I. The HyperGeometrical Universe Grand Unification Theory

Transcription

1 Abstat I Th HypGomtial Unis Gand Unifiation Thoy Mao A ia* This pap psnts a simpl Gand Unifiation Thoy latiity is xpandd to inopoat a d Bogli Wa Dsiption Quantum Gaity Eltostati and Magnti intations a shown in a unifid famwo Biot-Saat Law is did fom fist pinipls Unifiation symmty is dfind fo all th xisting fos In th famwo of this thoy th is only on Fo no masss hags Quas Cosmi Constants t Intodution H is psntd a thoy that mas us of Fou-Dimnsional Spatim d Bogli was to pliat all fos of Natu Quantum Gaity Eltostatis and Magntism a did as th sult of simpl onstuti intfn of fou-dimnsional spatim was olaid on an xpanding hypsphial Unis This wo is basd on th HypGomtial Unis Thoy On alulats th onstuti intfn of spatim was Th shift in th nod du to th onstuti intfn btwn patils fom on d Bogli Unis xpansion to th nxt dfins th alation and thus th magnitud of th fo Hypsupfiial was a assoiatd with Gaitation whil olumti was a assoiatd with ltomagntism Th thoy is alld a Gand Unifiation Thoy baus it poposs that th th quas whih a inxtiably onntd though gluons in th Standad Modl a atually quantum numbs assoiatd with th th lina dimnsions of th sou of th spatim was This sou is poposd to b a fou-dimnsional llipsoid of olution patil X fo simpliity Qua numbs bing just lngths of an llipsoid annot b spaatd by ollisions in th sam way on annot spaat th X dimnsion fom a th dimnsional body Ngati lngths a assoiatd with phas shifts 8 dgs of th spatim wa Sam olum patils a synhonizd by a Cosmologial Cohn ondition with ah oth thoughout th Unis and all th way to thi oigin In fat d Bogli phas is what distinguishs matt fom antimatt Wa fo nutino-indud day is a poposd to b a standad hadoni wa downonsion Th oth dimnsions of th Standad Modl a onsidd to b otational dgs of fdom of th X-patils Th HypGomtial Standad Modl will b psntd in anoth pap of this sis

2 Hypsphial Unis Th pitu shown in Figu psnts a oss stion of th Hypsphial Expanding Unis Th Unis is onsidd to b atd by an xplosion but not by a thdimnsional xplosion Instad it is onsidd th sult of a fou-dimnsional xplosion Th olution of a th-dimnsional xplosion is an xpanding twodimnsional sufa Th olution of a fou-dimnsional xplosion is an xpanding th-dimnsional hypsufa All tims a mad dimnsional by th multipliation by th spd of light φ θ τ τ' x Figu Shows th oss-stion Xτ fo th xpanding Unis Th Unis lngth along X is psntd by th band X o Y o Z is displayd along th pimt of th il Also shown in th diagam is Φ Cosmologial Tim and adial Tim This figu displays th two tim dimnsions and Φ and two tim pojtions τ and τ Eah fn fam has its own tim pojtion This figu also shows that th fou-dimnsional spatim is ud bing th adius of uatu gin by th dimnsional ag of th Unis This simpl figu liminats th nd fo Cosmologial Constant qustions onsidations about Gaitational ollaps o antigaitational alation of th xpansion of th th-dimnsional Unis sin th Unis is poposd to b fou-dimnsional plus a Cosmologial Tim Φ Dfinitions: Cosmologial Tim Φ psnts an absolut tim fam as nisiond by Nwton and Mah It is a fifth dimnsional in th HU modl adial Tim is also a dimnsional tim o an b sn as a fouth physial dimnsional of popagation It has a pfntial dition adial and it dfins a pfntial tim fam Sin on onsids th Unis xpansion loity to b th spd of light ps a simpl lationship with Φ idntial modul lationship τ is any oth popagation dition This maps ou loal fam dimnsional tim and it is th sou of th latiism in th Thoy of latiity Diffnt angls of popagation flt diffnt lati loitis

3 Th angl btwn and τ dfins th loal dfomation of spatim Th angl btwn τ and τ dfins th lati dg of loal dfomation of spatim Sin th hypsufa is ou th-dimnsional Unis a hypsupfiial spatim wa is a spatim distuban that popagats along th Fabi of Spa Th onpt of th Fabi of Spa will bom la as th thoy is dlopd Fabi of spa is usd in two manns: a as th non-dfomd spatim wh loal fn tim τ points in th adial dition and b th subjt of dfomation olumti was a spatim was that a f to dit thmsls without haing to dfom th Fabi of Spa This will also bom la as th thoy is dlopd In this modl th Hypsphial Unis is laly finit iula adius of uatu qual to th dimnsional ag of th Unis that is th spd of light tims th ag of th Unis It is also impossibl to tas sin it is xpanding at th spd of light Oigins of th Hypsphial Expansion Th lus fo th ation of this modls lis on latiity and Quantum Mhanis latiity stats that th ngy of a patil with st mass m and momntum p is gin by: E m p m A wh m is th mass in motion This quation has impliit assumptions whih an b bought into light by onsiding it a momntum onsation quation instad: m p m A Wh is th momntum of a patil in motion at th spd of light taling suh that its τ patil mas angl with th stati fn fam τ Obs Impliit in quation A is that th patil is atually taling along a foudimnsional spa timd by a fifth tim dimnsion and has two lina momntum omponnts: a Th-dimnsional momntum p b pndiula momntum m in th dition of adial Tim In addition th patil tals at th spd of light in along a hypotnus with an intial mass m

4 Now it stats to bom la that th motion of th patil is atually in a fi dimnsional spa fou physial dimnsions and a tim and at th spd of light bing th th dimnsion motion just a dift Th tigonomti funtions assoiatd with a latiisti Lontz tansfomation a gin in tms of loity by: osh A sinh A4 tanh A5 Manipulating quation A and using m m osh on obtains: m m m A6 m osh osh m m A7 m osh sinh m m A8 A9 τ x m τ im With m d Bogli walngth fo th patil on its own fn fam taling at h th spd of light in th dimnsional tim τ dition τ osh τ im τ sinh x im τ ojtion on th τim dition ojtion on th xim dition Equation A9 is th basi quation fo th Quantization of latiity It dsibs th motion of a patil as th intation of two was along dimnsional tim and th-dimnsional spa 4

5 Figu blow displays th patil as a d Bogli wa osillating as a funtion of Cosmologial Tim Φ popagating along τ This is a pop fn fam plot that is th patil is at st at th oigin and only tals along th dimnsional tim dition τ x D Bogli Tim-opagating Wa Φ τ Figu This modl shows a d Bogli osillation as a funtion of Cosmologial Tim Φ x xim x Th diagam blow psnts th sam obsation fom a moing fam of fn lati loity tims tanh: Φ τ d Bogli Obsd Tim- opagating Wa in th Moing fn Fam im Figu ojtion of d Bogli Wa in th moing fam of fn τim τ τ 5

6 Th τ im that is th pojtion on th τ axis of th wa popagating along th τ axis sting fn fam is gin by: τ τ im τ xim osh sinh A A This mans that th pojtd d Bogli Tim-Taling walngth is zo whn th lati loity ahs th spd of light Zo walngth mans infinit ngy is quid to twist spatim futh Th at of spatim twisting with spt to pop tim lats to th pow ndd to alat th patil to a gin spd Fom quation A5 alation in th moing fn fam an b alulatd to b: Alation im d tanh A dτ im In th patil fn fam th alation has to b gin by Nwton s Sond Law d tanh Fo M Alation im M A dτ im This mans that any fo loally twists spatim and not only Gaitation as it is onsidd in Gnal latiity It also shows th as th lati spd btwn th two fn fams inass towads th spd of light th quid fo to alat th patil appoahs infinit Th Maning of Intia Fom quation A it is la that intia is a masu of th sping onstant of spatim that is how diffiult it is to twist spatim In th Standad Modl pap of this sis it will bom la that Gaitational Mass is inidntally latd to Intial Mass Engy Consation of d Bogli Was: Th total inti ngy alulatd in tms of d Bogli momnta is qual to th latiisti Total Engy alu of a f patil Th total ngy is M in th pop fn fam and qual to: E M h x im h t im h M osh t sinh t h M M τ A4 6

7 in th moing fntial fam has Mathd d Bogli Wa Intptation of a atil Lt onsid a patil as a f d Bogli wa In its own fntial it just popagats in th dition of dimnsional tim τ On a moing fn fam th d Bogli wa is domposd in two: On with walngth x im A sond with walngth osh popagating along x Thi nonlina intations sults in: τ sinh popagating along τ τ im τ ψ x τ os xosh osh τ sinh A5 ψ x τ osh x xosh τ sinh os osh τ sinh A6 o two was popagating in th dition of and with walngth qual to osh Thus a patil an b dsibd as a phas mathd wa popagating along its dimnsional tim dition as th Hypsphial Unis xpands as a funtion of Cosmologial Tim Nxt on uss th intfn of spatim was to di Quantum Gaity and unify it to Eltostati intation Cosmologial Cohn Th Hypsphial Expanding Unis xpands in units of d Bogli yls Th figu shows that a patil stat of motion dos not modifis its phas lationship with th Unis Th patil is always phas mathd to th st of th Unis This is th maning of physial xistn this phas mathing ondition implis that all th Unis is in phas lid th sam numb of d Bogli yls as it popagats along th dimnsional tim This also mans that th Unis is thin along th adial dition of popagation on d Bogli walngth thin 7

8 Th numb of d Bogli yls a patil passs though is indpndnt upon th angl lati loity This mans that any patil of a gin typ is always in phas with anoth of th sam typ isptily of its tajtoy though th Unis It also mans that say potons atd in th Dawn of th Unis pt th sam phas lationship with all th oth potons of th Unis thoughout th ags Th sam is tu fo any patil atd at any tim D Bogli phas and intnsity a poptis shad by patil lasss Figu displays two intial systms with th sam oigin Systm with distint oigins would ha an additional phas-shift du to th tadd potntial intation This is th ason why all th was in a multi-patil body an ha thi amplituds addd togth as opposd to haing thi amplituds aagd out to zo du to a andom phas lationship This ohn is ssntial in ating a Quantum Gaity Thoy and it is ssntial to th HypGomtial Thoy In fat Cosmologial Cohn is a hypothsis and a oollay of th HypGomtial Thoy Quantum Gaity and Eltostati Intation Lt s onsid a body and a patil intating though thi fou-dimnsional was Th body will always ha a Kilogam of mass o hag and th patil will always b a on amu atomi mass unit patil ~nuton Fo th Gaitational intation this patil will ha zo spin whil it will ha spin half fo th ltostati intation Although th fou-dimnsional wa intation is taing pla on th hypsufa of a fou-dimnsional xpanding hypsph on will ma us of oss-stions to alulat intfn pattns Intfn is onsidd on ah d Bogli xpansion of th Hypsphial Unis Noti that spatim was and thi sous will b dsibd in dtail in a pap of this sis On an bifly dsib th sou of waing as a fou-dimnsional patil fou-dimnsional llipsoid of olution o patil X fo simpliity Th X patils a haatizd by fou axs lngths Th axs lngths olat with th Quas omposition of matt Th fouth-axis always points in th adial Tim dition Ndlss to say diffnt Quas axis lngths and diffnt otational stats aound th fou axis will b suffiint to maps all nown patils photons msons nutinos t olum mass tunnls in an out of th th-dimnsional spa fo spinning patils patils with non-zo spin and out and in towads th adial tim dimnsion Spin is onsidd to b a spial otation sin th otation axis is ppndiula to adial Tim and on of th spatial oodinats That gis spinning a diffnt fft; it bings th patils in and out of th Fabi of Spa thus allowing fo a alignmnt of th y to of assoiatd spatim was 8

9 9 Lt s onsid th intation though a two-dimnsional oss-stion X x τ atil on on amu nuton sits on x whil patil two th body of Kg sits on x Th fou-dimnsional spatim was a mbddd in a fifth dimnsion Cosmologial Tim A position in this spa is dfind by th following to: Φ τ using dito osins and B At tim zo th positions fo patils and a gin by: and B Aft a d Bogli yl on has ths th tos: and and B is th unptubd st of th fou-dimnsional wa of patil aft a d Bogli yl is th position of th sam st und th influn of patil Th -to is gin by: j ij g B4 Wh ij g is th mti of th fi-dimnsional spa Again osmologial distans would qui a futh finmnt whih is not quid in th alulation of na-

10 poximity fos In th diation of th Biot-Saat law g will b wittn with ij gad th osponding non-zo lati spds Noti th ½ phas dpndn on - to osponding to th fifth dimnsion fo a half-spin patil And fo a stati and nutal zo spin fowad tim taling wa Wh NKg of Matt Aogado s Numb6676E6 patils of typ h**aogado/ Kg x E-5 mts in th MKS systm Kg h/kg x E-4 mts in th MKS systm G Gaitational is th Gaitational Constant 667E- m Kg - s - Singl lti hag 6E 9 Coulomb q is th ffti alu of th singl lti hag hag diidd by a sning fato of E-9 Coulomb ε mittiity of auum 8854E- C N - m - MKS B5 Stating with th standad MKS quation fo ltostati fo btwn two on Kg bodis of ltons on amu ltons o potons x Coulombs on obtains: F F Eltostati Eltostati 4ε 4 ε xcoulomb N Kg mt 4ε Kg N Kg q * Coulombs * p * patil q * Coulombs * p * patil Kg mt mt G Eltostati 4ε N q E 5 B5

11 G G Eltostati Gaitational E E 6 667E B6 Th spatim wa fo a singl patil an b psntd by: os ψ x y z τ Φ f B7 wh mans absolut alu f θ absolut alu of th phas olum is 5 fo a patil with spin half and fo nutal matt Th maning of is that fo ah d Bogli walngth tasd path by th Hypsphial Unis a popagating spatim wa spad along by a fato of 7 fo hagd patils and 6 fo nutal-zo spin matt M fo nutal matt-matt o antimatt-antimatt intations o opposit hag intations M- fo nutal matt-antimatt intations o sam hag intations Similaly fo a Kg body loatd at position : M Nos ψ x y z τ Φ B8 f wh th fft of th g mass is impliit in th -to and xpssd by th fato N Th wa intnsity sals up with th numb of patils N On ilogam of mass has mols of amu zo-spin nutons o Aogado N To alulat th fft of Gaitational/Eltostati attation on nds to alulat th displamnt on th st of ah patil o body wa du to intation with th was gnatd by th oth body This is don fo th light patil by alulating th diati of th wafom and onsiding th xtmly fast aying gaitational wa fom th maosopi body always qual to on sin th maxima of ths osillations a too los to ah oth and an b onsidd a ontinuum Th total wafom is gin by: os M * N ψ x y z τ Φ total f f B9

12 Th tm f ontains th tatmnt fo tadd potntials but fo simpliity w will nglt diffns in dimnsional tim btwn and Equation B9 is th on and only Unifiation Equation that is it is th fou-dimnsional wa quation that yilds all th fos whn on onsid fou-dimnsional wa onstuti intation It shows that anti-matt will ha gaitational pulsion o anti-gaity with spt to nomal matt Th diati fo ψ is gin by: ψ x y z τ Φ ~ B x τ f du to << Similaly ψ x y z τ φ ~ N B x τ Soling fo x: x N N B Th a two gimn of spatim tal and thy a dpitd in Figu 4 blow: x Figu 4 This figu shows th gomty of a sufa bound patil This is a X sus τ oss-stion of th Hypsphial Expanding Unis Noti that th two ils psnt a on d Bogli xpansion of th Hypsphial Unis Nomally a wa atd in th inn d Bogli sufa will ha a st xatly in th adial dition in th out sufa If shiftd by a alu x it would ha its st dfind by th angl whih is xtmly small This is alid fo hypsupfiial was that

13 is was that popagat along th d Bogli sufa without laing it zo spin patils Fo th as of spin half patils th nw st is gin by th angl that is th - to of th wa is f to dit itslf without haing to bnd th d Bogli hypsufa Tan is gin by tan x/ o by tan x/ * / dpnding upon if th intation is suh that th patil -to shifts as in o it just aquis th adial pointing dition as in A futh finmnt intodud by Equation B will intodu a ll of loal dfomation of th d Bogli hypsufa o Fabi of Spa If th patil is apabl of taling longitudinally its dimnsional tim axis o -to will b displad by th angl Chagd patils and nutons a patils with nonzo spin This modl poposs that spin is a otation along a dition ppndiula to dimnsional tim and on of th spa dimnsions thus x y and z polaizations a possibl Th psn of spin also allows fo th patil to dtah fom th Fabi of Spa and to align its loal Fabi of Spa Loal Fabi of Spa alignmnt mans that th dition of spatim wa popagation hangs Nutal matt spin zo intating with non-hagd bodis will tal as hypsupfiial was that is thi dimnsional tim will align itslf aoding to angl fo a osponding displamnt x aft on d Bogli walngth hypsphial xpansion A hang in angl osponds to a muh small angl hang btwn th adial ditions by a fato / 985E-4 with as th dimnsional ag of th Unis Th xpimntal spatim tosion du to gaitational intation lis sompla in btwn and -4 thus showasing a ll of loal dfomation of th Fabi of Spa Fom figu 4 on alulat tan as: x N tan δ δ B -4 Wh 985 δ and M It will b shown that th upp limit is alid fo hagd patil intation whil th low limit modifid by a slight dfomation of th fabi of spa will b assoiatd with gaitational intation A dual way of thining about spatim tosion is to onsid that matt/olum tunnls btwn gaitational hypsupfiial and non-gaitational longitudinal o olumti stats Th amount of tim in th non-gaitational stat sults in diffnt gaitational masss fo th patils Fo th as of light on has th following quation: tan B4 That is light popagats with dimnsional tim τ at 45 with spt to th adial tim

14 To alulat th diati of tan with spt to τ on an us th following lationship: tan tan N τ δ Sin th wa intfn at th pious st happns at a null angl Alation is gin by: B5 N a tan δ B6 τ To alulat th fo btwn two Kg masss mols of amu patils spaatd by on mt distan on nds to multiply quation B5 by Kg N patils/kg* Kg: N * Kg Kg Kg F G Calulatd δ δ B7 mt mt Fo δ and 5 on obtains th G Eltostati B5 N Kg G Calulatd δ E 5 G Eltostati B8 wh on mad us of N and onsidd th absolut alu It is impotant to noti that th diation of th G Calulatd n mad us of any ltostati popty of auum hag t It only mattd th mass spatim olumti dfomation and spin Of ous on usd th lan onstant and th spd of light and Aogado s numb By stting δ on os th ltostati alu of G! To analyz Gaitational intation lt s onsid that Hubbl offiint masumnts stimat th Unis as bing aound 5 Billion Yas old o 48E6 mts adius To obtain th lastiity offiint of spatim lt s wit δ / ξ on quation B7 and quat th G Calulatd to G Gaitational fo two bodis of Kg spaatd by mt F G Gaitaion al 667 Kg E - mt N Kg Wh sin w a onsiding a spin-zo intation Kg ξ mt B9 4

15 Soling fo ξ: ξ G 4 N Kg 8567 Gaitaion al B If w onsid that th fo is gin by mass tims alation: F tan θ mmass mmass a x mmass ξ x B mmass F ξ x mmass Ω G Unis Th natual fquny of spatim osillations is: x B Ω G Unis ξ 4 KHz B Noti that this is not dpndnt upon any masss That should b th bst fquny to loo fo o to at gaitational was Of ous Hubbl d shift onsidations should b usd to dtmin th pis fquny fom a spifi gion of th Unis Chagd patils a apabl of taling along dimnsional tim ditions of du to th fat that a hagd patil is atually a spinning llipsoid of olution Th spin is a otation ppndiula to dimnsional tim and a spa dimnsion At ah d Bogli yl th phas of th wa in th dimnsional dition hangs sign This hang in sign olats with th attation and pulsion sn in hagd patils Spin zo matt dos not ha that phas hang and thus only psnts gaitational attation o antigaitational pulsion Whil spinning dimnsional tim and th physial dimnsion axis hagd patils a hagd-massi non-massi and sly-hagd-massi at ah d Bogli yl sly hagd patils follow th sam tajtoy with a 8 dgs phas shift A full dsiption of th modl fo nula patils will b psntd in th Hypgomtial Standad Modl pap of this sis At last on an alulat th alu of th auum pmittiity fom quations B5 and B8 as: ε 7 Nq E - B4 Not supisingly th is a pft math btwn thotial and xpimntal E- C N - m - alus Th sning fato usd to alulat th ffti hag p patil is du to th fft of non-zo spin on matt 5

16 6 It is impotant to noti that this diation only uss on paamt sning fato and that th fomula is did in tms of lton hag spd of light Aogado s Numb and lan s onstant to lat it to non-hypgomti hysis Th omplt quation fo Gaitation is gin by: m m Kg N F al Gaitaion ξ B5 Quantum aspts an b od by not using fast osillation appoximations It is also impotant to noti that quations B8 and B9 an b usd to alulat th intation btwn any patils matt o anti-matt o to pfom quantum mhanial alulations in a mann simila to molula dynami simulations Th Quantum haat is impliit in th d Bogli walngth stpwis quantization It is also latiisti in ssn as it will bom la whn on analyzs Magntism nxt Magnti Intation Th Diation of th Biot-Saat Law Lt s onsid two wis with unts i and i spaatd by a distan Lt s onsid i on th lmnt of lngth dl as th sult of a moing hag of mass of Kg of on amu ltons o potons This is don to obtain th ot saling fato Without loss of gnality lt s onsid that th distan btwn th two lmnts of unt is gin by: I and C Th loitis a: and C

17 7 Du to th spin half on has aft a two d Bogli yls: and and C Sin on xpts that th motion of patil will podu a dag on th lton along its dition of motion Th figu blow showas th gomty assoiatd with ths two unts x x' z y y' z' Figu 5 Diation of Biot-Saat Law using spatim was

18 8 Th -tos fo th two ltons on th stati fn fam a gin by: ~ ~ C4 Noti also that th fft of th ½ spin is to slow down th at of phas aiation along th dimnsional tim τ in half In th as of unts th loitis a not latiisti and on an ma th following appoximations to th fi-dimnsional otation matix o mti: osh and sinh ι i / wh i is th loity along th axis i Similaly: ~ C5 Th wa intnsitis at a: os f z y x Φ τ ψ C6 os f M z y x Φ τ ψ C7 Wh N Aogado d Bogli walngth of a on amu atomi mass unit patil d Bogli walngth of a Kg patil /N and d Bogli walngth of an lton diidd by th mass of on lton in amu

19 9 Now on an alulat: ~ C8 ~ C9 ~ C f du to << Similaly: ~ ~ C f ~ C

20 Hn: sin ~ f z y x Φ τ ψ C z y x ~ Φ τ ψ C4 And ~ ~ f f Φ τ ψ C5 Thus ~ ~ C6 ~ C7 ~ C8 ~ C9 Wh non-loity dpndnt and singl loity dpndnt ontibutions wh ngltd du to th ountbalaning wa ontibutions fom stati positily hagd nts

21 Th fo is gin by: tan F τ [ ] [ ] dl dl C Wh on too into onsidation that a patil with spin half has a yl of instad of Th Biot-Saat Law an b wittn as: µ I I dl dl x df C 4 x Compaing th two quations on obtains: µ C 4 q Thus µ q C Fom quation B4 ε Thus Nq Nq µ ε C4 q Thus on os th lationship btwn µ and ε Gand Unifiation Supsymmty As th dimnsional ag of th Unis boms small th lati stngth of gaitation intation inass Consly on xpts that as th Unis xpands Gaity will bom wa and wa This and th fou-dimnsional light spd xpanding hypsphial Unis topology xplain th alation of xpansion without th nd of anti-gaitational da matt Fo Gaitation th sping offiint is gin by: m nuton 4 θ F m a m tan 8566 x κ x D8 nuton x nuton g

22 Similaly fo Eltostati intation on has: F Thus m nuton m nuton θ a m tan x κ x D8 x nuton κ 4 g 8566 D9 κ Thus whn was small than tims 8E-9s Gaitational and Eltomagnti intations had qual stngth Thy w tainly indistinguishabl whn th adius of th Unis was on d Bogli walngth long Conlusions: Th HypGomtial Thoy a modl that onsids th intfn of foudimnsional wa on th hypsufa of a Hypsphial Expanding Unis was intodud Th omplxity of th psnt dsiption of th Unis in ou Sins is assignd to th fat that on is daling with fou-dimnsional pojtions of a fi dimnsional poss Ou inability to aliz that mad th dsiption unnssaily omplx Ths a th ingdints fo a nw and simpl fomulation of hysis: Quantum Gaity Eltostatis and Eltomagntism w did using th sam quations sam famwo Th thoy is inhntly quantum mhanial Two fundamntal paamts of th Unis w alulatd fom fist pinipls pmittiity and magnti susptibility of auum Biot-Saat law was did fom fist pinipls Gand Unifiation Supsymmty onditions fo th tim whn all fos w qual w did fom simpl Gomty onsidations Th Fabi of Spa an b onsidd to b th gions of th hypsph wh th nomal to its loal spa is pointing in th adial dition Any gion wh that happns has a distint and yt undistinguishabl haat It is distint baus it is pointing in th dition of Unis xpansion but it is indistinguishabl within th fou-dimnsional latiisti pspti All fn fams a quialnt within a fou-dimnsional pspti Thy bom distint but not distinguishabl und a fi-dimnsional analysis Nutons gaitational intation with a hagd patil is as stong as an attati hagd-hagd patil intation This xplains th nd fo nuton glu to at high Z nuli This is du to th Spin/ of a nuton This

23 mans that a nuton is also apabl of laing th fabi of spa btwn d Bogli stps A nuton will attat qually a poton o an lton as if it had th opposit hag Th natual fquny of spatim osillations is did to b 4 KHz Mah s no-loal gaitational intation xplanation fo intia is plad by a hypgomtial loal Fabi of Spa distotion agumnt Mah s and Nwton s absolut tims a assignabl to th Cosmologial Tim That tim is absolut but an only b masud by obsing th xpansion of th fou-dimnsional hypsphial Unis Chomodynamis Conlusions: This thoy jts th xistn of oth fos In fat th a no fos masss hag o anything oth than simpl gomti tms Masss hags w usd in this wo to onnt th modl to th psnt dsiption and poply sal th alulatd dynamis It is impotant to noti that although matt is bing modld as a sou of foudimnsional spatim was matt is dual to th was thmsls Wa intation mos th foi fo nw was stating on ah d Bogli yl in th sam way that intation btwn was in a pond ats nw nod gnating sous Matt is modld in HU as a fou-dimnsional llipsoid of olution with olum popotional to th mass and th axs lngth quantum numbs qual to th qua omposition of matt Sin quas a just quantum numbs of a olum thy annot b spaatd in th sam way on annot spaat th X dimnsion fom a th-dimnsional objt Oth dimnsions of th Standad Modl a modld as otations Spin is modld as a otation ppndiula to dimnsional tim and on spatial oodinat x y o z Th/two additional dimnsions a aptud as otational dgs of fdom fo otation along th th/two spatial axs Ellipsoids an ha two o th distint axs Th ons with only two axs will paalll Chomodynamis with only two nw dimnsions Matt and anti-matt should psnt anti-gaitational intation Summaizing: Up/Down assignd to th llipsoid axis lngths Stang/Cham assignd to otations and otational lls along th smallst momnt of intia axis Bottom/Top assignd to otations and otational lls along th lagst momnt of intia axis Th dtails of th modl will b psntd in Standad Modl pap of this sis

24 Cosmologial Conlusions: Th Hypsphial Expanding Unis has pofound Cosmologial impliations whih will b disussd in anoth pap of this sis Som of ths impliations will b mntiond h: Th xpanding hypsph laly shows in gomtial tms that any position Cosmologial angl in th Hypsufa -D Unis has a Hubbl ding loity Th Hubbll th Hubbl osmologial xpansion loity at a osmologial angl θ s Figu is gin by o Hubbll θ o This mans that th th-dimnsional spa is xpanding at th Hubbl osmologial xpansion loity spd of light p adian as th hypsph mos outwads along th adial tim dition o Th osponding liitd motions to all intations in th Unis a just sid-difts fom a light-spd tal along th adial Tim dition Anti-gaitational anti-matt Galaxis should xist in idntial abundan as matt Galaxis Anti-gaitational intation minimizs th hans fo atastophi ollisions Ealy Unis gaitation had muh high stngth thus th fomation of Galaxis should had bn xpditd whn ompad with modls that do not aount fo that Fundamntal Conlusion: A last onlusion woth mntioning is a modifiation of Nwton s Fist Law: In th absn of intations a body loally dfomd spatim gion will dift within th Hypsufa -D Unis until τ and a paalll again o onsly until it ahs a point wh its dift loity quals th Hubbl loity of that gion of spa Noti that th appant motion will still xist sin th spatim is xpanding and any pla in th Unis has a Hubbl xpansion loity Although moing latily to its oiginal position th body mains stati with spt to th Fabi of Spa τ paalll to At that point th loal dfomation ass to xist and th body difts with th xpansion at th Hubbl loity In oth wods motion is a way fo spatim to lax; in th sam way a Tsunami is th mans fo th Sa to gain a ommon ll 4

25 Final mas: Th modl of gaitational mass psntd h is just a bif dsiption on how to tal that poblm within th HU famwo It indiats that th quialn btwn Intial Mass and Gaitational Mass is aidntal Equialn inipl should b aluatd opning th doos to ontolling gaity and nula hmisty to a ll n bfo imagind Th disussion on gaitational and nula hmisty ontol will b psntd in anoth pap of this sis 5

26 fns: H A Lontz A Einstin H Minowsi nd Edition O inipio da latiidad Fundaao Caloust Gulbnian Shwazshild Btam "WMA Spaaft Maps th Enti Cosmi Miowa Sy With Unpdntd ision""wma Spaaft Maps th Enti Cosmi Miowa Sy With Unpdntd ision" hysis Today ol 56 No 4 Apil : auli W 958 Thoy of latiity Tanslatd by Fild London: gamon ss Landau L D and Lifshitz E M 975 Th Classial Thoy of Filds Oxfod: gamon ss Classial Eltodynamis JD Jason 975-John Wily & Sons Mao A ia an b ahd at ny9@yahooom 6