Cosmic Quantization with Respect to the Conservation of Upper-Limit Energy

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1 1 Cosmic Quanizaion wi Respec o e Conservaion of pper-limi Energy Collège De La Salle - Frères Absrac Te condiions of e early universe are no known wi any measure of cerainy ey are only eories. Terefore, using e assumpion a e esimaed oal energy of e observable universe is conserved, we propose a differen lower limi for e graviaional energy; we aemp o unify e subaomic and e large scale universe ino one coeren wole; us, sowing a e cosmos beaves like a quanum objec. I uses a form of Bor s quanizaion o srengen e unificaion of quanum graviy. Our model is simple, ye compreensive. Keywords Black Hole Cosmology Graviy Quanizaion 1 Inroducion Our approac agrees wi acceped cosmology on e upper limi esimaes, no only for esimaed oal energy of e observable universe E = M c, bu also for presen pysical properies, suc as e Hubble ime = R c; e caracerisic graviaional poenial / n 1 ; e criical densiy; lanck force f and ower ; and e upper bound of e Bekensein Hawking enropy. As as been noed, e universe can be quanized as a black ole (Alfonso-Faus 0). We sugges a e quanum of e graviaional poenial field energy (e energy of one cosmic bi) is e iniial cosmic poenial energy, E = m c, aloug we ge a differen esimae for is iniial value an e ordinary one. Our calculaions urn ou o occur a an infrared radiaion (IR) frequency. We poin ou a lanck leng; ime and emperaure are idenified wi e quanum of graviy. Tus, for example, ime is bounded below by emaroun85@omail.com

2 lanck ime and above by e caracerisic ime of e observable universe, ese bounds can be applied o eac propery of e graviaional quana. lanck ime can be viewed as an endpoin for lanck epoc wic is a radiional (non-inflaionary) era in Big Bang cosmology, is period of ime proposes a singulariy a breaks down all e laws of pysics. lanck ime is no only e saring poin of e Big Bang and e cosmic inflaion, bu i is also e saring poin of e universe. For is reason, e energy idenified wi e quanum of e graviaional poenial occurs merely a lanck ime. Accordingly, 6 kg can be viewed as an esimae a exised during lanck epoc. eraps, is esimae is e saring mass of e singulariy: e primiive aom. Cosmic Quanizaion Consider e quanum of e graviaional angular momenum, were m = E c is e mass equivalen o e quanum of e graviaional poenial energy rougou e age of e universe; similarly, radius rougou e age of e universe. r = c is e graviaional mcr = n (1) Assuming e conservaion of energy principle olds for e cosmos, e esimaed oal energy of e observable universe is consan; we ge, by considering e cenripeal force as being equal o e graviaional poenial. c m r M m = G r () Combining e above, afer simplifying, n = GM m r () Recall e bounds on m, GM l m n GR emaroun85@omail.com

3 Te quanized mass is equal o e graviaional mass. n c r (4) = cr G Convering o e lanck leng n = l = c, we ge r l (5) Te quanum of graviy n can be viewed as e informaion conen of e universe. You mig expec is o vary as e cube of e graviaional radius of e visible universe a ime, afer all e maerial of e universe appears o be fairly uniformly disribued rougou is volume. Te above equaion, owever, sows a i acually varies direcly as e square of is radius. Tis suggess one of wo ings: 1) eier e black ole singulariy from wic e universe emerged was roaing; or, ) all maer in e universe is acually disribued along e boundary of e ouer sell of e universe. Te firs case mig also explain wy mos galaxies seem o be relaively fla spirals. Te angular momenum of e original universe, ogeer wi differences in speed of e ejeca caused by collisions would cause a naural flaening ino spirals wi a bias in e direcion of e original roaion. Randomized collisions would end o dampen ou is bias over ime, bu i would no eliminae i. Tis roaion would cause e ejeca o flaen ou ino a more disc-saped universe and resul in e quanum number becoming proporional o area raer an volume. We canno see e universe as roaing direcly because ere are no ouside poins of reference. Tere is evidence, owever, a is is e case (Longo 011) as ere is an apparen 7% bias oward couner-clockwise roaing galaxies in e norern emispere. Tis discrepancy is oo large o aribue o cance and sows a e universe is no, as as always been assumed, isoropic. A roaing universe would ave o ave a cener for e roaion. Te problem is a e disances involved, and e slowness of roaion, mig make deermining is cener difficul. However, a does no mean i is impossible. emaroun85@omail.com

4 4 Te second possibiliy for is would be for all of e maer o be locaed on e surface edge of e expanding spere of e universe. Bu is sould mean we would see a brig spo in e direcion from wic we came surrounded by a dark band aving ings oo far away from us for lig o ave raveled, or a dim band as ings ge farer away from us on e edge. Eier way, ere would be a difference in e red sif as we view ings in differen direcions. Tis as no been observed, so is possibiliy is no likely. Subsiuing Eq. 5 ino Eq. and solving for m we ge m = l r GM (6) Subsiuing caracerisic ime), and E for energy. GM for c R, for r c (a lanck ime and e mc, we ge e quanum of e graviaional E = (7) Observe a for =, we obain E J, using lanck relaion we 1 find IR. Addiionally, is esimae is relaively close o e ig frequency of e cosmic microwave background radiaion (CMBR) and i can be close o one elecron vol. Tis means a e graviaional energy is proporional o e square roo of e cube of ime (and us radius). Tis also suppors e idea of a roaing universe as i is a direc consequence of Eq. 5. Heisenberg principle, E, can relae e uncerainy of massenergy and space-ime wiin e subaomic scale (a scale of E E and ). For example, E is lanck energy wen is lanck ime. Remember, E canno be E and canno be. For is reason, 46 J is ou of e cosmic limis because i corresponds 11 sec wic is 1. However, J can be a cosmic endpoin because i corresponds 14 sec wic is only. Moreover, i is wor menioning a m r c. emaroun85@omail.com

5 5 Densiy is proporional o e mass and inversely proporion o e volume; ence, ρ = 1 G 1 (8) Here e equaion of mass densiy assumes a e universe is sperical. However, if e black ole from wic i emerged was roaing en e rue sape would be an oblae speroid or a ickened disc. Tis means a e apparen spericalness mig be due o reflecion from e edge of e universe or may be a relaivisic effec from differen speeds of expansion in differen direcions. By edge we mean e limi of e observable universe. Tus, ings may no be were we ink ey are and ere mig be muliple images of e same objec. I mig be possible o es is reflecion eory. Te bias in counerclockwise urning spiral galaxies observed in e norern emispere mig be balanced by an equal bias in clockwise urning spiral galaxies observed in e souern emispere. Tis ceck is on-going and e resuls ave no ye become available. However, if e resuls are analyzed over e enire sky en jus suc a mirroring may be discoverable. Tis would also indicae a e universe is closed and increase e likeliood of a Big Crunc a e end of ime. Tere is anoer problem. Even if is is e case, i would no be conclusive if ere is a difference in ages beween e reflecions. Te problem is a e angle of e universe would only approximaely equal e angle of e solar sysem, so is bias may no be observable easily. Also, e reflecion of any paricular galaxy may roll off e edge (e imes a wic e lig from a galaxy i e edge would no all be e same) and cange e apparen angle we see a galaxy from. Te objec and is reflecion would no necessarily be viewed from e same poin in ime. Tis mig inroduce a second bias wic would make i almos impossible o verify e sape of e universe as being an oblae speroid or disc. Consider e amoun of cange our own sellar sysem as undergone in e las four billion years. Regarding Eq. 7 as being work done in e cosmic expansion, we ge for e quanum of e graviaional force, f = f (9) emaroun85@omail.com

6 6 and e quanum of e graviaional power, = () Bo of ese are proporional o e square roo of e graviaional radius and are a direc resul of Eq. 7. sing Scwarzscild radius, e emperaure of e graviaional quana can be given by Hawking relaion, T = 1 k (11) 9 Observe a for e caracerisic ime we obain T = K, is esimae is very close o. 7 K, an excepional emperaure of e CMBR. Acually, is difference in esimae may be more of a calculaion error raer an a resul derived from eory. Furermore, i is wor menioning a for lanck ime we obain lanck emperaure. Noe a e emperaure is inversely proporional o ime. From Clausius relaion, Tis yields e quanum of graviaional enropy. S = E T, we apply e above resul o Eq. 7. k S = 5 (1) Tis is by far e fases grow rae of any of e quana considered and is proporional o e square roo of e fif power. Table 1 sows e values of various graviaional quana a differen imes rougou e age of e universe. For insance, e graviaional mass varies from a poonic mass a lanck ime, o a solar mass in abou one second, o a galacic mass in abou four mons and finally reacing e cosmic mass in abou 14 billion years. sing pysical laws, we could exend e resuls o oer pysical quana. emaroun85@omail.com

7 7 Te propery of e graviaional quana Radius Quanum of graviy Energy Mass roporion o Time r 5 n / 1 E 44 / 8 m 7 Time ( sec.) SI nis 6 m J. 5 kg. Densiy / ρ 1/ kg / m. Force 1/ f N. ower 1/ W. Temperaure T 1/ K. Enropy 5 / S J / K. Table 1 Relaive canges in graviaional quana wi respec o ime Cosmic Quanizaion of Space-Time and Mass-Energy Space-ime is quanized, remember r = l n = n (1/a) Bu wy i appears a space-ime is coninues? Tis can be simply explained by undersanding = ( n n 1) (1/b) Space-ime appears coninues because e universe is reacing n 0 n In addiion, mass-energy is quanized. Te equaion resul from subsiuing Eq. 1/a in Eq. 7, or E 4 = n is a emaroun85@omail.com

8 8 m = c n 4 (14/a) Bu wy i appears a mass-energy is coninues? Tis can be simply explained by undersanding m m = c ( n 4 n 4 1) (14/b) Mass-energy appears coninues because e universe is reacing m n m 0 n 4 Conclusion 6 kg (Alfonso-Faus 0) is viewed as a value a exised during lanck epoc; is esimae could be e saring mass of e singulariy. Our model predics a e universe sared a lanck ime only, erefore, 8 kg is viewed as e mass idenified wi e quanum of e graviaional poenial. If our esimae is valid en our model unifies e essenial pysical properies a bo e subaomic and e large scale universe. Our approac gives anoer way of esimaing e oal energy of e observable universe under e assumpion a is oal energy is conserved. I describes e cosmic inflaion and e increase in enropy as an increase in e informaion conen given by is quanum of graviy. We need o poin ou a our rae of inflaion is differen from a derived by Alan Gu (Gu 1981). E Te energy idenified wi e quanum of e graviaional poenial 1 J is energy of IR a exised in a universe of a singulariy; i is e iges amoun of energy a is found before e Big Bang. Te universe only sared o inflae a lanck ime wi an amoun of IR energy, bu wi energy less an is ere was only a primiive aom. In addiion, is lower limi of cosmic energy is relaively close o e energy a is on e ig frequency of CMBR; is esimae can be close o one elecron vol as well. Acually, is difference in esimae menioned above may be more of were i is calculaed raer an from an acual difference in eory. emaroun85@omail.com

9 9 Te formulas, in paricular Eq. 5, suppor e idea a e universe is disc-saped and roaing, peraps resembling a super-sized spiral galaxy. Our conclusion, wic is based upon is model, corresponds wi e modern cosmological observaions. References Alfonso-Faus, A., Asropys. Space Sci., 1, 69, (009) Alfonso-Faus, A., Asropys. Space Sci., 5, 11, (0) Alfonso-Faus, A., Asropys. Space Sci., online: 1 Augus 01 (011a) Alfonso-Faus, A., arxiv:15.14 (011b) Barrow, J. and Sonoda, D.H., Mon. No. R. Asron. Soc., 1, 917 (1985) ys. Rev. D, 7, (197) Collins, C.B. and Hawking, S.W., Mon. No. R. Asron. Soc., 16, 07 (197) Egan, C.A. and Lineweaver C.H., Asron. J., 7, 185 (0) Fullana i Alfonso, M.J. and Alfonso-Faus, A., Asropys. Space Sci., 7, 19{0 (01) Gonza'alez-D az,.f., Na. Sci., (5), 87 (011) Gudder, S.., arxiv:18.96 (011) Gu, A.H., ys. Rev. D,, 47{56 (1981) Hagiwara, K. e. al., ys. Rev. D, 66, (00) Hawking, S.W., Commun. Ma. ys., 4, 199 (1975) He, X.G. and Ma, B.Q., Mod. ys. Le. A, 6, 99 (011) Lloyd, S., ys. Rev. Le., 88, 7901 (00) ys. Rev. B, 699, 4-9 (011) admanaban, T., Rep. rog. ys., 7, (0b) admanaban, T., Mod. ys. Le. A, 5, 119, (0b) Sanos, E., Asropys. Space Sci., 6, 7 (0a) Sanos, E., ys. Le. A, 74, 709 (0b) Sanos, E., Asropys. Space Sci.,, 4 (011) Verlinde, E.., J. Hig Energy ys., 14, 09 (011) emaroun85@omail.com

10 5 Te Elecric Carge Hypoesis of e Subaomic niverse From lanck relaion, E = ν, we apply e above resul o Eq. 7. Tis yields e quanum of graviaional frequency of e early cosmic Elecromagneic radiaion (EMR). ν = 1 (15) Corresponding Coulomb s poenial energy o Eq. 7, we ge e quanum of graviaional elecric carge of e early cosmic EMR. q = q 4 5 (16) Macing Eq. 15 wi Eq. 16, q = q (17) ν Tis is a relaion beween e elecric carge of e early cosmic subaomic paricles and is frequency. Observe a e range of e elecric carge for e early cosmic EMR is convenional esimae 4 C q 4 C, is differs from e q 5 e. Also noice a for =, we obain ν 1 Hz and q 1 C, on e oer and, ν Hz wen q 19 C. emaroun85@omail.com