Origin of the Expansive Homogeneous and Isotropic Relativistic-Quantum-Mechanical Universe

Transcription

1 Adv. Studies Theor. hys., Vol. 5, 011, no. 16, Origin of the Expansive Homogeneous and Isotropi Relativisti-Quantum-Mehanial Universe Vladimír Skalský Faulty of Material Sienes and Tehnology of the Slovak University of Tehnology, Trnava, Slovakia vladimir.skalsky@stuba.sk Abstrat hysial properties of the universe unambiguously determine also the physial onditions and mehanism of its origin. Keywords: General relativity and gravitation, Cosmology: Observational osmology, Theoretial osmology, Mathematial and relativisti aspets of osmology 1 Introdution At present time we reliably know that the universe has omplementary relativisti and quantum-mehanial properties. A relativisti quantum-mehanial universe is expanding, homogeneous and isotropi. It means that it originated before the finite time, under physial onditions that an be unambiguously identified by the reverse extrapolation of its expansive evolution. Aording to the present observations the age of our observed expansive homogeneous and isotropi relativisti quantum-mehanial Universe is approximately 13.7 Gyr [1,, 3]. The reverse extrapolation of the evolution of an expansive homogeneous and isotropi relativisti quantum-mehanial universe leads to an initial osmologial singularity (i.e. to the most perfet geometri objet: point), in whih assuming that it should have physial properties all the physial parameters of the universe would have zero or infinite values. But this neither from the standpoint of the general theory of relativity, nor from the standpoint of

2 784 V. Skalský the quantum mehanis in priniple is not possible. Therefore, the initial osmologial singularity is not a physial objet, but only an abstrat limit geometrial objet. From the quantum-mehanial standpoint the reverse extrapolation of the evolution of the expansive homogeneous and isotropi relativisti quantummehanial universe an be arried bak only to the lank era, when the universe had the following parameters [4]: lank length lank time t l m, (1) l = s, () lank mass lank mass density lank temperature m 10 8 kg, (3) ρ kg m 3, (4) T 10 3 K. (5) Origin of an expansive homogeneous and isotropi relativisti quantum-mehanial universe lankon, i.e. a matter-spae-time non-differentiate physial objet with the lank quantities (1)-(5), is a limit quantum-mehanial objet. Therefore, it annot be reated from something non-physial, by some kind of non-physial proesses. Aording to Stephen Hawking and Leonard Mlodinow:... if we want to go bak even further and understand the origin of the universe, we must ombine what we know about general relativity with quantum theory. [5, p. 131]. From the omplementarity between general theory of relativity and quantum mehanis results unambiguously that the matter-spae-time non-differentiate plankon an originate only by the quantum-mehanial proesses in the relativisti quantum-mehanial environment. We know only one global relativisti quantum-mehanial environment: an expansive homogeneous and isotropi relativisti quantum-mehanial universe, and only quantum-mehanial proesses whih may manifest an atualization and de-atualisation of quantum-mehanial objets: the quantum-mehanial flutuation origin and extintion of the partiles and radiation. Therefore: The plankon with limit relativisti and quantum-mehanial properties an originate only by quantum-mehanial proesses in the expansive homogeneous

3 Relativisti-quantum-mehanial universe 785 and isotropi relativisti quantum-mehanial universe there, where appropriate onditions arise. The matter-spae-time non-differentiate plankon has extreme relativisti quantum-mehanial properties; therefore, it an originate only under very speifi onditions. From the first nontrivial exat solutions of the Einstein field equations, whih were published in 1916 by Karl Shwarzshild [6], results that aording to the Einstein general theory of relativity massive objets might exist from whih neither the matter objets nor radiation annot esape. For this property John A. Wheeler in 1967 gave to them the name blak holes. The dimensions of the blak hole are determined by the event horizon (Shwarzshild sphere) with ritial (gravitational or Shwarzshild) radius [6]: Gm r =. (6) At the beginning of 1970 s, British theoretial physiist Stephen W. Hawking when he analysed thermodynami properties of blak holes from the quantum-mehanial point of view ame to an unexpeted and surprising disovery, now known as Hawking blak hole evaporation or Hawking effet. He published it on 1 Marh 1974 in the artile Blak hole explosions? [7], and a year later, in more detail, in the artile artile Creation by Blak Holes [8]. Aording to Hawking, blak hole evaporation an be desribed in several ways, whih at first sight may seem to be very different, but in fat they are equivalent. One from the desription is based on the fat that the unertainty relations allow partiles flutuation to transfer over a short distane at superluminal veloity. Therefore, partiles and radiation an esape via flutuation from the blak hole. By esape (evaporation) of partiles and radiation the blak hole loses mass [9]. In his bestseller A Brief History of Time [10] Hawking desribed the final phase of the evaporation of blak hole as follows: As the blak hole loses mass, the area of its event horizon gets smaller, but this derease in the entropy of the blak hole is more than ompensated for by the entropy of the emitted radiation, so the seond law is never violated. Moreover, the lower the mass of the blak hole, the higher its temperature. So as the blak hole loses mass, its temperature and rate of emission inrease, so it loses mass more quikly. What happens when the mass of the blak hole eventually beomes extremely small is not quite lear, but the most reasonable guess is that it would disappear ompletely in a tremendous final burst of emission, equivalent to the explosion of millions of H-bombs. [10, p. 107]. Blak holes an not evaporate (disappear) ompletely by the Hawking effet. The Heisenberg unertainty priniple (relations) [11] do not allow it. After evaporation of the blak hole a limit matter-spae-time unstrutured plankon remains with a relatively small, but non-zero mass. (The plankon has mass, determined by the relation (3), i.e. several hundred-thousandth of a gram.)

4 786 V. Skalský The plankon is a limit ( residual ) Shwarzshild undifferentiated in matterspae-time manner blak hole, whih in this limit state an exist only in the frame of unertainty relations. Therefore, in the shortest possible, i.e. lank time t, determined by the relation (), it is transformed by the flutuation into objet, whih is strutured in the matter-spae-time manner. Flutuation differentiation of the plankon is realized under extreme onditions, with the maximum possible, i.e. lank temperature T, determined by the relation (5), generating the maximum possible negative pressure of reating partiles. Therefore, reated partiles are drifting apart at high veloities, and the event horizon is moving away from them at the maximum possible veloity of signal propagation. The relativisti quantum-mehanial objet, strutured in matter-spae-time manner, with the event horizon moving away at the veloity, is spae-time limit-singularly losed. A baby universe, i.e. new spae-time limit-singularly losed expansive homogeneous and isotropi relativisti quantum-mehanial universe (EU), is reated. The EU during its whole expansive evolution expands at the boundary veloity of signal propagation. Therefore, for its gauge fator a and the osmologial time (age of universe) t is valid the relation [1]: a = t. (7) If in the relation (6) instead of the ritial radius r we put the gauge fator a := r, we reeive: Gm a =. (8) The physial-mathematial foundations of the present relativisti osmology are represented by the Friedmann equations of the homogeneous and isotropi relativisti universe dynamis [13, 14], whih using the Robertson-Walker metris [15, 16, 17, 18] an be expressed in the following form: 8π Gρa Λa a & = k +, (9a) 3 3 8π Gpa a a& + a& = k + Λa, (9b) p = wε, where a is the gauge fator, ρ mass density, k urvature index, Λ osmologial onstant, p pressure, w state equation onstant, and ε = ρ energy density. The Friedmann-Robertson-Walker (FRW) equations of the homogeneous and isotropi relativisti universe dynamis (9a), (9b) and (9) fulfil the restritive onditions, determined by the relations (7) and (8), only with k = 0, Λ = 0 and w = 1/3 [19]. Using the FRW equations (9a) and (9b) with k = 0 and Λ = 0 and (9)

5 Relativisti-quantum-mehanial universe 787 total zero energy state equation 1 p = ε, (10) 3 we an determine the parameters of the model of a flat (Eulidean) expansive homogeneous and isotropi relativisti universe (EU model), whih desribes the EU in the linear approximation, in whih we abstrat from its relativisti and quantum-mehanial properties [19]: 4 Gm GE 3 3 a = t = = = = =, (11) 4 H 8π Gρ 8π Gε where H is the Hubble onstant (parameter, oeffiient), and E energy. From the relations (11) results inrease of universe mass Δm = Δt = kg s. (1) G Hawking in his above mentioned bestseller A Brief History of Time wrote: in quantum theory, partiles an be reated out of energy in the form of partile/antipartile pairs. But that just raises the question of where the energy ame from. The answer is that the total energy of the universe is exatly zero. The matter in the universe is made out of positive energy. However, the matter is all attrating itself by gravity. Two piees of matter that are lose to eah other have less energy than the same two piees a long way apart, beause you have to expend energy to separate them against the gravitational fore that is pulling them together. Thus, in a sense, the gravitational field has negative energy. In the ase of a universe that is approximately uniform in spae, one an show that this negative gravitational energy exatly anels the positive energy represented by the matter. So the total energy of the universe is zero. Now twie zero is also zero. Thus the universe an double the amount of positive matter energy and also double the negative gravitational energy without violation of the onservation of energy. [10, p. 19]. In the EU model, determined by the FRW equations (9a), (9b) and (9) with k = 0, Λ = 0 and w = 1/3, the Eulid geometry is valid. Aording to the Einstein general relativity, for the total mass m tot of the Eulidean homogeneous matter sphere is valid the relation: 4 3 3p m tot = π r ρ +. (13) 3 For the total mass of the EU in the linear approximation m tot with the non-zero values of the gauge fator a := r, the mass density ρ and the pressure p an be valid:

6 788 V. Skalský m tot only on the ondition [0]: = 4 3 3p π a ρ + = 0 (14) 3 + 3p ρ 0. = (15) For the mass density ρ and the energy density ε is valid the relation: ε = ρ, (16) therefore, the relation (15) using the relation (16) an be rewritten into the form: ε + 3 p = 0. (17) If in the relation (17) we express the value of pressure p, we reeive the total zero energy state equation, mentioned above as the relation (10). From the above mentioned unambiguously results: The EU model is only one non-formal universe model of the expansive homogeneous and isotropi relativisti quantum-mehanial universe in the linear approximation with the total zero and loal non-zero mass (energy). The EU model is the only one model of the expansive homogeneous and isotropi relativisti Universe, whih in the frame of measurement unertainty orresponds with the results of the present observations [1,, 3, 4]. Note: The model and physial properties of the EU are analysed in more detail in the artile: The model of a flat (Eulidean) expansive homogeneous and isotropi relativisti universe in the light of the general relativity, quantum mehanis, and observations [3]. 3 Conlusions From the analysis given above it results unambiguously that after the evaporation of blak hole by Hawking effet, it remains matter-spae-time undifferentiated plankon, whih in the frame of Heisenberg unertainty relations is transformed by flutuation into a new spae-time limit-singular losed expansive homogeneous and isotropi relativisti quantum-mehanial universe with the total zero and loal non-zero mass (energy). From observations, physial and model properties of our observed Universe it results unambiguously that the expansive homogeneous and isotropi relativisti quantum-mehanial universe with the total zero and loal non-zero mass (energy), is the only one possible universe, in whih physial properties unambiguously determine also both the physial onditions and the mehanism of its physial, i.e. relativisti quantum-mehanial origin.

7 Relativisti-quantum-mehanial universe 789 Referenes [1] C. L. Bennett et al., First Year Wilkinson Mirowave Anisotropy robe (WMA) Observations: reliminary Maps and Basi Results, Astrophysial Journal Supplement Series, 148 (003), 1-7. [] G. Hinshaw et al., Five-year Wilkinson Mirowave Anisotropy robe (WMA) Observations: Data proessing, sky maps, and basi results, Astrophysial Journal Supplement Series, 180 (009), [3] N. Jarosik et al., Seven-year Wilkinson Mirowave Anisotropy robe (WMA) observations: Sky maps, systemati errors, and basi results, Astrophysial Journal Supplement Series, 19 (011), [4] M. lank, Über irreversible Strahlungsvorgänge, Fünfte Mittheilung (Shluss), Sitzungsberihte der Königlih reussishen Akademie der Wissenshaften, 6 (1899), [5] S. Hawking and L. Mlodinow, The Grand Design. New Answers to the Ultimate Questions of Life, Bantam ress, London (010). [6] K. Shwarzshild, Über das Gravitationsfeld eines Massenpunktes nah der Einsteinshen Theorie, Sitzungsberihte der Königlih reussishen Akademie der Wissenshaften, (1916). [7] S. W. Hawking, Blak hole explosions? Nature, 4 (1974), [8] S. W. Hawking, artile Creation by Blak Holes, Communiations in Mathematial hysis, 43 (1975), [9] S. Hawking, Blak Holes and Baby Universes and Other Essays, Bantam Books, New York (1993). [10] S. W. Hawking, A Brief History of Time. From the Big Bang to Blak Holes, Bantam Books, New York (1988). [11] W. Heisenberg, Über den anshaulihen Inhalt der quantentheoretishen Kinematik und Mehanik, Zeitshrift für hysik, 43 (197), [1] V. Skalský, Cosmologial onsiderations and the speial theory of relativity, Astrophysis and Spae Siene, 158 (1989), [13] A. Friedmann, Über die Krümmung des Raumes, Zeitshrift für hysik, 10 (19), [14] A. Friedmann, Über die Möglihkeit einer Welt mit konstanter negativer Krümmung des Raumes, Zeitshrift für hysik, 1 (194), [15] H.. Robertson, Kinematis and World Struture, I, Astrophysial Journal, 8 (1935), [16] H.. Robertson, Kinematis and World Struture, II, Astrophysial Journal, 83 (1936a), [17] H.. Robertson, Kinematis and World Struture, III, Astrophysial Journal, 83 (1936b), [18] A. G. Walker, On Milne s Theory of World-Struture, roeedings of the London Mathematial Soiety, 4 (1936),

8 790 V. Skalský [19] V. Skalský, A note of the problem of hoosing a model of the Universe, IV, Astrophysis and Spae Siene, 176 (1991), (Corrigendum: V. Skalský: Astrophysis and Spae Siene, 187 (199), 163.) [0] V. Skalský, Vesmír ako fluktuáia vákua (in Slovak), (The universe as a vauum flutuation), Slovak University of Tehnology ress, Bratislava (00). [1] V. Skalský, The Wilkinson Mirowave Anisotropy robe (WMA) onfirmed the model of our observed relativisti Universe, Astrophysis and Spae Siene, 95 (004), [] V. Skalský, The model of a flat (Eulidean) expansive homogeneous and isotropi relativisti Universe in the light of the Wilkinson Mirowave Anisotropy robe (WMA) observations, Astrophysis and Spae Siene, 31 (009), 1-4. [3] V. Skalský, The model of a flat (Eulidean) expansive homogeneous and isotropi relativisti universe in the light of the general relativity, quantum mehanis, and observations, Astrophysis and Spae Siene, 330 (010), This artile is also available via the artile-id: arxiv: v1, or the link: [4] V. Skalský, The model of a flat (Eulidean) expansive homogeneous and isotropi relativisti universe and the Wilkinson Mirowave Anisotropy robe (WMA) observations, Advaned Studies in Theoretial hysis, 5 (011), Reeived: July, 011