Ari Brynjolfsson: Nucleosynthesis in plasma-redshift cosmology

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Nucleosynthesis in plasma-redshift cosmology Ari Brynjolfsson

∗

Applied Radiation Industries, 7 Bridle Path, Wayland, MA 01778, USA

Abstract The plasma-redshift cross-section is a newly discovered interaction of photons with hot sparse plasma. This cross section is derived from conventional physics by more exact calculations than those conventionally used to derive the cross section for photo-electric effect, Compton scattering, and the Raman scattering. This new plasma-redshift cross-section explains the redshift of the solar Fraunhofer lines, the intrinsic redshifts of stars, quasars, and galaxies, the cosmological redshift, the magnitude-redshift relation for supernovae Ia (SNe Ia), the cosmic microwave background (CMB), the cosmic X-ray background, and the surface brightness of galaxies. There is no need for dark energy, dark matter, or black holes. In this article we show that plasma-redshift cosmology leads to hot quark-gluon plasma at the centers of black hole candidates and super-massive black hole candidates. The conditions are similar to those surmised ad hoc in the initial phases of the Big Bang. Plasma-redshift cosmology thus explains eternal renewal of matter and primordial like nucleosynthesis. We have failed to find any need or reasonable support for the Big Bang. We find that the observed nucleosynthesis and the many other phenomena are consistent with the plasma-redshift cosmology.

Keywords: Nucleosynthesis, cosmological redshift, plasma redshift, cosmic evolution, dark energy, dark matter, black hole. PACS: 52.25.Os, 52.40.-w, 98.80.Es

1

Introduction

Many assume that the predictions of the Big Bang model compare well with the observed concentration of the light elements; see Peebles’ monograph [1]; see also Schramm [2] who states: ”The bottom line remains: primordial nucleosynthesis has joined the Hubble expansion and the microwave background radiation as one of the three pillars of Big Bang cosmology”. However, others find large discrepancies between the observations and the predictions. Quoting Thomas et al. Rollinde et al. [3] find that: ”In effect, we are faced with explaining a 6 Li plateau at a level of about 1000 times that expected from BBN”. Thus it appears that the observed values of the elements often deviate from the predicted values; and it has been difficult or not possible to explain these deviations. Spergel (see section 11.2.3 of [4]) finds that: The ”observations appear to require either a significant modification of our ideas about Big Bang nucleosynthesis or the existence of copious amounts of non-baryonic dark matter” and ”all of the proposed modifications of Big Bang nucleosynthesis (BBN) appear to violate known observational constraints”. Similar concern is echoed by the authors of the Report of the Dark Energy Task Force [5]. The report states: ”Dark energy appears to be the dominant component of the physical Universe, yet there is no persuasive theoretical explanation for its existence or magnitude. The acceleration of the Universe is, along with dark matter, the observed phenomenon that most directly demonstrates that our theories of fundamental particles and gravity are either incorrect or incomplete.” In the following, we will explain how we may be able to explain the nucleosynthesis in a fundamental different way from that based on the Big Bang hypothesis. ∗ Corresponding

author: aribrynjolfsson@comcast.net

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We have previously shown [6-12] that the newly discovered plasma-redshift cross-section, which follows from basic laws of physics, explains the redshifts of the solar Fraunhofer lines, the intrinsic redshifts of stars, galaxies, and quasars, the cosmological redshifts, including the magnitude-redshift relation for SNe Ia. The plasma redshift cross section also explains the cosmic microwave background (CMB), and the X-ray background (see sections 5.10 and 5.11 and Appendix C of [6]). We have also shown that the observed variations of surface brightness with the redshift confirm the predictions of the plasma redshift, while contradicting the predictions of the Big Bang cosmology [12]. These explanations, which are all based on the plasma-redshift cross-section have no need for expansion of the universe, dark energy, or dark matter for explaining the observed phenomena. The failure to deduce plasma redshift has also lead to failure to recognize the plasma-redshift heating of the solar corona, galactic corona, and intergalactic plasma. In light of plasma-redshift cross section, we find that contrary to general belief, the photons are weightless in a local system of reference and gravitationally repelled as seen by an observer in a distant system of reference. Photons’ weightlessness became clear when predictions of plasmaredshift theory were compared with the great many solar redshift experiments; see sections 5.1 to 5.6 of [6] and the theoretical explanation in [9]. The designs and the interpretations of the many well-executed experiments that have been used in the past to prove the weight of the photon ignored well-established laws of quantum mechanics [9] and made it impossible to see the weightlessness of the photons. No conclusion about the photon’s weight could therefore be made [9]. Many consider the existence of ”black holes” (BHs) a proven fact. We refer to these objects as ”black hole candidates” (BHCs), because we consider BHs as hypothetical and not a proven fact; see Narayan [13]. In plasma-redshift cosmology, the weightless hot photon ”bubbles” are formed at the centers of BHCs during their collapse, as we will see. This prevents formations of BHs. The very high temperatures at the centers of BHCs cause the nuclei in burned out star matter to fission into primordial matter in accordance with conventional laws of physics. The weightlessness of photons in the local system of reference is also important for explaining the high temperatures in BHCs and the nucleosynthesis. Interestingly, together with the plasma redshift cross section, the weightlessness of the photon (with gravitational mass mg = 0, while its inertial mass as before is equal to mi = hν/c2 in the local system of reference) eliminates the need for Einstein’s λ; that is, the world can be quasi static without Einstein’s λ. For the readers unfamiliar with the plasma-redshift cosmology, we recap in section 2 some of the main elements of it. In section 3, we discuss: a) why plasma-redshift cosmology has no black holes; b) the collapsars; c) the super-massive black-hole candidates (SMBHCs) at the center of our Galaxy; d) supernova SN 1987A; e) the diamagnetic moments and the jets from BHCs; and f) the gamma-ray bursts. In section 4 we summarize the major conclusions.

2

Plasma redshift of photons

In addition to the cross sections for photo-electric effect, the Compton scattering, and the Raman scattering, we have the plasma redshift cross section. This last mentioned interaction is important only in hot sparse plasma. Photons energy loss through plasma redshift is in some aspects analogous to the fast charged particles’ energy loss through Cherenkov radiation. In both cases the additional energy loss is due to the dielectric constant. But there are also differences. Most of the fast charged particles’ energy loss through Cherenkov radiation is emitted and reaches large distances, while usually only a small fraction close to the interaction site is absorbed. In case of photons, the entire plasma-redshift energy is quickly absorbed close to the interaction site. This absorbed energy, which consists of very low energy quanta, results in significant heating of the plasma. Plasma redshift of photons is also related to double and multiple Compton scattering of photons. Regular Compton scattering consists of one incident photon and one scattered or outgoing photon; but double and multiple Compton scatterings consist of one incident photon and two or more outgoing photons. When one of these outgoing photons’ frequency approaches zero, the cross section approaches infinity. Heitler [14] thought that he had solved this so-called infrared problem. He estimated that the corresponding integrated product of the outgoing low-frequency photons’ energies

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and cross sections is small, or approximately 1/137 of the regular Compton cross section. This is usually correct in ponderable matter, gasses, and in laboratory plasmas. But Heitler overlooked the fact that when the incident photon penetrates very hot and very sparse plasmas, the very soft part of the spectrum of the outgoing photon will interact simultaneously with great many electrons in the plasma. The plasma redshift is about 50 % of the regular Compton cross-section multiplied by the photon energy. We call this energy loss of the incident photons ”plasma redshift”, because it occurs only in very hot and sparse plasma. The deduction of this plasma redshift and the necessary conditions for plasma redshift are given in sections 1 to 4 and in Appendix A of [6]. The results of the calculations are given by Eqs. (18) and (20) and Eq. (28) of that source, and are summarized in Eqs. (1) and (2) below.

2.1

Predictions of plasma redshift

The plasma redshift is given by ln(1 + z) = 3.326 · 10

−25

Z

R

Ne dx + 0

γi − γ0 , ξω

(1)

where Ne is the electron density in cm−3 and x is in cm. γi is the initial quantum mechanical photon width (half-width at half maximum in the Lorentz distribution for the line intensity. Lorentz distribution is the same as the Breit-Wigner distribution in nuclear physics or Cauchy distribution in mathematics). In the Sun, the Lorentzian form of the line dominates the Gaussian form of the line beyond about three half-widths. This has been used for experimental determination of the Lorentzian width of the solar photons. The variations in the photon width, γi , are due to variations in both the intrinsic photon width and the pressure broadening, which includes the Stark broadening. The classical photon width is γ0 = 2e2 ω 2 /(3me c3 ) = 6.266 · 10−24 ω 2 ; where ω is the center frequency of the incident photon. For the frequency range of main interest, we have that ξ ≈ 0.25.

2.2

The plasma-redshift cut-off

The plasma redshift is significant only when the plasma densities are low and the plasma temperatures high. This is the main reason why the plasma redshift was not discovered long time ago. Plasma physicists were usually dealing with relatively dense and cold laboratory plasmas. Plasma redshift is possible only if the following condition is fulfilled 2 T 5B √e ˚ A, (2) λ ≤ λ0.5 = 318.5 · 1 + 1.3 · 10 Ne Ne Angstr¨om units, B is the magnetic field in where λ is the wavelength of the incident photons in ˚ gauss units, Te is the electron temperature in degrees K, and Ne is the electron density in cm−3 . Accordingly, the plasma redshift is not possible in conventional laboratory plasmas or in the reversing layer and the chromosphere of the Sun, because the densities are too high and the temperatures too low.

2.3

The cosmic microwave background

The cosmic microwave background (CMB) is emitted by the intergalactic plasma. According to Eq. (1), the plasma-redshift absorption is κpl = 3.326·10−25 (Ne )av cm−1 . The absorption coefficient is independent of the incident photon’s frequency as long as the frequency exceeds the cut-off given by Eq. (2). From the observations of the supernovae Ia, we obtain Ne = 1.95 · 10−4 cm−3 . This corresponds to one Hubble length LH = c/H0 = 1/κpl = 1.542 · 1028 cm ≈ 5, 000 Mpc. The emission corresponding to the plasma-redshift absorption turns out to be the CMB. The plasma-redshift absorption is more than million times greater than the conventionally used free-free absorption at the CMB frequencies; see Appendix C of [6]. The dominance of the plasma-redshift absorption explains the beautiful blackbody spectrum of the CMB.

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Within the blackbody cavity with a radius of LH = 1/κpl ≈ 5, 000 Mpc, the corresponding blackbody radiation has a temperature obtained by equating in this case the radiation pressure with the plasma pressure. We have (for details; see section 5.10 and Appendix C of [6]) 4 a TCM B = 3N kT,

or

TCM B =

3N kT a

1/4 = 2.73 K,

(3)

where a = 7.566 · 10−15 dyne cm−2 K−4 is the Stefan-Boltzmann constant and k = 1.38 · 10−16 is the Boltzmann constant. TCM B is the temperature of the CMB radiation. The value of TCM B = 2.73 K, shown on the right side, is for N = Np + NHe++ + Ne = 1.917Ne and Ne = 1.95 · 10−4 cm−3 , and T = 2.7 · 106 K. The value of Ne is obtained from the measurements of the magnitude-redshift relation for supernovae SNe Ia. The good fit along the entire redshift range between the predicted and the observed magnitude-redshift relation [6, 11] for supernovae supports the contention that the density is correct, because otherwise the Compton scattering would cause the fits to deviate [6, 11]. The particle temperature T can be obtained independently from the measured X-ray background. The CMB has a well-defined blackbody spectrum, because plasma-redshift absorption is about 106 to 1014 times greater than the usually used free-free absorption . The plasma-redshift absorption determines the emission spectrum; see section C1.4 of Appendix C in [6]. The plasma around the galaxies and galaxy clusters have higher plasma densities and the product of Ne T ≈ Ne Te is higher due to the gravitational attraction. The peak of the CMB spectrum shifts therefore slightly towards higher temperatures in direction of clusters such as the great attractor. This shift in the peak of the CMB is seen also in the direction of the Galactic center plane. This perturbation from distant galaxies and galaxy clusters is rather small, because of the large Hubble length, LH = 1/κpl ≈ 5, 000 Mpc, and limited angular resolution.

2.4

Weightlessness of photons

Most important for the explanation of the renewal of matter and many phenomena associated with BHCs is the fact that the photons are weightless in a local system of reference (where the observer and the photons are), but repelled in a reference system of distant observer, such as an observer on Earth looking at photon experiments in the Sun or close to a BHC. This gravitational repulsion of photons cancels the gravitational redshift, when the photons emitted in the Sun are observed on Earth. This most remarkable discovery (because it contradicts general opinion) was made when the predicted plasma redshift, based on the known electron densities and photon widths in the solar corona, was compared with measured solar redshifts; see sections 5.6.1, 5.6.2 and 5.6.3, and Fig. (4) in reference [6]. The weightlessness of photons is theoretically unrelated to the plasma redshift. But only when comparing the observed solar redshifts with the theoretical predictions of the plasma redshift became it clear that the solar redshifts, when observed on Earth, are not caused by Einstein’s gravitational redshift. The great many other experiments that were believed to show that photons had weight have, due to disregard for the uncertainty principle, all been interpreted incorrectly. The details of the theoretical explanation of photons weightlessness are given in reference [9]. The weightlessness of photons is a fundamental discovery that has great consequences for cosmology. It eliminates the need for BH and Einstein’s Λ, it facilitates the explanation of the eternal renewal of matter, and it modifies, but does not destroy, the theory of general relativity; see [9].

2.5

The conservation of energy

In plasma-redshift cosmology, the energy is conserved at all times. In Big Bang cosmology the energy is not conserved. Instead, it may disappear into a black hole, or it may be created out of nothing in form of a variable dark energy. For illustrating the conservation of energy, let us consider a particle with mass m0 . At a large distance from a BHC, its rest energy is Eo = mo c2 = hνo , where c is the velocity of light and νo the frequency of the corresponding photon. When this particle falls, it transfers its change in

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gravitational potential energy, δE, to its surroundings in form of heat. The total rest energy of this particle at the lower gravitational potential is then m c2g = ε mo (c/ε)2 = mo c2 /ε = hνo /ε = hν, where ε = 1 + zg (see Møller’s Eq. (8.73) and Eq. 10.84 in [15]). When the redshifted photon returns from the lower potential to the original position, its redshifted frequency and energy hν = hνo /ε is reversed (blue shifted) resulting in energy equal to hνo to cancel the gravitational redshift. The BHC (or the star) pushes the photon outwards. In doing so it returns the energy δE to the photon. This shows that the energy is conserved in the present plasma-redshift theory. In the conventional theory, the photons redshift is not reversed, and the energy is not conserved. This underscores the beauty of the plasma-redshift cosmology.

2.6

Black holes in Big Bang cosmology

In the conventional Big Bang cosmology masses and all forms of energy have a gravitational mass. It can then be shown that objects should be formed that are so massive that nothing can escape them, not even light. These objects are called black holes (BHs). These bodies cannot emit blackbody radiation and their blackbody temperature must be zero, as seen by a distant observer on Earth. Nevertheless, the gravitational field and angular momentum is assumed to escape and affect surrounding objects. Principally, the time inside the BH can not be defined and the phenomena inside the BH appear beyond the realm of classical physics. However, close to the BH limit, the quantum mechanical uncertainty principle could play a role. Stephen Hawking has conjectured that due to the uncertainty principle in quantum mechanics some radiation could be emitted. This Hawking radiation from a black hole with a mass M has a blackbody temperature given by T =

¯hc3 M

K, ≈ 6.1 · 10−8 8πGM kB M

(4)

where M is the solar mass, kB the Boltzmann constant, G the gravitational constant, ¯h the Dirac constant, and c the velocity of light. This equation shows that the temperature T is very low unless the mass M is very small. The Hawking radiation has never been experimentally confirmed, nor has the existence of a BH ever been confirmed. According to Narayan [13], the black hole candidates (BHCs) are believed to have masses M greater than 3M to 5M . X-ray binaries appear to have BHCs with masses on the order of 5M to 10M ; and centers of galaxies are believed to have BHCs on the order of 106 to 109.5 times M .

3

Nucleosynthesis in plasma-redshift cosmology

This section shows that when the mass of a collapsar increases beyond about 3 solar masses, the collapsar does not form a BH, as usually conjectured. At the center, it forms instead a dense weightless photon ”bubble” that prevents the formation of a black hole and facilitates primordial like nucleosynthesis. The photon ”bubble” is surrounded by hot layers of quark-gluon plasma, then hot neutron layers followed by layers of hot and dense proton-electron plasma.

3.1

No black holes in the plasma-redshift cosmology

In the general theory of relativity (GTR), the gravitational time dilation and the redshift are both given by; see Møller’s Eqs. (8.114), (10.62) and (10.65) in [15] dt = r p

dτ 1−

2 G M/(R c2 )

− γι

2

uι /c

= ε dτ , −

(5)

u2 /c2

where the proper time τ is the time measured by an observer following the particle; and t is the time measured by a distant observer far away from the gravitating body. ε = (1 + zgr ) is the GTR

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factor replacing the transversal Lorentz factor (1 − u2 /c2 )−1/2 in special theory of relativity (STR). We have that λgr ε = (1 + zgr ) = (6) λ0 where zgr is the expanded gravitational redshift in Big Bang cosmology, which besides the usual gravitational redshift includes modification by the particles movements, as given by Eq. (5). When the reference system is not rotating, γι = 0, Eq. (5) takes the form dt = p

dτ 1 − 2 G M/(R c2 ) − u2 /c2

(7)

−1

where G = 6.673 · 10−8 cm3 g s−2 is Newton’s gravitational constant. The mass M of the BHC is defined from gravitational field when the radius R is large; and u is the velocity of the particle. For u ≈ 0, this equation is valid for 2GM/(Rc2 ) < 1. Eq. (7) is then valid for R > RS ≈

2GM M = 1.485 · 10−28 M = 2.95 · 105 cm . c2 M

(8)

where RS , the Schwarzschild radius of the BHC. When R approaches this limit, the time increment, dt, approaches infinity, and the frequency of light, the energy and the temperature approach zero. Besides the velocities and thermal motions, electrical and magnetic fields can also affect the limit. The limiting conditions for the different particles in the BHC have therefore a broad distribution. The gravitational field affects not only time as in Eq. (5). At a point P the rest mass m = m0 ε, the velocity of light c = c0 /ε, the frequency ν = ν0 /ε,, the photon energy hν = hν0 /ε, and the spatial dimensions. The rest-mass energy, as seen by a distant observer, is given by mc2 = (m0 ε)(c0 /ε)2 = m0 c20 /ε. The conservation of energy is valid at all times so that Ekin = (Ekin )0 /ε. We see thus that Ekin = (Ekin )0 /ε = (m0 c20 − mc2 ) = m0 c20 (1 − 1/ε),

(9)

which for ε 1 is close to m0 c20 . In a local system of reference at rest at P, we have thus that (Ekin )0 = εEkin = εm0 c20 − m0 c20 ,

(10)

which for large ε is much larger than the rest energy of the particle. Close to the center of the BHCs the very hot matter will transform therefore into photons, which are weightless. This conclusion does not require that ε = (1 + zgr ) is given by expressions in Eq. (5) and (7). This is important because the concept of a point mass may not have a real physical meaning. In quantum mechanics, the mass particle is always contained in a finite volume. Also, in plasma-redshift cosmology, the photons weightlessness means that the gravitational mass is not conserved when the mass changes to photons or photons change to mass. We have that the photon’s gravitational mass mg = 0, while its inertial mass is mi = hν/c2 . The limiting radius of the BHC will often be inside the collapsar; and it may therefore be difficult to define M and R. For interpreting Eqs. (9) and (10), we only require that ε increases towards the center of the BHC. The nuclear fusion, fission, and binding energies are insignificant, or less than 1 % of the rest-mass energy. The initial heating close to the singularity is therefore about equal to the rest-mass energy. All the equations in plasma-redshift cosmology are the same as the conventional equations. The difference is only the weightlessness of photons, and the way the photon frequency varies when the photon moves from the gravitating body (such as the Sun) outwards to a distant observer (for example on the Earth). In plasma-redshift cosmology, the photon frequency increases and cancels the gravitational redshift during the photon’s travel outwards (see section 2.6 above), while according to Einstein’s GTR the photon’s gravitationally redshifted frequency stays constant as the photons move outwards, for example, from the Sun to the Earth. Had Einstein known that the photons are weightless, he would never have introduced his cosmological constant λ, because the photons weightlessness in the local system of reference (repulsion in distant system of reference) eliminates the need for Einstein’s λ.

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The plasma-redshift cosmology accepts the conventional assumptions of physics, which demand that the energy is conserved at all times, and that the time t in Eq. (5) is real at all times. Therefore, in plasma-redshift cosmology we cannot have a black hole. Eqs. (9) and (10) show how the plasmaredshift cosmology can easily deny the existence of a black hole. From Eq. (8) we get that the average gravitational mass density ρg within a sphere with radius R must at all times in the local system of reference meet the condition that ρg · R2 < 1.6076 · 1027 g cm−1 .

(11)

When the product ρg · R2 approaches the limit 1.6076 · 1027 , at least some of the gravitational mass must convert into weightless photons. This prevents formation of a BH. Eq. (11) must be valid throughout the universe. On the other hand, in the Big Bang cosmology, the value of ρg · R2 may be equal to or exceed this limit, which results in a BH. Important is also the fact that when a particle with rest mass m0 moves from infinity to the surface of a BHC, the kinetic energy gained is not equivalent to the potential energy difference between the infinity and the surface, as usually believed. Instead, the total gain in kinetic energy is about equal to the particle’s rest-energy m0 c2 . It is as if the particle had fallen all the way to the brink of a BH. This correction of the conventional calculations is important, because it significantly increases the heating at the center of the BHC. This rule applies to collapsars with the hot photon bubbles at their centers. The weight of the particle at the surface will squeeze the mass of the collapsar to release, mostly close to the center of the BHC, a total energy close to m0 c2 . The accretion of matter may easily lead to growth of the BHC to SMBHCs. Before any large mass unit, such as an iron nucleus, transforms into photon energy, it usually will fission into hadrons, such as protons and neutrons, which in turn may fission into the fundamental particles, such as the quarks, the antiquarks, and the leptons (which include electrons (e), muons (µ), and tau particles (τ , ) and their antiparticles and the corresponding neutrinos), and the bosons (which include photons, gluons, Z-bosons, and W-bosons). The fission and fusion energies of nuclei amount to a small fraction of the rest-mass energy, or usually less than about 1 %. This is consistent with experiments, such as the Relativistic Heavy Ion Collider (RHIC) experiments at Brookhaven National Laboratory; see Shuryak [16]. The deconfinement of the quark matter occurs at temperature on the order of 170 MeV [16, 17, 18], or at about 192 MeV, as some other estimates indicate, see Cheng [19]. The transformations and heating will absorb most of the energy, which in the conventional Big Bang theory was assumed to disappear into the black hole. This hot quark-gluon plasma emits weightless photons [20, 21, 22, 23, 24, 25, 26]. The quarks and the leptons are fermions and are therefore governed by the Pauli exclusion principle. Identical fermions are pushed apart and therefore outwards. The photons, which are bosons, are not governed by the exclusion principle. They will then separate from the fermions and be squeezed inwards and concentrate at the center of the BHC. The gluons, Z-bosons, and W-bosons usually stay close to the quarks and the leptons. The weightless photons at the center of the BHC eliminate the black hole singularity in Eq. (5), because at the surface of the photon bubble the gravitational attraction is zero.

3.2

Collapsars

A large, burned out star will reach a point when the thermal pressure of the particles can no longer balance the gravitational attraction. The star will then shrink. However, even when all fusions cease, the exchange interactions between the identical fermions often can counter balance the gravitational attraction. Initially, the electrons (having the smallest mass) set the limit and prevent the collapse if the star mass M is less than about 1.4 M , the maximum mass for a white dwarf. If M increases beyond this limit, the star collapses further to a neutron star. In turn, the exchange interactions between the neutrons cannot prevent a collapse to a BHC if the mass exceeds about M ≈ 2.5 M . The Big Bang cosmologists assume therefore that the BH do exist, because the physical laws, as they know them, can’t circumvent their formation. In the plasma-redshift cosmology, on the other hand, the formation of the BH can be circumvented, as we saw in previous section. When the collapsar is large enough to form a BHC, the temperature at its center is high enough to transform the mass into photons. The exchange interactions, which

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involve identical fermions in the quark-gluon plasma layer and in the neutron layer, push the the fermions outwards, and squeeze thereby the photons (which are unaffected by the exchange forces) inwards. The weightless photons, which are bosons, collect therefore at the center of the BHC and prevent thereby the formation of the BH. The physics for collapsar below the mass limit for BHC is in plasma-redshift cosmology nearly identical to the physics in conventional Big Bang cosmology. We can then in plasma-reshift cosmology use the conventional models that have been used to describe the neutron stars and pulsars in Big Bang cosmology. For example, for a non-rotating neutron star with mass M ≈ 1.4 M , we can use the equation of state assumed by Akmal et al. [27], as modified by Olson [28], or by Kratstev and Sammarruca [29]. A neutron star with density equal to the normal nuclear energy density, which is about 153 MeV fm−3 or 2.73 · 1014 g cm−3 , would have a partial (along each axis) pressures of about px = 1.27·1033 dyne cm−2 . The energy density at the center of a 1.4 M star with radius of about 12.7 km will be about 317 MeV fm−3 , corresponding to a mass density at the center of 5.65 · 1014 g cm−3 . The corresponding partial pressure at the center would be px = 2.44 · 1034 dyne cm−2 ; see [28]. Akmal et al. [27] believe, based on laboratory experiments, that the neutron star becomes unstable when its mass increases and approaches M ≈ 2.2 M . They set an upper limit of M ≈ 2.5 M . Laboratory experiments make it likely that at the centers of such stars, matter transforms to quarkgluon plasma [29]. These predictions are crude but consistent with observations [29, 30, 31, 32]. They are also consistent with plasma-redshift cosmology, because we may have that in the transition zone 1.8 M ≤ M ≤ 2.5 M , a quark-gluon plasma is formed that emits and transforms into photons, which form a bubble that prevents any part of the star from reaching the black-hole limit. A small bubble has only a small effect on the conventional equations of state. The state will depend on the rotation. For a crude overview, we may use as a guide the models for ”Fast rotation of strange stars” developed by Gourgoulhon et al. [33]. From their estimates and their figures 2 and 4, it is clear that the star stretches in the equatorial direction as the rotation increases. When the surface at the equator exceeds the limit for bound orbit, the star loses mass at the equator. Such a BHC may accrete mass and the bubble at the center will grow. The bouncing back and forth across the bubble gradually reduces the angular momentum, and the BHC may grow into a slowly rotating super-massive BHC (SMBHC). The photons being bosons can be compressed at will. The photon bubble, which following the initial collapse is heavily compressed, will therefore bounce back. Some of the energy can result in a supernova eruption, some of it may be released in form of primordial plasma and some in a gammaray burst, confer SN 1987 A. Most important change from conventional physics is that collapsar will have a hot photon bubble at its center, which is surrounded by quark-gluon plasma, then neutron layers, and proton-electron plasma layers. The transition between the different layers is gradual; for example, mainly the outer layers of the photon bubble will be mixed with quark-gluon plasma.

3.3

SMBHC at the center of our Milky Way

Every galaxy is believed to contain a supermassive black hole candidate (SMBHC) with a mass often in the range of 106 to 3 · 109 solar masses. In our Galaxy the SMBHC in Sgr A∗ with mass of about M ≈ 3.7 · 106 M has been exceptionally well studied [34 - 42]. With help of inflation, dark energy, and dark matter many phenomena appear to confirm to the expectations of the Big Bang cosmologists. One of the phenomena that has been difficult to understand is the youth of the stars, such as, O8-B0 main sequence stars with masses of about 15 M

and ages less than 10 million years, in the immediate surroundings of the SMBHC [34, 35, 42]. Plasma-redshift cosmology indicates that BHCs and SMBHCs are very hot. The density in the photon bubble and in the surrounding quark-gluon plasma decreases as the BHCs grow. But the temperature in the photon bubble at the center surrounded by quark-gluon plasma will still be very high, and will exceed about 192 MeV, or 2.2 · 1012 K. Outside the quark-gluon plasma and the neutron layers, the electron-proton plasma is also very hot. In the inner layers all the heavier nuclei will have fissioned into protons and neutrons. The temperature of the outer layers decreases gradually. When the temperature decreases below about 15 MeV in the outer layers, some fusion can take place; first, with formation of helium and then lighter elements. Different disturbances can

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lead to release of high density primordial matter from the SMBHC at the center of our Galaxy. Such matter can result in star formation close to the Galactic center. Plasma redshift gives thus a natural physical explanation of the observations of youthful stars at the center of our Galaxy. Interestingly, the very high temperatures and densities in some of the layers of the SMBHC may lead to spallation and to formation of 6 Li and other isotopes that Big Bang scenario had difficulties in explaining. The observed dimness and infrared emission from the SMBHC at the Galactic center has also been difficult to explain; see [34 - 38]. In plasma-redshift cosmology, the plasma-redshift cross-section dominates the absorption and emission processes in the very hot coronal like plasma surrounding the SMBHCs. The black body emission temperature, Tbbem , from the fully ionized plasma around a SMBHC is given by Eq. (3) or 4 a Tbbem = 3N kT = 5.75Ne kT K,

(12)

where a = 4σ/c = 7.566·10−15 dyne cm−2 K−4 is the Stefan-Boltzmann constant and k = 1.38·10−16 is the Boltzmann constant, and N ≈ 1.917Ne . In the outermost corona, the densities may be Ne ≈ 4.6 · 104 cm−3 and the particle temperature T ≈ 2 · 106 K. The emission temperature is then Tbbem ≈ 100 K. For Ne ≈ 4.6 · 106 cm−3 and the particle temperature T ≈ 4.4 · 107 K. The emission temperature is then Tbbem ≈ 1000 K. If the emission areas have a radius of about 7.5 · 1015 cm and 7.5 · 1013 cm, respectively, the emitted energy would be about 1036 erg s−1 , as observed. These outer reaches of the corona are transparent to optical light. The limb effect and the variation of Ne and T with depth complicate the estimates. In addition, we must take into account synchrotron radiation, which increases the luminosity at frequencies around ν ≤ 1012 s−1 . These examples serve therefore only as rough indicators. Without going into elaborate details, however, they indicate that the plasma-redshift cross-section can explain the observed low-energy emission, which is about 1036 erg s−1 . In Big Bang cosmology, it is often assumed that the BHCs and the SMBHCs are relatively cold (mainly because the hot matter and energy are sucked into the BH). The low emission is often explained as due to low surface temperature. It was difficult therefore to explain the large X-ray flares often observed. Plasma-redshift cross-section dominates in the sparse outer layers of the corona. But in the deeper and denser corona the free-free emission and absorption may dominate at the higher temperatures and higher (X-ray) frequencies, because plasma redshift is proportional to Ne , while the free-free emission is proportional to Ne2 . Just like in the Sun we often have eruptions usually initiated (like in the Sun) by a strong magnetic fields which lower the plasma redshift cut-off frequencies, see Eq. (2). The cut-off region for these frequencies may then penetrate deep into the corona. Once the additional plasma redshift heating starts in these deep layers, the conversion of magnetic field energy to heat kicks in and augments the plasma-redshift heating and makes it explosive. (The physics of the solar flares are described in section 5.5 of reference [6], and the relevant free-free emissions and absorptions in Appendix C1 and C2 of that source.) Plasma-redshift cross-section gives thus a rather simple explanation of these difficult to explain observations of X-ray flares. The observations of the Galactic center are consistent with a SMBHC with a hot (about 192 MeV, or 2.2 · 1012 K) photon bubble at its center, which is is surrounded by quark-gluon plasma, neutron layers, and layers of electron-proton plasma corona, as predicted by the plasma-redshift cosmology. In the deeper layers of the SMBHC the temperature is so high that no heavy nuclei exist. Instead, we have a large reservoir of primordial matter at the center of the SMBH.

3.4

SN 1987 A

The excellent phenomenological descriptions of the collapse of Sanduleak −69◦ 202, a B3 I star, to form SN 1987A in a Type II core-collapse explosion show many phenomena that are at odds with that expected, as pointed out by Panagia [43], who is one of those that has studied this subject thoroughly. He writes: ”The early evolution of SN 1987A has been highly unusual and completely at variance with the wisest expectations.” The collapse of such a large star, M ≈ 20 M , was expected to result in a BH, but we see no indication of that. But the plasma-redshift cosmology gives a natural explanation. It suggests that

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before the limit of BH is reached, the matter transforms into weightless photons at the center of the collapsar. These weightless photons prevent formation of a BH. The collapsed SN 1987 A showed very fast brightening (within one day) and the fast decay of that ultraviolet flux; but no good physical explanation could be given But in plasma-redshift cosmology a huge pulse of brightness must follow immediately after the collapse. A star with mass of M ≈ 20 M , will during the collapse release at the center of the collapsar a large fraction of the gravitational potential energy in form of a thermal energy. A fraction of that energy transforms into photons that form a hot bubble at the center of the collapsar. Due to the fast rotation, the bubble will be thrown outwards and form a torus close to the periphery of a flattened disk. The photons may concentrate in one or more swellings along the torus. Due to rotational stresses, the enclosure around the torus is likely to burst and release some of the high-energy photons. These photons will interact with the quark-gluon plasma, the neutrons, and the proton-electron plasma on their way out and release hot primordial matter together with the high energy photons. This sudden release of primordial matter and intense high-energy photons will fall-off fast, as the pressure in the bubble decreases. The relatively short pulse of high-energy photons interacts with circum-stellar matter by producing huge amounts of electron-positron pairs, which also contribute to the ionization and excitation of the circum-stellar matter. This produces the light echoes and rings as suggested by Panagia [43]. Why the low luminosity following the relaxation of the initial brightness? Some of the primordial matter that gushes out will cover up the collapsar with hot electron-proton plasma. The Compton scattering and absorption in this hot and dense electron-proton plasma reflects and absorbs the high energy radiation from inside the collapsar. When relaxed after the initial pulse, the outer most layers of the plasma will cover up the BHC, and will emit infrared radiation that thermally insulates the BHC; see Eq. (12) in subsection 3.3. This equation explains why the luminosity is many orders of magnitude smaller than that from a hot excited atomic and molecular matter. We often see reference to barium and nickel lines emitted from the collapsar. I believe that these lines are from the pre-collapse surroundings and not from the proper collapsar, which consists mainly of primordial and youthful matter. How were the rings formed? Usually, it is assumed that the inner and outer rings are left over debris from explosions in the blue giant when it was a red giant. In the plasma-redshift cosmology this may be a correct explanation, but a modification of this conventional explanation may also be possible. Plasma-redshift cosmology shows that all stars must have a corona. Plasma-redshift initially transfers the energy loss of photons to the electrons [6], which then ionize the atoms. The sphere of ionization stretch far beyond the conventionally estimated Str¨omgren radii. All stars have plasma spheres analogous to the heliosphere. The radius of the heliopause is on the order of 2.2 · 1015 cm; see Fig. 5 of Opher et al. [44]. Plasma-redshift heating causes the radius of the plasma sphere around stars to increase with their luminosity. Sanduleak-690 202 had a luminosity of L ≥ 105 L , see Nathan Smith [45]. For interstellar densities and magnetic fields similar to √that in the solar neighborhood, we expect the radius of the star’s plasma sphere to be in excess of 105 = 316 times that of the Sun, or in excess of about 7 · 1017 cm. The radius to the colder and denser layers outside the plasma sphere is likely to be about 1.3 to 1.6 · 1018 cm, which is about equal to the distance to the outer rings of SN 1987, as determined by Panagia [43]. Many other factors affect the estimated radius, such as the direction and intensity of the magnetic field, the density and pressure of the interstellar matter, and the motion of the star relative to the interstellar medium. This is therefore a crude estimate. It merely makes the formation of the matter around SN 1987-690 202 reasonable without any particular explosions. Plasma redshifts initiates large flares in the Sun [6]. Similar flares are likely to be initiated, especially in large stars like B3 Ia star Sanduleak 690 202. These flares carry large amount of matter into the far reaches of the corona, especially, along the center plane of the rotation. This may explain the inner ring. Very intense high-energy photon beams will stream out through holes or ruptures in the swellings on the torus at the end of the collapse. The torus is unlikely to be uniform with photon bubbles concentrating in swellings at one or more places. Due to the centrifugal forces, the torus is likely

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to rupture a few places, especially in the equatorial plane, but it may also rupture at one or more places along the ridge of the torus. The fast rotation will spray a beam in a circle. This is suggested only as a possible explanation of the ring formation. The rings may diffuse and cool down and become dust rings, as confirmed by Bouchet et al. [46]. Most of the very high-energy photons and high energy particles released in the initial flash were not (and due to lack of proper instrumentation could not be) detected. The low grain temperature, about 166 K, observed by Bouchet et al. [46] does not conflict with the much higher, about 2 · 106 K, temperature in line forming elements observed by Gr¨oningsson et al. [47]. We see thus that plasma-redshift cosmology gives a reasonable physical explanations of many of the phenomena around SN 187 A. Many of these phenomena could not be easily explained in the Big Bang cosmology.

3.5

Diamagnetic moments and plasma jets from BHCs

In plasmas, the diamagnetic moments created by the charged particles encircling magnetic field lines are strongly coupled and oppose the magnetic field. On the average, the energy density of the field is about equal to the kinetic energy density of charged particles. When the magnetic field moves with the plasma from hotter region to a colder region, the energy density of the field usually exceeds the kinetic energy density of the particles. The plasma-redshift heating reverts then the magnetic field energy to heat, just as it does in the solar atmosphere; see subsection 5.5 and Appendix B of [6]. In and above the photosphere this energy conversion may cause solar flares like eruptions and hot bubbles. Plasma-redshift together with the magnetic field thus creates hot bubbles with denser plasma (or even ”clouds”), on the surface of these hot bubbles. The dense plasma may leak due to gravitation into the SMBHC, just as high velocity clouds leak into the Galaxy [6]. In the solar corona, we also have plasma-redshift heating push matter into arches. The condensed plasma leaks down both ends of these arches back into the Sun. These processes are the main source of accretion onto SMBHC. Divergence in the magnetic field accelerates the charged particles outwards. In Appendix B of [6], we show (see Eq. B9 of [6]) that the force, FP , on a charged particle at a point P is given by FP =

n m vP2 , 2 RP

(13)

which is independent of the magnetic field strength. The particle’s velocity, v⊥ , at right angle to the field is given by BP 2 v⊥ = vP2 , (14) B where the magnetic field B at the point P decreases outwards as n RP B = BP , (15) R The force given by Eq. (13) pushes the diamagnetic dipole of the charged particles outwards. Especially in the very hot plasma around the BHC, the value of vP2 may exceed GM/Rc , where Rc is the distance of the point P from the gravitational center, and M is the gravitational mass inside P . The force FP pushing the diamagnetic moment outwards may therefore exceed the gravitational attraction. The energy gained can exceed 1020 eV. We find it likely that this accounts for the fast jets often seen being pushed outwards from BHC. It may even account for the highest energy cosmic rays. These jets are fed mainly by the hot proton-electron plasma surrounding the BHC. Plasmaredshift cosmology thus gives a natural physical explanation of the jets seen streaming away from many BHC and SMBHC.

3.6

Gamma-ray bursts

As we have seen, the photon bubbles in large BHCs come in many sizes. Many triggers, such as passage of a star close the BHCs, can initiate an outburst. When the fragile containment opens up

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and releases the photons from the center, the photons may not have time to react with the quarkgluon plasma, the neutron layers, or the electron-proton plasma surrounding the BHC. A BHC may then suddenly release photons equivalent to a small fraction or a large number of solar masses. Such gamma-ray bursts therefore come in many sizes. A quiescent SMBHC at the center of our Galaxy releases the primordial matter and the photons usually in smaller bursts. Initially, the high energy photons interact with matter mainly by producing electron-positron pairs. The characteristic 511 keV annihilation line observed mainly in the galactic center is a clear indicator of this. The often surmised positron decay of isotopes seem inadequate for explaining the large intensities reported by Weidenspointner et al. [49]. Without the present plasma-redshift cosmology, it is difficult to explain the observations. This appears to be still another confirmation of plasma-redshift cosmology.

4

Summary and conclusions

The plasma-redshift cross section is not hypothetical, as it is derived theoretically from conventional laws of physics without any new assumptions. It explains great many cosmological phenomena that in the conventional Big Bang cosmology defied physical explanations. 1. Plasma redshift explains the solar redshift, the cosmological redshift, and why all stars, galaxies and quasars have intrinsic redshifts, due to the fact that when a photon penetrates a hot sparse plasma, it is redshifted in accordance with Eq. (1) and (2) ; see the deduction in [6]. Plasma redshift also explains the heating of the solar corona, the galactic coronas, and the intergalactic space. The energy the photons lose in the plasma redshift is absorbed in the plasma and transformed into heat [6]. 2. The cosmological redshift is not due to expansion as assumed in the Big Bang cosmology, but to plasma redshift of photons in intergalactic plasma with average temperature of 2.7 · 106 K, and electron density of 2 · 10−4 cm−3 . Plasma redshift explains the observed magnitude-redshift relation for supernovae Ia without any expansion, dark energy, or dark matter [6, 7, 11, 12]. 3. Big Bang cosmology assumes cosmic time dilation. Perusal of the experiments, which were thought to prove cosmic time dilation, shows that the proofs are invalid [6, 7, 11]. Consistent with all observations, the plasma-redshift theory shows that there is no cosmic time dilation. 4. According to the Big Bang cosmology, the cosmic microwave background (CMB) originated in a plasma at a redshift of about z = 1400 [1]. In contrast to this, plasma-redshift cosmology explains that the CMB with its beautiful blackbody spectrum is emitted from the intergalactic hot plasma without any expansion; see subsection 5.10 of [6]. The required average density and average temperature are exactly the same as those required to explain the cosmological redshift and the X-ray background; see subsection 5.11 and Appendix C of [6]. 5. In the Big Bang cosmology, we cannot explain the X-ray background, because the intergalactic space is assumed cold and practically empty. In plasma-redshift cosmology, the observed X-ray background follows from the same densities and temperatures of the intergalactic plasma as those needed to explain the cosmological redshift and the microwave background radiation; see subsection 5.11 of [6]. 6. Scrutiny of solar experiments shows that most of the redshifts, when observed on Earth, are not due to the gravitational redshifts, but are due to the plasma redshifts given by Eq. (1) and (2); see [6] and [9]. 7. The experiments in laboratories and in space that have been assumed to prove photons gravitational redshift did not allow adequate time for the change in photons frequency. Heisenberg uncertainty principle shows that the time difference between emission and absorption of the photons was too small for the given potential difference. The experiments were therefore incorrectly designed and the observations incorrectly interpreted [9]. The plasma redshift shows clearly that the photons redshift is reversed when they move from the Sun to the Earth [6].

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This reversal of the gravitational redshift means that the photons are weightless in the local system of reference, but repelled by the gravitational field in the reference system of a distant observer; see [9]. 8. The weightlessness of photons shows that Einstein’s equivalence principle is wrong [9]. The gravitational mass, mg = 0, of a photon is not equivalent to its inertial mass, mi = hν/c2 . The enormity of this finding for gravitational theory should be appreciated. Presently, we modify the equivalence principle to apply always, except to photons (possibly to all elementary bosons). 9. When a mass particle approaches the BH limit of a BHC or a SMBHC, its kinetic energy, in the local system of reference (see Eq. 10), may exceed significantly its rest mass energy. Mass then converts to photons that accumulate at the center of the collapsar due to repulsive forces on the fermions. The weightless photons at the center prevent the formation of a BH. 10. Time is described with a real number everywhere and at all times, because there are no black holes; see subsection 3.1. The problem of ever-increasing time and ever-increasing entropy is resolved when we realize that we are usually observing only one half of the material-photon cycle. We usually focus on the physical changes from creation of matter through its changes (which define the time) towards burned out stars and their transformation in large BHCs, while often disregarding the other half of the time cycle; the creation of photons and their transformation to matter in an ever lasting renewal process. 11. Although the universe is quasi-static, infinite and ever lasting there is no Olbers’ paradox. The reduction of the light intensity in the plasma-redshift absorption resolves this problem; see [6]. 12. In the Big Bang cosmology, the stars will run out of energy and will have a finite lifetime. Plasma-redshift cosmology by contrast leads to eternal renewal of matter and stars, as we have seen in this article. The plasma-redshift cosmology leads to transformation of burned out matter to photon bubbles at the centers of BHCs and SMBHCs. The hot photon bubbles and the hot centers of BHCs and SMBHCs lead to renewal or recreation of primordial matter. This primordial matter leads to the nucleosynthesis and to formation of new stars for ever. We have demonstrated that plasma redshift, which is based on fundamental and basic conventional physics without any new or additional assumptions, leads by necessity to renewal of matter in BHC and thereby to fundamental changes in our cosmological perspective.

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