)But her eMt f r epr esent sal l t hef or msof mass- ener gyi ncl udi ngr adi at i on. Thenwe cansay: Rf =C/ Ht f Rf =GMt f / C^2 andt her ef ore:Ht =Ht f / ( si ne) ^( 3- a2) ( 1- 4) R=Rf ( si ne) ^( 3- a2) ( 1- 5) M=Mt f ( si ne) ^( 3- a2)( 1- 6)p=pt f / ( si ne) ^2( 3- a2) ( 1- 7) densi t y andal so: q^2=qf ^2/ ( si ne) ^a2( 1- 8)wher eal l t hef i nal val ues( subi ndexf ) meanst hef i nal st at eat t hemoment ofmaxi mexpansi onof t heUni ver se.Andt heval uesf or R, H, M, par ef or t heact ual moment andt heyi ncl udeal l t he mass- ener gy.Thel ongi t ude: L=C/ w=2Rf / pi I sexpr essedi nf unct i onof t hemassas: L=2G Mt f / pi C^2 I ment i ont hi sl ast expr essi onbecauseA. Ei st ei ncal cul at edasr adi oof t he Uni ver sewhat I i dent i f yas:L=t hewavel engt h/ 2piWewi l l seenowhowt or el at et hemassof t heal l Uni ver se, wi t hi st het ot al mass-ener gyandt het her mal ener gyandt hemassof al l t hepar t i cl est oeachot her .weknowt hat :pt =8pi ^( KT) ^4/ 15h^3C^5=( KT) ^4/ h^3C^5) ( 3Z^4/ 4pi 2^4) ( 512pi ^6/ 45Z^4)( t her mal densi t y)i f =512pi ^6/ 45Z^4andKT=2mC^2/ ZB^( 1/ 4)Thenwi t hj ust t hepr evi ousequat i onswededucet hef ol l owi ngr esul t s:pt m=pt ot / A^2( 1- 9) ( t her mal densi t y)andi f t her adi usof t heUni ver sei st hesamef or t her adi at i onandf or t hemass t hen:Mt m=Mt ot / A^2( 1- 10)2. - I f wer emember edt hedef i ni t i onsgi venont hePl ank' st i menowwehave:mp=( hC/ G) ^( 1/ 2) t p=( hG/ C^5) ^( 1/ 2)andf r omt hedef i ni t i ons: B=hC/ Gm^2m^2C^4=h^2/ t ^2weobt ai n: mp/ t p= C^3/ G=Mt / Ht =Mt / t 't her ef or e: mp/ t p=C^3/ Gi st her hyt mof mat t er cr eat i on. Onwhi cht ' =( si ne) ^( 3-a2)I t i si mpor t ant t omakenot i ceher et hat I pr oposest heexi st enceof t wot ypesoft i me, oneof t hemwhi chI wi l l cal l r el at i ve, i t i sanel ast i ct i mei t i st ' , i sel ast i c,goesupanddownandceasest oexi st but al waysr ebor n. i t i saf unct i onof t he ot her t i me, t heabsol ut et i met a=/ wt hen:t ' =( si newt a) ^( 3- a2) / HfSo, t ot al massasf unct i onof t heabsol ut et i mei s: M=Mt f ( si newt a) ^( 3 - a2) and asf unct i onof t her el at i vet i mei s:M=C^3t ' / G Sowemaysayt hat f r omt hepoi nt of vi ewof t heabsol ut et i me, t hecr eat i onofmat t er goesaccompani edbyi t sdest r uct i onaf t er t heUni ver sear r i vest oi t smaxi m expansi on. wecoul dal sodeduceeasi l yt hat t hespeedof expansi oni s:v=( 3- a2) C( si ne) ^( 3- a2) / Tg 3. - Now, i f t hepot ent i al gr avi t at or yener gyi s: Ep=- GMt ^2/ R andi f t heener gyof t hemassandt het her mal ener gyi s: Mt C^2=Mt f C^2( si ne ) ^( 3- a2)t hat addedt o- - GMt ^2/ Rgi veus: Tot al Ener gy=0 Weshoul ddi st i ngui shbet weent het ot al massof t heUni ver seandt hemassof t he par t i cl es. f or t hi sweshoul dconsi der ( r epeat i ng) :- t hat t het ot al mass- ener gywi t hout i ncl udi ngt ot hegr avi t at i oni t i sMt .- t hat t het hermal mass- ener gyi sMt m.- t hat t hemassof t hepart i cl esi sMm - t hat t hemass- ener gyof t hegr avi t at i oni sMg - t hat t hemass- ener gyat t heendof t heexpansi onwi t hout t hegr avi t yi sMt f- t hat t het hermal mass- ener gyat t heendof t heexpansi oni sMt mf- t hat t hemass- ener gyof t hepar t i cl esat t heendof t heexpansi oni sMmf- t hat t hef i nal mass- ener gyof t hegr avi t at i oni sMgf- t hat t hegr owt hof t hespacedoesn' t meant hat t heexpansi onof t heUni ver se t r anspor t ski net i cener gy, t hi si szer o.- t hat t hemassof t hepart i cl esaret hedi f f erencebet weenMt andMt m=Mm - t hat t het ot al gr avi t at or yener gyi ncl udest hepot ent i al ener gyof t her adi at i onand t hat of massandi t i snegat i ve.- t hat t het ot al ener gyof t heUni ver sei ncl udi ngal l t hef or msof ener gyi sequal t o zer o. andt hebal anceof massi s:Mm+Mt m=Mt =- Mg Mm+Mt m- Mg=0 i nconsequence"Mm"t hat i t i st hemassof t hepar t i cl esi s:Mm=Mt - Mt m=Mt - Mt / A^2 Mm=Mt ( 1- / A^2)4. - Wewi l l seet hat consi der i ngwhat I cal l edt ot al massast hesumof t hemasses of t hepar t i cl eswi t hnonzer or est massandt het her mal massi sj ust i f i edi nf unct i on of somesi mpl eequat i onsof t heGener al Rel at i vi t yappl i edt ot heUni ver seont he whol e. Mr . M. Rober t Wal di nhi sbook"SpaceTi meandGr avi t at i on"def i nest he Hubbl e' sconst ant as:H=1/ ada/ dt ( 4- 1)i nwhi ch"a"det er mi nesanscal eof l ongi t udei nf unct i onof whi cht heUni ver se expands, weal soknowt hat Hi sdef i nedby:H=V/ L( 4- 2)wher eVi st hespeedof expansi onof adi st ant gal axyand"L"t hedi st anceof an obser ver t oi t .I wi l l demonst r at et hat "a"andLar epr opor t i onal :f r om( 4- 1) ( dH/ dt ) a=- 1/ a^2( da/ dt ) ^2+1/ a( d2a/ dt 2) ( 4- 3)f r om( 4- 2) ( dH/ dt ) L=- 1/ L^2( dL/ dt ) ^2+1/ L( d2L/ dt 2) ( 4- 4)Supposet hat "L"i spr opor t i onal t o"a", t hen: a=k! L( 4- 5)wher ek! i sanumer i cconst ant wi t hout uni t s. nowweobt ai nt hef i r st andt hesecond der i vat i vesof ( 4- 5) andweobt ai n:da/ dt =k! - dL/ dt =k! - Vd2a/ dt 2=k! - dV/ dt =k! - Ac wher eAci st heaccel er at i onof t hegal axyt hat i sonL.( dH/ dt ) a=- 1/ L^2( dL/ dt ) +1/ L( d2L/ dt 2)t hesamebookdef i nest hedesacel er at i npar amet er "q"( donot conf usei t wi t ht he el ect r i cel ement ar ychar ge) as:q=ad2a/ dt 2/ ( da/ dt ) ^2=Lk! ( k! xAc) / k! ^2/ V^2=AcL/ V^2Now, A, L, andVar er el at edwi t hHas: dV/ dt =HdL/ dt =A=HV=HL^2AL= H^2L^2andq=H^2L^2/ V^2=1 wef oundt hat t hedesacel er at i npar amet er i suni t ar y.Thi sal l owsust odeducet hef ol l owi ngr el at i vi st i cequat i on:q=4pi G/ 3H^2( pm+3P/ C^2) =1 Onwhi chpmi st hedensi t yof t hemassandt headdi ng3P/ C^2i st hedensi t yof t he mass- ener gyof t hepr essur eof r adi at i onP, t hat i st osayt het her mal densi t y, so:1=4pi G/ 3H^2( pm+pt )H^2=Gk( pm+pt ) =Gkptpt =pm+pt m pt meanst ot al densi t y pmmeansmassdensi t y pt mmeansmassequi val ent t her mal densi t y Andsi ncet hevol umei st hesamef or t hemassandf or t her adi at i on, t hen:Mt =Mm+Mt m t hat i t i sequal t ot heoneI f oundbef or eandt hi si swhat I want edt odemonst r at e.That i sbysupposi ngt hat "a"andLar epr opor t i onal , wear r i vet oat r ul yconcl usi on.Aswel l asf r omt heequat i on( 4- 2) youar r i vedt o( 4- 4) , of t hei nt egr at i onof ( 4- 3) we ar r i vedt o:H=- Va/ a( ai ssubi ndexi nVa) and: Va/ a=V/ L. Now, anot her r el at i vi st i c equat i oni s: H=2Gkpt - KC^2/ a^2 wher eKi st hef act or t hat def i nesi f t heUni ver sei spl ane, spher i cal or hyper bol i c.Fr omt hepr evi ousequat i onandasH^2=Gkpt t hen: KC^2/ a^2=H^2k=4pi / 3 K=Va^2/ C^2 i t canbecl ear l yseet hat Ki sposi t i veandl esst han1( Vai sal wayssmal l er t haC) ,t hat meansacl oseUni ver se. andt heconst ant i sl esst han1.5. - Thei mpor t ant t hi ngher ei st oexpl ai nt heor i gi nof t hemat t er . Theequat i onsoft hepr evi oust opi csshowshowi t var i eswi t ht het i meangl e, but i t doesn' t i nf or m usabout t heor i gi n. For t hi s, I post ul at et heconcept t hat t hemat t er andt heener gy of t heUni ver sear enot et er nal , but r at her t heyhavebeencr eat edi nf unct i onof t he uncer t ai nt ypr i nci pl eof Hei sember g. But si ncet hi spr i nci pl ewoul dr equi r et hat t he spont aneouscr eat i onof asi ngl epar t i cl ebeat empor ar yphenomenonandt hat i tmust di sappear at at i menol onger t han:t =h/ mC^2 t hat i t obvi ousl yver ymuchl esst hant heageof t heUni ver se, t henhowi st hat t he pr ot onsandt heel ect r onsexi st per manent l y?. Oneopt i oni st ot hi nkt hat eachnew i nst ant newpar t i cl esar ecr eat edandt heol donesdi sappear , andi nconsequence t heUni ver sei sr ecr eat edeachmoment andi f i t i sr ecr eat edi neachmoment , who needsaBi g- Bang?Thepr evi ousanswer i st omuchspecul at i ve, andal t hought he peopl et hat ar edevot edt ot heset opi csar enot wal ki ngi nt hebr anchesat t het i me of gener at i ngnewi deas, I don' t l i ket hi sone.SoI pr ef er t ocont i nuet hi nki ngt hat t hepr i nci pl eof uncer t ai nt yi sbeenwor t hbut Ishoul dexpl ai nwhymat t er doesn' t di sappear i nt heuncer t ai nt yof t het i meof t he pr i nci pl eof Hei sember g.I f i ndt hat t her ewoul dnot becont r adi ct i onwi t ht hepr i nci pl ei f I post ul at et hat att hesamet i met hat mat t er i sf or medwi t hposi t i veener gy, i t i sf or medsomeanot herf or mof ener gyt hat i snegat i veandt hat compensat esexact l yt hemat t er , i nsuch wayt hat t henet cr eat edener gyi szer oandt her ef or et het i meonwhi cht hemat t ershoul ddi sappear i nor der t oagr eewi t ht hepr i nci pl ei t i si nf i ni t eor at l east asl ong asanuni ver sal cycl e. I bel i evet hat t hi sener gyi st hegr avi t at i on, I bel i evet hat t he gr avi t at i oni st hei nvent i onof Nat ur ei nor der t oper mi t t hecuasi per manentexi st enceof mat t er , besi desbei ngt her esponsi bl ef or i t sevol ut i on. I al r eadyf ound howt hi shappenwhenI f oundt hat t het ot al ener gyof t heUni ver sei szer o.Let ust hensupposet hat wi t ht hecr eat i onof apar t i cl ewi t hener gy ( m+) C2i scr eat edanener gy( m- C^2) sucht hat : mi i st hedi f f er encebet weent hi s t womasses.mi =h/ C^2t ionwhi chmi i st heuncer t ai nt yof t hemassandt i t heuncer t ai nt yof t het i me. Si nce t heuncer t ai nt yof t het i mehast obeequal or mi nor t ot het ot al ageof t heUni ver se andt hi si s2/ Hf , t hen:mi =hHf / 2C^2=0. 86e- 65gr m THATWOULDBE! THENETMASSOFTHEUNI VERSE! . i t seemst obei ncr edi bl e t hat asosmal l massi st henet massof t heUni ver se, but i f wecal cul at edt he l ongi t udeof t hecor r espondi ngwavewewoul dhave:l =h/ 2mi C=2hC/ Hf h=2C/ Hf =2RfThat i s, t hedi amet er of t heUni ver sei st hel ongi t udeof t hewaveof t hi sonl y par t i cl et hat r epr esent si t .I want t oaddt hat I havesomucht r ust i nt heequat i oni nor der t ocal cul at et he cosmi cbackgr oundt emper at ur eof r adi at i ont hat when( accor di ngt ot hel asti nf or mat i ont hat I have) t hi si sof 2. 735Kel vi ndegr ees, t hat t hedi f f er ences bet weent hi sf i gur eandmi ne( 2. 7374kel vi ndegr ees) I at t r i but ei t t o: er r or si nt he measur ement of Tor t oer r or si nt hemeasur ement of t heconst ant st hat i nt er vene i nt hecal cul at i on( ver ypr obabl yt heconst ant of Bol t zmanandG) . or t ot hat t he t emper at ur et hat I cal cul at ecoul di ncl udeot her par t i cl eswi t hzer or est mass( notphot ons) as; gr avi t ons, neut r i nset c.Anot her t hi ngI want t oaddi st hi s: t heequat i onsI haveshownar ef or al ar ge amount of par t i cl es, t hat i s, somehour saf t er t heBi g- Bang. For t hever ymoment oft heBi g- Bang( dur i ngt hePl ank' st i me) t heyar eal i t t l edi f f er ent becauset he const ant . I amnot expl ai ni ngher et hedet ai l sbecauseI woul dhavet ousemor e space, andt hi ssupposet obeanabst r act . Thef ul l paper i sof near ahundr ed pages, andI aml eavi ngout al ot of det ai l sabout t het emper at ur e, t her mal ener gy densi t y, t henumber of phot onsandt her at i owi t ht henumber of nucl eons, et c. ButYwi l l sayonet hi ngf or t hat moment ( Pl ank' st i me) , t henumber Nwasexact l y1,al soal l of t hecoupl i ngconst ant s, t hemass- ener gyof t heUni ver sewasexact l yt he Pl ank' smass.Theonl yot her t hi ngI wi l l add, i sagr aphwhi chshowsaccor di ngwi t ht he equat i onst hat I haveshownhowt hef our par amet er sof t hef or cesvar ywi t ht he ener gy. not i cespeci al l yt hat t heonl yf or cewhi chi sget t i ngbi gger i st hest r ong f or ce( t hepar amet er i sgoi ngdown) .Youshoul dobser vei nt hegr aphst hat I at t acht hat t heuni f i cat i onof t he4f or ces happensi nf act whent hemassof t hemasni st hemassof Pl ank. t hegr aphsar e exposedasl ogar i t hmi cgr aphssot hat onecoul dappr eci at et hevar i at i on.Thecosmi cbackgr oundt emper at ur ecanbeexpr essedasi seasyt oded uceas:T=Tf / ( si ne) ^( 3/ 2)Nowwewi l l expr esst hi st emper at ur easaf unct i onof Pl ank' st emper at ur eT1, as t hi shappenedwhensi ne=1/ Bf ^( 1/ 2) t hen:T=T1/ Bf ^( 3/ 4) ( si ne) ^( 3/ 2)T1=2m1C^2/ ZKbeenm1t hePl ank' smassm1=( hC/ G) ^( 1/ 2) a nd:si ne=( T1/ T) ^( 2/ 3) x1/ Bf ^( 1/ 2)For ever yoneof t he4par amet er sof t hef or cest her eexi st anexponent ( a1, a2,a3, a4) i nsuchawayt hat i ngener al :k=kf ( si ne) ^an wher ekr epr esent sanyof t hef our par amet er sandkf i t sf i nal val ue, and"an"i s t hecor r espondi ngexponent ( n=1, 2, 3, 4) so:( si ne) ^an=( T1/ T) ^( 2an/ 3) X1/ Bf ^( an/ 2) and: k=kf ( T1/ T) ^( 2an/ 3) x1/ Bf^( an/ 2)Whi chexpr essedasaf unct i onof t heval ueof t hepar amet er of t hef or cesi n Pl ank' st i me( whenal l of t hepar amet er swer euni t ar y) i s:k=( T1/ T) ^( 2an/ 3)Thi sl ast equat i oni sgoodf or al l t hepar amet er s, andyouj ust get t oknowt he t emper at ur ei nanyepocht oknowwhat wast heval ueof t hepar amet er ( andofcour seal sot heexponent "an"of t hecor r espondi ngf or ce)T1=2( hC/ G) ^( 1/ 2) C^2/ ZK=1. 430694953e32Kel vi nsI seasyt odeduceal sot hat t hepar amet er sof t hef or cesvar ywi t ht heener gyof t he masonandt hat i nt hePl ank' st i met hecor r espondi ngener gywas:3. 0607e+19Gev.Theequat i onshowst hat t heuni f i cat i onhappenswhent hemasonener gyhadt hi s val uei nt hePl ank' st i me.E=E1/ k^( 1/ an)BeenE=mC^2i nanyepochandE1=m1C^2 Concl usi on: t hi smodel i sver ysi mpl eandi t doesnot r equi r edmor emat ht hanwhatI haveal r eadyshown. Thesear et hegener al concl usi onsf or t het heor y:a) TheUni ver sebegant oexi st 1/ Ht sec. agowi t hnot mass - ener gyandwi l l endi n aBi g- Cr unchal sowi t hout mass- ener gy. TheUni ver sepr oper t i escanbededuced f r omt heat omi cpar t i cl esandf r omsomef undament al const ant s.b) Par t i cl esbegant oexi st exact l yat t hePl ank' st i me, t heycamet ot heexi st ence becauset heuncer t ai nt ypr i nci pl eandcont i nueexi st i ngbecausegr avi t y count er bal ancet heener gyof t hemi nsuchawayt hat t het ot al ener gyof t he Uni ver sei szer oal waysexcept by"mi "whi chi sal most zer ot o.c) Thecosmi cbackgr oundt emper at ur eandt het her mal densi t yhadbeencomi ng downsi ncet hePl ank' sepoch, but t het ot al t her mal ener gywasl i t t l eat t hat t i me,andevenbeent het emper at ur ever yl owont hesedays. t ot al t her mal ener gyi s hi gher now.d) Theori eswhi chdonot accept t hecycl i ngof t heUni verseargui ngt hat :- TheBi g- Crunchwoul dbet heonl yandbi ggest of t heBl ackHol esand t heref orei t won t bounceback.- Therei snot enoughmass( densi t y) i nt heUni verset ost opi t andbri ngi tbackt ot heBi g- Crunch.- Ent ropyal waysgoupt heref oret hecl ockwi l l st opf orever.Theprevi ousobj ect i onsarecorrect i f ( andt hi si si mport ant ) : t hemass-energyi sconst ant i nal l epochs. But f romwhat wej ust haveseen, t hi si snott hecase, t heref oret heobj ect i onsarenot val i d. Andbesi desheat , creat es di sorder, gravi t ycreat esorder. I not herwords, whent heUni versei s expandi ng, cosmi ct emperat uregoesdownandent ropyi sgoi ngupont hebul k , whent heUni versei sshri nki ng, t emperat urei sgoi ngupspont aneusl y, so ent ropyont hebul ki sgoi ngdown. Thi sdoesn t meant hat hot bodi eswi l lreci veheat f romcol dbodi es, t hesenseof t heheat t ransmi si onwon t change , but t aki ngt hecompl et eUni verse, ent ropywi l l godownandmat t erwi l l be di sappeari ngbecausegravi t at oryenergyi sgoi ngdownal so.I nf act , ri ght knowi shappeni ngt hat i ngeneral ent ropyi sgoi ngup, but t here aresomebodi esi nwhi chent ropyi sgoi ngdown, whi chbodi es?wel l , besi des t hel i vi ngbeens, everynewst ari sreduci ngi t sent ropywheni t i sf ormi ng,becausei t t akesi t smassf romcol dmat t er, i t wi l l changet oahot mat t er becausegravi t y. Of course, t hi si shappeni ngj ust duri ngi t sbi rt h, af t ert hat ,ent ropyagai nwi l l goup.e) Ther ear et woki ndsof t i me, t heabsol ut e, andpr obabl yj ust amat hemat i cal butnot r eal t i me, andt her el at i ve, t het i mewhi chbegant oexi st andt hat wi l l end.f ) Theuni versei sal most exact l yf l at j ust becauset heexi st enceof "mi ,ot herwi sei t woul dbeexact l yf l at . ( k=1)g) Equat i onsar enot cont r adi ct or ywi t h( asf ar asI f ound) t hegener al r el at i vi t y.h) Thef ourparamet ersof t hef orcesof Nat urevarywi t ht i meandwi l l reacha f i nal val ue. Theyhadt hesameval ue"1"at t hePl ank' st i me. Andt heyare numeri cal l yrel at ed. Al l of t hemchangewi t ht heCBT, t hat wi l l reacha mi ni mumnonzeroval uebef orei t st art st ogoupagai n. Therei snot reasont o di scusst hat i f t hecoupl i ngconst ant swoul dbedi f f erent , t heUni versewoul d not exi st . That i snot correct , t hepoi nt herei showdot hecoupl i ng const ant schange, t herat eof changeof t hem, whi chwi t ht heexcept i onofgravi t y, t heot hert reeareal most const ant . Besi des, nobodycansaywhat i twoul dhappeni f some"const ant s"varywi t ht i mebecausenobodyknowswhatot herconst ant swoul dal sochanget ocompensat eandkeept heUni verse exi st i ng.i ) El ect r i cchar gevar i eswi t hener gy. but muchmor el esst hanmass, i nabout 10e -40t i mesl ess.j ) Li ght speed, Pl ank' sconst ant , Newt on' sconst ant , DandJ, Bol t zman' sconst ant, ar et hemai nconst ant sof Nat ur e. Theydef i neal l t her est of t hepr oper t i esof t he Uni ver se.k) Ther eal Cosmol ogi cal pr obl emi st oexpl ai nt heval ueof t hef undament alconst ant s. I t i sut opi ct ot hi nkt hat someki ndof mat hemat i csor t heor ywi t houtconst ant si t sel f wi l l expl ai nt hese, why?Becauset heseconst ant shaveuni t s(gr am, cm, sec. ) andt her ei snoanyr easonabl emeanof get t i ngt heseuni t sf r om anyl ogi cor mat hemat i cal pr i nci pl es, unl esswest opst udyi ngphysi cswi t huni t s andst ar t t hest udyphysi cswi t hj ust pr opor t i ons. t hent her ei sonl yonet hi ngwe cansayabout t hepr oper t i esof t hepar t i cl es; t heyaresomanyt i messmal l eror bi gert hansomepropert i esof t heUni verse, orvi ceversa.AsI sai dat t hebegi nni ng, t hi spaper i sanabst r act , andf or t hat r easonI di d nti ncl udemanyt hi ngs, but i f t her eader havesomequest i onsregardi ngt hi spaperIwi l l gi vehi mmoredet ai l si f hecal l smet omye- mai lAnyonewhoreadt hi spapercanusei t f orPhysi csandCosmol ogy purposes, but i f myi deasareexposedi nanyf orm, mynamemust beci t edon i t . RamnGar zaWi l motE- mai l : r agawi @hot mai l . com Oct . 7of 1998 Mont er r ey, N. L. Mexi co