A Cosmological Model with Variable Constants (Functions of the Gravitational Potential)

Transcription

1 A Cosologial Model with Variable Constants (Funtions of the Gravitational Potential) Guoliang Liu Independent Researher London, Ontario, Canada. Eail: Version 1 on Deeber 4, 1. Version 4 on April 8, Abstrat: Based on several assuptions to dedue a osologial odel with three fundaental onstants along with the diensionless eletroweak oupling onstant turned into funtions of the gravitational potential. Initial researh of this odel has indiated solutions to several longstanding osologial puzzles. Key words: Gravitational Waves, Blak Hole, Quasar, Galaxy, Neutron Star, Cosi Rays 1. Introdution The quantu field theory of the standard odel for partile physis is based on a flat spae-tie referene frae without onsidering gravitational fields, so it annot explain the phenoena involved gravitational fields. The eletroweak oupling onstant is a variable diensionless onstant, whih iplies the priniple of general ovariane is breaking down in irosopi sale. A physial law expressed in a general ovariant fashion takes the sae atheatial for in all oordinate systes, so any diensionless onstant should take the sae value in all oordinate systes as well, beause the nuerial values of diensionless physial onstants are independent of the units used. So it is ipossible to fit the quantu theory into the fraework of general relativity based on the priniple of general ovariane [1]. Hene we try to odify the quantu theory in order to desribe the phenoena inside a gravitational field in irosopi sale. So we assue that the speed of light in vauu and Plank onstant are funtions of the gravitational potential, whih are defined in a universal flat spae-tie referene frae sitting far away fro any gravitational fields. People had ade siilar proposals before [1, ], but they ould not reahed self onsistent onlusions, beause they had not identified all fundaental onstants ontrolled by the gravitational potential. And our assuption on the ative and passive gravitational ass in setion is quite unique and ritial in order to derive equation (.1). In setion and, we will design a thought experient whih is a photon traveling in a still gravitational field, and write down three equations to desribe it based on several assuptions, and derive funtions for those variable onstants by solving these equations. We will investigate the physial signifiane of the funtions in setion 4 and eventually dedue a osologial odel in setion 5 to solve several long-pending osologial probles, suh as the ehanis

2 of the gravitational waves, the essene of the osi irowave bakground, and the origins of the osi rays. We will derive a saller Hubble onstant fro the gravitational oupling onstant in setion 6.. Assuptions The speed of light in vauu is a funtion of the gravitational potential. A vauu infinitely far away fro any ative gravitational rest ass is a flat spae-tie perfet vauu; the speed of light in this perfet vauu has a axiu speed. We assue that the inertial ass of partiles is equivalent to the passive gravitational ass whih is subjeted to the gravitational fore, and only the rest ass of ferions is equivalent to the ative gravitational ass whih an produe the gravitational potential, so the funtions of the gravitational potential should be valid to the sale of ferions. Sine a photon does not have a gravitational field assoiated with the ative gravitational rest ass, a photon propagating in a gravitational field will not produe any gravitational waves; the hange of the gravitational potential energy of a photon is absolutely equal to the hange of the kineti energy of the photon. These assuptions will yield equation (.1) in setion. Based on the priniple of general ovariane, the fine struture onstant as a diensionless oupling onstant for the arosopi eletroagneti fore should be invariant in the gravitational field. And beause of the onservation of eletri harge, we have to assue Plank onstant and the pereability of vauu being funtions of the gravitational potential [11], while keep the eleentary harge and the perittivity of vauu as true onstants. These assuptions will yield equation (.) in setion. Sine the frequeny of light will not hange during its propagation through different edius, so we assue the frequeny of a photon will not hange when it travels in a gravitational field. This assuption will yield equation (.) in setion. We have to assue all of our easureents are referring to a lok sitting in the universal flat spae-tie referene frae, whih is sitting infinitely far away fro any gravitational fields, but still should be full of Higgs field. Atually it is the only valid inertial referene frae in reality; if we talk about tie dilation without referring to the preferred referene frae, then it an only lead to all kinds of paradoxes. By the way, general relativity urved spae-tie is inopatible with hoogeneity of spae; isotropy of spae; unifority of tie, and will violate the onservation laws assoiated with those syetries [9].. Derive Variable Constants as Funtions of the Gravitational Potential The speed of light in vauu is a funtion of the gravitational potential showed as (, where ( ) ; is the speed of light in perfet vauu where the gravitational potential equals to zero. The Plank onstant is a funtion of the gravitational potential showed as h (, where h( ) h. The ass of a photon is a funtion of the gravitational potential showed as (,

3 where ( ). Derive three equations (.1), (.) and (.) aording to the assuptions disussed in setion. u ( ( ( u ) du (.1) This equation also an be written as: ( ( ( du (.1.1) u The left hand part of this equation represents the hange of the photon s kineti energy; the right hand part represents the hange of the photon s gravitational potential energy. If we deal with a ferion with an ative gravitational rest ass assoiated with its intrinsi agneti field, then we have to add ters to represent the gravitational and eletroagneti radiation energy on the left hand part of equation (.1.1), and a ter to represent the hange of the eletroagneti potential energy on the right hand part. In this ase the equation an be written as: Gravitational Radiation Eletroagneti Radiation u Eletroagneti Potential [ ( ( ] E E ( du E (.1.) Gravitational We notie E when u, this iplies that ferions will not have gravitational Radiation radiation energy in perfet vauu, and we will prove the essene of the gravitational radiation energy is theral energy in setion 4.4. So in this ase equation (.1.) has hanged into: Eletroagneti Eletroagneti E Radiation E (.1.) Potential is the kineti energy of ferions in speial relativity. h( ( h (.) This is based on the fine struture onstant is a true onstant invariant in a gravitational field. ( ( (.) h( h This is based on the frequeny of a photon defined by a universal lok sitting in the perfet vauu is invariant during its propagation in a gravitational field. Cobine (.) and (.) to get ( / ( (.4) Put (.4) into (.1) to get

4 1 u du 1 ( (.5) ( Differentiate both sides of equation (.5) to get d( 1 ( du ( (.6) Derive fro (.6) ( d( du (.7) Integrate both sides of equation (.7) to get ( / u K (.8) where K is a onstant to be defined. Sine ( ) (.9) Cobine (.9) and (.8) to get K / (.1) Substitute (.1) into (.8) to derive a funtion for variable speed of light in vauu: 1/ ( (1 u / ) (.11) Substitute (.11) into (.) to derive a funtion for variable Plank onstant: 1/ ( h (1 u / ) h (.1) Sine 1 and ( 1/ ( ) / u where the pereability of perfet vauu and is the perittivity of vauu. Cobine this with (.11) to derive a funtion for variable pereability of vauu: 1 ( ( 1u / (.1) ) The rest energy of a partile should be invariant in a gravitational field due to the onservation of energy. E ( ( (.14) where is the rest ass of a partile in perfet vauu, put (.11) into (.14) to derive a funtion for variable rest ass of a partile:

5 1 ) ( (1 u / (.15) Also based on the onservation of energy, the energy easuring unit suh as Plank energy should be invariant in a gravitational field. E P 5 1/ 5 [ ( ( / G( ] ( / G ) 1/ (.16) where G is gravitational onstant in perfet vauu, h/ is redued Plank onstant in perfet vauu. Substitute (.11) and (.1) into (.16) to derive a funtion for variable gravitational onstant: G (1 u / ) G (.17) ( Funtion (.11), (.1), (.1), (.15), and (.17) are five basi funtions of the gravitational potential, and we will abbreviate these funtions to desribe variable onstants as FGP fro here after. 4. Investigate the Physial Signifiane of FGP 4.1. FGP as a Unified Mirosopi Explanation to Tie Dilations Plank units are defined in ters of five fundaental physial onstants; they are the speed of light in vauu, redued Plank onstant, gravitational onstant, Coulob onstant, and Boltzann onstant. Even though three out of five fundaental onstants have turned into funtions of the gravitational potential, Plank length; Plank harge and Plank teperature; three out of five base Plank units are invariant in a gravitational field, only Plank tie and Plank ass turn into funtions of the gravitational potential: t 1/ P ( ) (1 u / 1 P ( ) (1 u / t P P (4.18) where t P is Plank tie in perfet vauu (4.19) where P is Plank ass in perfet vauu. Funtion (4.18) and (.11) indiate that tie slowdown in the gravitational field exatly athes the slowdown of light in vauu, FGP an dedue that all kinds of loks should slow down to the sae pae at the sae bakground gravitational potential; no atter they are atoi loks or just siple pendulus, or even the ean lifetie of a deay partile. Hene if we loally easure the speed of light in vauu using loally defined Plank units or SI units in a loal referene frae, whih has a lose to onstant bakground gravitational potential, then we atually annot detet any hange. Funtion (.15) and (4.19) indiate that the gravitational oupling onstant is a diensionless true onstant siilar to the fine struture onstant, so the priniple of general ovariane is onfired to be valid in arosopi sale. An inertial referene frae travels with a onstant speed V in a perfet vauu, the tie easuring unit will be affeted by the speed aording to speial relativity:

6 1/ t ( V) (1 V / ) t (4.) where t is any tie easuring unit in perfet vauu. Copare (4.) to (4.18), we an dedue a relationship between a onstant speed V and a onstant gravitational potential U as following: V U (4.1), this forula iplies these two referene fraes are equivalent. Therefore, FGP an provide a unified irosopi explanation to speial relativity tie dilation and gravitational tie dilation or gravitational redshift. So let s reonsider the thought experient in a referene frae with a onstant bakground gravitational potential U, in this senario the equation (.1) will be as below: u ( u U) ( u U) ( u U) du ( U) ( U ) (4.) Based on (.4) and (.11), equation (4.) an be rewritten as below: u ) 1/ ( u U) ( u U) du (1 U / ( u U) (4.) Use the total gravitational potential u u U (4.4) to do a substitution in (4.) ( u ) 1/ ( ( du (1 U / U (4.5) While the other two equations (.) and (.) an be as below: h( ( h (4.6) ( ( (4.7) h( h Cobine (4.6) and (4.7) to get ( / ( (4.8) Put (4.8) into (4.5) to get 1 u du 1 u U 1/ ( ) ( (1 U / ) (4.9) Differentiate on both sides of equation (4.9) to get d( ( du 1 ( (4.) Derive fro (4.) ( d( du (4.1)

7 Integrate on both sides of equation (4.1) to get ( / u K (4.) where K is a onstant to be defined. Sine ( ) (4.) Cobine (4.) and (4.) to get K / (4.4) Substitute (4.4) into (4.) to derive a funtion for the variable speed of light in vauu: 1/ ( (1 u / ) (4.5) Substitute (4.5) into (4.6) to derive a funtion for the variable Plank onstant: 1/ ( h (1 u / ) h (4.6) Coparing (4.5) to (.11) and (4.6) to (.1), we onlude that all funtions will take sae fors for the total gravitational potential u as for the loal gravitational potential u, so for onveniene fro now on when we talk about the gravitational potential u, it will be the total gravitational potential by default. Let s onsider another senario whih is a gravitational field traveling with a onstant speed V in perfet vauu. Based on forula (4.1), a onstant speed in perfet vauu is equivalent to a onstant bakground gravitational potential, so the total bakground gravitational potential onsidering both senario will be: U U V / (4.7) 4.. FGP Fator as an Explanation to g-fator Deviation The Bohr agneton is defined in SI units by e / where e is the eleentary harge, is the redued Plank onstant, and (.15) ( u ) B ( 1u / ) 1/ e B e is the rest ass of an eletron. Aording to funtion (.1), the Bohr agneton as a easuring unit of the agneti B oentu turns saller in a gravitational field. So the g-fator [] experiental value should equal to the stander odel theoretial value whih has not aounted the effet of the 1/ ( gravitational field ultiplied by a FGP fator 1 u / ). After investigate the results fro experients easuring the g-fator of a uon, I onlude the FGP fator has a value of approxiately 1., whih will yield the total gravitational potential on the ground of the earth: 8 U E.7 1 ( / s) (4.8)

8 Put the average ground gravitational potential assoiated with the rest ass of the earth 7 U E 6.41 ( / s) into forula (4.7) to get a onstant speed: V E 76 / s whih will be interpreted as the speed of a flux assoiated with the osi gravitational field in paragraph 5. If the gravitational potential desribes soe kind of flux in the vauu, then V in forula (4.1) is the speed of the flux. A ferion with half-integer spin has an intrinsi agneti field with agneti flux, and has a rest ass with an intrinsi gravitational field with soe kind of flux as well. So I dedue that the agneti flux not only desribe the intrinsi agneti field in one aspet but also desribe the gravitational field in another aspet. The agneti flux is neutrino flux with a speed defined by the gravitational potential. Ferions and anti-ferions have rest ass equivalent to ative gravitational ass, while photons and gauge bosons, neutrinos and Higgs bosons only have inertial ass equivalent to passive gravitational ass. Even though soe neutrinos or bosons ay have rest ass, but only ferions an have ative gravitational rest ass to produe gravitational potential. The gravitational fore between ferions and anti-ferions is repulsive fore [1], so their rest ass anels eah other after they annihilate into a pair of photons without rest ass. Anti-ferions will attrat eah other; just the sae way as ferions will attrat eah other; while photons and Higgs bosons will be attrated by both ferions and antiferions. 4.. Eletroweak Coupling Constant as a Funtion of the Gravitational Potential Experients have proved the ean lifetie of a beta deay partile travelling at high speeds will beoe longer to ath the slowdown of tie, whih is predited by the speial relativity. Forula (4.1) iplies this should also happen when the tie is slowdown in a gravitational field. Sine the ean lifetie of a uon deay relates to the Feri onstantgf in following 5 6 forula: 19 /( Q ) GF /( ) (4.9) whereq, is the rest ass of a uon. Based on funtion (.11), (.1), (.15) and (.18) to onlude the Feri onstant should be invariant in a gravitational field. The relation between GF and W the oupling onstant of the eletroweak interation is desribed by this forula: G F ) W / (4.4) [] where W /( W is the rest ass of a W boson. Aording to funtion (.11), (.1), (.15), (4.9) and (4.4), we an derive the diensionless oupling onstant of the eletroweak interation as a funtion of the gravitational potential: 1 W ( (1 u / ) W (4.41) Based on the eletroweak oupling onstant 1 7 and the eletroagneti oupling onstant 5 1/17, funtion (41) gives u (1.71 1) / when (. Aording to the eletroweak theory the eletroagneti fore and weak fore will erge into a single W W

9 eletroweak fore when the teperature is high enough, so funtion (4.41) not only delares the priniple of general ovariane breaking down in irosopi sale, but also iplies that a gravitational field should have teperature. Beause a gravitational potential is related to the speed of a neutrino flux by forula (4.1), neutrino flux an arry theral energy. So the energy hange of a photon with a speifi frequeny in a gravitational field an represent the ean kineti energy of the neutrinos whih have a teperature of T, whih an be desribed as below: [ h( h] f kbt (4.4) where k B is Boltzann onstant, f is the speifi frequeny of a photon. Sine the osi irowave bakground has a theral blak-body spetru at the teperature of T. 7548K (4.4), if we onsider this as the teperature of the 1/ ( gravitational field on the earth, then we an put the FGP fator 1 u / ) 1. alulated fro the g-fator experients, (4.6) and (4.4) into (4.4) to get the speifi frequeny: f k / B h, whih an orrespond to a photon of 78KeV at perfet vauu. Put f bak into (4) to derive the teperature of a gravitational field: T [( 1 u / ) 1/ 1] K (4.44) This yields a teperature of T U K when (. Sine the strong interation 7 oupling onstant S 1, funtion (4.41) gives u (1 1) /, when (, the W S teperature of the gravitational field will reah about K aording to funtion (4.44). Funtion (4.41) defines an upper liit for the teperature and a lower liit for the gravitational potential, beause the eletroweak oupling onstant should not be bigger than one, otherwise the eletroweak fore will be stronger than the nulear fore. Forula (4.4) plus radiative orretions set an upper liit of rest ass for any gauge boson inluding Higgs boson at15 GeV, and set a lower liit at 15 W GeV as well. If Higgs bosons an arry ajor portion of the vauu zero-point energy, the vauu atastrophe will disappear. The inertial ass density of bosons in spae will be so high that it is oparable to Plank density, so we have to redefine the vauu as a spae with zero ative gravitational rest ass density, and define the perfet vauu as pure Higgs field. Hene, ferions with ative gravitational rest ass are siilar to vortexes in the sea of Higgs bosons; the vauu is siilar to the sea without vortexes, while neutrinos are siilar to fluxes, and photons are siilar to waves. The perfet vauu is siilar to the quietest sea of Higgs bosons without vortexes, without fluxes, and even without waves. Beause any blak-body avity an only be onstruted by ondensed atter, so all blak-body radiation experients an only prove that Plank's law an be applied to arbitrary ondensed atter. Sine the sea of Higgs bosons is super fluid ondensed atter, if a ferion is a bubble in the enter of a vortex in the sea of Higgs bosons, then the size of the bubble an define as the size of the ferion, and the vortex with neutrino flux an define the gravitational field assoiated with the ferion, so it is possible for a ferion with gravitational rest ass to eit blak-body radiations. W

10 4.4. The Mehanis of Gravitational Waves is Blak-Body Radiation Funtion (4.4) indiates the teperature of a gravitational field is proportional to variable Plank onstant; the kineti energy of a partile is stored in the intrinsi agneti field assoiated with its spin defined by Plank onstant. The flutuation of the intrinsi agneti fields will produe blak-body radiations assoiated with the teperature flutuation in the gravitational field; it will redue the kineti energy of a partile traveling in the gravitational field aording to equation (.1.). Beause the rest energy of a partile is stored in its intrinsi agneti field as well, so it is possible for a partile to lose its rest energy by the gravitational blak-body radiation when the teperature is high enough. The essene of gravitational waves as blak-body radiations sees to be onsistent with the proposal of gravity as an entropi fore [4] and gravitoagnetis [7]. The blak-body radiation energy density: E d 8 kbt /15h at (4.45) where a is 16 4 the radiation density onstant equal to J / K, is a true onstant invariant in a gravitational field. Put (4.44) into (4.45) to get the gravitational blak-body radiation energy density: E d 1/ 4 [( 1 u / ) 1] J / (4.46) The gravitational blak-body radiation energy plays a very iportant role to ounterbalane the gravitational attration. If the teperature reahes the upper liit to T H K then the 4 gravitational radiation energy density reahes the axiu of J /, whih is ties higher than the nulear fission energy density of uraniu; only the annihilation an produe suh high energy density. So I onlude the partile and anti-partile annihilation ust be the energy soure to power the gravitational blak-body radiation near the blak hole event horizon. Sine the Plank s law has turned into a funtion of the gravitational potential, the wave lengths of theral radiations near the upper liit of teperature will be signifiantly shorter, so they will look like X-ray bursts or gaa ray bursts. The vauu flutuation near the event horizon an be very big due to the Plank onstant turning bigger sharply; there are a lot of virtual partile-antipartile pairs that pop up fro the vauu and then anel eah other near the event horizon. Beause the gravitational fore works oppositely on partiles and anti-partiles, they are separated before they an anel eah other. The virtual anti-partile ust either annihilate with a real partile or esape, so the blak hole has to lose ass to ensure the onservation of energy. Beause of the onservation of harge, only the virtual anti-partiles without harges an be turned into real anti-partiles, so only antineutrinos and anti-neutrons an be ejeted fro a blak hole. Even though the onservation of baryon nuber sees to be broken, but the nuber of anti-neutron being produed by a blak hole should equal to the nuber of neutron inside a blak hole being onverted into energy, so the proess looks like a phase transition fro neutron to anti-neutron. So if siultaneously a 16 1

11 phase transition fro anti-neutron to neutron an happen soewhere in the universe, then the onservation of baryon nuber an be saved, and it an be the origin of the osi rays when I establish y osologial odel. The phase transition fro neutrino to anti-neutrino or fro neutron to anti-neutron near the event horizon is siilar to the so-alled blak hole evaporation [5], but it is uh ore intense beause the gravitational repulsive fore towards the antipartiles and beause the Plank onstant and the teperature inrease sharply aording to funtion (4.6) and (4.44). Stellar objets oe near the event horizon will ause intense vauu flutuations to produe large aount of anti-neutrons, whih will then annihilate and turn everything into heat energy. Even though the blak hole will lose ass due to the onservation of energy, the oentu and angular oentu of the falling partiles are transferred to the blak hole due to the onservation of oentu and angular oentu. Funtion (4.46) iplies that the gravitational blak-body radiations are extreely intense near the event horizon, so a blak hole whih will suk everything inside is ipossible to be fored. The ritial gravitational potential u / to for a blak hole annot be reahed. FGP have liits set 7 by a lower liit gravitational potential atu L (1 1) / when u W ( ) S aording to funtion (4.41). Otherwise photons will stop oving aording to funtion (4.5), the Plank onstant will turn infinitely large aording to funtion (4.6) and the teperature will be infinitely high aording to funtion (4.44). Hene, blak holes should be alled quasi-blak holes aurately. Quasi-blak holes an be used to define the aro rest ass quanta fored by gravitation, so they provide iportant lues to establish a new osologial odel. 5. Dedue a Cosologial Model fro FGP 5.1. Revised Hubble s Law fro the Cosi Bakground Gravitational Potential FGP is based on an universal flat spae-tie perfet vauu referene frae, so I assue this should be the initial state of the universe, with an equal aount of hydrogen atos and antihydrogen atos along with photons and Higgs bosons spread evenly in the spae, with an ative gravitational rest ass density lose to zero and a teperature lose to absolute zero as well. After a long period of tie, beause the atos and anti-atos were subjeted to the two types of gravitational fores, eventually hydrogen atos separated fro anti-hydrogen atos and individually fored a huge sphere of hydrogen atos and a huge sphere of anti-hydrogen atos. These two spheres eventually sit still in a perfet vauu far away fro eah other beause the gravitational repulsive fore is offset by their oon gravitational attrative fore towards the photons and Higgs bosons. We have to use a funtion to desribe the gravitational potential inside a sphere: u( r) 4 G r / (5.47) where r is the distane fro the enter of ass, is the average density of the ative gravitational rest ass within the sphere with a radius of r. Only the rest ass inside a sphere has ontribution to the gravitational potential on the surfae of the sphere, beause the neutrino flux assoiated with the gravitational potential on the surfae is the

12 extension of the intrinsi agneti fields assoiated with the rest ass of the ferions inside the sphere. So it is iportant to define the axiu size of a gravitational field by oparing its gravitational field strength with the nearby gravitational field strength. For exaple the earth has a axiu sphere radius of about.61 8 where the gravitational strength is about.6n / kg and equals the one of the sun. The oon is loated outside the axiu sphere of the earth, so its axiu sphere radius is about.91 7 where the gravitational field strength also equals the one of the sun. While the sun has a uh bigger axiu sphere beause the losest star to it known today is four light years away. We an use the ass of the earth or the oon to alulate the gravitation potential of the earth or the oon up to the axiu sphere only, outside the sphere we have to use the ass of the sun to alulate the gravitational potential of the sun. The gravitational potential has points of disontinuity on the axiu sphere, so the teperature and the radiation energy density of the gravitational field have points of disontinuity on the axiu sphere as well aording to funtion (4.44) or (4.46). Even the speed of light in vauu has points of disontinuity on the axiu sphere as well, and this will ake the gravitational lensing effet bigger and lead to overestiation on the ass of stars. It is iportant to identify the boundary of a gravitational field for alulating or easuring the speed of light in vauu. Theoretially only the perfet vauu referene frae is an inertial referene frae, whih is suitable for quantu theory and speial relativity. But in pratie, based on forula (4.1), we an apply those theories in a loal referene frae with a very lose to onstant bakground gravitational potential, suh as the ground of the earth referene frae. If we use funtion (5.47) to desribe a osi sphere, then we an take square root on both side of this funtion to derive the revised Hubble s law: v( r) H r (5.48), sine we onsider the speed v (r) as the speed of the neutrino flux assoiated with the osi gravitational field, so aording to forula (4.1) we an obine (5.47) and (5.48) to get the density of the osi sphere: H / 8G (5.49), use the Hubble onstant H 67.8( k/ s) / Mp to 7 alulate the value of kg/. This is exatly the ritial density predited by general relativity to for a stable universe. Put the ritial gravitational potential u / and the ritial density into funtion (5.47) to get the radius of the osi sphere: 6 R C / H (5.5) and this also is the radius of the so-alled Hubble sphere; it is about billion light years. If it is a osi blak hole event horizon, then anything inluding lights is trapped inside, but FGP has a lower liit gravitational potential u L (1 7 1) /, so the osi sphere annot be a true blak hole and it should still have interation or partile exhange with the faraway anti-osi sphere. The Hubble onstant and the osi density should have been uh saller in the past, and eventually settle down to today s value after the osi sphere and the anti-osi sphere ahieved a dynai balane. So the heat death of an open universe will never happen in this senario, and there is no reason to break the dynai balane to reate the so-alled Big Bang or Big Crunh senario.

13 5.. Gravitational Redshift is Proportional to the Teperature Funtion (5.47) along with the ritial density in forula (5.49) indiated that a quasar ay have a osi bakground gravitational potential of.5 if it is away fro the enter of the osi sphere, whih is about ten billion light years. The irowave bakground or the gravitational field teperature in that loation is extreely high at K aording to funtion (4.44); it an produe the wide range ionization, whih annot be explained before. Also, beause the bakground gravitational potential is oparable to the ritial gravitational potential, a quasi-blak hole fored in this quasar takes only half aount the rest ass than one in the Milky Way galaxy. This quasar an easily output huge aount of energy, beause the gravitational blak-body radiation energy density ounted on the osi bakground 19 gravitational potential itself reahes1.5 1 J / aording to funtion (4.46), whih is already ten ties higher than the nulear fission energy density of uraniu. Lights fro this quasar should have a gravitational redshift of Z. 414, beause just onsidering the osi bakground gravitational potential already yields a loal Plank onstant ties bigger than the one in a perfet vauu aording to funtion (4.6). A osi bakground gravitational redshift yields a distane signifiantly different fro the distane given by onsidering the redshift as a Doppler shift. The redshift oes fro a osi bakground gravitational potential: Z (1 u / ) 1/ 1, only the redshift of spetrus fro interstellar plasa louds, whih is the sallest redshift fro the sae galaxy, is reliable for the estiation of distane. Aording 8 to funtion (4.44), the teperature is proportional to the redshift: T Z K, so a bigger redshift ost likely iplies higher teperature, but not neessarily relates to a larger distane. The teperature of the osi irowave bakground with the biggest redshift 11 observed so far at Z 189 is T CMB K, whih is loated near the edge of the osi sphere. CMB 5.. Foration of Galaxies Sine a spiral galaxy is oposed by billions of stars siilar to the sun, and I assue they all evolved fro a huge hydrogen gas ball, I use the solar ass 1 kg and the distant to the ost faraway dwarf planet Eris about as the radius of a hydrogen gas ball to estiate a density at g kg/ quasi-blak hole of hydrogen gas, substitute this into funtion (5.47) to get the radius to for a r g whih will give a ass of 7. 1 kg ; this is an estiated ass for a spiral galaxy. Sine the ass of the osi sphere given by the ritial density is about kg, the total nuber of spiral galaxy is about one hundred thirty billion. Beause only about 6% of the galaxies are spiral galaxies, other types of galaxies are saller, so the total nuber of galaxy ay be over two hundred billion. Therefore the average

14 ass of a spiral galaxy should be kgwhih is 4% less than the original estiation, and is about two hundred billion solar asses. This huge hydrogen gas ball will shrink by gravitational attration; the teperature and density keep rising in the ore, and nulear fusions start to for other abundant light eleents. The galaxy at this stage is a giant quasi-star whih is a huge hydrogen plasa ball shrinking without spinning. Beause the ore of a quasi-star is like a giant sun, I use the average density of the sun S 148kg/ to estiate the size of a super assive quasi-blak hole with a radius r S.81 whih will give a ass of.8 1 kg, whih is about solar asses. It an be even bigger if its average density is saller; the biggest one so far has about twenty one billion solar asses. One the super assive quasi-blak hole is fored in the enter of a giant quasi-star, everything falling inside is turned into heat, so its angular oentu grows larger as the partiles annihilate and their spin oentus transfer to the quasi-blak hole. The spinning speed of the giant quasi-star will inrease as the angular oentu ontinues to be transferred fro the super assive quasi-blak hole by its agneti field. The high speed spinning will flatten the hydrogen plasa loud into a big aretion dis; about 4% of the original estiated ass of a spiral galaxy has spun off to for the globular luster or dwarf galaxies, and the spiral struture has fored at this stage. Beause of the heat fro the super assive quasi-blak hole, the hydrogen plasa in the aretion dis starts the nulear fusions to for other abundant light eleents and shrinks loally by gravitation to for stars inside a spiral galaxy The Origins of Cosi Rays The plasas falling into a quasi-blak hole are turned into heat energy arried away by high energy anti-neutrons and anti-neutrinos. All anti-neutrinos will esape easily, while ost of the anti-neutrons lose their kineti energy by knoking partiles out of the surrounding plasa loud, then annihilate to release intense gravitational heat radiation aording to funtion (4.46). But a tiny fration of anti-neutrons not hitting anything will join with the partiles being knoked out to for the so-alled osi rays. The anti-osi sphere should be the final destination of those anti-partiles in the osi rays, while ost of the partiles in the osi rays are fro the antiosi sphere event horizon. This not only an explain the origins of the osi rays, but also explain why the energy of the anti-protons and positrons whih have been deayed fro the antineutrons in the osi rays are signifiantly higher than the energy of the protons and eletrons, and explain why they oe so evenly fro every diretion. The partile exhange with the antiosi sphere by osi rays is ritial to ahieve the dynai balane of the universe. Beause the quasi-blak holes are onverting huge aount of neutrons into energy and anti-neutrons at all ties, the partile exhange with anti-osi sphere is ritial to save the onservation of baryon nuber whih sees to have been broken by the neutron phase transitions near the event horizon of quasi-blak holes. Most of the protons and eletrons in the osi rays are fro the event horizon of the anti-osi sphere, they have been aelerated by the gravitational fields between

15 two osi spheres to the average energy of 1 GeV. Hene, the estiated distane between these two osi enters should be larger than four ties the radius of the osi sphere Neutron Stars and Its Relationship with Stars and Planets Aording to funtion (4.41) the eletroweak oupling onstant inreases as the ass of a star inreases, so the nulear fusions to for heavy atoi nuleus will keep going as long as there are enough plasas to feed into it, until it turns into a quasi-blak hole of neutron. Put the 17 average nulear density.1 kg/ into funtion (5.47) will get the radius to for a n 1 quasi-blak hole of neutron r N 646 and the ass is N kgwhih is about nine solar asses. A star with ore than nine solar asses ost likely will end up with a supernova. Usually the explosion will be triggered by a fast oving outer shell sashed by a lagging quasiblak hole inside it; the asyetri explosion ejets its reains out of the supernova enter to beoe a pulsar. In ase a supernova is triggered by the ollapse of a heavy outer shell, then its reains stays in the enter after a syetri explosion due to large aount of atter being annihilated fro every diretion, whih beoes a agnetar or a pulsar. If the outer shell is extreely heavy, then the quasi-blak hole has to lose ost of its ass in order to power a soalled hypernova explosion, and its reains will disappear after intense radioative deays as a gaa ray burst. In the enter of a super assive quasi-blak hole, the hypernova explosion as a power soure to withstand the gravitation attration will happen fro tie to tie. Older super assive quasi-blak holes should have less ass and higher density than younger ones. The radioative deays eventually will bring down the ass of a agnetar, it will turn into a pulsar, and then it will split into several sall neutron stars, beause the heavy nuleus is not stable without a strong gravitational field. The deayed sall neutron star attrats and spins the surrounding hydrogen gas and supernova debris or saller neutron stars into an aretion dis, the nulear fusion starts again in the enter with highest teperature and density. Finally it beoes a newborn star with or without planets Estiations Based on Zero Cosi Bakground Gravitational Potential The agneti field of a star or a planet oes fro a deayed sall neutron star buried in its enter, so let s study the agneti field of a neutron star. Sine M H (5.51) where M is the agneti dipole oent per unit volue, H is the agneti field strength, v is the volue agneti suseptibility of a neutron star, and the neutron star agneti pereability (1 ), oparing this to funtion (.1) and we notie that the vauu in a v 1 gravitational field has a volue agneti suseptibility ( (1 u / ) (5.5). It is very big near the event horizon, so I assue is very big as well, and this also iplies the v agneti dipole oent of ost neutrons in a neutron star will take the sae diretion of the neutrino flux assoiated with the gravitational field. Hundred perent of the neutrons will take the sae spin diretion, sine the suseptibility beoes infinitely large when a neutron star v

16 beoes a quasi-blak hole, so I siply assue the square of the ass ratio between a neutron star and a quasi-blak hole to equal the ratio of the neutrons taking the sae spin diretion, hene M ( n / n ) Mn[ N ( / N ] (5.5) where neutron star, n 17.1 kg/ is the density of a kgis the ass of a neutron, M n J / T is the agneti n 7 dipole oent of a neutron, N ( is the rest ass of a neutron star with a surfae gravitational potential of u, N is the rest ass of a quasi-blak hole of neutron. Aording to funtion (5.47) we get[ ( / ] ( u / ) (5.54), put this into (5.5) then obine with (5.51) and N N (5.5) to get the agneti field strength on the surfae of a neutron star as below: 18 H 1.61 ( u / ) / v A/ (5.55) Sine B (1 ) v H, where B is the agneti flux density on the surfae of a neutron star, 7 and 4 1 T / A is the perfet vauu pereability, and v 1 v we an derive 1 B ( u / ) T (5.56) The agneti flux density reahes a axiu about T on the surfae of a quasiblak hole of neutron, and it has a iniu angular oentu of J s fro the spin of aligned neutrons. Consider a neutron star as a solid sphere with even density to get the oent of inertia: I N 5 ( r ( /5 8 r ( / (5.57) where ( is the radius of a neutron star with N N n N a surfae gravitational potential ofu. Fro funtion (4.47) we get r N ( n ( u / 4G ) 1/ (5.58), and based on funtion (.11) to get the theoretially axiu angular speed of a neutron star as below: r N ax 1/ ( / r ( [ G (1 u / )/( ] N n 1.41 (1 u / ) 1/ /( 1/ rad / s -- (5.59) Then derive the theoretially axiu angular oentu of a neutron star as below: L 1/ 1 1/ I ( (1 u / ) /G.81 ( (1 u / J s (5.6) ax N ax n ) 7 Put liit gravitational potential (1 1) / into funtion (5.59) and (5.6) to get the u L axiu angular oentu of a quasi-blak hole of neutron is J s with a spin frequeny of.5698hz. A neutron star ost likely will retain this angular oentu after a supernova explosion, so I an estiate the atual upper liit of its spin frequeny. Let s estiate how long a T agnetar will take to deay into a T pulsar by the gravitational blak-body radiation. Aording to funtion (5.56) and (4.44) the agnetar has

17 a teperature 7.61 K and the pulsar the pulsar has a teperaturet p.1851 K. T 8 Aording to funtions (5.47), (5.56), (5.57) and (5.6) this agnetar ay spin up to.88hz, has a radius of r 189 and a ass of kg; this pulsar ay spin up to18 Hz, 9 has a radius of r p 571 and a ass of p kg. Aording to Stefan-Boltzann 4 law the blak-body radiation power P AT, where the surfae area of a blak-body is A, and T is its teperature, and based on funtion (.11) and (.1) the Stefan-Boltzann onstant is a funtion of the gravitational potential: 1/ 5 4 1/ 8 4 ( (1 u / ) kb /15h (1 u / ) J / sk (5.61) So the net radiation power: P net A T 4 A T p p 4 p [ r (1 u / ) 1/ T 4 r (1 u p p / ) 1/ T 4 p ] J / s ---- (5.6) where u is the gravitational potential on the surfae of the agnetar andu p is the one of the pulsar. Fro funtion (5.56) we get / u.1 and u p /.1 ; put all data into (5.6) 6 11 to get P net.751 J / s and deterine t ( ) / p.71 s (5.6) deay Thus a agnetar with three solar asses takes about seven thousand five hundred years to deay into a pulsar with one tenth of a solar ass. Now let us replae the agnetar with a quasi-blak hole of neutron; this will be a senario for an extreely intense hypernova explosion. Sine we already know r N 646 and 1 N kg, the highest teperature of a quasi-blak hole at the liit gravitational potential is T H K at (1 1) /, so we an substitute the data of the u L agnetar with the data of a quasi-blak hole of nuleus in funtion (5.6) to get: p net P net [ r (1 u N L / ) 1/ T 4 H r (1 u p p / ) 1/ The tie for the extreely intense hypernova explosion will be: T 4 p ] J / s J / s (5.64) t ( ) / p. s (5.65), the powerful hypernova an onsue a typial hyper N p net 148 super assive quasi-blak hole with one hundred illion solar asses in about eleven trillion years if it repeats every illion years. Sine the super assive quasi-blak hole in the enter of the Milky Way galaxy has only four illion solar asses left now, this suggests that it is about eleven trillion years old. Usually a supernova explosion happens when the teperature of a neutron star reahes the teperature T U K when W ( and u (1.71 1) / aording to funtion (4.41) and (4.44). In this senario 45 P net 6.61 J / s andtsuper 4. s, it takes about four inutes to power a supernova explosion. All estiations above are based on an equal to

18 zero osi bakground gravitational potential, whih are suitable for those galaxies in the Loal Group. If the supernovae are far away fro the enter of the osi sphere, then the estiations will be different, hene using supernovae as standard andles will lead to wrong onlusions. Knowing the ore teperature of the sun is about K ; we assue this to be the teperature of a deayed sall neutron star in the ore, and use funtion (4.44) and (5.47) to get the radius of the deayed sall neutron star to be about Hene its ass is about kg, whih is about 5.5% solar ass, and this iplies the standard solar odel has to be revised [8]. Aording to funtion (5.56) the deayed neutron star in the enter of the sun has a agneti field of T. Knowing the ore teperature of the earth is about 7 K ; we also an derive that a deayed 4 sall neutron star with a radius of 14 and a ass of 1.81 kgis buried in the enter of the earth, whih has 18% of the ass of the earth. The deayed neutron star in the enter of the earth has a agneti field of6.1 1 T, and on the surfae of the earth the easured average agneti flux density still has T, probably beause the earth inner ore onsists priarily by an iron-nikel alloy whih has high pereability. Substitute the nulear density in funtion (5.5) with the density of rest ass in funtion (5.47), then we an transfor funtion (5.56) into a funtion to desribe the agneti field assoiated with a gravitational field desribed by funtion (5.47): 1 B ( / )( u / ) T (5.66) n The Milky Way super assive quasi-blak hole has a ass of about kg, aording to funtion (5.47) it has a radius of about and its density is about1.1 1 kg/. And aording to funtion (5.66) the agneti flux density on the surfae of a quasi-blak hole is proportional to its density, so the agneti flux density of this super assive quasi-blak hole: u ( / ) T (5.67) whih is 8 T on its surfae and dereases to 81 T at B ilky our loation. The agneti flux density falls off inversely with the ube of the distane fro its enter; this is a harateristi of a dipole field. This agneti field plays a very iportant role in the foration of a spiral galaxy, and I suggest that the stars near the galaxy enter have heavier deayed neutron star ores with stronger agneti fields, and that they also have higher overall densities than those stars far away fro the galaxy enter. The deayed neutron stars hiding in the enter of stars ould be the so-alled dark atter, and this an explain why the stars in the globular luster show no evidene for dark atter. A neutron star ore an have up to nine solar asses, whih an explain the typial ass to light ratios up to ten ties the ass to light ratio of the sun. Even though the agneti field assoiated with the osi sphere is extreely weak,

19 the so-alled osi axis ight be due to it [6], and f C / should be the typial spin frequeny of the neutrino fluxes assoiated with the gravitational field and the agneti field of the osi sphere Total Gravitational Blak-Body Radiation Energy of the Cosi Sphere Aording to funtion (4.46) and (5.47) we an estiate the total gravitational blak-body radiation energy inside and outside the osi sphere: E Inside / / 1/ 1/ G ( [(1 u / ) 1] d( J / (5.68) u L H E Outside 1 4 1/ G C ( [(1 u / ) 1] d( J / (5.69) u L where 7 C is the rest ass of the osi sphere and is its density, u ul (1 1) / 7 16 Fro forula (5.49) kg/, we derive E Inside J. Aording to 7 funtion (5.47) the lower liit of the gravitational potential (1 1) / whih gives the rest ass of the osi sphere u L kg to derive E Outside J. The average C 5 7 radiation energy density inside the osi sphere is about J /. The lowest density is zero in the enter of the osi sphere and in the spae infinitely far away fro it; the highest 4 density is J / at the edge of the osi sphere. The gravitational blak-body radiation energy is the portion of the vauu zero-point energy arried by gravitational fields, while the ajor portion of the vauu zero-point energy is arried by Higgs field. 6. Conlusions 6.1. Suary The osologial odel dedued fro funtions of the gravitational potential (FGP) has provided proper answers to several long pending osologial probles, suh as gravitational wave, irowave bakground radiation, osi rays, neutron stars and quasars. The universe is stable and the osi evolution will ontinue forever, beause the true blak hole, the heat death of the open universe, Big Bang or Big Crunh is ruled out by FGP. 6.. Dedue Aurate Eletroweak Coupling Constant fro the Nulear Density The highest radiation energy density at the edge of the osi sphere is produed by the annihilation of neutrons and anti-neutrons fro the neutron phase transitions near the event horizon, so it should equal the rest energy density of the neutron 4.71 J / derived fro 17 the nulear density.1 kg/. Fro funtion (4.46) we derive the aurate lower liit n

20 7 of the gravitational potential ( ) / (6.7). Fro funtion (4.45) we u L get the aurate axiu teperature T H K [1]. Then fro funtion (4.41) we 7 get the aurate eletroweak interation oupling onstant in perfet vauu , and get the aurate teperature T U 11 derive the orresponding radiation energy density K whenw (. Fro funtion (4.45) we E U 1.81 J / W. If it is produed by the annihilation of left-handed neutrinos and left-handed anti-neutrinos fro the neutrino phase transition near the event horizon, then we an derive the orresponding density of neutrino as kg/, and that will be a assive neutrino with an inertial ass about ties the rest ass of a neutron, whih is about5 KeV. Forula (4.4) also indiated a boson with a rest ass about ties the rest ass of a Higgs boson whenw (, whih is about6.7mev. So this ight iply a one to one relationship between ferions and bosons, we notie that the rest ass of a neutron is about ties the rest ass of a Higgs boson. 6.. Derive Hubble Constant fro the Gravitational Coupling Constant Copare the gravitational oupling onstant: ( G e / P ) ass ratio between the quasi-blak hole of neutron and the osi sphere: ( / N C ) to the square of the, they are quite lose to eah other. The eletron is the sallest iro ass quanta, while the quasi-blak hole of nuleus is the sallest aro ass quanta; Plank ass is the biggest iro ass quanta, while the osi sphere is the biggest aro ass quanta. And the gravitational oupling onstant should be the link between the iro and aro ass quanta, so I dedue that their ass ratio should be equal to eah other, and then we an alulate Hubble onstant and the ritial rest ass density aurately. Fro forula (5.49) and (5.5) we derive C / G H (6.71), fro funtion (5.47) and the nulear density 17 1 n.1 kg/ we get N kg H, and then derive Hubble onstant as below: 1/ 19 1 / G s 14.68( k/ s) Mp (6.7) G N / And then the ritial rest ass density defined by the derived Hubble onstants should be H. Sine the newly derived Hubble onstant is saller than 8 /8G 4.51 kg/ the urrent estiated value, the radius of the osi sphere is larger: 6 R C / H 6.81, whih is about 66.6 billion light years; the rest ass of the osi sphere is bigger as well: 5 C / G H 4.51 kg. We notie / R / G. C C The gravitational onstant in perfet vauu is indeed interrelated with the properties of the osi sphere, whih has atually proved Mah s priniple: Loal physial laws are deterined by the large-sale struture of the universe, or in our words by funtions of the gravitational potential. Aording to funtion (6.68) and (6.69) the total radiation energy of the osi sphere

21 depends on the ritial density or the rest ass assoiated with Hubble onstant, and the total radiation energy is inversely proportional to the ube of Hubble onstant. The g-fator experients indiate the osi bakground gravitational potential on the earth is 8 quite sall at.761 ( / s), whih has an equivalent neutrino flux speed of.76 k/ s aording to forula (4.1), put this into (4.48) to get the distant fro the earth to the enter of the osi sphere, whih is about one illion light years based on the urrent estiated Hubble onstant. But it should be 4.5 illion light years based on the newly derived saller Hubble onstant, and of ourse all distanes estiated by gravitational redshift have to be adjusted aordingly. The irregular galaxy Sextans B is 4.44 illion light years away fro the earth, thus ight be the ost distant eber of the Loal Group, and ould be the galaxy losest to the enter of the osi sphere. 7. Disussion Sine we have proposed agneti flux essentially is neutrino flux, and a photon ontains agneti flux, so this iplies every photon inside our osi sphere should be oposed by one pair of left-handed neutrino and left-handed anti-neutrino, while every photon inside the antiosi sphere should be oposed by one pair of right-handed anti-neutrino and right-handed neutrino. The issing left-handed anti-neutrino is always hiding inside a photon in our osi sphere, beause in the vauu of our osi sphere is doinated by left-handed neutrinos; annihilation will lok the left-handed anti-neutrinos inside photons forever, while the issing right-handed neutrino is always hiding inside a photon in the anti-osi sphere for the sae reason. Neutrino is a speial kind of ferion without rest ass, so it does not have an intrinsi agneti dipole field assoiated with its spin. But a pair of neutrinos an for a Cooper pair with integer spin, whih should be the agneti flux quantu inside a superondutor, and neutrino flux oposed by neutrino Cooper pairs should be superfluid. Neutrino Cooper pairs ight even turn into frationally harged quasi-partiles whih ontain ore than one pair of neutrinos when the teperature is old enough, that ight be able to explain the frational quantu Hall effet. Aording to Pauli Exlusion Priniple, a pair of ferions ust have opposite spins to exhange virtual photons, this not only an guarantee the onservation of angular oentu, but also an ensure their intrinsi agneti oentus are anti-parallel, hene the agneti fore between their intrinsi agneti field is always attration; while a ferion-antiferion pair ust have opposite spins to ensure the onservation of angular oentu when they exhange virtual photons, but their agneti oentu are parallel, hene the agneti fore between their intrinsi agneti field is always repulsion. The gravitational fore ight be the long range quantu entangleent effet fro the intrinsi agneti field of ferions. Hene only ferions with rest ass an produe the De Broglie atter waves, whih should be the so-alled gravitational waves in for of eletroagneti radiations with blak-body spetru.