Quantum Mechanics, Cosmic Acceleration and CMB Radiation by U

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Global Journal of Science Frontier Research Physics and Space Science Volume 12 Issue 4 Version 1.0 June 2012 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Inc. (USA) Online ISSN: 2249-4626 & Print ISSN: 0975-5896

Quantum Mechanics, Cosmic Acceleration and CMB Radiation By U. V. S. Seshavatharam & S. Lakshminarayana Andhra University, Visakhapatnam, India Abstract - Based on the big bang concepts - in the expanding universe, rate of decrease in CMBR temperature is a measure of the cosmic rate of expansion. If universe is accelerating, CMBR temperature must decrease continuously. It is noticed that, Bohr radius of hydrogen atom, quanta of the angular momentum and the fine structure ratio - are connected with the large scale structure of the massive expanding universe. In the accelerating universe, as the space expands, in hydrogen atom, distance between proton and electron increases and is directly proportional to the size of the universe. ‘Rate of decrease in the laboratory fine structure ratio’ is a measure of cosmic rate of expansion. Considering the integral nature of number of protons (of any nucleus), integral nature of ℏ can be understood. Obtained value of the present Hubble constant is 70.75 Km/sec/Mpc. Instead of the Planck scale, initial conditions can be represented with the Coulomb scale. Finally it can be suggested that, if the primordial universe is a natural setting for the creation of black holes and other non-perturbative gravitational entities, throughout its journey, the whole universe is a primordial (growing and rotating) black hole. Keywords : Reduced Planck’s constant, Fine structure ratio, Bohr radius, Cosmic mass, Coloumb scale, CMB radiation, Cosmic acceleration, Light speed rotation and Primordial cosmic black hole.. GJSFR-A Classification : FOR Code: 020106, 020103, 020602 Quantum Mechanics, Cosmic Acceleration and CMB Radiation

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Quantum Mechanics, Cosmic Acceleration and CMB Radiation

U. V. S. Seshavatharamα & S. Lakshminarayanaσ

Abstract - Based on the big bang concepts - in the expanding 2 M c  universe, rate of decrease in CMBR temperature is a measure 0 ≅   of the cosmic rate of expansion. If universe is accelerating, me Gm pe m CMBR temperature must decrease continuously. It is noticed (2) that, Bohr radius of hydrogen atom, quanta of the angular Considering both the number of electrons and momentum and the fine structure ratio - are connected with positrons, it is noticed that, June 2012 the large scale structure of the massive expanding universe. In the accelerating universe, as the space expands, in hydrogen 11M 17 atom, distance between proton and electron increases and is ln ·20 ≅≅137.024 directly proportional to the size of the universe. ‘Rate of Nme α  (3) I decrease in the laboratory fine structure ratio’ is a measure of cosmic rate of expansion. Considering the integral nature of Where N is the Avogadro number and α is number of protons (of any nucleus), integral nature of  can the fine structure ratio. V be understood. Obtained value of the present Hubble constant is 70.75 Km/sec/Mpc. Instead of the Planck scale, initial b) To understand the quanta of the angular momentum IV conditions can be represented with the Coulomb scale. Finally Giving a primary significance to the existence of ersi on ue it can be suggested that, if the primordial universe is a natural mm,,G&c, and con sidering the Machian concept of ss setting for the creation of black holes and other non- ep the distance cosmic back ground [6] in the form of perturbative gravitational entities, throughout its journey, the XII I whole universe is a primordial (growing and rotating) black ‘distance cosmic mass’,  can be considered as the compound physical constant [7,8,9]. hole. Keywords : Reduced Planck’s constant, Fine structure M Gm m ratio, Bohr radius, Cosmic mass, Coloumb scale, CMB  ≅0 pe ≅×−34 · 1.0572 10 J.sec (4) ) radiation, Cosmic acceleration, Light speed rotation and mce

Primordial cosmic black hole. (

From the atomic structure point of view also this I. The Reduced Planck’s Constant - a idea can be strengthened. If electron is revolving round

m se arch Volume Strange Coincidence the nucleus, naturally p and me both are the characteristic physical inputs. By considering the origin arge dimensionless constants and compound of the Bohr radius of Hydrogen atom this proposal can physical constants reflects an intrinsic property of be given a chance. If so: in the expanding universe nature [1,2]. Whether to consider them or discard L ‘quanta’ increases with increasing mass of the universe. them depends on the physical interpretations, Any how this is a very sensitive problem to human experiments and observations. The mystery can be thoughts and observations. Considering the ‘integral resolved only with further research, analysis and nature’ of number of protons, integral nature of n· can discussions. If m and m are the rest masses of e p be understood. Considering any two successive electron and proton respectively, it is noticed that, integers n and (n +1), their geometric state is

c r na l of Science Fr on tier Re ≅ 0.99753 (1) nn( +1·.)  if this logic is true, it can be suggested that Gm M m ou pe0  is connected with the large scale structure of the 3 expanding universe. The laboratory fine structure ratio is Where M00≅ c2 GH and the best value

+1.3 Global J [3,4,5] of H0 is 70.4−1.4 Km/sec/Mpc. Surprisingly this m e2 α ≅ e · (5) ratio is close to unity! How to interpret this ratio? M4πε Gm m 00pe a) Number o f electrons or positrons in the universe Number of electrons or positrons in the present It is the strength of electromagnetic interaction universe can be expressed as and is an intrinsi c property of nature. Cosmic

acceleration and dark energy constitute one of the most Author α : Honorary faculty, I-SERVE, Alakapuri, Hyderabad-35, AP, important and challenging of current problems in India. E-mail : [email protected]

Author : Dept. of Nuclear Physics, Andhra University, cosmology and other areas of physics [10]. If so ‘rate of σ Visakhapatnam-03, AP, India. E-mail : [email protected] increase in  ‘ or ‘rate of decrease in α ‘ can also be

considered as a measure of the cosmic acceleration. density of the (closed) rotating and expanding universe. With reference to relation (4), magnitude of the Hubble’s Not only that, by considering the universe as a constant can be fitted as primordial growing and light speed rotating black hole, 3 (c2 GH0 ) can be obtained and the growing cosmic Gm2 m c pe (6) size can be minimized to (/cH0 ). H0 ≅≅70.75 Km/sec/Mpc 22 d) The Coulomb scale: alternative to the Planck Scale c) Bohr radius of the Hydrogen atom By any chance, if  is a cosmic variable, then what about the validity of ‘Planck mass’ and ‘Planck In hydrogen atom, potential energy of electron in Bohr radius [7, 8] can be expressed as scale’? Answer is very simple. c can be replaced G e2 ec22 E ≅− × (7) 2 P 44πε Gm M πε Gm with e It can be called as the ‘Coulomb mass’. 0pp00 . 4πε0G 24

June 2012 ec

Thus, total energy of electron in Bohr radius is Its corresponding rest energy is . It can be 4πε G 2 22 0 18 e ec (8) called as the ‘Coulomb energy’. Planck energy can be ET ≅− × 48πε0Gmpp M 00πε Gm replaced with the ‘Coulomb energy’. I

on Considering the integral nature of number of e2 M ≅ ≅×1.859211 10−9 Kg (13) protons (of any nucleus), above relation is C πε V 4 G 0 2 22 IV e ec (9) ET ≅− × 24 2 ec 18 ue ersi ue 4·πε G nm M 8·πε G nm 0()pp 00() McC ≅ ≅×1.042941 10 GeV (14) ss 4πε G 0 4 XII I where n = 1, 2, 3, .. Thus in a discrete form, Here e is the elementary charge and (cG /)is 2 22 the cla ssical limit of force. How to interpret this mass 1 e ec (10) ET ≅− × × unit? Is it a primordial massive charged particle? If 2 n2 48πε Gm M πε Gm 0pp 00 such oppositely charged particles annihilates, a large

) Hence ‘Bohr radius of hydrogen’ atom is amount of energy can be released. Considering so

( many such pairs annihilation hot big bang or inflation

2 can be understood. This may be the root cause of 44πε00GmppM Gm 1 πε0Gm p c a ≅≅··(11) cosmic energy reservoir. Such pairs may be the chief 0 222  2H

se arch Volume ec e 0 constituents of black holes. In certain time interval with a well defined quantum rules they annihilate and release a

This is a very simple and natural fit. The real large amount of energy in the form of γ photons. In the

beauty of the Mach’s principle can be seen here. expanding universe, with its pair annihilation, origin of

c the CMBR can be understood. aM∝∝ (12) It is widely accepted that charged leptons, 00H 0 quarks, and baryons all these comes under matter or mass carriers and photons and mesons comes under In this way, independent of the telescopic force carriers. If so what about this new mass unit? Is it a observations, the exact value of the present Hubble’s fermion? or Is it a boson? or else is it represents a large constant can be estimated from the ground based potential well in the primordial matter or mass

r na l of Science Fr on tier Re dα d laboratory experiments and thus or repr esents generation program? Is it the mother of magnetic ou dt dt monopoles? Is it the mother of all charged particles? By a measure of the cosmic acceleration. Since its origin, any suitable proportionality ratio or with a suitable scale  is assumed and observed to be a fundamental factor if one is able to bring down its mass to the

Global J d quantum constant. It means, at present, = 0.Hence observed particles mass scale, very easily a grand dt unified model can be developed. it can be suggested that, at present there is no Clearly speaking ec, and G play a vital role in expansion or acceleration in the universe. fundamental physics. With these 3 constants space-time To establish this fact, one must derive the curvature concepts at a charged particle surface can be characteristic cosmic mass M ≅ c3 2GH independent studied. Characteristic ‘Coulomb size’ can be expressed 00 2 as of the cosmic critical density 38HG0 π concepts. If one is able to show that, H is a cosmic angular velocity 0 2GMC −36 2 R ≅≅2.716354 × 10 m (15) variable, then 38HGπ represents the geometric C 2 0 c

Quantum Mechanics, Cosmic Acceleration and CMB Radiation

Considering ‘light speed rotation’, characteristic II. The Critical Density and Its ‘Coulomb scale angular velocity’ is Dimensional Analysis 3 cc 44 ωC ≅≅ ≅1.085672 × 10 rad/sec (16) Assume that, a planet of mass (M) and size (R) RCC2 GM rotates with angular velocity ()ωe and linear velocity e) To understand the CMBR temperature (ve ) in such a way that, free or loosely bound particle of mass (m) lying on its equator gains a kinetic energy Pair particles creation and annihilation in `free equal to potential energy as, space'- is an interesting idea. In the expanding universe, by considering the proposed charged MC and its pair annihilation as a characteristic cosmic phenomena, 1 2 GMm mve = (23) origin of the isotropic CMB radiation can be addressed. 2 R

Where the free space is occupied by a large massive body, there the pair annihilation of MC cannot be seen 22GM ve GM (24) June 2012 and this may be a reason for the observed anisotropy of Rvωωee= = ande = = RRR3

CMB. At any time t, it can be suggested that

19 MC 2 i.e Linear velocity of planet’s rotation is equal to free kBtT≅ ·2 MCc (17) particle’s escape velocity. Without any external power or M I t energy, test particle gains escape velocity by virtue of Where M is the cosmic mass at time t and T planet’s rotation. Using this idea, ‘Black hole radiation’ t t is the cosmic temperature at time t. Please note that, at and ‘origin of cosmic rays’ can be understood. Note that V present if Earth completes one rotation in one hour then free particles lying on the equator will get escape velocity. IV 2 MCC2 Mc 0 MR= (43π) 3ρ ersi on ue T0 ≅≅· 3.5175 Kelvin (18) Now writing, e ss Mk 0 B XII I vGee88πρ 2 πρ Ge(25) Qualitatively and quantitatively this can be ωωee= = Or = R 33 compared with the present CMBR temperature 2.7250 Kelvin. It seems to be a direct consequence of the 2 3ωe Mach's principle. It means - at any time, the cosmic Density,ρ = (26) ) mass or cosmic size play a critical role in the pair e 8Gπ

( annihilation energy of Initial temperature of the . MC In real time, this obtained density may or may universe can be expressed as not be equal to the actual density. But the ratio,

2 2 se arch Volume 2McC 31 0 (8πρG 3 ω ) may have some physical meaning. T ≅ ≅×2.42 10 Kelvin (19) real real C The most important point to be noted here, is that, as kB far as dimensions and units are considered, from With reference to the present observed CMBR equation (26), it is very clear that, proportionality temperature, considering the 3 dimensional average constant being 38πG , thermal energy 3 above relation can be expressed kTBt, 2 as 2 density∝ ( angular velocity) (27)

Equation (26) is similar to ‘‘flat model concept’’ 3 MC 2 kT≅ ·2 M c (20) of cosmic ‘‘critical density’’ 2 Bt M C t

2 r na l of Science Fr on tier Re Thus, 3H0 ρc = (28) ou 8πG 2 M2 Mc2 ≅≅CC 0 (21) T0  · 2.345 Kelvin Comparing equations (26) and (28) 3 Mk0 B Global J dimensionally and conceptually, 22 3ωe 3H0 In this way, origin of the CMB radiation can be ρρe = withc = (29) 8πG 8Gπ studied. But it has to be discussed in depth. Now, initial temperature of the universe can be expressed as 22 HH→→ωωand (30) 0 e 0e 2 2 2McC 31 0 In any physical system under study, for any one TC ≅ ≅×1.61 10 Kelvin (22) ‘simple physical parameter’ there will not be two 3 kB

different units and there will not be two different physical temperature is a measure of the cosmic rate of meanings. This is a simple clue and brings ‘‘cosmic expansion. Modern standard cosmology is based on rotation’’ into picture. This dimensional analysis cannot two contradictory statements. They are - present CMBR be ignored. temperature is isotropic and the present universe is accelerating. In particle physics also, till today laboratory III. Modified Hubble’s Law evidence for the existence of dark matter and dark Ever since the late 1920’s, when Edwin Hubble energy is very poor. Recent observations and thoughts supports the existence of the cosmic axis of evil. discovered a simple proportionality between the redshifts in the light coming from nearby galaxies and Independent of the cosmic red shift and CMBR their distances, we have been told that the Universe is observations, cosmic acceleration can be verified by expanding. Hubble found the recession speed v of a measuring the ‘rate of decrease’ in the fine structure nearby galaxy was related to its radial distance r, ratio. In this connection an attempt is made to study the = universe with a closed and growing model of v Hr0 , where H0 is the constant of proportionality. This relationship- dubbed the Hubble law- has since cosmology.

June 2012

If the primordial universe is a natural setting for been strengthened and extended to very great distances in the cosmos. This was the incomplete the creation of black holes and other non-perturbative 20 interpretation that changed the destiny of the modern gravitational entities, it is also possible to assume that throughout its journey, the whole universe is a primordial I cosmology. Based on this interpretation modern cosmologists arrived at the conclusion that - at present, (growing and rotating) cosmic black hole [12-16].

on universe is flat and is accelerating. Later in his life Instead of the Planck scale, initial conditions can be represented with the Coulomb scale. V Hubble varied from his initial interpretation [11] and said that the Hubble law was due to a hitherto undiscovered

IV c) Light speed rotating Black Holes: The special holes mechanism, but not due to expansion of space - now Origin of ‘rotating black hole’ formation can be ue ersi ue called cosmological expansion. ( 5 ) ss understood with the classical power limit cG/ and For the same observations it can also be 2 ( Mc ) within 3 steps. For any rotating celestial body

XII I possible to state that, in a closed and expanding universe, from and about the cosmic center, rate of 2 increase in galaxy redshift is a measure of cosmic rate torque,τ ≤ Mc (31)

of expansion. This statement includes 3 points. 1) Light c5 from the galaxy travels opposite to the direction of =τω ≤ ) power, P (32) cosmic expansion and shows redshift and thus redshift G

( is a measure of galaxy distance from the cosmic center. cc33 thus, ωω≤ and = max (33) 2) In the expanding universe, increase in redshift is GM GM instantaneous due to instantaneous increase in galaxy se arch Volume When the celestial body rotates at light speed, distance (which is due to instantaneous increase in to have maximum angular velocity, size should be cosmic volume) and 3) Rate of increase in redshift minimum as, indicates the cosmic rate of expansion. c GM a) The proposed 4 assumptions R = = (34) min ω 2 Starting from the Coulomb scale, it is assumed max c that, at any time (t), This expression is similar to the ‘Schwarzschild 1) The universe can be treated as a primordial rotating radius’ of a black hole. The only change is that and growing black hole. coefficient 2 is missing. This is really a very interesting 2) With increasing mass and decreasing angular case. This obtained expression indicates that, to get

r na l of Science Fr on tier Re velocity, the universe is always rotating with speed ‘light speed rotation’, celestial body should have a ou of light. ‘minimum size’ of 2 Clearly speaking this 3) ‘Rate of decrease’ in CMBR temperature is a GM c . proposal is entirely different from the existing concepts measure of cosmic ‘rate of expansion’. of General theory of relativity. It is not speaking about Global J 4) ‘Rate of decrease’ in laboratory fine structure ratio is the gravitational collapse of stars or space-time also a measure of cosmic ‘rate of expansion’. curvature or singularity. Now this is the time to re- At time t, cosmic size is R≅ 2 GM c2 and tt examine the foundations of modern black hole physics. 3 cosmic angular velocity is ωtt≅≅c R c 2.GM tThus If the concept of ‘Schwarzschild radius’ is believed to M≅ cG3 2.ω be true, for any rotating celestial body or black hole of tt rest mass (M) the critical conditions can be stated as b) Universe – the primordial cosmic black hole follows. 1) Magnitude of ‘kinetic energy’ never crosses Based on the big bang concepts- in the ‘rest energy’. 2) Magnitude of ‘torque’ never crosses expanding universe, rate of decrease in CMBR ‘potential energy’ and 3) Magnitude of mechanical

Quantum Mechanics, Cosmic Acceleration and CMB Radiation

power never crosses ( cG5 /.) Note that, based on the 14. Nikodem J. Popéawski. Radial motion into an Virial theorem, potential energy is twice of kinetic energy Einstein-Rosen bridge. Physics Letters B. Volume 2 and thus, τ ≤ 2Mc . 687, Issues 2-3, 2010, p110-113. 15. Zhang T.X. Cosmic microwave background IV. Conclusion radiation of black hole universe, Astrophysics and The proposed methodology is very simple. Space Science, Vol. 330, 2010, p.157-165. Searching, collecting, sorting and compiling the cosmic 16. Roger Penrose. Chandrasekhar, Black Holes, and code is an essential part of unification. Further research Singularities. J. Astrophys. Astr. 1996, 17, p 213-231 and analysis in this new direction may reveal the facts.

V. Acknowledgements

The first author is indebted to professor K. V. Krishna Murthy, Chairman, Institute of Scientific Research on Vedas (I-SERVE), Hyderabad, India and June 2012

Shri K. V. R. S. Murthy, former scientist IICT (CSIR) Govt. of India, Director, Research and Development, I-SERVE, 21 for their valuable guidance and great support in I developing this subject.

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