Ari Brynjolfsson Plasma Redshift Cosmology Theory by Ari Brynjolfsson

Website for

Plasma Redshift Cosmology A new cosmology, which is radically different from the conventional big-bang cosmology (Last edited: October 2, 2010)

Ari Brynjolfsson

Most of the details for plasma redshift and its consequences are discussed in the supporting articles. The following summarizes the major results. For questions and information, please, contact Ari Brynjolfsson at aribrynjolfsson@comcast.net Here is my CV

This website is copyrighted ÂŠ by Ari Brynjolfsson, Applied Radiation Industries, 7 Bridle Path Wayland, MA 01778, USA ====================== Keywords: Plasma redshift, plasma-redshift cosmology, solar redshifts, galactic redshifts, redshifts of quasars, narrow line, broad line, cosmological redshifts, time dilation, cosmic microwave background, CMB, cosmic X-ray background, cosmic nucleosynthesis, gamma-ray bursts, big bang, inflation, dark energy, accelerated expansion, dark matter, black hole, black hole candidates, expansion of the universe, static universe. ======================

Supporting articles [1]. arXiv:astro-ph/0401420 [ps, pdf, other] : Title: Redshift of photons penetrating a hot plasma Author: Ari Brynjolfsson [2]. arXiv:astro-ph/0406437 [ps, pdf, other] : Title: Plasma redshift, time dilation, and supernovas Ia Author: Ari Brynjolfsson [3]. arXiv:astro-ph/0407430 [ps, pdf, other] : Title: The type Ia supernovae and the Hubble's constant Author: Ari Brynjolfsson [4]. arXiv:astro-ph/0408312 [ps, pdf, other] : Title: Weightlessness of photons: A quantum effect Author: Ari Brynjolfsson [5]. arXiv:astro-ph/0411666 [ps, pdf, other] : Title: Hubble constant from lensing in plasma-redshift cosmology, and intrinsic redshift of quasars Author: Ari Brynjolfsson [6]. arXiv:astro-ph/0602500 [ps, pdf, other] : Title: Magnitude-redshift relation for SNe Ia, time dilation, and plasma redshift Author: Ari Brynjolfsson [7]. arXiv:astro-ph/0605599 [ps, pdf, other] : Title: Surface brightness in plasma-redshift cosmology Author: Ari Brynjolfsson [8]. Title: Nucleosynthesis in plasma-redshift cosmology Author: Ari Brynjolfsson Comment: Presented at APS meeting April 17, 2007 [9]. Title: High density plasma in black hole candidates Author: Ari Brynjolfsson Comment: Presented at HEDP/HEDLA at the APS meeting April 12, 2008 [10] Title: Plasma Redshift Cosmology: A Review Author: Ari Brynjolfsson Astronomical Society of the Pacific CONFERENCE SERIES, Volume 413, pp. 169-189 , 2 nd Crisis in Cosmology Conference in Port Angeles, WA, USA; September 7 to 11, 2008.

[11] Title: Nucleosynthesis in Plasma-Redshift Cosmology Author: Ari Brynjolfsson Astronomical Society of the Pacific CONFERENCE SERIES, Volume 413, pp. 209-218 , 2 nd Crisis in Cosmology Conference in Port Angeles, WA, USA; September 7 to 11, 2008. [12] Title: Plasma Redshift, Dark Matter and Rotational Velocities of Galaxies. Author: Ari Brynjolfsson Comment: Presented at APS April meeting in Denver, Colorado, May 2 to May 5, 2009.

Table of Contents INTRODUCTION CHAPTER I. PLASMA REDSHIFT AND ITS CONSEQUENCES 1. Theoretical deduction of plasma redshifting………………………………………......… 9 1.1 Plasma redshift as a function of the electron density..………………………………...16 1.2 Angular scattering ………………………………………………………………….… 18 2. Solar experiments confirm the plasma redshift ………………….. ………………… . 20 2.1 Plasma-redshift heating ……………………………………………………… …….…20 2.2 Redshifts of the solar Fraunhofer lines...……………………………………. .………..24 3. Galactic corona………………………………………….……………………………......…29 4. Hubble constant derived from plasma redshift …………………………………………. 31 5. Cosmological distances Rpl and Rbb ……………………………………………………. …33 6. Magnitude-redshift relations for SNe Ia ………………………. …………………………36 7. Surface brightness of galaxies ………………………………………………………….. …41 8. Cosmic microwave background ………………………………………………………….. .42 8.1 Intensities of the CMB for frequencies below 109 Hz ……...………................................47 8.2 Redshift of 21 cm wavelengths in the coronas of different objects....................................48 9. Cosmic X-ray background …………………………………………………………….……50 10. Solar wind and cosmic jets………………………………………………………………….52 11. Densities and temperatures in intergalactic space……………………………………..….56 12. Dark matter, dark energy, and accelerated expansion..……….………………….....….. 60 12.1 Dark matter and rotational velocities of galaxies ……………………………………....62 13. Plasma-redshift heating of the Galactic corona. ………..…………………..………….....67

CHAPTER II. THE REPULSION OF PHOTONS AND ITS CONSEQUENCES 14. Gravitational repulsion of photons…………….………………………………………….....68 14.1 Repulsion of photons ……………….…………………………………………….……..72 15. Black hole candidates are not black holes, but engines for eternal renewal of matter.......77 16. The singularity limit in BHC ………………………………………………………………...80 17. Densities in and around black hole candidates...………………………………………... …85

CHAPTER III. SUMMARY OF PLASMA REDSHIFT COSMOLOGY 18. Summary……………………………………………………………………………………...90

INTRODUCTION When discussing the uncertainty principle Bohr said to Einstein: Donâ&#x20AC;&#x2122;t tell God how to make the world go around. But let us find out how He does it! In recent years the advances in technology have greatly expanded observation technology. We are no longer limited to the optical spectra, but can observe the spectrum from radio waves, microwaves, infrared, optical, ultra violet spectra to high energy x-rays and gamma rays with unprecedented accuracy. This then gives us opportunities to improve and test cosmological theories. The newly discovered plasma-redshift cross-section of photons penetrating hot sparse plasma leads to a new cosmology, which is radically different from the conventional big-bang cosmology. The plasma redshift cross section is derived from conventional axioms of physics by using more exact calculations than those usually used. No new physical assumptions are made. The conventional equations are adequate for conventional laboratory systems, but when the plasma is very hot and sparse (low density) like the plasma in the coronas of stars, galaxies, and quasars and the plasma in intergalactic space, the conventional equations are inadequate. The plasmaredshift cross section must then be taken into account. We find then that plasma redshift and its consequences explain the intrinsic redshifts of the Sun, stars, galaxies, quasars and the cosmological redshift. It explains the cosmic microwave background, the X-ray background, and the eternal renewal of matter. It indicates that the universe is non-expanding, infinite, and quasi-static. Plasma redshift cross section explains: 1. The transition zone to the solar corona 2. The densities and the temperatures in the solar corona 3. The intrinsic redshifts of the Sun, stars, quasars, and galaxies 4. Cosmological redshifts 5. Cosmic microwave background 6. Cosmic X-ray background 7. Gamma-ray bursts 8. The star-forming regions at the centers of galaxies 9. The cosmic nuclear-synthesis 10. The eternal transformation of old star matter to primordial-like matter 11. A great many other phenomena 12. How the world (through conventional physics) renews itself forever Consistent with plasma-redshift cosmology, we find that: 1. The big-bang cosmology is false. The universe is not expanding 2. There never was a cosmic inflation 3. There is no need for: Einsteinâ&#x20AC;&#x;s cosmological constant, cosmic inflation, dark energy, accelerated expansion, dark matter, black holes, or super-massive black holes

The solar redshift experiments and plasma redshift cross section show that photons are weightless in a local system of reference and repelled by the gravitational field when observed in a distant system of reference. It is generally thought that a great many experiments have proven beyond reasonable doubt that photons have weight, and that the gravitational mass m g of each photon is equal to its inertial mass mi; that is, mg = mi = hν/c2. However, in the design and evaluation of these many experiments, the researchers failed to take properly into account the quantum mechanical effects including the uncertainty principle and the finite nonzero time required for all transitions. The proper evaluation of all the experiments, including the solar redshift experiments, shows that photons are weightless. The weightlessness of photons, which was derived from the solar redshift experiment, appears related to the fact that photons are primary bosons without a rest-mass. Experiments show that while photons are weightless, the electrical fields (and their Fourier harmonics) of charged particles have weight. The weightlessness of photons makes it possible to explain why the world can renew itself forever without Einstein’s cosmological constant , as we will see in Section 15 in Chapter II. I have failed to find any experiment or observation contradicting the predictions of the plasma-redshift cosmology. In 1913 and 1915 Bohr derived the stopping power for fast charged particles penetrating matter. This worked well until about 1930 when it was discovered that for higher-energy fast particles, the stopping power was greater than that predicted by Bohr‟s equations. It also was observed that Cherenkov radiation was emitted. The physicists were puzzled. For a long time they could not understand what was going on. Then came Enrico Fermi with his 1939 and 1940 articles, which in essence said: Bohr! You forgot to take the dielectric constant properly into account. The dielectric constant explains the increased stopping power and the Cherenkov radiation. Bohr immediately agreed and elaborated the subject. The dielectric constant is important only at high particle energies that were not in focus when Bohr introduced his equations in 1913 and 1915. Similarly, the equation that we have been using for calculating the stopping power of photons in laboratory plasmas disregards the dielectric constant and results only in the Compton scattering (Arthur Holly Compton, Sept. 10, 1892 - March 15, 1962, is the 1927 Nobel laureate in physics for his discovery of the Compton effect). When we apply these equations to the hot sparse plasmas of intergalactic space, they fail to explain the plasma redshift, as well as the Raman scattering on the plasma frequency, which require that we take the dielectric constant into account. When we insert the dielectric constant, we discover that in the hot sparse plasmas of space we get, besides the conventional Compton scattering, two additional cross sections: the plasma redshift cross section and the Raman scattering on the plasma frequency. These two additional cross sections explain many cosmological phenomena, including the cosmological redshift, as we will see.

CHAPTER I PLASMA REDSHIFT AND ITS CONSEQUENCES 1. Theoretical deduction of plasma redshifting The deduction of the plasma redshift is shown in sections 1 through 4 and in Appendix A of reference [1] arXiv:astro-ph/0401420, “Redshift of photons penetrating a hot plasma”. Plasma redshift is deduced theoretically from well-founded axioms of physics by using more accurate calculations than those usually used. It is an inescapable consequence of conventional laws of physics. The main results are given by Eqs. (12) and (13) below. A photon is a pulse of light (a “packet” of energy). It is a quantum mechanical concept of an electromagnetic interaction and a basic "unit" of light. We may use mathematics to Fourier analyze the pulse. The effect of a photon pulse is the result of the effects of all the Fourier harmonics in the pulse. Many monographs on this subject teach that a photon consist of one Fourier harmonic. This is wrong. Such a photon does not exist in nature. Nothing in nature is infinitely sharp or consists of a single Fourier harmonic, as that would contradict the uncertainty principle. In nature, the Fourier components of the photon pulse usually have a Lorentzian distribution (equal to the Cauchy distribution in mathematics) of the Fourier harmonics. Below, we summarize the deduction. In “Redshift of photons penetrating a hot plasma”[1], I explain in greater details the calculations. I explain also in numbered comments how and why in the past physicists failed to deduce this cross section. (It is not possible to deduce plasma redshift when using classical physics methods, which are usually used.) When expressing the force from the action of the electrical photon field on the electron, we must apply the complex dielectric constant ε. Use of quantum mechanical photons, a photon pulse, is also essential. In quantum physics, the photon frequency, νo, means the center frequency of Fourier harmonics in the Lorentz frequency distribution. The width of this distribution depends on the lifetime for the emission of the photon, Δν = 1/τ, that is, the half width is the reciprocal of the time constant τ. It is important in the following to keep this in mind. We must also use the correct complex dielectric constant for each component of this Fourier distribution, and not approximate it with the real part as is often done in plasma physics and plasma cosmology. It is the complex part (the friction-like part) of the low frequencies in the Lorentz distribution that cause the plasma redshift. The classical dynamical equation of motion of an electron with charge e acted on by a Fourier electrical field, A · exp(iωt), in Gauss (cgs) units, is at the position r = 0 usually approximated by

mr  m0 r  mq2 r  e  A  exp(it ) ,

(1)

where the radiation damping constant is β0 = 2e2 ∕(3mc3) = 6.266·10–24, and m0 r  m0 2 r is the “friction” caused by the radiation emitted by the electron when it is forced to oscillate, and where r , r , and r are the first, second, and third time derivatives of the complex distance r in the oscillation of the electron having charge e and mass m in the electrical Fourier field harmonic with modulus and frequency ω. On the right side of Eq. (1), we have, as is usually done, approximated the force on the electron with mass m and charge e by e·A· exp(iωt), instead of using the actual force (e·A/)· exp(iωt), where  is the dielectric constant around the electron. The first term on the left side gives the acceleration of the electron with mass m, the second term is the energy loss caused by the radiation emitted when the electron is accelerated. The third term gives the oscillation of a bound electron. In the fully ionized plasma this term third term is zero. This usual approximation, Eq. (1) above, is usually permissible in laboratory media, including all laboratory plasmas, where the free electron density usually exceeds about Ne = 1014 cm-3. But in the hot and sparse plasmas of coronas of the Sun with Ne<109 cm-3 and temperature of about 2·10 6 K and in coronas of stars, quasars, and galaxies, and in the sparse hot plasma of the intergalactic space with Ne ≈ 2 ·10-4 cm-3 and an average temperature of about 2.7·10 6 K, this approximation is not permissible. Instead, we must for the low frequencies of each and every photon pulse use a more accurate form for the dielectric constant. Instead of Eq. (1) above, we then have

mr  m r  m p r  mq2 r  e

A exp(it ) ,  ( )

(2)

where on the right side we have taken into account the fact that the dielectric constant varies with the frequency of the Fourier harmonic of the photon field. On the left side, the first term is the acceleration of the electron. In Eq. (2), we have separated the damping term in Eq. (1) into two terms, the damping m r due to collisions, and the damping m p r  m p 2 r due to the forced oscillations of the electron. The collision damping is usually characterized by α=2/τ where τ is the average time between collisions. βp is a measure of the quantum mechanical radiation damping emitted when the electron (including its spin) oscillates in the photon field; see section A3 in Appendix A of [1] arXiv:astro-ph/0401420, “Redshift of photons penetrating a hot plasma”, where we show also how Eq. (2) can be solved exactly to give us the radius r. See also reference [10] above in Supporting Articles. In his articles in Phil. Mag. 25 (1913) 10 and ibid. 26 (1913) 1 and ibid 30 (1915) 581, Niels Bohr (Niels Henrik David Bohr; 7 October 1885 – 18 November 1962, my mentor, received the Nobel Prize in Physics in 1922 for his contributions to our understanding of atomic structure and quantum mechanics) calculated the stopping power for fast charged particles. He used an equation similar to Eq. (1) above. In case of fast charged particles, the Fourier forms of the electrical field consist of the Modified Bessel Functions, and not the Lorentz distribution valid for photons. Bohr set the dielectric constant equal to one,  = 1, because that approximation was permissible for calculating the stopping power of fast charged particles with the low energy used at that time in relatively cold media. The improved quantum theory developed in the 1920s did not change this. But when in the 1930s the energy of the fast charged particles increased significantly (especially when the velocity increased beyond the speed of light in the matter the particles penetrated), it was observed that the stopping power increased and that the Cherenkov radiation was emitted. Nobody could understand this increased stopping power, nor the emitted Cherenkov radiation. Then in Phys. Rev. 56 (1939) 1242, and ibid 57 (1940) 485, Enrico

Fermi (Enrico Fermi, 29 Sept. 1901 – 28 Nov. 1954, was awarded the Nobel Prize in Physics in 1938 for his work on induced radioactivity) pointed out that we could not ignore the dielectric constant. He changed the right side of Eq. (1) to the right side of Eq. (2), and could then explain both the increased stopping power and the Cherenkov radiation for fast charged particles with much higher speed than those imagined by Bohr in his 1913 and 1915 articles. Subsequently, Niels Bohr (see: Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 18, No. 8 1948) and his son Aage Bohr (see: Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 24, No. 19, 1948) wrote important articles elaborating the subject (Aage Niels Bohr, born June 19, 1922, my mentor in nuclear physics, was awarded the Nobel Prize in Physics in 1975 together with Mottelson and Rainwater for the discovery of the connection between collective motion and particle motion in atomic nuclei and the development of the theory of the structure of the atomic nucleus based on this connection.) In my thesis in 1973 at the Niels Bohr Institute, I elaborated further on this subject by more accurate theoretical estimates of the stopping power. Even when the dielectric constant is included, the damping terms (the second and the third terms on the left side of Eq. (2)) are usually omitted. But for accurate calculations of the stopping power and for deriving the plasma redshift it is essential to include these damping terms. It is important to take note of the fact that nobody questions that Eq. (2) is more accurate than Eq. (1). The correctness of plasma redshift, which follows from the more accurate Eq. (2) (and not from Eq. (1)), should therefore not be questioned. It must predict more accurately than the old equations the cross section for interactions of photons with matter. I first deduced the plasma-redshift cross section three days before Christmas 1978 in response to questions about the big-bang cosmology from two of my sons then in High School. They were asking me about the big-bang theory. I explained it to them and some of the alternative cosmologies, and said: “I don‟t believe any of these explanations. This is not the way nature behaves”. They continued to question me about it. I was familiar with interactions of radiation with matter. I knew all the equations. I grabbed an envelope and did a few calculations on the back of it. I saw that the physicists had overlooked an important cross section, the plasma redshift of photons. The improvement I made was to take the dielectric constant, including the damping terms, properly into account in the equations of motion for interactions of photons with electrons. Conventionally, the dielectric constant is set equal to one or, at very best, equal to the real part. These approximations can never lead to the “plasma redshift”. I thought it would be easy to explain it to others, but have found it anything but easy. At the Niels Bohr Institute in Copenhagen, I had defended my thesis on a closely related subject: “Some Aspects of the Interactions of Fast Charged Particles with Matter”; and I have worked with all kinds of radiation interaction with matter. I suspect the reluctance to accept my theoretical deduction of the plasma redshift cross section is rooted in its revolutionary consequences. It explains through simple physics many solar phenomena, the cosmological redshift, and many other cosmological phenomena without cosmic time dilation, inflation, dark energy, accelerated expansion, dark matter, or black holes. Both professors and graduate students are heavily committed to the big-bang cosmology and are thoroughly convinced that it is correct. The cardinals of physics in the 17th century were the most learned men and were convinced that they knew all about the heavens, and that the Ptolemaic geocentric model with its epicycles for planetary movements was correct. So when Galileo Galilei showed a new perspective they rejected it and were not interested. The reluctance to accept a simple deduction of plasma redshift most likely has similar causes.

The solution of Eq. (2) is well known and is given by

r

e ( A /  )  exp(it ) e ( A /  )  exp(it ) ,  m q2   2  i (   p 2 ) m q2   2  i 3 

(3)

From this solution we derive the polarization, P() = Neer, where Ne is the electron density in cm–3, and where we have set  + p 2   2 , because the emission spectrum of  is very similar to the spectrum of p2 . From the polarization we derive the dielectric constant

 ( )  1 

4 Ne er , ( A /  ) exp(it )

(4)

From Eqs. (3) and (4), we then get that

 ( )  1 



2 q

4 N e e2 / m



   i    p   2

 1



 p2

2 q

  2  i    p 2  

 , (5)

where the cyclic “plasma frequency” is

4 N e e2  p  2 p   5.642 104 N e . m

(6)

We should take note of the fact that imaginary part in the denominator of Eq. (5) is closely related to the second and third terms in Eq. (2); that is, it is closely related to the energy losses of electrons when they oscillate in the collision field and the photon field. The corresponding “friction” losses of the photon energy (resulting in the plasma redshift) as we will see, have been disregarded in the past, because researchers, instead of the more exact calculations, used approximations. Usually these approximations were adequate, because all the low energy states in the conventional laboratory plasmas and in colder media were fully occupied. But in the corona of stars, quasars, and in intergalactic space the energy states are mostly unoccupied. The photons can then transfer low energy quanta to the plasma. The free oscillator strength is given by Table 1 in the following. When writing the complex dielectric constant in the form ε = (n – iκ)2 , we get from Eq.(5) that

2n



(   p 2 ) p2 2

 p2   4   2 . 2 2 2 2 2 6 (q2   p2   2 )2     p 2   2 (q   p   )   

(7)

We have replaced the factor (α+βpω2) by βω2, because the collision damping results in an analogous emission to the conventional emission from accelerated charges. When we normalize the average photon flux to one photon per cm2, we get for the energy flux decrease

0 dS d 0   dx dx 2 c



2n exp(2 x / c)  d .    2 / 4  (  0 )2  

When we insert Eq. (7) for the value for the dielectric constant  at x = 0, we get for the

(8)

photon‟s energy loss:

d 0 0  dx 2 c

 p2  4  d







 

2 q



  p2   2    2 6   2 4    0   2



(9)

The first factor comprising the bracket in the denominator of the integrand is due to the dielectric constant,   1 , while the factor comprising the braces corresponds to   1 and to the conventional cross section; that is, the Compton cross section. Eq. (9) can be solved by using integration in the complex plane. We integrate along the xaxis and along a semicircle in the upper half-plane. The integral along the semicircle is zero. The integral from – to + along the x-axes is then equal to the sum of the residues of the four complex roots in the upper half-plane; see section A5 in the Appendix A in reference [1] arXiv:astro-ph/0401420. When evaluating the different quantities, we can set: 1) q = 0; 2)   0 = 6.26610–24; 3) p  1; 4) 0  p ; and 5)   0 . We find then that the four roots in the complex plane are

 a   p   b   p :  c  d  0 

 i   p2 2    i   p2 2    i 1    i   2 

(9a)

The integration in the complex plane is important, because the conventional approximations fail to include the cross section due to the purely complex root, which results in the plasma redshift cross section. The integral is then given by the residues of a, b, c and d, and we get:

d 0   2 i  0   Re s  a   Re s  b   Re s  c   Re s  d   dx 2  c

(9b)

The integration of Eq. (9) is then given by: (see also Eq. (A35) of [1] arXiv:astro-ph/0401420)

 

 

2   1  1/    0 d 0   1     0  6.65 1025  N e    2 2 dx 2 2 0 1  1/   2 1    00    0 0 

(10)

Within the brackets, the first term represents the Raman scattering on the plasma frequency.

The conventional calculations fail to include the corresponding roots, because of the classical physics approximation used. The second term represents the plasma redshift term. The conventional calculations have failed to include this term due the approximations used. This important cross section is due to the purely imaginary root, which is due to the complex part of the dielectric constant, and thus due to the energy losses occurred when the electrons oscillate in the collision and photon field. This cross section is purely an absorption cross section without any scattering. The third or last term represents the conventional Compton scattering. The two first terms, the Raman scattering term and the plasma redshift term, are thus a consequence of ε ≠1, while the third term, the Compton scattering term, is independent of the dielectric constant and is about the same when ε =1. The small value (β0 ω0) 2 in the denominator of the third term (β0 = 6.266·10·–24) is usually not included, but it follows from more exact calculations. We emphasize that we have made no new assumptions and have not introduced any new physics. The deduction of these cross sections follows only from more exact calculations. The two first terms inside the brackets in Eq. (9b), the Raman scattering terms on the plasma frequency, are usually very small or nearly insignificant, because the oscillator strength for an emission and absorption are nearly equal and cancel each other when the plasma is nearly in thermodynamic equilibrium. However, there is a concurrent small angular scattering, which sometimes is observed at large cosmological distances, for example in the high redshift SN Ia studies; see Eq. (52) of [1] arXiv:astro-ph/0401420. The third term inside the brackets of Eq. (10), the Compton scattering term, is the conventional scattering term and is nearly independent of the dielectric constant. The concurrent redshift (due to the recoil) of the scattered photon is small, and affects only the scattered photons, which in the case of optical photons is practically all lost from starlight‟s intensity. The second term inside the brackets in Eq. (10), the plasma-redshift term, is due to a pure imaginary root in the integral of Eq. (9). It is therefore a pure absorption term (friction term) and does not scatter the incident photon. But when the low energy levels in the hot sparse plasma are not occupied, they can absorb small energy quanta from the photons. The corresponding energy absorption heats the plasma. However, this redshift is possible only if the plasma can absorb the very small energy quanta. In ordinary laboratory plasma all the low-energy levels are occupied and cannot absorb the small quanta involved in the plasma redshift of photons. T his fact explains why the plasma redshift was not discovered before, and why the approximations,  = 1, used by Bohr were assumed to be adequate. On the other hand, in hot sparse plasmas of the corona of stars and in intergalactic space, the plasma oscillations in the plasma are highly excited, and most of the states with low energy are empty and can absorb the low energy quanta that result in the plasma redshift of photons. At lower plasma temperatures, the low energy levels in the plasma are occupied. These

occupied levels can occasionally transfer small energy quanta to the photons and cause a blueshift of the photons. The cross section for this blue shift (negative redshift) is small, as shown in the last column of Table 1 for a3.633. At still higher densities and lower temperatures, such as in the solar chromosphere, the plasma blue shift is usually insignificant.

a   p /  00 kT   3.65 105 0 Ne / T ,

(11)

For calculating the degree of occupation of the important levels in the plasma, we must calculate the energy levels and each one‟s occupation by using quantum mechanics; see section 3.2 of [1] arXiv:astro-ph/0401420. The calculations show then that plasma redshift of photons starts to be important at about the densities and temperatures in the transition zone to the solar corona. The plasma-redshift heating and cooling (by heat conduction and emission) in the transition zone can be calculated exactly by use of extensive computer programs, which I have used. This has been done as shown in sections 5.1 to 5.6 of [1] arXiv:astro-ph/0401420, and the prediction of temperature and densities through out the transition zone and the solar corona are found to match extensive observations. This match is a strong confirmation of the plasma redshift. The value of  in the plasma redshift term, the second term within the brackets of Eq. (10), depends mainly on the collision frequency, the temperature and the density, and on the magnetic field. The magnetic field causes the electrons to gyrate around the magnetic field lines, whereby the interacting electrons lose (emit) energy and cause broadening of the emitted energy losses. In Eqs. (1) and (2), we could include the magnetic field in the dynamic equations. We get then twice as many roots in Eq. (9), but the sum of the residues has nearly the same form as in Eq. (10). We also find that the magnetic field increases the value of . Table 1. Oscillator strength function F(a), where a   p /  00 kT   3.65 105 0 Ne / T a F(a) a F(a) a F(a) 0.0 0.1 0.2 0.3 0.344 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.163 1.2

1,000 0.990 0.962 0.921 0.900 0.872 0.821 0.769 0.717 0.667 0.618 0.571 0.527 0.500 0.485

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.2 2.4 2.6 2.671 2.8 3.0 3.5

0.445 0.407 0.372 0.339 0.309 0.280 0.253 0.228 0.183 0.144 0.111 0.100 0.082 0.057 0.010

3.633 4.0 5.0 6.0 7.0 8.0 9.0 10.0 20.0 40.0 50.0 100 200 ∞

0.000 -0.022 -0.057 -0.070 -0.073 -0.071 -0.067 -0.061 -0.024 -0.0071 -0.0047 -0.0012 -0.0008 -0.0000

Quantum mechanical treatment of the plasma leads to a more reliable estimate of this “friction” term. This term is rather complicated to calculate, but the details are found in sections 3 and 4 of [1] arXiv:astro-ph/0401420. The variations of the oscillator strength function, F(a), in the plasma redshift cross section is given in Table 1 as a function of the parameter a given by Eq. (11). Table 1 shows that the plasma redshift cross section for values of a < 3.633 results in a positive oscillator strength, Ne·F(a), and therefore in a plasma redshift. But for relatively high values of a (>3.633), the oscillator strength F(a) is slightly negative, which corresponds to a blue shift. This small blue shift has been seen in some experiments, such as in the Pioneer experiments, which used 13 cm microwaves to penetrate the outer reaches of the solar corona. But the plasma blue shift is usually small and usually dismissed by big-bang cosmologists as noise in the experimental data, because they cannot understand it. In the evaluation of the Pioneer 10 and 11 experiments, it is incorrectly surmised that the photon frequency is constant during the photons travel from Earth to the Pioneer and back to the Earth. The actual tiny blue shift of the photons during their travel (confer the last column in Table 1 in reference: arxiv:astro-ph/0401420, which for a > 3.633 shows negative redshifts; that is, blue shifts) is in the range measurements assumed incorrectly to be due to a Doppler shift and indicating that the space craft is continuously accelerated towards the Earth. The gravitational blue shift (reversal of the gravitational redshift) of photons when moving outwards is not fully compensated when the photons move back to Earth. Also this contributes to the anomalous acceleration. But this contribution is much smaller (less than 10 %). In relatively cold and dense plasma, the oscillator strength function, F(a), is zero or slightly negative, because almost all of the low energy levels in the plasma are occupied. The photons cannot therefore transfer energy to the plasma, and only a very few of the occupied electron states in the plasma can transfer their energy to photons, corresponding to the negative values of F(a) in the last column of Table 1.

The 21.1 cm wavelength is not plasma redshifted (or even slightly blue shifted) in the corona of the Sun, the stars, and quasars, because the value of the parameter, a, is too high. When observed, the 21.1 cm line therefore always has a significantly smaller redshift than the optical lines from the quasar. If the 21.1 cm line comes from hydrogen atoms surrounding the quasar, its redshift is a rough measure of the distance to the quasar, provided the hydrogen atoms have low velocity. The difference between the redshift of the optical lines and the 21.1 cm line is then also a rough measure of the intrinsic redshift of the quasar, while the redshift of the hydrogen line is a rough measure of the cosmological distance, because the 21.1 cm line is plasma redshifted in intergalactic space with its low density and high temperature.

1.1. Plasma redshift as a function of the electron density The relation between the plasma redshift z and the electron density Ne in hot sparse plasma with the incremental distance dx in cm integrated from the observer to the star at a distance R is; see Eq. (20) in “Redshift of photons penetrating a hot plasma” [1] arXiv:astro-ph/0401420:

ln(1  z )  3.3262 10

25

  N e  dx 0



 i   0   

(12)

where z is the plasma redshift, Ne = Ne (x) is the electron density in cm─3 at the distance x in cm from the observer, γi = 1/τ the initial quantum mechanical photon width and τ the lifetime of the emitting state, which includes the effect of the collisions. The photon width γ 0 in sparse plasma is equal to the classical photon width γ0 = 2e2ω2 /(3mec3) = 6.266·10–24· ω2, where ω = 2πν and ν is the photon‟s frequency, e and me the electronic charge and mass, c the velocity of light. All the photon widths, γi, gradually (for column density Ne < 3·1017 cm─2) approach the classical photon widths as they penetrate hot electron plasma. For optical photons, we have that ξ ≈ 0.25. All the optical photons from the Sun, the stars, and the galaxies will therefore have the classical photon width when observed on Earth. The fact that all optical photons from the Sun have the classical photon widths when arriving on Earth can be confirmed by experiments. To best of my knowledge this has not been done. But such experiments could confirm or modify the factor ξ ≈ 0.25 in the plasma redshift. The widths of the photons emitted from the Sun often deviate significantly from the classical photon width γ0 = 2e2ω2/(3mec3). It is usually surmised, incorrectly, this photon width is unchanged from that in the Sun when it arrives on Earth. The sufficient and necessary condition for the redshift given by Eq. (12) is that the wavelength λ is shorter than a certain cut-off wavelength limit, λ0.5 , given by (see Eq. (28) of [1] arXiv:astroph/0401420):

  0.5

2  Te 5 B   318.6  1  1.3 10  ,  N N e   e

(13)

where λ is the wavelength in Å, B the magnetic field in Gauss and Te the plasma temperature in Kelvin. This value corresponds to a = 1.163 in Table 1. Eq. (13) is valid for the center of the spectrum (about 500 nm). In the transition zone to the corona the heating is so steep that nearly the entire spectrum becomes plasma redshifted. We usually call λ0.5 the cut-off wavelength for plasma redshift. It marks the wavelength when the oscillator strength is 0.5 ·Ne. Often, as in the transition to the solar corona, the oscillator strength function changes steeply in the transition zone. We can then often assume that for wavelengths λ ≥ λ0.5 the plasma redshift is nearly zero; and for λ ≤ λ0.5 that the oscillator strength function is F(a) = 1, or that the probability for the photons energy loss hν (plasmaredshift of photons, or photons‟ energy loss) is close to its maximum value, 3.326·10 −25·hν cm2·erg per electron. The exact value of the oscillator strength, F(a), in the cut-off region around λ0.5 is given in Table 1 above and by Eqs. (15) and (16) of [1] arXiv:astro-ph/0401420. Once initiated the plasmaredshift heating increases the temperature and decreases the density. The transition from no redshift to full redshift is therefore rather sharp, as it is in the transition zone to the solar corona; see section 2.1. Solar redshifts increase with frequency, because at higher frequencies the redshift integral reaches deeper into the transition zone. Although the cut-off for plasma redshift in the transition zone to the solar corona is fairly sharp, the solar redshifts of shorter wavelengths should be slightly greater than that of longer wavelengths. Eq. (13) shows that the shorter wavelengths in the solar spectrum should be redshifted slightly more than the longer wavelengths. This is consistent with observations, and thus another independent confirmation of the plasma-redshift theory.

The solar flares. The magnetic field B in the transition zone to the solar corona is often about 6 Gauss. But occasionally it can reach much higher values of 1000 or even 1600 Gauss. The cut-off may then reach to higher densities well below the usual transition zone. Ultraviolet photons may then initiate plasma-redshift heating resulting in plasma â&#x20AC;&#x153;bubblesâ&#x20AC;? that grow below the usual transition zone. These bubbles may grow huge and become large and explode into the transition zone. These predicted phenomena are consistent with the observed flares; see section 5.5 of [1] arXiv:astroph/0401420. Spicules are related to the flares, but arise as smaller magnetic fields cause bubbles to form low in the transition zone. Low in the transition from the chromosphere to the solar corona, the magnetic field creates instabilities similar to those in the flares. Smaller plasma redshift heated bubbles form between the colder plasma. These result in the spicules; see sections 5.1 and 5.5 of [1] arXiv:astroph/0401420. Arches. It has been difficult to explain the arches often seen stretching far into the corona and lingering there, often for an extended time. When the field is horizontal and strong, large bubbles are initiated just below the usual transition zone. The diamagnetic moments reduce the field mainly I the center where the temperatures are the highest, while the return field of the diamagnetic moments may strengthen the surface field of the bubbles. The low densities due to the high temperatures push the bubble outwards. The relatively strong surface field may split into arches as the bubble moves into the corona. The plasma redshift heating of the plasma surrounding the arches may actually push the plasma from outside the arches into the arches. This extends the lifetime of the arches. We may even have plasma move down both ends of the arch; see the last two paragraphs of section 5.5 of [1] arXiv:astro-ph/0401420. Only the plasma redshift gives a reasonable account of these complex phenomena. Destruction of the magnetic field and concurrent heating. It is often seen that where the magnetic field is strong in the Sun, the overall field decreases concurrently with flare-like phenomena. In the literature this is usually described incorrectly as reconnection of field lines causing destruction of the magnetic field, which causes the corresponding heating. This is clearly incorrect. Reconnection of the field lines is not the cause but the consequence of the destruction of the magnetic field. In plasma the electrons and ions encircle the field lines and cause diamagnetic moments that oppose the field. The strong magnetic field due to Eq. (13) facilitates the plasma redshift. The associated plasma redshift heating increases the diamagnetic moments, which reduce the field and cause reconnection of the field lines. This is thus another case where plasma redshift facilitates explanation of the observed phenomena. The solar wind. The diamagnetic moments of electrons and ions are pushed outwards by the outward divergent magnetic field; see section 5.3 and Eq. (B10) of [1] arXiv:astro-ph/0401420. This magnetic force on the diamagnetic moments increases the outward directed velocity of the particles and is one of the principal causes of the solar wind. Plasma-redshift heating enlarges the diamagnetic moments and enhances significantly the repulsive force on the diamagnetic moments; see Eq. (28) in section 10 below. The plasma redshift causes charge separation because the plasma redshift heating is transferred first to the electrons, some of which become very hot and diffuse outwards (because they can only slowly transfer their energy to the other particles). This charge separation causes the electrons to

diffuse outwards ahead of the protons and helium, and thereby drag the protons and helium outwards.

1.2. Angular scattering Concurrent with the energy losses we usually have angular scattering. In case of the last term inside the brackets of Eq. (10) above, the Compton scattering term, the angular scattering for optical photons is nearly isotropic. In case of optical photons, the angular scattering of the incident photon on the plasma electrons removes the photon from the light intensity from the star. In case of big-bang cosmology this reduction is insignificant, because of the very low electron density ( 1.410–7 cm–3) in intergalactic space. But in the plasma-redshift cosmology the electron density in intergalactic space, about Ne  0.0002 cm–3, is about 1600 times higher than that in the big-bang cosmology. This reduction in the light intensity is then very significant. It eliminates the need for the accelerated expansion in the big-bang cosmology. In case of magnitude-redshift relation for SNe, the redshift and time dilation in the big-bang cosmology cause a reduction in intensity by 1/(1+z) 2. But in the plasmaredshift cosmology the corresponding intensity reduction for redshift and Compton scattering is 1/(1+z) 3. The big-bang cosmologists have therefore to introduce accelerated expansion, while the plasma redshift predicts the observed reduction. In case of surface brightness, the big-bang cosmologists require a reduction in intensity by a factor of 1/(1+z) 4 , while plasma redshift requires the factor to be 1/(1+z) 3. Also in this case, the plasma redshift predicts the observed reduction. The angular scattering in the first term in Eq. (10), the Raman scattering term, is much smaller, because the energy of the plasma frequency-quanta is usually much smaller than the energy of the incident photon. In intergalactic space the plasma frequency is p = 5.64104Ne1/2  800, which is small compared with   3.771015 for 500 nm light. The Raman scattering results in individual angular scatterings of optical light on the order of p/  2.12 10–13. After many interactions, see Eq. (52) of [1] arXiv:astro-ph/0401420, the scattering has a Gaussian distribution with an average angle of:

  ( p /  )  ln(1  z)

(14)

which corresponds to

R 

7.14 1026  [ln(1  z )]3/2 cm, Ne

(15)

where R is the distance in cm to the star or the supernova. For a supernova at z =1.7, the value of   4.59 10 7 , and the radius of the supernova appears to be R  4.59 1020 cm. The density variations will make these values slightly larger. For plasma in thermodynamic equilibrium, the average energy change is insignificant, but the small angular scattering is still detectable at very large redshifts. These predictions of the present theory are also consistent with observations.

The center term within the brackets of Eq. (10), the plasma-redshift term, is not a scattering term but a true absorption term. This term is due to the imaginary parts of the dielectric constant and is a true friction term. The second law of thermodynamics does not apply to friction. It is therefore possible for the energy to move from the cold photosphere, T ≈ 5800 K, to the much hotter corona with T ≈ 2.2·106 K. This plasma redshift term can thus explain the heat transport to the transition zone and to the solar corona without breaking the second law of thermodynamics, which forbids transport of heat from one place to a hotter place. The plasma redshift heating of intergalactic space to multi-million degree temperatures is thus consistent with these important laws of physics.

2. Solar experiments confirm the plasma redshift The plasma redshift is based entirely on conventional physics and has no adjustable parameters such as the energy and density parameters ΩΛ and Ωm in the big-bang cosmology. It follows from more accurate calculations than those usually used. The predictions of the plasma redshift equations can be compared with many hundreds of good experiments. The energy is conserved at all times. For example, the energy lost by the photons in the plasma redshift is transferred to the plasma in form of equivalent heat. The plasma redshift heating is important for explaining the heating of the coronas of the Sun, the stars, the quasars and the galaxies, and of the plasmas in intergalactic space. Due to the closeness of the Sun, many solar phenomena have been studied most thoroughly. Therefore, we will first compare the predictions of the plasma redshift equations with solar phenomena; see sections 5.1 to 5.6.3 of reference [1] arXiv:astro-ph/0401420 for greater details.

2.1. Plasma-redshift heating It has been impossible to explain how the solar photosphere, which is only 5,800 degrees Kelvin, could supply heat to the solar corona enough to heat it to about 2.2 million degrees Kelvin. The ultraviolet photons resulting in Strömgren spheres around the Sun and stars can not explain the high coronal temperatures of about 2 million degrees K. A Strömgren sphere (named after Bengt Georg Daniel Strömgren, (January 21, 1908 – July 4, 1987), my mentor in astrophysics) around the Sun would result in temperatures usually less than about 10 5 K. The heating by Compton scattering of optical light, as suggested by some, would result in an insignificant temperature increase. The X-ray cooling of the solar corona is significant, but the heat conduction from the corona inward to the solar surface and outwards to outer space is much larger than the X-ray cooling. In the plasma redshift each photon transfers a small fraction of its energy to the electrons in the coronal plasma. This energy transfer is possible only if the low-energy quantum states in the plasma are not occupied. In ordinary laboratory plasmas, all the low-energy quantum states are occupied. In such plasmas there is then no plasma redshift. But in the sparse hot plasmas of the Sun, the stars, the quasars, and in intergalactic space, the temperature is so high that the low-energy states are unoccupied

and the plasma redshift is then possible. The heating of the coronal plasma is caused by the imaginary part (the “friction” part) of the dielectric constant. It is thus caused by the energy losses in the forced oscillations of the electrons, which in turn are caused by the photon field and by the collision field; see Eq. (2) above. This energy transfer from each photon accounts for most of the coronal heating. Most of the remaining heating is supplied by conversion of the magnetic field energy to heat. But this conversion of the magnetic field is initiated mostly by the plasma-redshift heating, which increases the diamagnetic moments and produces, thereby, a strong electromotive force that reduces the magnetic field. The total heating, about 5.3·10 5 erg cm–2 s–1, balances the heat losses, which are due mainly to heat conduction and x-ray emission; see section 5.1 of [1] arXiv:astro-ph/0401420. Table 2. Temperatures T and electron densities Ne in the quiescent solar corona as a function of distance R/R0 from the solar center in units of the solar radius R0. Distance R/R0 in units of the solar radius R0 1.001 1.002 1.005 1.01 1.02 1.05 1.1 1.2 1.3 1.4 1.6 1.8 2.0 2.2 2.4

Temperature Electron T in degrees densities Ne Kelvin in cm–3 5.70 ·105 8.81 ·105 1.10 ·106 1.27 ·106 1.45 ·106 1.69 ·106 1.88 ·106 2.06 ·106 2.14 ·106 2.17 ·106 2.19 ·106 2.19 ·106 2.17 ·106 2.14 ·106 2.09 ·106

Distance R/R0 in units of the solar radius R0

7.45 ·108 4.73 ·108 3.65 ·108 2.99 ·108 2.38 ·108 1.60 ·108 1.03 ·108 5.49 ·107 3.40 ·107 2.29 ·107 1.23 ·107 7.67 ·106 5.85 ·106 4.72 ·106 3.92 ·106

2.6 2.8 3.0 3.2 3.4 3.6 5.0 6.0 7.0 8.0 10.0 30.0 60.0 100.0 215

Temperature T in degrees Kelvin

Electron densities Ne in cm–3

2.02 ·106 1.92 ·106 1.78 ·106 1.60 ·106 1.29 ·106

3.35 ·106 2.89 ·106 2.54 ·106 2.12 ·106 1.78 ·106 1.55 ·106 7.36 ·105 1.85 ·105 8.12 ·104 4.45 ·104 1.81 ·104 6.16 ·102 1.23 ·102 3.77 ·101 6.38

Sometimes, it is suggested that magnetic fields are primordial. There is no physical basis for this. Magnetic fields are produced by moving charges; and in plasmas, the magnetic fields are both created and counteracted by diamagnetic moments. These diamagnetic moments tend to strengthen each other and collectively counteract the external magnetic fields and may even dominate (reverse) them. The balance depends on the rate of cooling and the heating. Either the external fields or the collective diamagnetic moments dominate. These forces sometimes cause reversal of the observed magnetic field both on Earth and in the stars. In plasmas, the maximum magnetic field‟s energy density is often nearly equal to the total kinetic energy density of the charged particles; see Appendix B of [1] arXiv:astro-ph/0401420. It is often stated that reconnection of the magnetic field lines causes the destruction of the magnetic field, which in turn results in the corresponding heating. But reconnection can never cause the destruction of the field. Instead, as shown above, the plasma redshift heating increases the diamagnetic moments and causes thereby an electromotive force that destroys the magnetic field. This destruction of the magnetic field causes the reconnection.

Besides the direct heating by the plasma redshift, the conversion of magnetic fields to heat must be

taken into account in the transition zone and in the corona. Without the magnetic fields the Sun would still have a transition zone to a corona with a temperature of about T ≈ 106 K. The temperatures would thus be lower than T ≈ 2.2 ·106 K with the magnetic field. These phenomena are analyzed in sections 5.1 to 5.5 and in Appendix B of [1] arXiv:astro-ph/0401420. I used large Excel programs to make the extensive calculations (by a small step iteration method) of the heating profile in the transition zone and the solar corona. The cooling is partly due to X-ray cooling, but mainly due to heat conduction from the corona and the transition zone down into the chromosphere. Heat conduction in the transition zone increases significantly the temperature of the chromosphere; see [1] arXiv:astro-ph/0401420. Eqs. (12) and (13) and the heat conduction predict the profiles shown in Table 2 and in Figure 1 and 2. For greater details of the calculations, see Table 2 and Figs. 1 and 2 in [1] arXiv:astro-ph/0401420. It is possible to determine independently the temperature and electron density profiles from accurate X-ray measurements, and thereby confirm the predicted temperatures and electron densities of the coronal plasma; see section 5.2 of [1] arXiv:astro-ph/0401420..

Temperature of the coronal plasma in degrees Kelvin

Temperature in the solar corona as a function of the distance R/Ro from the solar center 3000000 2500000 2000000 1500000 1000000 500000 1

1.5

2.5

Distance R/Ro from the solar center Figure 1. From reference [1]. Figure 1 in: arXiv:astro-ph/0401420 [ps, pdf, other], “Redshift of photons penetrating a hot plasma” by Ari Brynjolfsson. The ordinate shows the temperatures of the plasma in the transition zone and the corona as a function of the distance from solar center in units of solar radius on the abscissa. The lower and upper curves correspond to NeT = 5·1014 and NeT = 4·1014 cm−3 K, respectively. The solar wind at the distance of Earth is assumed to be Nevp = 3.2·108 cm−2 s−1.‟ and the magnetic field is assumed to be 5.5 and 6.3 Gauss, respectively, and it is assumed to decrease about inversely with the square of the radius to the solar center.

The plasma redshift predicts well the measured temperature, see Figure 1, and electron density profiles, see Figure 2, in the transition zone and in the corona as a function of the radius R. In the middle of the transition zone to the solar corona, the temperature and density are: T ≈ 5·105 K and Ne ≈ 109 cm–3. According to Eq. (13), the cut-off wavelength is then λ0.5 ≈ 5000 Å, which is about in the middle of the solar spectrum. These values thus confirm the plasma redshift Eq. (12) and the cutoff zone given by Eq. (13) and Table 1 above; see also section 5.2 of [1] arXiv:astro-ph/0401420. For the quiescent solar corona, the predicted maximum temperature of about Tmax ≈ 2.2 million K is obtained when the heating balances the cooling processes. This temperature maximum, which matches the measured value, is predicted to be at about R ≈ 1.9 solar radii, which also matches the observed values. These values are independent confirmations of the plasma redshift. The conventional theory could not explain the observed steep profile in the transition zone, or the high temperature maximum in the corona; see Fig. 1. Plasma redshifting on the other hand gives a beautiful quantitative explanation of the observations. The plasma redshift gives also a wonderful explanation of many other important but difficult-to-explain solar phenomena, such as, spicules, solar flares, the arches mentioned in section 1.1. Plasma redshift heating is a first order process in the density, while the cooling processes such as X-ray cooling and recombination cooling are second order processes. This creates instabilities. The hot plasma seeks to get hotter while the cold plasma seeks to become colder. We will therefore have explosive expansions that create the spicules, the flares and the arches, as described in details in section 5.3 and Eq. (B10) of the Appendix B2 of [1] arXiv:astro-ph/0401420. The solar wind, which had defied reasonable explanations, is easily explained; see section 5.3 of [1] arXiv:astro-ph/0401420 for the detailed explanations of these phenomena. The expert solar physicist professor Eugene N. Parker, of the University of Chicago (see for example: “Heating Solar Coronal Holes,” Ap.J., 372, 719 (1991)), once remarked to me: “We have long wondered how the solar surface can transfer energy to the much hotter corona. This appears to contradict the second law of thermodynamics, which forbids transfer of energy from a cold place to a hotter place.” Plasma redshift explains these strange phenomena. Plasma redshift is a “friction” process. Plasma redshift is entirely due to the pure imaginary part of the dielectric constant. The photons lose energy in a “friction” with the plasma, the second and third term on the left side in Eq. (2). The energy that the photons lose is immediately absorbed in the form of very small energy quanta and transformed to heat. Like friction this is not a reversible process. The second law of thermodynamics does not apply to “friction” processes. It therefore does not apply to the plasma redshift of photons. We can also ask: How does the heating transport jump from the photosphere to the transition zone? Eq. (13) above explains this. There is practically no plasma-redshift heating between the photosphere and the lower transition zone, because the electron density Ne in the intervening layers is too high and the temperature T too low according to Eq. (13). We can also say that all the low energy states are occupied in the cold and dense plasma below the chromosphere. However, some of the plasma-redshift heating leaks by conduction down into the chromosphere and increases its temperature. When the magnetic field is relatively strong, the plasma redshift may then lead to initiation of flares below the transition zone. Only plasma redshifting can explain these atypical phenomena. The ultraviolet photons and X-rays contribute to the heating and cooling; confer the “Strömgren spheres”. But the corresponding heating and cooling result in temperatures usually in the range of 104 to 105 K. Once in a while ultraviolet photons can, according to Eq. (13), with help of the magnetic field initiate creation of plasma bubbles below the transition zone. As these bubbles grow and become hotter the plasma redshift increases, because more of the spectrum can be plasma redshifted. It can take a long time for these “bubbles” to grow. Finally they erupt and create flares and arches.

Like the Sun, all stars, quasars, and galaxies must have intrinsic plasma redshifts, and a plasmaredshift heating in their analogous corona, and associated flares and arches. The conventional denial of intrinsic redshifts of these objects has caused not only difficulties, but also misinterpretations when

explaining many cosmological phenomena. In large hot stars, the first term in Eq. (12), which is proportional to the electron density integral, usually dominates. It also dominates in the case of the cosmological redshift by the plasma in intergalactic space. In these cases the plasma redshifts are nearly independent of the wavelength above the plasma-redshift cut-off, λ0.5, given by Eq. (13).

Electron density 1.E+09 1.E+08

Electron densities

1.E+07 1.E+06 1.E+05 1.E+04 1.E+03 1.E+02 1.E+01 1.E+00 1

100

1000

Distance from solar center

Figure 2. From reference [1]. Figure 2 in: arXiv:astro-ph/0401420 [ps, pdf, other], “Redshift of photons penetrating a hot plasma” by Ari Brynjolfsson. The ordinate shows the coronal electron density as a function of the distance R from solar center in units of solar radius R0 = 6.96·1010 cm. The cut-off for 5000 Å is at NeT = 4.75·1014 cm−3 K. Solar wind flux is assumed to be Nevp = 3.2·108 cm−2 s−1. The magnetic field is 6 Gauss in the transition zone. It decreases slightly faster than inversely with the square of the distance to the solar center. Between about 3 and about 5 solar radii the temperature drops significantly while the density decreases slowly. This is an unstable region and leads sometimes to condensation or “cloud” formation. Beyond this region the divergent magnetic field accelerates the charged particles‟ diamagnetic moments and causes thereby the observed acceleration of the solar wind. Also, the plasma redshift energy is transferred to the electrons. The electrons are therefore hotter than the protons and diffuse outwards ahead of the protons and pull the protons outwards. Both effects contribute to the solar wind.

In collapsars, such as the white dwarfs and the quasars the pressure broadening is large and the intrinsic redshift is often dominated by the second term on the right in Eq. (12). Because the pressure broadening varies from line to line, the plasma redshift varies from line to line in white dwarfs. Quasars, as we will show later, are related to super-massive black hole candidates (SMBHC). They are surrounded by hot high density extended corona. Their electron density integral (first term in Eq. (12)), and the pressure term (second term in Eq. (12)) are in this case exceptionally large. Their redshift is therefore exceptionally large. Plasma redshift explains also peculiar line widths (such as the broad lines), and redshift variations in quasars. Only the plasma redshift gives a reasonable explanation of these difficult-to-explain phenomena.

2.2. Redshifts of the solar Fraunhofer lines The redshifts of more than a thousand solar Fraunhofer lines (Joseph von Fraunhofer (1787-1826)) have been measured since about 1900. Most of the observed redshifts deviate significantly from Einstein‟s gravitational redshift. The redshifts are observed to vary not only from line to line, but also across the solar disk, and with time of the measurements. Many believe that the deviations from the predicted gravitational redshift are due to Doppler shifts in the line-forming elements. Others, such as M. G. Adam who researched this thoroughly, had difficulty believing that. Using conventional physics, she found prior to 1959 that the required Doppler shifts are too large. Also, these Doppler shifts should average out to about zero. But when Pound and Rebka Jr. in 1959 and Pound and Snider in 1964 thought, incorrectly, that they had confirmed Einstein‟s gravitational redshift, it was generally assumed that the observed deviations from the gravitational redshifts in the Sun were due to Doppler shifts in the line-forming elements. An elaborate system of currents in the line-forming elements of the photosphere was subsequently invented; see for example D. Dravins, L. Lindgren, and Å. Norlund in Astron. Astrophys. 96 (1981) 345, and a review by D. Dravins in Ann. Rev. Astrophys. 20 (1982) 61. However, there are significant discrepancies between observations and predictions of this conventional theory. For example, no reasonable current system can produce the excessive redshifts at the limb for the lines shown in Figure 4. Other discrepancies are discussed in section 5.6.3 of [1], arXiv:astro-ph/0401420. My analysis, which is similar to that of M. G. Adam, shows that in the photosphere the line shifts caused by currents in the line-forming elements average out and that the resulting average Doppler line shifts are nearly insignificant.

Excitation Functions for Collision Broadenings Relative collision broadenings

1.E+05 3 eV excitation level 4 eV excitation level

1.E+04 1.E+03

5 eV excitation level

1.E+02

6 eV excitation level

1.E+01 1.E+00 1.E-01 1.E-02 1.E-03 -100

400

900

1400

1900

The height in km in the solar atmosphere Figure 3. From reference [1]. Figure 3 in: arXiv:astro-ph/0401420 [ps, pdf, other], “Redshift of photons penetrating a hot plasma” by Ari Brynjolfsson. The ordinate shows how the relative collision broadening for each line varies with the height of formation in the solar atmosphere.

The main reasons for the variation in the plasma redshifts from line to line and across the solar disk are due to the second term in Eq. (12). The experimental determinations of the photon widths, γi = 1/τ, with Lorentzian distribution of the frequencies (same as the Cauchy distribution in statistics or the Breit-Wigner distribution in nuclear physics), are obtained by measuring the absorption beyond about three half-widths of the Gaussian line width. The Fourier components in the wings of the Lorentzian distribution, /([2 + ( – 0)2]), will then dominate the Gaussian distribution, exp [−A(ω – ω0)2/(2RT ω02)], of the line width, which is due to thermal movements in the line-forming elements. It is thus possible to distinguish experimentally the actual photon width from the width of photons from an undisturbed atom. SOLAR REDSHIFT Comparing plasma redshift theory with experiments 3.0E-06

2.5E-06

Redshift

2.0E-06

1.5E-06

1.0E-06

5.0E-07

0.0E+00 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Distance from the center of solar disk

Figure 4. From reference [1]. Figure 4 in: arXiv:astro-ph/0401420, “Redshift of photons penetrating a hot plasma” by Ari Brynjolfsson; see also reference [4]. arXiv:astro-ph/0408312 : “Weightlessness of photons: A quantum effect” by Ari Brynjolfsson. The ordinate shows the solar redshift as a function of the distance from the center of the solar disk on the abscissa. The horizontal blue line shows the expected gravitational redshift. The black curve shows the predicted plasma redshift, and the red squares the experimentally measured average redshifts of the 6297.8, 6301.5 and 6302.5 Å lines of Fe-I as measured by Adam and Higgs; see Table 3 below and section 5.6.1 of [1], arXiv:astro-ph/0401420. These variations shown in this figure are typical for strong lines with high excitation potentials for both lower and higher levels. The high excitation potentials cause the second term in Eq. (12) to be relatively small. For low excitation potentials, the second term in Eq. (12) is usually significant; and the center-to-limb effect very different. The depth of the line formation also influences the center-to-limb variations.

The photon widths can also be determined theoretically. The quantum mechanical photon widths of

the free atoms are usually broadened significantly by collisions resulting in the photon width, γ i. The simple estimates of the collision broadenings are illustrated in Figure 3. These rough estimates show the essence of the variations in the broadenings of γi with the height of the line formation in the solar atmosphere. This is important as it affects γi in the second term on the right side of Eq. (12). This broadening varies with the strength of the transition in the free atom, and with the excitation potential, pressure, and temperature in the line-forming elements. Interestingly, when the lower excitation potential is more than 2.5 to 3 eV and the line is so strong that it is formed relatively high in the photosphere, the collision broadening is small at all positions. For these lines, such as those shown in Figure 4 with lower excitation levels in excess of 2.223, 3.654, and 3.686 eV formed high in the photosphere, the center-to-limb effect is large due to the long path through the corona at the limb, in accordance with the first term of Eq. (12). This is a systematic effect and valid for all lines with high excitation potentials. For resonance lines, such as  = 5896 Å of sodium and  = 7699 Å of potassium (with lower excitation potential equal to zero eV), the large collision broadening decreases significantly with formation height (strength of the line); that is, towards the limb of the Sun. For these lines, the second term in Eq. (12), the collision broadening term, is then much greater at the center of the solar disk than at the limb, because at the center the lines are formed deeper in the photosphere where the densities are greater. At the limb the collision broadening is then much smaller than at the center, because of the much smaller densities at the limb. This decrease in the center-to-limb effect in the second term of Eq. (12) may nearly balance the increase in the center-to-limb effect from the first term in Eq. (12); for example, the total center-to-limb redshift of the resonance lines of sodium and potassium is nearly constant. This is also a systematic effect, which is easily confirmed. Thus, strong lines with high excitation potential, such as the iron lines in Figure 4, have generally a small second term in Eq. (12) and therefore a large center-to-limb effect; while lines with low excitation potentials, such as the resonance lines of sodium and potassium, have relatively broad collision width at the center and small collision widths at the limb. The second term in Eq. (12) is therefore much stronger at the center than at the limb. The summation of the two terms in Eq. (12) has therefore much smaller center-to-limb effect. The redshifts of weak lines are formed relatively deep in the photosphere. These weak lines are usually weak because of their high excitation potentials and therefore rather small collision broadenings. However, because they are weak and formed deep in the photosphere, there is at the very center often a small collision broadening, which increases the redshift at the very center of the solar disk. This collision broadening may then decrease and becomes insignificant as we move towards the limb. The redshift may even have a minimum about halfway towards the limb. Closer to the limb, the first term in Eq. (12) causes the redshift to increase steeply towards the limb due to longer path lengths in the solar corona. These systematic and predictable variations could not be explained before, but plasma redshift gives a simple and consistent explanation. My analyses of hundreds of lines shows that when the excitation potentials were high, the collision broadening is small, as is to be expected from Fig. 3. It follows that all lines with relatively high ionization potentials (lower level greater than about 3 eV, depending on the strength of the line and its

wavelength) will have significantly larger redshifts at the limb than at the center of the solar disk, because the second term in Eq. (12) is small. These predictions are consistent with observations, and a strong confirmation of the plasma redshift given by Eq. (12). Lines with low excitation potentials, such as the 5890 Å resonance line of sodium, which is collisionbroadened by a factor of about 10 to 18 has relatively large center redshift. It also has a small center to-limb effect, because the second term in Eq. (12) is large and its decrease towards the limb compensates roughly for the increase in the first term towards the limb. This applies also to the potassium 7699 Å resonance line. In both cases the predictions match the observations. A great many other lines were investigated in detail in this way. Surely, the plasma redshift explains the variations in center redshifts and the center-to-limb effect from line to line. The redshifts of the 6297.8, 6391.5 and 6302.5 Ǻ lines of iron serve well for illustrating the plasmaredshift in the Sun; see Table 3 above and Fig. 4, see Table 3 and Fig. 4 in [1] arXiv:astro-ph/0401420. The upper level excitation potentials of the lines are: 4.191, 5.620, and 5.653 eV, respectively, while the corresponding lower levels have excitation potentials of 2.223, 3.654, and 3.686 eV. These lines have thus rather high excitations potentials. They are also strong, and are therefore formed high in the photosphere where the collision broadening is small. These lines have been studied by many, but exceptionally thoroughly by M. G. Adam (Mon. Not. R. astr. Soc. 119 (1959) 460), and subsequently by Lloyd Higgs (Mon. Not. R. astr. Soc. 121 (1960) 421). It was important that they measured the redshift thoroughly close to the limb, where the redshift exceeds significantly the gravitational redshift. The differences between Adam‟s and Higgs‟ data are typical for good measurements. Table 3. Solar redshift experiments by Adams and Higgs and plasma redshift theory. Distance r/R0 from the center of the solar disk in units of solar radius R0 0.999 0.998 0.995 0.990 0.985 0.980 0.975 0.974 0.970 0.950 0.949 0.925 0.900 0.875 0.800 0.700 0.600 0.500 0.000 1

Measurements by Higgs (/) · 106

Measurements by Adam (/) · 106

Average of Higgs and Adam data (/) · 106

3.03 2.83 2.62 2.47 2.36 2.27

2.67 2.56 2.44 2.35 2.35 2.21

2.85 2.69 2.53 2.41 2.35 2.24

2.19 1.96

2.15 1.96

2.17 1.96

1.80 1.70 1.64

1.77 1.61 1.48

1.78 1.66 1.56

1.08

The values in the parentheses are obtained by interpolation.

Predicted1 by plasma redshift (/) · 106 3.12 (3.03) (2.86) (2.66) (2.53) (2.43) (2.36) 2.35 (2.27) (2.08) 2.04 (1.84) 1.72 (1.60) 1.40 1.24 1.14 1.08 1.00

Table 3 and Figure 4 illustrate the general trend of the first term in Eq. (12). The uncertainty in the data of Table 3 is usually ill-defined. The observer must select observation times when the solar atmosphere is relatively quiescent. The redshifts vary slightly with magnetic field and the sunspot cycle. The differences in the estimates by Adam and Higgs shown in Table 3 are indicative of the variations in good measurements. The slightly higher redshifts measured by Higgs are likely due to slightly higher electron densities in the corona, because Higgs‟ data were collected closer to the maximum of the sunspot cycle. The center-to-limb effects are usually measured relative to the redshift at the center of the solar disk. I used the absolute value of 1.08·10 −6 at the center as measured by Higgs. Analyses of the experiments illustrated in Table 3 and Figure 4 show that the solar lines are not gravitationally redshifted, but plasma redshifted. Had I selected the center-to-limb redshifts for the sodium 5896 or potassium 7699 Ǻ lines, the redshift would not have been as far from the gravitational redshift. Having investigated a great many lines, it became clear to me that plasma redshift predicted the variations in the redshift from line to line and across the solar disk without the gravitational redshift. The light intensities are high close to the surface of B-stars with temperatures about 3.5 times that of the Sun, and of O stars with temperature about 8 times that of the Sun. The plasma redshift heating at a small region around a point P in the corona is about proportional to NeTp4, where Ne is the electron density at P and Tp is the photosphere temperature. The Xray cooling is proportional to Ne2  T –1/2, where T is the temperature at P. But the Lyman Spitzer‟s conduction cooling, which often dominates, is proportional to   10–6 T 5/2. At high maximum temperatures in the corona the outflow also contributes to the cooling. These stars can maintain electron densities in their coronas that are significantly higher than those in the Sun. Their larger radii usually extend their coronas. Detailed estimates of their redshifts require knowledge about their magnetic fields and the gravitational pressure in the corona. The redshift, however, should be significantly higher than that in the Sun. They could easily be on the order of or exceed about 3 to 20 km/s, which is on the order of the observed K-effect, which has defied explanation since its discovery nearly 100 years ago; see Halton Arp (MNRAS, 258(1992) p.800-810. When observed on Earth, the lines from white dwarfs are not gravitationally redshifted, but plasma redshifted. Due to the large pressure broadenings the second term on the right side is responsible for most of the observed redshifts. The lines are gravitationally redshifted in the white dwarfs, but when the photons travel to Earth this gravitational redshift is reversed, and the redshift that we observe is the plasma redshift. It is of course difficult to expel the strong belief that it is the gravitational redshift that we observe; but the variations in the pressure broadenings from line to line explain the observed variations in the redshifts from line to line. From each white dwarf, the gravitational redshifts should be about the same for all lines, which contradicts observations.

3. Galactic corona The plasma redshift heating is first order in the electron density, Ne , while X-ray cooling is second order in density. The hot regions tend then to get hotter and the cold regions colder. This causes large temperature variations in intergalactic space and within the galactic coronas. The extremes of the temperatures are limited mainly by heat conduction. The cold temperatures are also limited by X-ray heating. In intergalactic space the average temperature is about 2.7·10 6 K, but the temperatures vary

significantly. We may have huge bubbles (sometimes even exceeding 100 Mpc in diameter) with center temperatures on the order of 30 million K surrounded by colder plasma at the surfaces of these “bubbles” with temperatures of about 0.3 million K, where the galaxies are usually formed. Within galaxies the temperatures vary significantly, with hot regions containing million K temperatures surrounded by colder, much denser clouds with temperatures below 10 4, or even 103 K. The temperature inhomogeneity has caused much confusion in the interpretation of the observations, especially since the important plasma-redshift heating was unknown. Already by the late thirties, extended areas in the Milky Way Galaxy were observed to emit Balmer lines and such lines as the 3727 Å-line from O II, which showed that oxygen and hydrogen and other atoms existed in ionized states in large regions of interstellar space. The interstellar density of hydrogen was estimated to be on the order of 3 cm–3, and the temperatures in the range of 10 4 to 105 K. This indicates a pressure corresponding to Ne T ≈ 3·104 to 3·105 cm-3 K. In 1939 (ApJ 89(1939)526S), my mentor, Bengt Strömgren (1908-1987) showed that the ultraviolet photons from stars A0 (T =10,700 K) to O5 (T =79,000 K) would ionize their surroundings, and form so-called Strömgren spheres around these hot stars. Without the plasma-redshift heating the temperatures in the Strömgren spheres would usually be between 104 to105 K. Later, the pulsar measurements have shown that the H II regions around bright stars within our Galaxy stretch far beyond the conventional Strömgren radii. Without the plasma redshift, it has not been possible to explain these extended hot H II regions or their high temperatures. One of the first to propose a Galactic corona was Lyman Spitzer, Jr.: ApJ. 124 (1956) 20. He had, however, great difficulties in finding a source for the heating of the corona. He suggested that maybe plasma bubbles produced by supernovae heating drifted into the Galactic corona. It became also clear that these H II regions were very hot, producing such ions as Fe X, which requires million-degree temperatures. The heating difficulties lead Spitzer to underestimate the density of the corona by a factor of about 20; see references in section 5.7.1 of [1] arXiv:astro-ph/0401420; see also sections C2 and in particular C2.1 of Appendix C of that source. Using conventional physics without plasma redshift, it has not been possible to explain the milliondegree temperatures and the large extent of the H II regions. Nor has it been possible to explain the heating of the solar corona, the Galactic corona, and the intergalactic space. Some astrophysicists still question the existence or minimize the importance of the galactic corona, because they cannot find sources for the necessary heating. Pettini et al. found clear evidence that the 6374.5 Å line from iron atoms that had lost 9 electrons (Fe X) caused a broad trough in the spectrum of the bright light from SN1987A in the Large Magellanic Cloud (LMC); see: Million-degree gas in the Galactic halo and the Large Magellanic Cloud. II - The line of sight to SN1987A, M. Pettini, R. Stathakis, S. D'Odorico, P. Molaro and G. Vladilo., ApJ. 340, p 256-264 (1989). This line could only be produced by hot plasma (about or exceeding 106 K) in an extended corona. Similarly, Sun et al., in arXiv;astro-ph/0606184v2 showed clearly that some clusters of galaxies have hot and relatively dense coronas with (T ·Ne > 104 Kcm-3). Only plasma-redshift cosmology (usually helped by X-rays and hot electrons from plasma redshift in intergalactic space, and by cosmic gamma rays and fast cosmic particles) explains the necessary heating to about million K in the Galactic corona.

Pettini et al. estimated that the column density of hydrogen is NH  3.2·1021 cm−2 . Over a distance of 50 kpc to LMC, this corresponds to an average density of (Ne)av ≈ 0.021 cm−3 and a high temperatures of T ≈ 1.0·106 K, which corresponds to an average pressure of p/k ≈ (NH+ + NHe++ + Ne) · T ≈ 1.917 · Ne ·T ≈ 4·104. The temperatures and densities along the line of sight will vary between hot and cold regions due to the instabilities created by the plasma-redshift heating, which is proportional to Ne , while the X-ray cooling is proportional to Ne2. The temperature inhomogeneity means that the densities will be significantly greater in the cold regions than in the hot regions. The hot regions will stretch over shorter distances than 50 kpc. The average density in the high-temperature regions will therefore be significantly higher than the (Ne)av ≈ 0.021 cm−3. In the hot regions, the average density along the line of sight to LMC is likely to be (Ne)av ≈ 0.03 to 0.07 cm−3, which is significantly higher than the density (Ne)av ≈ 0.021 cm−3, which obtained by averaging over the column densities estimated by M. Pettini et al.. W. I. Axford and S. T. Suess (see:http://web.mit.edu/space/www/helio.review/axford.suess.html) point out in an article on “The Heliosphere” that observations of Faraday rotation and dispersion of pulsar emissions indicate an average electron density of (Ne)avg ≈ 0.03 cm−3. Radio observations of the 21 cm interstellar line, however, indicate neutral hydrogen is (NH)avg ≈ 0.7 cm−3 , and observations of Lyman alpha absorption in spectra of nearby stars indicate a density of hydrogen of about 0.1 cm −3. Plasma redshift makes it clear that the temperatures must vary greatly in the corona due to the instability caused by plasma redshift heating being proportional to the electron densities, while the Xray cooling is second order in electron density. All these estimates may therefore be reasonably accurate. The value of (Ne)avg ≈ 0.021 cm−3 from Pettini and coworker‟s experiments applies to the fully uniformly ionized plasma, while (NH)avg ≈ 0.7 cm−3 applies to the colder plasma and condensed clouds. As shown in section 5.7.1 of [1] arXiv:astro-ph/0401420, even the plasma-redshift heating of direct light from the Galaxy is not adequate for the heating of the plasma. It is essential therefore to take the ionization and heating by X-rays and hot electrons from the intergalactic plasma into account. These low-energy X-rays are produced by the hot plasma in intergalactic space, which is heated by the plasma redshift to an average temperature of about 2.7·106 K; see Eq. (C19) of [1] arXiv:astroph/0401420. The cosmic gamma rays and the fast particles also contribute. As we will see later, this high density corona appears to remove the need for dark matter in producing constant Galactic rotational velocities beyond a certain distance from the Galactic center. Plasma redshift also predicts that the average densities of the hot intergalactic plasma are about 1600 times higher than those in the big-bang cosmology. These relatively high-density plasmas in intergalactic space leak into the galaxies and galaxy clusters, making dark matter unnecessary; see section 11. These intergalactic plasmas are so hot that they are difficult to detect.

4. Hubble constant derived from plasma redshift In the plasma-redshift cosmology, the Hubble constant H0 in km s−1 Mpc−1, the distances Rpl in Mpc to a star or a galaxy, and the cosmological redshifts z are all determined from the average electron density, (Ne)avg in cm−3 , along the line of sight to the object. In intergalactic space, the second term on the right side of Eq. (12) is usually insignificant compared with the first. We have then that:

H 0  3.077 105  ( Ne )avg

km s−1 Mpc−1.

(16)

For (Ne)avg  2 ·10–4 cm−3 in intergalactic space, we get that H0  61.5 km s−1 Mpc−1. We obtain the Hubble constant by determining the average electron density, (Ne)avg in cm−3 . We can obtain the average electron density from the distance relation, Eq. (17), for example, by using Cepheid stars. The Cepheid stars are relatively close, the average electron densities may then be relatively large, and the Hubble constant determined from Cepheid variables tends therefore to be relatively large. We can also obtain the Hubble constant and the average electron density from the magnitude-redshift relation for supernovae, Eq. (19) in section 6. These determinations would tend to result in slightly smaller values, because a greater fraction of the track goes through intergalactic space, where the electron density is lower. We can also determine the electron density from the surface-brightness redshift relation; see Eq. (21) in section 7. We can also obtain (Ne)avg from measurements of the cosmic X-ray background (CXB) and the cosmic microwave background (CMB). These measurements depend also on the temperature. We can then use the measurements to determine both the temperature and electron density. Big-bang cosmologists use several parameters to determine the different quantities. Still, there are significant differences. For example, Sandage et al. (arXiv:astro-ph/0603647v2, ApJ 653 (2006) 843) find H0 = 62.3 ± 1.3 (random) ± 5.0 (systematic) km s −1 Mpc−1, while Riess et al. (arXiv:astroph/0905.0695v1) find H0 = 74.2 ± 3.6 km s−1 Mpc−1. These differences are caused partially by the absolute calibration of the distances. The calibrations are affected by the cosmic time dilation, the Dark Energy and the Dark Matter. But due to the low densities assumed in the big-bang cosmology, the relations are assumed to be independent of the Compton scattering. In plasma redshift cosmology, the universe is not expanding, and the Hubble constant is not a measure of the expansion but of the electron density as indicated by Eq. (16). In intergalactic space, the electron densities are relatively high, Ne  0.0002 cm–3 . There is no time dilation because the universe is considered quasi static. Due to the high densities, the Compton scattering is important. The equations such as: the distance-redshift equation, the magnitude-redshift relation, the surfacebrightness- redshift relation predict then correctly the experimental results without the use of any mystical parameters like the inflation, dark energy, dark matter, and the accelerated expansion. When the line of sight passes through galaxy clusters, which have higher densities than intergalactic plasma, the Hubble constant will appear relatively large. As the measurements improve these variations in H0 can be used to improve the distance estimates. Plasma redshift explains the cosmological redshift and shows that the universe is not expanding. In the plasma-redshift cosmology, there is therefore no cosmic time dilation. This is consistent with the

experiments; see subchapter 5.9 of [1] arXiv:astro-ph/0401420. As shown by David F. Crawford‟s analysis of the gamma-ray bursts, also they are consistent with no cosmic expansion; see: http://arxiv.org/PS_cache/arxiv/pdf/0901/0901.4169v1.pdf. In the case of the magnitude-redshift relation for SNe Ia, the concurrent attenuation of the light intensity by Compton scattering in the plasma-redshift cosmology causes the magnitude-redshift relation in the plasma-redshift cosmology to differ from that of the big-bang cosmology; see the difference between Eq. (19) and Eq. (20) in section 6 below. This difference (caused mainly by the attenuation by Compton scattering) causes supernovae researchers to think that the expansion of the universe is accelerating. Had they used the correct Eq. (19), there would be no need for accelerated expansion. In he case of surface brightness, Eq. (21) in the big-bang cosmology differs significantly from the corresponding Eq. (22) in the plasma-redshift cosmology. The comparison with experiments shows that the plasma redshift equation, Eq. (22), predicts well the experimental results, while Eq. (21), valid in the big-bang cosmology, clearly conflicts with the experiments results; see reference [7] Ari Brynjolfsson http://arxiv.org/PS_cache/astro-ph/pdf/0605/0605599v2.pdf.

5. Cosmological distances Rpl and Rbb For the cosmological redshifts, we can usually disregard the small second term on the right side of Eq. (12). From Eq. (12) we derive then that the distance Rpl to a star in the plasma-redshift cosmology is :

R pl 

c 0.9746 ln(1  z )   ln(1  z ) Mpc, H0 ( N e )avg

(17)

For details of the deduction of Eq. (17), see Eqs. (49) and (50) in reference [1] arXiv:astroph/0401420. From Eq. (16), we have set H0 = 3.076·105 · (Ne)avg in km s−1 Mpc−1. The velocity of light is c = 2.9979·105 in km s−1. (Ne)avg in cm−3 is the average electron density over the distance Rpl in Mpc. For a measured redshift z and distance Rpl to a star, we derive the average value of the electron density (Ne)avg ≈ 0.0002 cm−3 in intergalactic space, and then from Eq. (16) the value of H0 ≈ 61.5 km s−1 Mpc−1 in intergalactic space We can thus check the plasma-redshift theory by independent estimates of (Ne)avg, such as from X-rays and from CMB, as we will see later. In the big-bang cosmology the comoving distances, Rbb in Mpc, are sometimes given by Hubble‟s law, that is, by Rbb = (c/H0)  z. But usually it is given by a rather complicated integral. We have that

z  1/2 k dz ' c 1   Rbb    sinn   1/2 1/2  2 H 0 k 0 1  z '  1   z '   z '  2  z '       m 

(18)

For k = constant we may write Eq. (18) in the form

z  c dz '   Rbb   sinn   1/2  3 2 H0  0 m 1  z '   k (1  z ')     

(18a)

where the parameters H0 , k, m , and  are adjusted to fit the experiments. For k = constant, we have that |k |1/2 in the denominator and in the integrand cancel each other. We have that sinn(x) = sinh(x) for k > 0, that sinn x = x for k = 0, and sinn x = sin x for k < 0. Usually, we set (for a flat universe) k = 1 – m –  = 0. In the limit of k = m =  = 0, Eq. (18) becomes identical to Eq. (17), which is valid for nonexpanding cosmologies, such as plasma redshift cosmology. For a constant H0, figure 5 shows the distance as a function of the redshift. Often, supernovae researchers adjust the parameters Ω m and ΩΛ to be about m = 0.3 and  = 0.7, so as to let Rbb be slightly greater than the predictions of Rpl in the plasma-redshift cosmology. This reduces slightly the effect of their omission of Compton scattering. The plasmas around supernovae and galaxies containing supernovae have densities greater than the average density in intergalactic space. These higher electron densities increase (Ne)avg and the value of H0 in km s−1 Mpc−1 , as given by Eq. (16). As the distance Rpl increases, a larger fraction of the path penetrates intergalactic space where the average density is lower. The Hubble constant, H0 , is then also slightly lower for distant objects than for nearby objects. When from the redshift of an object, we deduct the intrinsic redshifts that are caused by plasma redshift in the corona of the Milky Way and in the object‟s galaxy, we will find a reduced value of H0  61.5. This reduced value corresponds more closely to the average value for H0 in intergalactic space. The intrinsic redshifts may also be increased due to reddening by dust, as indicated by the analysis of Jha, S. et al. 2007, ApJ 659, 122, and Conley et al. arXiv:astro-ph/0705.0367 accepted ApJL. It is difficult but not impossible to distinguish the contributions from the plasma redshift and the dust. In the big-bang cosmology, we must distinguish between the comoving distance Rbb given by Eq. (18), the angular diameter distance, Ra = Rbb/(1+z), the luminosity distance, Rlu = Rbb(1+z), and the surface brightness distance: Rsb = Rbb(1+z)2, see Eq. (6) and Fig. 1 of reference [5] arXiv:astroph/0411666; “Hubble constant from lensing in the plasma-redshift cosmology, and intrinsic redshift of quasars”, and Eq. (A14) in [7], “Surface brightness in plasma-redshift cosmology”, arXiv:astroph/0605599. The comoving big-bang distance Rbb given by Eq. (18) is the distance between two points measured along a path defined at the present cosmological time. In the big-bang cosmology, we also have the

angular diameter distance Ra = Rbb/(1+z), which is the distance between the observer and the object at the time the object emitted the light. Due to the expansion, the angular diameter distance, Ra , is shorter than the comoving distance, Rbb, by a factor of 1/(1+z). In the plasma-redshift cosmology, the “angular diameter distance” is equal to the Euclidean distance Rpl, as defined in Eq. (17). The universe is not expanding, and there is therefore no difference between the two distances; that is, so that (Ra)pl = Rpl.

Distances versus redshift 7000

Distance in Mpc for Ho=100

6000

5000

4000

3000

Plasma redshift Big Bang param. (0.0, 1.0) Big Bang param. (0.3, 0.7) Big Bang param. (0.4, 0.6) Big Bang param. (0.5, 0.5) Big Bang param. (1.0, 0.0)

2000

1000

0 0

Redshift z

Figure 5. Same as Figure 1 in reference [7]: arXiv:astro-ph/0605599 [ps, pdf, other], “Surface brightness in plasma-redshift cosmology” by Ari Brynjolfsson. The ordinate gives the distance to an object as a function of its redshift. The heavy dark curve gives the distances Rpl in Mpc for plasma redshift cosmology. All five different colored curves give the comoving distances Rbb in Mpc for the big-bang cosmology corresponding to the different values of the parameters for dark matter (Ωm) and dark energy (ΩΛ) as functions of the redshifts z on the abscissa. The Hubble constant is in all cases set equal to H0 = 100 km s−1 Mpc−1. The blue dash-dash curve is for the parameter values (Ωm, ΩΛ ) = (0.3, 0.7) that are frequently used. The straight red dashed curve is for (Ωm, ΩΛ) = (0.0, 1.0), which corresponds to Rbb = (c/H0) z, which is the Hubble law. For small redshifts z, all the curves give nearly the same distance-redshift relation, the usual Hubble law.

In the big-bang cosmology, the light intensity from an object decreases with distance squared, or proportional to 1/Rbb2. It decreases also proportional to 1/(1+z), because of the redshift (lower energy of the photons); and it decreases by another factor of 1/(1+z) due to time dilation (more time elapses between photons). The total decrease in light is thus proportional to 1/[R bb(1+z)]2, which corresponds to a luminosity distance: Rlu = Rbb(1+z). In the plasma-redshift cosmology, the light intensity from an object decreases with distance squared, or proportional to 1/Rpl2. Due to the redshift (lower energy of photons), it decreases also proportional

to 1/(1+z); and it decreases by another factor of 1/(1+z)2 due to Compton scattering. The total decrease in light is thus proportional to 1/[Rpl 2(1+z) 3]. For this reason, we define the luminosity distance in the plasma-redshift cosmology as Rlu = Rpl(1+z)1.5. This difference between big-bang and plasma-redshift cosmologies is one of the main reasons that in the plasma-redshift cosmology the data from supernova observations do not need any accelerated expansion with decreasing z, as is required in the big-bang cosmology; see section 6 below. In the big-bang cosmology, the surface brightness (the observed luminosity per unit area) of an object decreases with the luminosity distance squared; it is proportional to 1/[Rbb(1+z)]2 and inversely proportional to the area of the object, which, due to the expansion, appears to increase proportional to (1+z)2. We get thus that the surface brightness decreases as 1/[Rbb(1+z)2]2. That is, the surface brightness distance is given by Rsb = Rbb(1+z)2. In the plasma-redshift cosmology, the surface brightness decreases with luminosity distance squared, or is proportional to 1/[Rpl(1+z)1.5]2. We find thus that in the plasma-redshift cosmology the surface brightness distance varies as Rsb = Rpl(1+z)1.5. The experimental data again confirm plasma redshift cosmology and contradict big-bang cosmology; see section 7 below. The experiments show also that in the plasma-redshift cosmology, the angular size is constant, or that the product of angular size and red shift is independent of the redshift. This contradicts big-bang cosmology, which predicts that the angular size of galaxies should decrease as 1/(1+z) (the area as 1/(1+z)2) with increasing z. These experiments thus indicate that there is no “time dilation” and therefore no expansion as required by the big-bang cosmology.. The distances are usually estimated from an object‟s absolute and observed magnitudes (such as supernovae Ia, and Cepheid variable stars). From such measurements, the big-bang cosmologists have determined the parameters (k, m,  ) to nearly equal (0.0, 0.3, 0.7). These parameters result in comoving distances that are nearly equal (see Fig. (5)) to the distances derived from Eq. (17), which are valid for the plasma redshift cosmology.

6. Magnitude-redshift relations for SNe Ia The magnitude-redshift relation is one of the most important relations in cosmology. Therefore, it has been studied most thoroughly. The predictions of the plasma-redshift cosmology can be tested against many good observations, such as those in the SNe Ia experiments. Due to the failure to deduce the plasma redshift, cosmologists were lead to assume that cosmological redshifts were due to Doppler effects. This then lead to the big-bang cosmology with the galaxies moving away from each other. Subsequently, when the big-bang cosmology did not fit the data, it was necessary to introduce besides the big bang the assumptions of: inflation, dark energy, accelerated expansion, dark matter, and black holes for explaining the experimental results. All

these assumptions with adjustable parameters defied physical explanation. Plasma redshift, on the other hand, explains the cosmological redshift without the need for cosmological expansion, and without any adjustable parameters, such as: inflation, dark energy, accelerated expansion, dark matter, and black holes, which all defy physical explanation. In the plasma-redshift cosmology, the relation between the cosmological redshift and the average electron density in intergalactic space is given by Eqs. (12) and (13) above. Eq. (16) gives the relation between the Hubble constant, H0 in km s−1 Mpc−1 , and the electron density, (Ne)avg , in cm–3, while Eq. (17) gives the relation between the distance Rpl in Mpc and the electron density, (Ne)avg and the redshift z.

In the plasma-redshift cosmology, the magnitude-redshift relation is given by

 c  106  m  M  5  1.086a  5  log   ln(1  z )   7.5  log(1  z ) ,  H0 

(19)

where m is the observed magnitude of an object with the absolute magnitude M; z is the cosmological redshift, c is the velocity of light in km s−1 , and the Hubble constant H0 is in km s−1 Mpc−1. The factor “a” in the third term on the right side is the optical absorption coefficient along the line of sight. It is due mainly to absorption in our Milky Way and in the host galaxy; see Eq. (54) in reference [1] arXiv:astro-ph/0401420. The absorption “a” does not include the redshift absorption or the Compton effect, which are therefore included in the 5 th term on the right side. The 4 th term on the right side shows how the observed magnitude, m, increases with the distance, Rpl = (c ∕H0)· log (1+z) in Mpc, as given by Eq. (17). The distance, Rpl, in the 4th term of Eq. (19) is in units of parsec (pc), while in Eq. (17) it is in units of Mpc. This explains the factor 10 6. The last term takes into account the increase, 2.5·log(1+z), in the observed magnitude caused by the lost redshift energy, and the increase, 5·log(1+z), in the observed magnitude caused by the lost energy in Compton scattering on the electrons along the track to the object (star or galaxy).

In the big-bang cosmology, the magnitude-redshift relation is usually approximated by

 c  106  m  M  5  1.086a  5  log   d ( z )   5  log(1  z )  H0 

(20)

In Eq. (20), the big-bang cosmologists sometimes set the factor d(z) = d(z, H 0, ΩΛ, Ωm ) in the fourth term on the right side equal to z (that is, the Hubble distance Rbb = (c/H0)  z); see for example Alan Sandage, ApJ. 133 (1961) 355. But more often they set it equal to the integral within the large brackets of Eq. (18). In Eq. (55) of reference [1] arXiv:astro-ph/0401420, I used the value d(z) = z. In Fig. (5) above, this corresponds to the straight red dashed curve for (Ω m, ΩΛ) = (0.0, 1.0). When we use d(z) = z, there is not much difference between predictions of plasma-redshift cosmology and those of the big-bang cosmology; see Table 4 of reference [1]: arXiv:astro-ph/0401420.

But subsequent to employing d(z) = z, as Sandage did in 1961, big-bang cosmologists realized that in the their cosmology the distance d(z) should be given by Eq. (18) with (Ω m, ΩΛ) ≈ (0.3, 0.7), see Fig. 5 above, which results in a distance that is close to the distance given by plasma-redshift theory; but which for large z-values differs significantly from the distance d(z) = z. This causes then a significant difference between the big-bang and plasma redshift cosmologies, which big-bang cosmologists call “accelerated expansion”.

Magnitude m-M

Supernova's magnitude versus their redshift 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32

Data with time dilation Data without time dilation Plasma redshift theory

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Redshift z Figure 6. From Figure 6 in reference [1]: arXiv:astro-ph/0401420 [ps, pdf, other], “Redshift of photons penetrating a hot plasma” by Ari Brynjolfsson; The magnitudes, m-M, of supernovas on the ordinate versus their redshifts, z, from 0.0 to 2 on the abscissa. The data include all 186 supernovas reported by Riess et al. ApJ., 607 (2004) 665 (see the expanded Table 5 of that source). The lower data points noted with blue squares and a blue curve show the absolute magnitudes, Mexp, as reported by Riess et al. The data points noted with red triangles and a red curve show the same absolute magnitudes back-corrected for the time dilation, M ≈ Mexp −2.5 ln(1+z). The black curve shows the theoretical predictions of the plasma redshift given by Eq. (19).

The fictitious “Accelerated Expansion” in the big-bang cosmology When the distances in the big-bang cosmology and the plasma-redshift cosmology are about equal, we get, for the curvature parameter k = 0, that d(z) = d(z, H0, ΩΛ, Ωm ) = d(z, H0, 0.7, 0.3 ) in Eq. (20) is roughly equal to ln(1+z). The magnitude m is in plasma redshift cosmology given by Eq. (19), which is 2.5 . log (1+z) greater than the magnitude given by Eq. (20), which is valid for the big-bang cosmology. The experiments agree with Eq. (19), which is valid for the plasma redshift cosmology. Big-bang cosmologists correct the discrepancy with experiments by adjusting the

distances. They do this by requiring H0 to increase with decreasing z. This increase in H0 with decreasing z corresponds to “Accelerated Expansion”. They sometimes also increase slightly the value of ΩΛ. In the plasma-redshift cosmology no such adjustment is needed, because the data fit the prediction of the plasma redshift theory. The “Accelerated Expansion” is thus a consequence of the incorrect Eq. (20) in the big-bang cosmology. The last term, 5 log (1+z), in Eq. (20) needs to be replaced by about 7.5 log (1+z) if it is to fit the observations.

The fictitious “cosmic time dilation” in big-bang cosmology If the universe is expanding, then there must be a “cosmic time dilation”; but if there is no cosmic time dilation, the last term in Eq. (20) would be only 2.5 log (1+z) instead of 5 log (1+z). This would exaggerate the difference between Eq. (19) and Eq. (20). It is important therefore for bigbang cosmologists to have the cosmic time dilation. They contend that it has been proven independently that there is a “cosmic time dilation”; see e.g., Goldhaber et al. ApJ. 558 (2001) 359: http://arxiv.org/PS_cache/astro-ph/pdf/0104/0104382v1.pdf. “Cosmic time dilation” is an integral part of the big-bang expansion of the universe. Without “cosmic time dilation” there is no expansion. I have pointed out that the “experimental proof” by Goldhaber et al. is invalid, because Goldhaber‟s proof disregards “Malmquist bias”, which affects the interpretation of the relevant data; see section 5.9 in reference [1]: arXiv:astro-ph/0401420 and section 1 in reference [6]: arXiv:astroph/0602500. But experiments show that there is a significant variation in the size of the SNe Ia. Therefore the “Malmquist bias” must be taken into account. “Cosmic time dilation” in the experimental data used by Goldhaber et al. assumes that the “Malmquist bias” is zero, which is impossible, because it is thoroughly proven that the luminosities of the supernovae vary with the size of the explosions. The supernovae type Ia are nearly but not completely standard candles. They must therefore show “Malmquist bias”; that is, the most distant supernovae will have slightly larger explosions and must therefore be slightly brighter than average nearby supernovae. The difference between Eq. (19) and Eq. (20) is exaggerated by a difference caused by intrinsic redshift. The intrinsic redshift in the Milky Way and the host galaxy for the SNe Ia causes the Hubble constant for nearby supernovae (Cepheid galaxies) to appear greater than for distant supernovae (and distant Cepheid galaxies); compare Eq. (17). Recently, also, David F. Crawford (see: “No Evidence of Time Dilation in Gamma-Ray Burst Data”; http://arxiv.org/PS_cache/arxiv/pdf/0901/0901.4169v1.pdf) has given a rather conclusive proof that gamma-ray bursts show no cosmic time dilation. Just as in the magnitude redshift relation for SNe Ia, the gamma-ray bursts must show cosmic time dilation if the universe is expanding. Thus the plasma-redshift theory predicts, and both the SNe Ia experiments and the gamma-ray bursts experiment confirm that there is no cosmic time dilation; that is, the universe is not expanding. When we measure the observed magnitude m and the redshift z for a given absolute magnitude M, we can for each supernova determine the Hubble constant H0. From Eq. (16), we obtain then the average electron density (Ne)avg = 3.251·10−6 ·H0 ≈ 0.0002 cm−3. This average electron density in the plasma-redshift cosmology is about 1600 times greater

than the average density in the big-bang cosmology. It is therefore no wonder that the big-bang cosmologists had to “sprinkle” some dark matter here and there, such as in galaxies and in galaxy clusters. We will see later that due to the high densities of hot plasma in intergalactic space much more plasma leaks into the gravitational depressions created by galaxies and galaxy clusters and some gravitational lenses. The almost invisible hot plasma is mixed with relatively cold hydrogen clouds (due to the temperature instabilities created by plasma redshift heating, which is first order in density, and X-ray cooling, which is second order in density). These plasmas and hydrogen clouds in the coronas of galaxies and in galaxy clusters usually have significantly greater total mass than the visible stars and dust. We could say that the dark matter consists of dense, nearly invisible hot plasma mixed with cold hydrogen clouds. Besides its mass, which influences the rotational velocities of galaxies, the hot plasma is not completely invisible, as it can be detected through the X-rays it emits and through the CMB and intrinsic redshifts. These X-rays are heavily absorbed in the Galaxy. though.

Magnitude versus redshift for SN Ia 46.000

Magnitude m-M

44.000 42.000 40.000

magnitude without time dilation Plasma redshift theory

38.000 36.000 34.000 0.000

0.200

0.400

0.600 Redshift

0.800

1.000

1.200

Figure 7. The black curve is that predicted by the plasma redshift, while the blue squares show the experimental data points from the Supernovae Legacy Survey (SNLS) project as reported by Astier et al. (2005), Astron. Astrophys, 447 (2006) 31-48. http://www.arxiv.org/PS_cache/astro-ph/pdf/0510/0510447v1.pdf. This figure corresponds to Fig. 1 in http://www.arxiv.org/abs/astro-ph/0602500; “Magnitude-Redshift Relation for SNe Ia, Time Dilation, and Plasma Redshift” by Ari Brynjolfsson.

The good fit between the predictions of the plasma-redshift cosmology and the SNe Ia measurements along the entire z range is a strong confirmation of the plasma-redshift cosmology; see Figs. 6 and 7, above or Fig. (1) in [2] and Fig. 1 in [6]. From the data by Astier et al. in Astron.Astrophys. 447 (2006) 31-48, we estimate that in intergalactic space the Hubble constant is H0 ≈ 62.6 ± 0.14 ± 7 km s−1 Mpc−1, where the ± 7 km s−1 Mpc−1 stands for the uncertainty in the absolute calibration. For this value, we derive from Eq. (16), an average electron density (Ne)avg = (2.04± 0.2) · 10−4 cm−3 in intergalactic space, which is thus the average value for the long distances to the most distant supernovae. The estimates based on the data reported by Riess et al. Astrophys.J. 607 (2004) 665-687 (arXiv:astro-ph/0402512) are H0 ≈ 59.44 ± 0.14 ± 7 km s−1 Mpc−1. The average of 62.6 and 59.44 is H0 ≈ 61.0 ± 0.14 ± 7 km s−1 Mpc−1. From Eq. (16), we get that the average electron density in intergalactic space is then equal to (Ne)avg = 61/307600 = (2.00 ± 0.23) · 10−4 cm−3.

The Hubble constant and intrinsic redshifts The Hubble constant H0 ≈ 61.0 ± 0.14 ± 7 km s−1 Mpc−1in the plasma-redshift cosmology is significantly lower than the estimates of H 0 in the big-bang cosmology, which often exceeds about H0 = 70 km s−1 Mpc−1. From Eq. (16) we get for H0 = 70 that the average electron density is then (Ne)avg = 70/307600 = (2.28 ± 0.23) · 10−4 cm−3. These higher estimates of H0 are usually based on objects that are closer than the supernovae. We have also that the intrinsic redshift in nearby objects have greater weight. The difference between Eq. (19) and Eq. (20) increases the value of H0 in the big-bang experiments. The average electron densities along the tracks to these closer objects are higher, and according to Eq. (16) the average values of H0 are therefore larger. The big-bang cosmology, which denies intrinsic redshifts, can not explain the differences between nearby and distant objects, while plasma-redshift cosmology explains them as a natural consequence of intrinsic redshifts. (Also this effect contributes to the apparent “Accelerated Expansion” of the universe in the big-bang cosmology.) All the predictions of the magnitude-redshift relation, Eq. (19), in the plasma-redshift cosmology are consistent with observations. No fictitious parameters, such as: dark energy, dark matter, and accelerated expansion are needed to explain the observations. The observations show that there is no “cosmic time dilation”. The universe is thus quasi-static, as can be seen from Figs. 6 and 7 above, and references [1]. arXiv:astro-ph/0401420 and [6]. arXiv:astro-ph/0602500 : In the 80‟s, I compared the observed magnitude redshift relation with the prediction of the theory. The highest redshifts data, at about z = 0.5, were those by Sandage and Hardy in AP. 183 (1973) 743-757. The predictions of the plasmaredshift cosmology were then about equal to that of the big-bang. Since then it has, with the addition of the supernovae, been possible to expand the data set to about z ≈ 1.7. The new data fitted the prediction of the plasma redshift theory equally well, but the big-bang cosmologists had to introduce the “dark energy” (DE) and “dark matter” (DM) parameters and accelerated expansion parameter (in addition to cosmic inflation) to make the data fit the predictions.

7. Surface brightness of galaxies The surface brightness of galaxies has been studied thoroughly; see for example the following articles: Sandage and Lubin: A.J. 121 (201) 2271; ibid. page 2289; A.J 122 (2001) 1071; and ibid p.1084. We can therefore check the experimental results of these highly experienced researchers against the predictions of plasma-redshift cosmology; see: “Surface brightness in plasma-redshift cosmology” by Ari Brynjolfsson, in [7]: arXiv:astro-ph/0605599. The big-bang cosmology predicts that the surface brightness, isb, should decrease with an increase in the redshift z as 1/[Dbb2(1 + z) 4], where Dbb is the comoving distance defined by Eq. (18). In big-bang cosmology, we have therefore that the surface brightness is given by

isb 

(isb )0 (isb )0 (isb )0   2 4 Dsb2 Dlu2 1  z  Dbb2 1  z  41

(21)

In contrast, the plasma-redshift cosmology predicts that the surface brightness should decrease with the redshift z as 1/[ Dpl2(1 + z)3], where Dpl is the plasma redshift distance defined by Eq.(17). In the plasma-redshift cosmology, we have thus that the surface brightness is given by

isb 

(isb )0 (isb )0  3 Dsb2 Dpl2 1  z 

(22)

These predictions of Eqs. (21) and (22) can be compared with observations.

Surface brightness predictions compared with experiments The thorough analyses of the experiments by Sandage and Lubin: A.J. 121 (201) 2271; ibid. page 2289; A.J 122 (2001) 1071; and ibid p.1084 show that the observed surface brightness, besides decreasing with the square of the distance as given by Eq. (17) above, also decreases proportional to 1/(1 + z)3, in agreement with the prediction of the plasma-redshift cosmology. For greater details of the analysis, see in particular Table 3 of [7] Ari Brynjolfsson: “Surface brightness in plasma-redshift cosmology”, in arXiv:astro-ph/0605599. Table 3 of [7] shows that for the Petrosian values  = 1.7 and 2 as recommended by Sandage and Lubin, the Tolman signal (1+z) n corresponds to an average of n = 2.88, n = 2.91, and n = 2.93 (or about n = 3) for each of the two I-band galaxies and one R-band galaxy groups. It is also of interest that when using plasma-redshift cosmology the I-band galaxies give the same Tolman signal, 3, as the Rband galaxies. In the big-bang cosmology there is a significant difference between the I-band and R-band galaxies, because this difference is sensitive to the expansion. The experimental evidence is thus strongly in favor of the non-expanding plasma-redshift cosmology. Big-bang cosmologists cannot explain this discrepancy. Instead, they explain it as a kind of “surface brightness evolution”; or by asserting that at higher z-values the surface brightness (for some mystical reasons) is much greater for R-band than for I-band galaxies. This evolution of surface brightness is not supported by other experiments.

Thus the surface brightness experiments clearly contradict big-bang cosmology, while supporting plasma-redshift cosmology.

8. Cosmic microwave background The cosmic microwave background (CMB) has been investigated thoroughly “Most cosmologists consider this radiation to be the best evidence for the big-bang model of the universe”; see Cosmic microwave background radiation in Wikipedia. But plasma-redshift cosmology, which uses only conventional axioms of physics and more exact calculations than those usually used, shows that the

CMB (without any big bang) is emitted by the hot intergalactic plasma in accordance with wellestablished laws of physics. For deducing this CMB emission it is essential to use the plasmaredshift cross section for the absorption. The big-bang cosmologists who do not know about the plasma redshift cross section have no chance to deduce the CMB correctly. Importantly, the densities of the hot plasma in intergalactic space in the plasma-redshift cosmology are about 1600 times higher than in the big-bang cosmology. Important for deriving the beautiful black-body spectrum is the fact that the plasma-redshift cross section is independent of the frequency for frequencies above about 10 9 Hz. For frequencies below 10 9 Hz, the CMB intensities increase as predicted by the plasma redshift, but not by the big-bang cosmology. In section 5.10 and Appendix C of reference [1]: arXiv:astro-ph/0401420, I show that the CMB with blackbody temperature TCMB is emitted by the hot intergalactic plasma. At the plasma density of (Ne)avg  210–4 cm–3 in intergalactic space, the pressure of free-free emission is an insignificant fraction (less than 10 –6) of the pressure in the CMB emission. We should therefore equate the pressure of the CMB emission with the particle pressure in the plasma. When we then equate the photon pressure p, which is given by: 



u 4 4 2h 3 d 4 4 p    B  d    2  h / kTCMB   TCMB 3 3c 0 3c 0 c e  1 3c

ergcm–3 ,

(23)

with the plasma pressure kNT, we find that the energy density u is given by: (see Eq. (61) in section 5.10 of reference [1]: http://www.arxiv.org/PS_cache/astro-ph/pdf/0401/0401420v3.pdf.)

4 4 4  TCMB  7.566 1015  TCMB  3NkTe c

ergcm–3,

(23a)

where N  1.917· Ne with (Ne)avg  2.0·10−4 cm−3, k = 1.3806·10−16 erg K−1 is the Boltzmann constant,  = 5.6704·10–5 erg cm–2 s–1 K–4 is the Stefan-Boltzmann constant, c is the speed of light, and the average thermal particle temperature in the plasma is Te  2.7·106 K. By inserting these values (which are obtained from the supernovae, SNe Ia data, and from X-ray experiments) into Eq. (23a), we see that the blackbody temperature is TCMB  2.73 K, in agreement with that observed. We should realize that the photon pressure p in Eq. (23) is always correct, where TCMB  2.73 K is the blackbody temperature of the microwave radiation background. In the literature it is customary to equate this black-body temperature with the temperature of the particles, because that is what we did when we measured the blackbody temperature from a hole in a solid block. Many physicists are inclined therefore to equate TCMB with the particle temperature. We should realize, however, that more generally for obtaining equilibrium (no work) we should equate the photon pressure with the plasma pressure kNT, as we did in Eq. (23a).; see Appendix C of reference [1]:

http://www.arxiv.org/PS_cache/astro-ph/pdf/0401/0401420v3.pdf. The plasma-redshift cross-section in sparse hot plasma has the interesting characteristic that it is independent of the frequency above the cut-off frequency. This is what causes its beautiful black-body spectrum of CMB. Eq. (23a) for the CMB is obtained by equating the radiation pressure (a/3) · TCMB4 with the plasma pressure p = k(NT)avg, which is roughly isotropic and uniform in intergalactic space, although the densities and the temperature vary greatly. The constant a = 4/c, where  is the Stefan-Boltzmann constant. In free-free emission, which is used in the big-bang cosmology, the absorption coefficient varies strongly with the frequency, and we can not use simple relations therefore to obtain the blackbody spectrum. The relationship given by Eq. (23a) is unusually simple, because the plasma redshift cross section has the same optical depth, which for Ne  0.0002 is R = (3.32610– 25

Ne)–1 1.51028 cm for all frequencies of CMB above the cut-off at 109 Hz.

Contrasting this, the free-free emission for   1.6041012 Hz and at the same density has an absorption length at about R  1.851042 cm, for   1.6041011 Hz it is about R  2.151040 cm, and for   1.6041010 Hz it is about R  2.571038 cm; see Appendix C1.4 of [1]: http://www.arxiv.org/PS_cache/astroph/pdf/0401/0401420v3.pdf.

The plasma in intergalactic space is fully ionized and has a fairly uniform pressure. In the frequency range of interest, the plasma redshift dominates all other reactions, such as the free-free emission, by many orders of magnitude. Also, this fact explains the beautiful blackbody spectrum of the CMB. When deriving the analogous relation for the approximate blackbody spectrum of the Sun (or the stars), we must take into account the different optical densities  (or relaxation lengths 1/) for the different parts of the spectrum. We must also take into account the different depths and different pressures in the line-forming elements, and we must take into account that usually only a small fraction of the atoms are affected by the photon pressure. The calculations of the emission spectrum in this case are therefore very elaborate. When we do them, we find only a rough approximation to the blackbody spectrum of the Sun (and the stars). It is usually surmised that the spectrum from the Sun (and the stars) is a blackbody spectrum, although the actual measurements in the laboratory and the corresponding theoretical deductions differ significantly. Big-bang cosmologists base their explanation of the CMB on the free-free emission and absorption, which vary significantly with frequency and temperature. The calculations of the CMB spectrum in the big-bang cosmology are therefore difficult, because the free-free absorption coefficient is   NeNi–2Te–3/2.

Usually, the relaxation length 1/ for free-free emission far exceeds (by several orders of magnitude) that for the plasma redshift. For obtaining the beautiful black-body radiation, the big-bang cosmologists have had to assume cosmic inflation in addition to the big bang, and hypothesize that the universe cooled and condensed at about z = 1400, and then re-ionized at about z = 6, etc. Attempts are being made presently to validate some of these assumptions. Plasma-redshift predicts that these attempts will fail, because the intergalactic plasma in the plasma-redshift cosmology has always been hot and fully ionized. It predicts that no extraordinary condensation for z between 6 and 1400 will be found. In the CMB range of frequencies, the plasma-redshift absorption in the intergalactic plasma exceeds the free-free absorption by a factor greater than 10 6; see section C1.4 in Appendix C of [1] arXiv:astroph/0401420. In the plasma-redshift cosmology, the CMB is averaged over a huge volume with a radius of lCMB = CMB = 1/  ≈ 1/(3.326·10−25· Ne) = 1.5·1028 cm (approximately 5000 Mpc). This long distance reduces the effect of the plasma inhomogeneity, which is large on a much smaller scale, usually a fraction of a Mpc. The CMB radiation is also Compton-scattered on the individual electrons with a Compton length Compton = 0.5· CMB ≈ 7.5·1027 cm ≈ 2500 Mpc. This scattering helps homogenize the CMB and make it more isotropic. The variations in the plasma temperature, Te , and densities in intergalactic space are significant, but the energy density on the left side of Eq. (23) is proportional to the pressure, or to Ne·Te , which is about constant. This constant pressure helps reduce the variations in the blackbody temperature, TCMB, of the cosmic microwave background. The absorption length lCMB = 1/(3.326·10−25 ·Ne ) ≈ 1.5·1028 cm ≈ 5000 Mpc (one Hubble length) for all frequencies of the CMB in the intergalactic plasma can be considered to be the radius of a “blackbody cavity”. It is obtained from Eq. (12) by setting 3.326·10−25 ·Ne · lCMB = 1. In the case of big-bang cosmology, the low densities and the small absorption coefficient in the free-free emission means that the CMB emission must originate far beyond one Hubble length. In free-free emission, the absorption length varies significantly with the frequency (about proportional to 1/2). In the big-bang cosmology, this is overcome by assuming that CMB originates when matter was relative hot and relatively dense, so that blackbody radiation dominated and the matter was very dense, and hence the absorption length was small. (Still the temperature and the densities must vary significantly with the relaxation length.) The big-bang cosmologists then assume that at a redshift z equal to 1000 to 1500 the intergalactic plasma cooled to neutral hydrogen followed by reionization at a redshift between 6 to 3. This period of neutral hydrogen circumvents to some extent the problem of distortion of the spectrum by free-free emission and absorption. This scenario is not supported by facts, but is pure speculation about the supernatural big bang. Presently, there are ongoing attempts being made to confirm this by measuring, for example, the 21 cm H I line expected at these redshifts. So far, this has not been successful. This scenario contradicts the predictions of the plasma-redshift cosmology, which is based on pure physics.

Some good physicists (for example, P. J. P. Peebles, “Principles of physical Cosmology”, Princeton University Press, 1993, http://press.princeton.edu/titles/5263.html; see Eq. (7.15) and Fig. 7.1 of that source) have incorrectly thought that the beautiful, perfect blackbody spectrum proved that the CMB is not absorbed in intergalactic space, because any absorption would deform the spectrum. However, this argument is faulty, because when the emission is equal to the absorption and the absorption independent of the frequency, as it is in the plasma-redshift cosmology, the spectrum will continue to be a perfect blackbody spectrum.

The main deviations from the average TCMB are due to variations in p = kNTe caused by the variation in gravitational potential. In the corona of galaxies and galaxy clusters the plasma pressure kNTe is significantly higher than in intergalactic space. The dimensions of these high-density regions are usually a small fraction of 5000 Mpc. Still, the densest regions shift the frequency to slightly higher frequencies than those that make up the CMB. The increased emission from these high-density regions is counteracted by increased Compton scattering of the background radiation. These highdensity regions will nevertheless result in minuscule series of blackbody spectra that contaminate the CMB and increase slightly the frequency and make the CMB appear to have a slightly higher temperature in directions pointing towards the high-density regions. While, in regions of low densities, the plasma pressure is slightly lower, and therefore TCMB slightly lower. These fluctuations average to a reasonably uniform and isotropic TCMB. The anisotropy created in this way is related to the intrinsic redshifts, which for many galaxies is on the order of 0.001, which corresponds to fluctuations in CMB temperature of about 0.0006 K. The higher plasma densities in clusters absorb and scatter the background CMB slightly, and thereby reduce slightly the increase in TCMB. Nevertheless, the high density of nearby clusters, such as the Centaurus cluster at (l, b) = (302°, 22°), the Virgo cluster at (l, b) = (284°, 74°), and the Great Attractor at (l, b) = (280°, 6°) should cause slightly increased intensity in their directions. The measurements then also indicate that CMB has a significant dipole moment; that is, the CMB temperatures are slightly higher in one direction than in the opposite direction. The big-bang cosmologists interpret this as showing that our Milky Way Galaxy is moving at the very high speed of about 627 ± 22 km s−1 in the direction of the Galactic coordinates (l, b) ≈ (276º ± 3, 30º ± 3); see Charles H. Lineweaver, “The CMB Dipole: The most recent measurement and some history”, arXiv:astro-ph/9609034v1.pdf. A more resent analyses by Jha, S. et al. 2007, ApJ 659, 122 found that the Local Group moved with the velocity of 541 ± 75 km s−1 in the direction of (l, b) ≈ (258 ± 18°, 51 ± 12°). They found that this is consistent with the amplitude and position of the CMB dipole moving at 635 km s −1 towards (269°, +28°). These direction are reasonably close to the direction to the hot and relatively dense hot plasma around the Virgo cluster at (l, b) = (284°, 74°); the super-cluster Great Attractor at (l, b) = (280°, 6°) and the Centaurus cluster at (l, b) = (302°, 22°). The higher plasma densities caused by the higher gravitational potentials of these galaxy clusters are therefore likely to be the main cause of the CMB dipole. In the big-bang cosmology these high velocities, 635 km s−1 , were unexpected and remain unexplained. This velocity corresponds to 2.1 keV, or a proton temperature of about 25 million K. By contrast, the plasma redshift appears to give a reasonable explanation. In the plasma-redshift cosmology, not only will the higher intra-cluster plasma densities in these directions increase the CMB temperature slightly, but also the large gravitational attractions by the Virgo cluster, the Great Attractor, and the Centaurus cluster will affect, slightly, the electron densities, and therefore the intrinsic redshifts. Future experiments and analyses may resolve this issue; see http://www.atlasoftheuniverse.com/galgrps/vir.html Similarly, there exist cold clouds that do not emit CMB but which may Compton scatter the CMB. This may reduce the intensity in the directions of the cold clouds. For example, a cold spot in the CMB is found in the direction of (l, b) ≈ (207.8°, −56.3°). This coincides with low source counts in the NRVO VLA Sky Survey (Condon et al. in AJ.115 (1998) 1693) in this direction; see: Rudnik, Brown, and Williams in arXiv:astro-ph/0704.0908v2 3 Aug. 2007. This cold spot in the CMB, which

can not be explained by the big-bang cosmology, could actually be due to colder or condensed plasma in this direction which scatter the CMB more than it increases the emission. The exact cause is still to be determined. The plasma densities in intergalactic space are much higher (Ne ≈ 2.0·10−4 cm−3) than that (about 1.4·10−7 nucleons cm−3 for ·h2 = 0.13) surmised by the big-bang cosmologists; see Eq. 6.27 in P. J. P. Peebles, “Principles of physical Cosmology”, Princeton University Press, 1993, http://press.princeton.edu/titles/5263.html . Big-bang cosmologists cannot find a way to heat the plasma to the high average per particle temperatures of Te ≈ 2.7·106 K. (The average temperature per volume unit is much higher than the average temperature per particle.) Due to the transparency of the hot plasma, they assume that the plasma density is very low. Even when they assume that the universe is hot, they usually assume too low temperatures. (Even the plasma within the Strömgren radii is much colder than that heated by plasma redshift). They sometimes object that the high densities would cause much too fast a gravitational concentration of intergalactic matter. They did not realize that heat fluctuations are much more powerful than gravitational attraction. In fact, it is mainly the heating imbalance between plasma redshift heating, which is first order in density, and the X-ray cooling, which is usually second order in density, that causes the concentration of matter into colder regions, where galaxies are formed, and huge hot bubbles, with temperatures often in excess of 30 million degrees, that separate the cold regions. The gravitational attraction plays of course an important role within the galaxies and in the formation of black hole candidates which concentrate and transform old star matter to primordial matter, which is then pushed outwards, as we will see. Plasma redshift transfers some of the photon energy to the electrons, which thereby become hot. The electrons diffuse outwards and drag the positive particles outwards. Also, the divergent magnetic field pushes the diamagnetic moments of the particles outwards. There are thus forces that push the particles outwards and counteract the gravitational attraction, thus conferring the solar wind and often-seen jets that stream away from high-density objects.

8.1. Intensities of the CMB for frequencies below 10 9 Hz In intergalactic space, the plasma-redshift heating is proportional to Ne, while the X-ray cooling and recombination cooling are proportional to Ne2. The hot regions will then get hotter and the cold regions colder until other processes, such as heat conduction, counteract the spread in temperature. This causes instabilities leading to huge hot “plasma bubbles” surrounded by colder plasma on the surfaces of the hot “bubbles”. Galaxies and the bridges between the galaxies are usually at the colder edges of these hot “plasma bubbles”. The temperature variations are damped mainly by the heat conduction, cooling from the hot spots to the cold spots, and by X-ray heating of the cold spots. These bubbles are consistent with observations; see M. J. Geller & J. P. Huchra, Science 246, 897 (1989) and “The CfA Redshift Survey” by Huchra; http://www.cfa.harvard.edu/~huchra/zcat/. Big-bang cosmologists have had difficulties explaining these structures, because the heating by plasma-redshift was unknown to them. In spite of these instabilities, the pressure and the product (Ne · T) ≈ 540 are nearly constant. The blackbody emission temperature TCMB, given by Eq. (23), depends only on the pressure and is nearly constant, or independent of the temperature variations. For (Ne)avg ≈ 2·10–4 cm–3 and (Te)avg ≈ 2.7·106 K, and insignificant magnetic fields B, the cut-off wavelength, λ0.5, as given by Eq. (13) is then

  0.5  3.185 106 

Te  1.37 107  Te1.5  608 Ne

cm,

(24)

where (Ne · Te) ≈ 540 and Te ≈ 2.7·106 K. However, in the cold regions where Te  2.7·106 K, the cut-off wavelength can be much shorter. For the same average pressure, (Ne · Te)avg ≈ 540 and for Te ≈ 2.7·105 K at the surfaces of the bubbles, the 50% cut-off wavelength, λ0.5, is only about 19.3 cm (or 0.5 = 1.55·109 Hz). Therefore, in the colder regions of intergalactic space, the 50 % cut-off wavelength λ0.5 for plasma redshift may be about 19.3 cm, or less. Within the galaxies where the pressure is significant, the cut-off wavelength is even shorter. In colder regions of space where Te ≈ 2.7·105 K, the 21 cm wave length will then be redshifted about 56% less than the optical lines (see the oscillator strength function in Table 1). Within the coronas of stars and galaxies the reduction in the redshift of the 21 cm line is more significant. For λ 19.3 cm this effect is more significant. The intensity of the CMB with reduced redshifts will accumulate and increase the intensity mainly between about 20 cm and 20,000 cm; that is, for wavelengths λ >20 cm, the intensity of the CMB decreases less steeply with increasing wavelengths than the CMB intensity i(λ) ≈ 2kTCMB ν 2∕c2 ≈ 2kTCMB λ2. These predictions of the plasma-redshift theory are consistent with observations of increased intensities of the CMB at low frequencies; see for example Fig. 6.4 in: P. J. P. Peebles, “Principles of Physical Cosmology”, Princeton University Press, 1993. This figure shows clearly that the intensities start to increase at the wavelengths predicted by plasma redshift cosmology. This is an important confirmation of plasma redshift cosmology. See also Table 2 of Giardino et al. (in: arXiv:astro-ph/0202520v1 28 Feb 2002), who had to use the CMB temperatures of 2.75, 2.83, and 5.92 K for matching the observed intensities at the frequencies 2.326, 1.420, and 0.408 GHz, respectively. The excess intensities may stretch down to wavelengths λ0.5 ≥ 6 cm, or up to ν0.5 ≤ 5·109 Hz; see for example Fig. 6 in Hinshaw et al. ApJS., 170 (2007) 288, (arxiv:astro-ph/0603451v2), and Fig.10 in Bennett et al. Ap.J.S.148(2003) 97; http://www.arxiv.org/PS_cache/astroph/pdf/0302/0302208v2.pdf In the low frequency region the intensity of the CMB should be proportional to i(ν) ≈ 2kTCMB ν2∕c2 ≈ 2kTCMB λ2 which is consistent with observations except for frequencies below the cut-off at about 1 GHz (ν ≤ 109 Hz or λ ≥ λ0.5 = 30 cm). It has been difficult to explain the observations without plasma redshift and the cut-off frequencies. Big-bang cosmologists usually surmise that this increased emission at long wavelengths is due to(and close to the observed galaxies and the Milky Way) radio sources, or to thermal emission from grains, or dust, or that it is due to synchrotron radiation.

8.2. Redshift of 21 cm wavelengths in the coronas of different objects In spite of the high temperatures in the solar corona, the long wavelengths, such as the 21 cm line, are not (or are barely) plasma-redshifted, because the T/Ne1/2 values are too small; see Eq. (13) and Table 2 above. At a height of R/R  1.8, or at the temperature maximum in the corona, the cut-off wavelength λ0.5 is 0.0025 cm, and at R/R  3.4 it is about λ0.5 = 0.0031 cm. The redshift of the 21 cm wavelengths in the solar corona would thus be insignificant. More generally, in objects with intrinsic redshifts, including stars, galaxies and quasars, the cut-off wavelengths λ0.5 in their coronas are usually much less than 21 cm due to the high densities in the coronas. The plasma redshift predicts therefore that in the Sun and in other objects with intrinsic redshifts, such as stars and quasars, the 21 cm line will be redshifted less than the optical lines. The difference in redshifts between the

optical lines and the 21 cm line (provided that the 21 cm line comes from condensation just outside the corona of the objects) should be about equal to the intrinsic redshift of the quasar. The smaller redshift, z, of the 21 cm line from a quasar (usually, from a cloud surrounding the quasar) should be used to estimate the cosmological distance to quasars in accordance with Eq. (17). Due to the large intrinsic redshifts of quasars, the redshifts of the 21 cm lines from clouds just outside the quasar are usually not recognized as coming from the quasar. When the 21 cm line is observed towards the quasar, it is surmised by big-bang cosmologists to be from an object between the quasar and the observer. In the case of stars and common galaxies, the intrinsic redshifts are often so small that the 21 cm and 18 cm lines from H-I and OH respectively may be recognized as coming from the same object as the optical lines, but the smaller redshifts of the 21 cm and the 18 cm lines are then usually interpreted as being due to outward-moving flares or jets. When the object is very bright, the corona is more extensive and the intrinsic redshifts larger. Quasars and bright objects often push coronal plasma outwards (conferring the solar wind). This plasma may condense beyond the corona in a way similar to how the plasma from the Sun condenses at the heliopause. These condensations are likely to have a higher-intensity 21 cm absorption line, and besides the colder plasma emitting and absorbing the 21 cm line, may contain some hotter plasma ionized by X-rays from the surrounding intergalactic plasma. These faint absorption lines will then have approximately the same redshifts as the 21 cm line. This all is consistent with observations such as those discussed by P. Tzanavaris et al.; see their article: http://arxiv.org/PS_cache/astro-ph/pdf/0412/0412649v3.pdf. See also the article “Where is the Cold Neutral Gas in the Hosts of High Redshift AGN” by Curran, Whiting, and Webb: http://arxiv.org/PS_cache/arxiv/pdf/0807/0807.4983v1.pdf, which shows that extensive surveys fail to find 21 cm lines from highly redshifted objects such as quasars. This may be considered as an important confirmation of plasma redshift theory. In their Table 1, Tzanavaris et al. list several quasars with 21 cm-line absorption redshifts much less than the main emission redshifts from the quasar. For example, the quasar Q0952+179 has the main emissions lines at redshift of z = 1.478, while the redshift of the 21 cm absorption line is at z = 0.237803. They also detected some absorption lines of the Mg I and Ca II with the same redshifts as the H I 21 cm line. Knowing plasma redshift, I suspect that the redshift of the H I line is coming from a heliopause-like sphere surrounding the quasar (and not an independent object), while the redshift difference, z = 1.478 – 0.2378 = 1.24, is the intrinsic redshift of the quasar. The redshift of the 21 cm line represents the distance given by Eq. (17), R = (c/H0 ) ln(1+z) = 1,066 Mpc for c = 3·10 5 km/s and H0 = 60. The distance derived from the redshift of the optical emission lines is about 4,537 Mpc. The light intensity, corresponding to the absolute magnitude, will then be reduced by a factor of (1066/4537)2[(1+0.2378)/( 1+1.478)]3 = 0.00688 = 1/145.3, which corresponds to a change in absolute magnitude by about 5.4. If the magnitude of the quasar 0952+179 was estimated in the big-bang cosmology to be about –25.4 (see Table 3 of Rao et al.: http://arxiv.org/PS_cache/astro-ph/pdf/0211/0211297v3.pdf), then the absolute magnitude of quasar 0952+179 in the plasma-redshift cosmology is about M = –25.4+5.4 = –20. So it is nearly as bright as our Milky Way, whose absolute magnitude is –20.5. The intrinsic redshifts of other quasars would similarly correspond to reductions of their distances and brightnesses as determined in the big-bang cosmology.

Presently, there are plans to improve the measurements of the 21 cm H I-line so that galaxies at z ≈ 6 to 15 can be measured; see Barkana and Loeb (submitted 2007 to MNRAS): http://www.arxiv.org/PS_cache/arxiv/pdf/0705/0705.3246v1.pdf. In the future, the comparison of the redshift of the 21 cm line with the optical lines at high redshifts is likely to give a better confirmation.

9. Cosmic X-ray background In the plasma-redshift cosmology, the average electron density in the intergalactic plasma is equal to (Ne) avg  2 ·10−4 cm−3, and the average per particle temperature is (Te)avg ≈ 2.7·106 K. These densities and temperatures explain the cosmological redshift, the cosmic microwave background (CMB), and the measured X-ray background; see section 5.11 and Appendix C3 of reference [1]: arXiv:astroph/0401420. For example, at hν = 729 eV, the predicted X-ray intensity is Iν = 8.7 keV cm−2 s−1 sr−1 kev−1 (see Eq. (C21) in Appendix C of [1]: arXiv:astro-ph/0401420). When this value is extrapolated to hν = 750 eV, we get Iν = 8.0 keV cm−2 s−1 sr −1 kev−1, which is comparable to Iν = 7.5 ±1 keV cm−2 s−1 sr−1 kev−1 in the hν = 750 eV band measured by Kuntz et al.; see Kuntz, Snowden, and Mushotzky: (arXiv:0011552v1.pdf). It is important to take into account the absorption length for plasma redshift in the intergalactic plasma, which is l = lCMB = 1/(3.326·10−25 · Ne ) ≈ 1.5·1028 cm ≈ 5000 Mpc, see section C1.4 and Table C1 of [1]: arXiv:astro-ph/0401420. Above the plasma-redshift cut-off (which is slightly below 10 9 Hz), this absorption length is inversely proportional to the density and independent of the frequency and the temperature. The absorption lCMB for plasma redshift is usually much shorter than the absorption length for free-free emission. lCMB is simply the radius of the blackbody cavity emitting the X-rays. One can show theoretically that in a blackbody cavity, the radiation intensity is independent of the density. The intensity is simply given by the Planck law: :

2h 3 1 I  2 ( h / kT ) c e 1

erg cm−2 s−1 sr−1 Hz−1

(25)

which is independent of the plasma density; see Eq. (C2) in Appendix C of [1] arXiv:astroph/0401420. In free-free emission given by Eq. (26), the emission density of the X-rays is proportional to Ne2 ( Ni Ne) and inversely proportional to the temperature Te1/2 ; see Eq. (26). In the big-bang cosmology, these variables vary with time due to the expansion. In the big-bang cosmology the absorption distance, due to the low densities in intergalactic space, would be much larger than in the plasma-redshift cosmology. For example, for a plasma temperature

of Te = 3·106 K and Ne ≈ 1.95·10−4 cm−3, the absorption length for free-free absorption at the frequency  = 3·1012 Hz is 1.85·1042 cm, or about 1014 times as large as the absorption length in the plasmaredshift cosmology, which is about1.5·1028 cm. It is also important to properly take into account the increased absorption in our Milky Way Galaxy and how it varies with the spectra. The densities in the interstellar space and in the corona of the Milky Way are much greater than those usually assumed in the big-bang cosmology. The emission density of the X-rays is given by:

j 

5.444 1039  g ff  Zi2  N e  Ni  eh

)

erg cm−3 s−1 sr−1 Hz−1 ,

(26)

T 1/2

where Ni and Zi are the number density and the ionic charge of the positive ions and <g ff> is the Gaunt factor. The X-ray absorption is given by:

 

3.692 108  g ff  Zi2  N e  Ni  (1  e h T

1/2



)

cm−1,

(27)

see Eq. (C11) of [1]: http://www.arxiv.org/PS_cache/astro-ph/pdf/0401/0401420v3.pdf. For h << kT, we have that, see Eq.(C12) of [1]: http://www.arxiv.org/PS_cache/astroph/pdf/0401/0401420v3.pdf.

 Te3/2  Zi2 Ne Ni   0.173 1  0.130log    Te3/2 2 

cm−1.

(27a)

In the plasma-redshift cosmology, we have at least six independent relations for determining the two parameters, the density Ne and the temperature Te in intergalactic space. We can determine: 1) the electron density from Eq. (16) by measuring the Hubble constant; 2) the electron density from Eq. (17) by measuring the distances and the redshift; 3) the electron density, Ne, from the magnitude-redshift relation from Eq. (19) for SNe Ia data; 4) the product Te · Ne from the measured TCMB given by Eq. (23); 5) the ratio Te /Ne1/2 from the cut-off frequency given by Eq. (13) or (24); and 6) the ratio Ne2/ Te1/2 from the measured CXB intensity. In the plasma-redshift cosmology, all six of these independent relations are consistent with the same values for: (Ne)avg = 2·10−4 cm−3 and (Te)avg ≈ 2.7·106 K. The averages are per particle, and not per volume.

The X-ray intensities confirm the density and temperature estimates that were obtained from SNe Ia measurements and the CMB measurements in intergalactic space; see section 5.11 in [1]: http://www.arxiv.org/PS_cache/astro-ph/pdf/0401/0401420v3.pdf . The high densities and temperatures in intergalactic space that are derived in the plasma -redshift cosmology are believed by many to result in a much-too-high X-ray intensity. These opinions usually disregard that the absorption distances in free-free emission are many orders of magnitude greater than the absorption distances lCMB in the plasma-redshift cosmology; see Appendix C1.4 and X-ray intensity in C3, and Table C1 in [1]: arXiv:astro-ph/0401420. The low densities in intergalactic space surmised in the big-bang cosmology sometimes lead to difficulties in explaining the unusually high X-ray intensities often observed, such as those in the bridge between the Abell 222 cluster and the Abell 223 cluster (see: J. P. Dietrich, P. Schneider, D. Clowe, E. Romano-Diaz, J. Kerp, “Weak lensing study of dark matter filaments and application to the binary cluster A 222 and A 223” in Astron.Astrophys. 440 (2005) 453-471; arxiv.org/PS_cache/pdf/0406/0406541v2.pdf ). The densities in such “filaments” are close to those predicted by the plasma redshift. When evaluating the data, we must take the Galactic absorption into account, especially the absorption of the softer part of the X-ray spectrum. This bridge is obvious because the gravitational attraction and the plasma redshift heating from both galaxies combine to result in relatively dense plasma and high temperatures. The resulting high-energy X-rays are less absorbed in our Galaxy. This results in unusually high observed X-ray intensities. These dense “filaments” are part of the denser “filaments” at the surface of the hot plasma “bubbles” in intergalactic space. The bubbles are caused by the imbalance between the plasma -redshift heating (which is first order in density) and the X-ray cooling (which is second order in density). Usually, the X-rays from the colder and denser plasma at the surface of the bubbles are largely absorbed in our Galaxy. But in this case the two clusters increase the temperature and the high-energy X-rays. The X-ray intensity is a key factor for the X-ray heating of the Galactic corona and the coronas in and around galactic clusters, and for heating of cold filaments in intergalactic space, because the entire optical energy emitted by the galaxies is transferred to the intergalactic plasma with the help of the plasma-redshift heating. This heating of the intergalactic plasma then returns the energy back to the galaxies, mostly in the form of X rays. For heating the coronas of galaxies and galaxy clusters, the absorption heating by X-rays is an important addition to the direct plasma redshift heating; see section 5.7.7 in [1]: arXiv:astro-ph/0401420. The big-bang cosmology cannot explain the required heating of the intergalactic plasma, the intra cluster plasma, and the coronas of galaxies, quasars, and stars. In contrasts, plasma redshift heating together with X-ray heating does explain the heating of these plasmas.

10. Solar wind and cosmic jets Without plasma redshift, it has not been possible to explain many solar phenomena, including the

heating of the solar corona, the solar flares, protuberances, and the outward acceleration of the solar wind. There are many good review articles on the subject; see for example “The Heliosphere” by W. I. Axford and S. T. Suess: http://web.mit.edu/space/www/helio.review/axford.suess.html. But while these articles are of good quality, the authors do not have a clue as to the plasma redshifts in the Sun, the stars, the galaxies, and in intergalactic space. They therefore don‟t have a clue as to the plasma redshift heating of the corona of the Sun and the stars. Nor do they have a clue as to the significant heating by X-rays (mainly soft X-rays) from intergalactic space, where practically all starlight is converted (by plasma-redshift heating) to heat. All of this affects the density and pressure estimates in the Galactic corona, including those of the very local interstellar medium (VLISM). We should not be surprised, therefore, when plasma-redshift cosmology leads to significantly higher pressures in the VLISM than those derived from the conventional cosmology. It is often claimed that magnetic reconnection results in a conversion of magnetic field energy to heat. But the reconnection of the magnetic field lines is not the cause but a consequence of the magnetic field destruction. The reconnection of the field lines, which is initiated and caused by plasmaredshift heating, which, as explained in section 2.1 above and section 5.3 of [1]: arXiv:astroph/0401420, increases the diamagnetic moments that oppose the magnetic field. The electromotive force from the plasma-redshift-heated diamagnetic moments reduces and can even reverse the magnetic field. The real cause is thus the plasma-redshift heating, which is due to gradual loss of the photon energy as the photons penetrate hot sparse plasma. It is sometimes claimed that the A. N. Kolmogorov (Dokl. Akad. Nauk SSSR. 30 (1941) 301) equation: Q  V3/, explains the heating, where  is the mass density, V is r.m.s. fluctuation velocity at the largest scale, and  is a representative outer-scale length (i.e. the size of the largest turbulent eddies); see Steven. R. Cranmer, http://arxiv.org/PS_cache/arxiv/pdf/0409/0409724v1.pdf. But some energy sources must cause the turbulence fluctuations. There has also been a fascination with Alfvén waves explaining this and that, including coronal heating and the solar wind. Alfvén waves, with a speed of about B/(4)1/2, cannot explain the acceleration of the solar wind close to the Earth‟s distance (1 AU) when the speed of the solar wind is 10 times that of the Alfvén waves. What drives the Alfvén waves? The energy doesn‟t come out of the blue. Consistent with observations, the plasma redshift gives a quantitative explanation of the coronal heating and of the solar flares, as described in section 5.1 to 5.6 of [1]: arXiv:astroph/0401420. It has been difficult to understand the forces that cause the solar wind. In spite of the strong gravitational attractions, the coronal mass particles are found to accelerate outwards. There are mainly two causes for this outward acceleration: 1) In their thermal motions in a magnetic plasma, the charged particles will gyrate around the magnetic field lines and produce thereby diamagnetic moments; see Sections 5.3.1 to 5.3.5 and Appendices B1 and B2 of [1]: arXiv:astro-ph/0401420. Usually the magnetic field decreases

outwards. It is thus divergent, and the magnetic forces on the diamagnetic moments of charged particles encircling the divergent magnetic field lines may exceed the gravitational attraction and accelerate the charged particles outwards. Let us assume that at a point P the magnetic field decreases outwards with the distance R as B = Bp·(Rp/R)n, where Bp is the magnetic field at P. Then a charged particle with mass m and velocity vp perpendicular to the field at P will have a diamagnetic moment at P given by m·vp2/(2·Bp), where vp is the particle velocity perpendicular to the field; see Eq. (B10) in Appendix B of [1]: arXiv:astro-ph/0401420. The force on the diamagnetic moment of the particle is then

n m  vp Fp   2 Rp 2

(28)

This force Fp is independent of the strength of the magnetic field B, because the diamagnetic moment increases when the magnetic field decreases, as long as the field B is strong enough to produce a diamagnetic moment. The repulsive force Fp on the diamagnetic moments m·vp2/(2·Bp) may exceed the gravitational attraction, which decreases as 1/R2 . Near the Sun this occurs usually at or beyond about 3 solar radii. But occasionally, when n is large (because the magnetic field originates high in the atmosphere, but below the transition zone) this diamagnetic force exceeds the gravitational force closer to the transition zone to the corona. The plasma-redshift heating enhances this force Fp by increasing the velocity vp. 2) The energy lost by the photons in the plasma redshift interaction is transferred to the electrons, which therefore become hot. In sparse plasma the energy transfer from very hot electrons to protons and other positive ions is a rather slow process. Although most of the electrons are nearly thermal there will be a high-energy tail in the distribution. The electrons in this highenergy tail are according to Eq. (28) pushed outwards ahead of the protons. This high-energy tail of hot electrons comes about because the plasma redshift heating (above the cut-off) is independent of the electron temperature, while the X-ray cooling deceases rather steeply with increasing electron temperature (below about 3 MeV). The hottest electrons diffuse outwards ahead of the protons and create an electrical field that pulls the protons and other positive ions outwards. The plasma redshift heating is first order in density, while the transfer of the heating from the electrons to the protons is a second order process in density. This effect is therefore more pronounced when the plasma is sparse. At very large distances in the heliosphere the redshift heating decreases more steeply than the electron density due to interstellar pressure, and the protons will catch up with the electrons. Although the solar dipole field is expected to be horizontal at the equatorial plane, the plasma redshift heating causes the magnetic field lines to stretch radially outwards. This is caused by plasma -redshift heating, as described in section 5.4 of [1]: arXiv:astro-ph/0401420. The field decreases therefore about as 1/R2 instead of proportional to 1/R3. Still, the solar wind will be slower around the equatorial directions of the dipole field than in the polar direction of the magnetic dipole field. At the distance of Earth‟s orbit (1 AU) the solar wind may be 450 km/s, while in the polar direction it is about 750 km/s. This solar wind is in addition to the isotropic velocities of the thermal motions in the plasma. The magnetic field from the Sun stretches beyond Earth‟s orbit, where it is usually between about 20

and 100 G, or 2 to 10 nT (nanotesla). For this low field at 1 AU, the relatively high kinetic energy density of the particles, therefore, exceeds the energy density of the magnetic field. This reduces the diamagnetic moments and the repulsive force Fp. Even between about 0.3 AU and 1 AU the force Fp in Eq. (28) may be reduced for this reason. Beyond 1 AU, the acceleration given by Eq. (28) is usually insignificant. This depends on the magnetic field strength. We observe therefore significant oscillations in the particle velocity or the solar wind coherent with the magnetic field strength. At 1 AU, the solar wind speed is about 450 km/s close to the equatorial plane and about 750 km/s over most of the remaining sphere. The plasma redshift heating of each electron is proportional to time. At these high velocities the plasma redshift of the fast-moving solar wind is then small relative to the large energy flux at 1 AU. This is due to the small dwell-time of the electrons at each location. The interstellar medium surrounding the solar wind (the heliosphere), however, is moving much slower. The heliosphere moves through the local interstellar medium at about 26 km/s. At this slower speed the plasma redshift heating of each electron is more important, but still rather small. But the interstellar medium closest to the interface with the heliosphere will stop the solar wind, and is thereby ionized by the solar wind. This plasma moves with the heliosphere. Plasma redshift heating of this interstellar medium becomes then significant and extends the ionized sphere around the solar wind. This, as the preliminary IBEX (Interstellar Boundary Explorer) experiments indicate, may call for asignificant revision of the conventional theory. This interstellar medium at the interface with the solar wind is thus nearly constant, and is thus constantly exposed to both the solar wind and the plasma-redshift heating, which both will ionize it if it was not ionized already. Due to the low densities, nearly all of the frequencies of the solar light will be plasma redshifted (see Eq. (13)), and will then augment the heating by the solar wind energy significantly. The ionized sphere around the Sun may thus stretch far beyond the usually surmised heliopause that has been assumed to be between 50 and 100 AU. Also, because of the relatively high temperatures and pressures, the nearby interstellar medium may reach inward more than that usually assumed. The relatively high pressure of the interstellar medium may penetrate close to 30 to 50 AU. Due to the instabilities in the plasma-redshift heating (which is 1 st order in density) and the X-ray cooling (which is 2 nd order in density), the densities and the temperatures at the interfaces may be uneven, as IBEX experiments indicate; see D.J. McComas et al. in Science 326 (2009) 959, and Dave McComas, http://ibex.swri.edu/, 15 October 2009. If the number density in the low speed wind at 1 AU is about 6 protons cm−3 , and in the high-speed wind about 3 protons cm−3, then the corresponding solar wind pressures of the protons alone at 1 AU are about 6 ·2· mp·vp2 = 4.1 ·10−8 to 3 ·2· mp·vp2 = 5.6·10−8 dyne cm−2 , respectively. If for a moment we disregard any increase in the velocity beyond 1 AU, we find at a distance of about 40 AU that the partial proton pressure of the solar wind is: pp  4.1 ·10−8/402 = 2.55·10−11 dyne cm−2 for the low speed wind, and for the high speed wind about 3.53 ·10−11 dyne cm−2. At 40 AU these proton pressures correspond to: pp /k = Np ·Tp = 1.84·105 and 2.56·105 cm−3 K. In the plasma-redshift cosmology, the temperature is not uniform. For 5 % helium the average temperature in the hot regions may be T ≈ 0.82·106 K, (see section 13 for 5 % helium). In these hot regions the average proton density is then about Np = 0.22 and 0.31 cm−3. This does not include pressure from magnetic fields and plasma redshift heating beyond 1 AU. If we include the colder

regions the average density may be about Np = 0.4 cm−3, as indicated by the rotational velocity in the Galaxy; see Section 13. This does not include pressures from the increase in the particle speed beyond 1 AU, and it does not include the pressure of the magnetic field, nor does it include the electron pressure, or the thermal pressure in the solar wind. The distance to the heliopause is not known. We also do not know the temperature in the heliopause. These are a crude estimates. But they show that in the plasma-redshift cosmology the interstellar pressure in the solar neighborhood may be significantly larger than that often surmised, which is usually less than p/k = N·T = 2·104 cm−3 K; see Edward B. Jenkins: http://arxiv.org/PS_cache/arxiv/pdf/0805/0805.2700v1.pdf. While the estimates by Jenkins are of good quality, he could not take into account the very significant modifications of the evaluations of the many observations caused by plasma redshift. The imbalance between the plasma redshift heating and the X-ray cooling has a tendency to create a “bubble” structure and an uneven interface at the heliopause (at about 60 to 120 AU) between the heliosphere and the interstellar medium. Presently, only preliminary data of the “Interstellar Boundary Explorer” (IBEX) program (see: http://ibex.swri.edu) are available, but the observed arc-shaped region in the sky creating a large amount of “energetic neutral atoms” (ENAs), and showing up as a bright, narrow ribbon on the maps, appears easily explained by plasma-redshift theory. It will be interesting to watch for further results of the IBEX program. It will be difficult to explain the observations without the use of plasma redshift theory. Over the sunspots the magnetic field is unusually strong and nearly radial. The outflow is then large and the field stretches unusually far out. This helps lower the temperature over the sunspots, and the solar wind is usually more intense over the sunspots. Scattering of the charged particles helps transform the velocity gain in the direction of the field lines into transversal velocities. Due to their double charge, the helium ions scatter more than the protons. As the particles gain energy, the helium ions‟ velocity component perpendicular to the field gains more than that of the protons. The average force on the helium ions may therefore exceed that on the protons. For greater details, see section 5.3 and the deduction of Eq. (B10) in [1]: arXiv:astro-ph/0401420. In other stars and in galaxies, phenomena analogous to these solar phenomena are widespread. They are especially important in collapsars, which can be very hot and have very large magnetic fields. Their relativistic charged particles form large magnetic dipole moments. In these objects the wind, similar to the solar wind, can form jets mainly in the polar directions of these objects. Where ions move around, there will be magnetic fields surrounding their orbits. The particles will encircle the field lines. While the field inside the particles orbit is weakened, the field outside the orbits is strengthened. Therefore the dipole moments are coupled, and can form large domains that may stretch thousands of kilometers. An ion encircling the magnetic field opposes and weakens the magnetic field. The diamagnetic moments are coupled, so as to coherently oppose any external field. These diamagnetic moments increase due to any heating, including the plasma-redshift heating. Thereby they may destroy or even reverse the initial field. The 11 year cycle of the solar magnetic field most likely has similar causes.

11. Densities and temperatures in intergalactic space In the big-bang cosmology, the average intergalactic baryon density divided by the proton mass is

 avg mp

 N equiv  1.124 105    h 2

protons cm−3 ,

(29)

see Eqs. (5.68) and (6.27) in “P. J. P. Peebles, “Principles of Physical Cosmology”, Princeton University Press, 1993, http://press.princeton.edu/titles/5263.html). If for the baryons we have ·h2 = (0.013±0.003), as assumed by Peebles, then the number density of the baryons in the big-bang cosmology is about Nequiv = (1.46±0.3)·10−7 cm−3, which corresponds to avg = 2.4410–31 g·cm−3. (If in the big-bang cosmology, we include dark energy and dark matter; that is, if we set  = 1, and h = 0.72 as is sometimes done, we get avg = 9.7510–30 g·cm−3, which is about 40 times greater than avg = 2.4410–31 g·cm−3.) In plasma-redshift cosmology, the electron number density is Ne ≈ 0.0002 cm−3, the mass density is then avg = 0.0002(1.4/1.2)  1.672610–24 = 3.910–28 g·cm−3, which is about 1600 times larger than the baryonic density, avg = 2.4410–31 g·cm−3, in the big-bang cosmology; and about 40 times larger than avg = 9.7510–30 g·cm−3 in the big-bang cosmology, which includes dark energy (DE) and dark matter (DM) parameters. For Ne/Nequiv ≈ 1.2 /1.4, we get from Eq. (29) that Ne ≈ (1.25±0.3)·10−7 cm−3. If h = 0.7 (that is, the Hubble constant is H 0 = 70 km s−1 Mpc−1), then  = 0.0265 for the baryons; and if h = 0.6, we get  = 0.0361; but the electron density is the same as before; that is, Ne ≈ (1.25±0.3) ·10−7 cm−3 in the bigbang cosmology. In the plasma-redshift cosmology, the average electron density is (Ne)avg ≈ (2.0±0.02)·10−4 cm−3 , or about 1600 times higher than the average electron densities Ne ≈ 1.25·10−7 cm−3 , that Peebles assumed in the big-bang cosmology. Big-bang cosmologists sometimes refer to “critical density”, which corresponds to  = 1, which for h = 0.74 and Ne /Nequiv ≈ 1.2 /1.4 corresponds to an electron density of Ne ≈ 5 ·10−6 cm−3. The electron density in the plasma-redshift cosmology is about 40 times this “critical density”. With the high density in the plasma-redshift cosmology the big-bang cosmologists are inclined to think that the universe would quickly collapse into a black hole (BH). These much higher densities in the plasma-redshift cosmology therefore startle big-bang cosmologists. But, as we will see, the experimental evidence supporting the plasma redshift is overwhelming. For example, all the predictions of relations such as the distance-redshift relation, magnitude-redshift relation, and the surface-brightness-redshift relation match the experiments without any artificial adjustment parameters such as the non-physical big bang, the non-physical inflation, the non-physical dark energy, the non-physical dark matter, or the non-physical accelerated expansion parameters. Proper physics also explains the cosmic microwave background (CMB), and the X-ray background

(XRB) without any non-physical parameters, such as cosmic inflation. In the plasma-redshift cosmology, wherever and whenever matter concentrates in a black hole candidate (BHC) or a super massive black hole candidate (SMBHC), it (usually old star matter) becomes so hot that it turns into primordial matter and weightless photons. The exchange forces between the fermions cause the weightless photons to accumulate at the center of the BHC and prevent the formation of the BH. In the plasma-redshift cosmology, the BHs are thus never formed; instead, in the BHCs and SMBHCs the old star matter transforms into primordial matter for eternal renewal of the universe. On occasions, for example when the BHC is hit by an incoming star, the hot primordial matter may escape. It is therefore understandable that we have a star-forming region surrounding the SMBHC at the Galactic center. When photons escape they are seen in a distant system of reference as if they are being pushed outwards (although the photons are weightless in the local system of reference). The high-energy photons will recreate primordial matter. The primordial matter and the photons can thus renew the world forever. In plasma-redshift cosmology, the transformation of old star matter to primordial matter in BHCs thus results in a very stable, everlasting self-regulating cosmology. Actually, it is the big-bang cosmology which is very unstable, because the attracting and repelling forces cannot balance exactly. Due to the transparency of intergalactic space, cosmologists usually assumed that the densities were low and the medium relatively cold, because, not knowing plasma-redshift theory, they saw no way to heat the intergalactic plasma to millions of degrees K. However, recent observations using the Chandra X-ray Observatory confirm that the intergalactic medium is mainly in hot gas filaments strewn throughout the universe. Also, absorption lines in background light are usually from highly ionized species. It is now common, therefore, to assume that the temperatures for the “warm-hot intergalactic medium” (WHIM) are in the range of 10 5 to 107 K, which is reasonably close to the values 3105 to 3107 K predicted by plasma redshift cosmology. In the big-bang cosmology, it is still impossible to understand the very high temperature of these hot filaments. In http://en.wikipedia.org/wiki/Outer_space - see section “Intergalactic”- they are described in this way: “Surrounding and stretching between galaxies, there is rarefied plasma that is thought to possess cosmic filamentary structure and that is slightly denser than the average density in the universe. This material is called the intergalactic medium (IGM) and is mostly ionized hydrogen, i.e. a plasma consisting of equal numbers of electrons and protons. The IGM is thought to exist at a density of 10 to 100 times the average density of the universe (10 to 100 hydrogen atoms per cubic meter). It reaches densities as high as 1000 times the average density of the universe in rich clusters of galaxies” The temperatures, 10 5 to 107 K, which are often derived from the absorption lines in light towards quasars, are significantly higher than those in the usual Strömgren spheres with temperatures usually between 3·103 and 105 K. It has been impossible to explain these hot dense filaments. For example, the remark: “…there is rarefied plasma that is thought to possess cosmic filamentary structure and that is slightly denser than the average density in the universe”, is strange and indicates the difficulty in explaining the filament structure. This hot filamentary structure is of course embedded in colder and

denser plasma. An average density of 100 hydrogen atoms per cubic meter corresponds to (Ne)avg ≈ 1.17·10−4 cm−3 , but then it may be 1/10 of that or even 1000 times more. These values are in the range of that estimated in the plasma-redshift cosmology, (Ne)avg ≈ 2·10−4 cm−3 , and indicate that the measurements may be closer to that predicted by plasma-redshift cosmology than the values estimated in the big-bang cosmology by Peebles; see Eq. (29). The observations of the “bubble” structure, the filament structure, the high ionizations stages, the absorption of highly ionized species, and the X-ray emission are all consistent with the predictions of plasma-redshift cosmology. Plasma redshift gradually transforms the photon energy from stars and galaxies into heat. This plasma-redshift heating in intergalactic space results in average plasma temperatures of about Tavg = 2.7·106 K. However, the plasma redshift heating is first order in the densities, and both the X-ray cooling and recombination cooling are second order in the densities. This causes the hotter regions to become hotter and the colder regions to be come colder. This continues until other processes such as heat conduction and X-ray absorption limit the imbalance. This imbalance nevertheless causes large temperature variations in the plasma from one location to another. We will have huge hot “bubbles” surrounded by colder plasma at their surfaces. The bubble surface is much less transparent when observed tangentially to the surface than when observed at right angle to the surface. Thus, when the colder and denser plasma surfaces are viewed tangentially, they may appear as “filaments”. These “filaments” form the web-like structures often seen in pictures. This explains the web-like structure often seen. The so called “hot filaments” in the big-bang cosmology consist, usually, of colder plasma at the surfaces of the hot plasma bubbles. These structures in intergalactic space are consistent with observations; see for example: M. J. Geller & J. P. Huchra, Science 246, 897 (1989) and “The CfA Redshift Survey” by John Huchra: http://www.cfa.harvard.edu/~huchra/zcat/. Big-bang cosmologists could not explain these structures because the plasma-redshift heating was unknown to them. The temperatures in the colder plasma filaments at the surfaces of the “bubbles” are about 3·10 5 K (usually about 3·10 4 to 3·106 K), but at the centers of the hot bubbles the temperatures may reach about 3·107 K (usually 3·106 to 3·108 K). The heat conduction limits the highest temperatures, and the X-ray heating (together with the heat conduction) will limit the lowest temperatures. The average pressure corresponds to Ne·T  540 cm−3 K. For N = Np + NHe++ + Ne  1.917·Ne, we get p/k = N·T  103 cm−3 K in intergalactic space. The density in the cold filaments may often be Ne ≈ 2.0·10−3 cm−3 and the density at the center of the hot bubble may often be Ne ≈ 2.0·10−5 cm−3. Within galaxies and galaxy clusters the temperatures and densities will be higher due to the gravitational pressure. In clusters and in the space between two or more galaxies the plasma redshift heating can be exceptionally large. Due to the gravitational attraction, the plasma may simultaneously be relatively dense. This explains the hot and relatively dense filaments in Galaxy clusters.. The higher densities at the surface of the bubbles may lead to condensation of the plasma and to galaxy formations in the colder regions at the surfaces of the hot bubbles. Galaxies and the bridges between the galaxies are therefore usually grouped at the colder surfaces of these hot plasma bubbles. The observations appear to confirm the temperatures predicted by plasma-redshift cosmology for the

observed bubble and filament structure.

12. Dark matter, dark energy, and accelerated expansion Big-bang cosmologists have many reasons to introduce mystical dark matter (DM), dark energy (DE) and accelerated expansion (AE) into their equations. In section 11, we showed that the actual electron densities in intergalactic space are (Ne)avg ≈ (2.0±0.02)·10−4 cm−3, or about 1600 times greater than the electron densities, (Ne)avg ≈ 1,25·10−7 cm−3, in intergalactic space derived by big-bang cosmologists. Plasma redshift transfers energy from photons to the plasma. This heats the plasma to the high average (per particle) temperature of about Tavg = 2.7·106 degrees K. In contrast, the adiabatic expansion in big-bang cosmology cools the intergalactic medium so much that it is difficult to explain the observed high intergalactic temperatures. In the plasma-redshift cosmology, the galaxies are formed in colder (often about 0.3 million degrees K) regions at the surface of huge hot (often about 30 million degrees K) plasma redshift heated “bubbles” in intergalactic space. The high surface densities (often more than (Ne)avg ≈ (2.0±0.02)·10−3 cm−3) will leak into the gravitational wells created by galaxies and galaxy clusters, including gravitational lenses. When the densities increase in these potential wells, the X-ray cooling which is proportional to NeNi (that is, density squared) has a tendency to cool the plasma and form neutral clouds. These condensations of the plasma to relatively cold neutral clouds further increase the mass density in the coronas of the galaxies. It is therefore not surprising that the big-bang cosmologists had to sprinkle some DM here and there.

Dark matter and dark energy from the distance-redshift relation. Eqs. (18) and (18a), and Figure 5 of Section 5 show how big-bang cosmologists have to adjust the dark matter (DM) and the dark energy (DE) parameters (m, ) in Eq. (18) to obtain a reasonable fit to the actual distance, Rpl, given by Eq. (17). In the plasma-redshift cosmology, the simple distance-redshift relation given by Eq. (17) fits the experimental data without a need for any such parameters.

Dark matter and the Coma cluster. The high-velocity spread v ≈ 1000 km/s within the Coma cluster lead Fritz Zwicky (see his article in Helvetica Physica Acta 6 (1933) 110-127), to suggest dark matter as one of possible explanations for this high-velocity spread. Many others have elaborated on this subject, and now all galaxy clusters are believed to have significant dark matter. This cluster is at a distance of about 93 Mpc, and contains about 1000 galaxies within a sphere with a diameter of about 1 to 1.5 Mpc. Zwicky observed that the velocities were too high for retaining some of the galaxies. Now, X-ray observations have shown that the temperatures of the coronal plasma within this sphere are often in the range of 30 to 120 million degrees K. The coronal plasma has an average density of

about 0.003 electrons cm−3. Using Eq. (12), we find that the plasma redshift caused by this density across a diameter of 1 to 1.5 Mpc in the cluster is from z ≈ 0.003 to z ≈ 0.0046, which corresponds to Doppler velocities given by v ≈ 920 km/s to v ≈ 1385 km/s. In addition to the apparent increase in the velocities caused by the plasma redshifting, the coronal density of the plasma, although small due to the high temperatures, is significant. The coronal plasma densities of about 0.003 electrons cm −3 within 1 to 1.5 Mpc correspond to about 4·1013 to 1014 solar masses. Without the plasma redshifting, it would be difficult to explain the large redshifts and the high temperatures in the corona of the cluster, while plasma redshifting gives a reasonable explanation. The future improvements in X-ray technology will improve the measurements of the plasma densities.

Dark matter and galaxy clusters. Due to the low gravitational potentials in galaxy clusters, the intracluster plasma densities are usually much higher than the densities in intergalactic space. The corresponding intrinsic redshifts are often significant. This denser intracluster plasma may appear as dark matter because the plasma is often nearly invisible. The intrinsic redshifts of the individual galaxies vary significantly within the cluster. When these intrinsic redshifts are interpreted as Doppler shifts some of the cluster members often will be estimated to have excessive velocities; see for example: Bode, Ostriker, Weller, and Shaw: ApJ. 663 (2007) 139-149; (arXiv:astro-ph/0612663v2). These incorrect interpretations of the observations lead to the assumption that dark matter is required to explain the assumed large intracluster velocities. The high velocities of the cluster members are often considered a proof of dark matter. In the plasma-redshift cosmology no mystical dark matter is needed to explain the observations.

Dark matter and Fingers of God. It is observed that galaxy clusters are elongated preferably in the direction towards the observer. In the big-bang cosmology, this has been difficult to explain. The most reasonable explanation was that velocity distribution caused the elongation. Big-bang cosmologist then invented (see the paragraph above) dark matter to explain the high velocities. But plasma redshift gives a simple explanation. The potential well created by the cluster causes the intergalactic plasma to fall into the well and increase plasma densities and the plasma redshifts in and around the clusters. Both the plasma redshifts and the extra mass density of the plasma increase the redshifts and the apparent elongation in the radial direction. The plasma redshifts of the galaxies at the back side of the cluster are relatively large, and when interpreted as due to Doppler shifts indicate elongation in the radial direction, mainly towards positive redshifts. The additional plasma densities show that the actual volume of the cluster is smaller than indicated. Both the increased densities and the smaller volumes lead to a wider velocity distribution, including both positive and negative velocities. In the Virgo cluster most of the galaxies will have a positive velocity (larger redshifts than the actual cosmological redshift) and fewer will have a negative velocity (smaller redshifts than the actual cosmological redshift). The increased width of the velocity distribution caused by the extra plasma redshifting and the increased Doppler shifts both increases the elongation; see: Figures 3-9 and 3-10 in “Seeing Red: Redshifts, Cosmology and Academic Sciences”, by Halton Arp (published 1998, Apeiron, Quebec H2W 2B2 Canada, ISBN 0-9683689-0-5).

Dark matter and gravitational lenses. Galaxy-clusters, galaxies and quasars are often observed to have unusually large mass. The potential well produced by the gravitational mass of the cluster

members is augmented significantly by the plasma mass falling from intergalactic space into the potential well created by the cluster. Both the increased mass and the outward decreasing plasma density will augment the power of the lens. This indicates also that the density in and around single galaxies is significant. We will study the corresponding rotational velocity of galaxies more extensively in the next section.

Dark energy and accelerated expansion of the universe. Initially, it was believed in the bigbang cosmology that the expansion of the universe would slow down, because of gravitational attraction. Scientists soon learned however that the slowing down was questionable, and it appeared that some forces might continue to maintain the outward expansion. But when the magnitude-redshift relation for supernovae improved in the nineties and beyond, it appeared that the expansion of the universe was accelerating. During the last decade, astronomers have found that for a given redshift, distant supernova explosions look dimmer than expected. Redshift measures the amount that space has expanded. By measuring how much the light from distant supernovae has redshifted, cosmologists can then infer how much smaller the universe was at the time of the explosion as compared with its size today. See Timothy Clifton and Pedro G. Ferreira: “Does Dark Energy Really Exist” in “Scientific American”, April 2009, Vol. 300, No 4, pp.48-55. In the big-bang cosmology, the extra absorption of distant SNe Ia thus leads to an accelerated expansion of the universe. But in the plasma-redshift cosmology, the explanation is very simple. The difficulty in big-bang cosmology is rooted in the wrong Eq, (20), which follows from the big-bang hypothesis. If instead we use the correct magnitude-redshift relation valid for plasma-redshift cosmology, Eq. (19), we get a predicted extra absorption, 2.5log(1+z), which, when disregarding the small difference between the 4 th term in the equations, explains the extra absorption observed by the researchers. This is one of the important confirmations of plasma redshift cosmology. The strange nonexplainable accelerated expansion of the universe disappears when using the correct magnituderedshift relation, Eq. (19), valid in plasma-redshift cosmology.

12.1. Dark matter and rotational velocities of galaxies In plasma-redshift cosmology, the average electron density of (Ne)av ≈ 2·10−4 electrons cm−3 in intergalactic space is about 1600 times greater than the densities usually conjectured in the bigbang cosmology; see sections 11 and 12 above. This much higher density than that assumed by big-bang cosmologist leads to much higher densities in interstellar space than those derived in the big-bang cosmology. In plasma-redshift cosmology, there is then no need for dark matter (DM) for explaining the rotational velocities of galaxies, as we will see. The average per particle temperature in intergalactic space is according to plasma redshift cosmology (Te)av ≈ 2.7 ·106 K. The galaxies and galaxy clusters are usually formed at the surface of huge “plasma bubbles” with temperatures T ≈ 3 ·107 K (3 ·106 to 2 ·108 K) . At the surface of the “bubbles”, the plasma is colder with temperature of T ≈ 3 ·105 K (3 ·104 to 3 ·106 K). For a number of particles in the

plasma equal to N = 1.92·Ne, we find that the pressure p in intergalactic space corresponds to p/k = (N)av ·(T)av = 1.92 · 2·10–4 · 2.7· 106 = 1035 cm–3 K. But due to gravitational attraction, the intracluster and interstellar pressures are significantly higher than the pressures in intergalactic space. The plasma from intergalactic space falls into the gravitational depression created by galaxies, galaxy clusters, and gravitational lenses. These structures contain a coronal plasma and neutral clouds (often caused by increased X-ray cooling at the higher densities) with a total mass that often far exceeds the mass in visible stars and dust particles. The gravitational field produced by the hot plasma, and by the cold and neutral associated clouds, has lead to the assumption of dark matter, because the hot plasma and colder clouds are largely transparent and difficult to detect except through their gravitational mass and X-rays. It has been difficult to determine the distances to the X-ray sources, but steadily improving technology is making it easier to localize the X-ray sources and reveal the missing gravitational mass. In some cases, the evidence for the hot X-ray-emitting plasma has been there for a long time; but not knowing the plasma-redshift heating, big-bang cosmologists could not explain the necessary heating that causes and maintains the temperature of such plasmas. At the distance R from the center of the Galaxy the gravitational potential of a particle with mass m is G·M(R) ·m/R, where M(R) is the total isotropic mass within the radius R. Usually, the mass distribution is not isotropic but a flattened ellipsoid or disk-like distribution. The equations are then more complicated. The assumed isotropic distribution serves only to simplify the equations, which can subsequently be corrected to fit the actual distribution. At the position R the mass m has a rotational velocity v so, that the particle‟s kinetic energy (½)m v2 = (½)G·M(R) ·m/R. Thus when the particle falls from infinity to the distance R from the center, it loses only one half of its potential energy; the other half of the potential energy transforms into kinetic energy. In the corona of a galaxy, the distribution of density  and plasma pressure p (when disregarding the magnetic and electrical fields) is determined by the Boltzmann distribution. We have then that:

dp d  m G  M ( R)     dR , p  kT 2  R2

(30)

where m is the average mass of the particles. On the right side, the factor 2 in the denominator takes into account that the particle‟s energy changes by only ½ of its energy when it moves to the distance R from the center. In a hot plasma (where the electrons contribute to the pressure), the average mass per particle is m ≈ 0.609·m p (for a number of helium atoms equal to 10 % of the number of protons), where: mp = 1.6726 · 10– 24 g is the proton mass; G = 6.674·10– 8 in dyne cm2 g–2 is Newton‟s gravitational constant; and M(R) in g is the galactic mass inside the radius R, in cm. The Boltzmann constant is k = 1.3807 · 10–16 in erg K–1 , and T in K is the temperature. If the rotational velocity v is constant for the radii R  R0 , and if the centrifugal force balances the gravitational attraction, while the repulsive plasma pressure outside R0 is insignificant (as it would be for a star or a massive relatively cold cloud), then the velocity v of that cloud or a star is given by:

v2 

G  M ( R) G  M 0  R G  M 0   R R0 R R0

(31)

where M(R) in g is the total galactic gravitational mass of the star or cloud and the plasma inside the radius R. Eq. (30) then takes the form:

dp d  m G  M0     dR p  kT 2  R0 R

(32)

Assuming that m/T is roughly a constant, we can integrate Eq. (32) from R0 to R1 and get that:

R  mG  M0 p  R ln 1  ln 1   ln 1  ln  0  p0 0 2  k  T  R0 R0  R1 

mG M 0 (2k T  R0 )

(33)

For a nearly constant rotational velocity beyond R0 , the mass between R0 and R must increase as M(R) = M0 · (R/R0 ), that is, M/R = M0/R0. The density  must then decrease outwards approximately proportional to 1/R2. The exponent on the right side of Eq. (33) must then be equal to about 2; that is, the value of the exponent is mGM0 /2kTR0 ≈ 2. The plasma temperature is then given by

T

G  M0  m  0.818 106 4  k  R0

(34)

where, for 5 % helium in the plasma, we have m ≈ (1.2/2.15)·mp = 0.558·mp, which results in T ≈ 0.818·106 K. For 10 % helium, we have m ≈ (1.4/2.3) ·mp = 0.609·mp, and that T ≈ 0.893·106 K. From Eq. (31), we get that the rotational velocity of the solar system is v = (GM0 /R0)1/2 ≈ 220 km/s at about R0 = 8 kpc from the galactic center. This velocity corresponds to M0 = 9·1010 solar masses; that is, M0 = 1.79·1044 g inside R0. Coronal clouds with about 0.15 of solar abundance have been observed. For this very low value, we get m ≈ 0.52·mp and a temperature of T ≈ 0.76·106 K. These temperatures in the interstellar plasma are lower than the value T ≈ 1.25·106 K that was assumed using the uniform distribution by M. Pettini et al.. But the temperature variations explain why we have relatively high concentration of Fe-X ions in the corona, as observed by M. Pettini et al. The 6374.52 Å line from Fe-X should not be too heavily absorbed in the colder and denser plasma. At these temperatures (colder than those assumed by M. Pettini et al.), the average column density of H per FeX is significantly greater than that estimated by M. Pettini et al. The condensations, such as clouds of neutral atoms and molecules, formed from the plasma are initially likely to continue to move with the plasma at a constant velocity and at right angle to the gravitational force. Large and relatively dense bodies are not affected significantly by the plasma pressure or the Eqs. (30) to (34) In Eqs. (31) and (32), some of the mass, M, is due to the stars and the dust, which have a different mass distribution from that of the plasma. This is especially important for small radii. The rotational velocity then increases more steeply for small radii R (as observed).

If the rotational velocity is constant and the density is spherical and isotropic, we derive from Eq. (31) that

M  R  avg 2 M0 v2    R  R  R2 4 G 4 R0 4 R 3

(35)

We made use of the fact that the density  R at R is about equal to 1/3 of the average density avg inside R. For v ≈ 220 km/s at R = R0 = 8 kpc, we get that the plasma density is R = 9.47 · 10–25 g cm–3. In case of solar abundance, this corresponds to a proton density at 8 kpc of Np = 0.40 cm–3 . Due the great inhomogeneity in density caused by structures such as the large and small Magellan Clouds (LMC and SMC), the streamers, and the arms of the Galaxy, relations such as ρ(R)  1/R2 are only crude approximations. The proton density at 8 kpc of Np = 0.40 cm–3 is close to the proton densities Np derived from the solar wind measurements in section 10, and the values of Np derived from the measurements of M. Pettini et al. who found that their measured column density of Fe X ions towards 1987 A in LMC corresponds to column density of hydrogen equal to (NH) av ≈ 3.2·1021 cm−2. Assuming temperatures of about or exceeding 1.25106 K, this corresponds to an average plasma density over 50 kpc of (NH)av ≈ 0.021 cm−3 . However, if the temperature is lower, the column density estimate would increase. From plasma-redshift theory we know that the temperature is not uniform, but alternates between hot and rather cold regions. If the hot regions fill about 20, 40 or 80 % of the distance, the a verage density in the hot regions would increase to (NH)av ≈ 0.104, 0.052 or 0.026 cm −3. Because the line of sight to SN 1987 A is nearly tangent to the orbit of the solar system, the density along the line of sight varies roughly as NH  1/(82+R2). At the distance of 8 kpc from the Galactic center, the density in the hot regions should then be NH ≈ 0.44, 0.22 or 0.11 cm−3. In the cold regions of the corona and in the coronal clouds the temperatures are much lower and the densities much higher. The actual average density at 8 kpc could therefore be significantly higher, and might even double to NH ≈ 0.88, 0.44 or 0.22 cm−3. Although these equations are in reasonable agreement with the observations, they should only be considered rough approximations. The optical spectrum of stars indicates that the galaxies have a highly flattened elliptical or a flat disk-like form. However, interstellar and intergalactic plasma matter usually contains more mass and is nearly invisible. Beyond a few kpc from the galactic center, this mass has the more isotropic and spherical distribution determined by the Boltzmann distribution. Sometimes, big-bang cosmologists argue that the concentration of dark matter initiated the formation of galaxies. Actually, the instabilities caused by plasma-redshift heating and X-ray cooling are more powerful than gravitational forces in creating condensations that initiate the formation of galaxies. The inhomogeneity in our Galaxy is caused by: 1) clusters of stars, 2) small satellite galaxies, such as SMC and LMC, and streamers, 3) the arms of the galaxy, 4) the magnetic and electrical fields, 5) the temperatures, 6) the different heating functions and cooling functions, which vary within the Galaxy

(and from one galaxy to another). Inclusions of these effects can be provided by future improvements. The relatively high density plasma in the corona of the Galaxy gives a reasonable explanation of the missing mass; especially in light of the high average density of intergalactic plasma, with (Ne)avg ≈ 2·10−4 electrons cm−3 , and a pressure corresponding to p/k = (N)av ·(T)av = 1035 cm–3 K. If the rotational velocity of our Galaxy is constant beyond 8 kpc at v = 220 km/s, the mass density  of the coronal plasma at R  8 kpc must be equal to about 9·10 10· M R per volume of 4R2·R, where R is in kpc. For solar abundance, the mass per proton is about 1.4·1.67·10 –24 = 2.34·10–24 g, and the density corresponds then to Np  26/R2 protons cm–3, where R is in kpc. Thus at a distance of R = 8 kpc, the average density is Np ≈ 0.4 protons cm–3 , and at R = 30 kpc it is Np ≈ 0.029 protons cm–3 . If the helium abundance is 5 %, or about 0.5 of that in the Sun, then N p ≈ 30/R2 protons cm–3. These are average densities. The average densities in the hot regions are then Np ≈ 0.04 to 0.1 protons cm–3 at 8 kpc, as derived from the experiments of M. Pettini, et al. (“Million degree gas in the Galactic Halo and the Large Magellanic Cloud II. The line of sight to supernova 1987A”; ApJ 340 (1989) 256-264); see also Eqs. (8) and (9) in reference [12]: Ari Brynjolfsson “Plasma Redshift, Dark Matter and Rotational velocities of Galaxies”. At R ≈ 8 kpc, the stars and dust in the galactic disk may contribute about 20 % of the mass. Disregarding (for a moment) the rotational velocities in the Galaxy, the gravitational potential well formed by the Galaxy at large distances R from the center should be nearly isotropic, and the outward gas and plasma pressure will counteract the gravitational attraction. The Boltzmann distribution given by Eq. (30) is then also isotropic and varies outwards, mainly with the radius of the sphere containing the coronal plasma and the clouds, as given by Eqs. (30) to (34). If we then consider a rotation of the Galaxy, the centrifugal forces in the direction perpendicular to the rotational axis will decrease the inflow and increase the outflow, resulting in a net outflow perpendicular to the axial direction. The components of inflow and outflow in the axial direction will be largely unaffected by the rotation. The inward flow will of course come to an approximate halt in the galactic plane, where the mass concentration will be highest, and lead to the formation of stars and dust in the galactic plane. This description appears to be consistent with our observations and Eqs. (29) to (33). But it is surely subject to significant modifications, as many non-gravitational factors have not been considered adequately, including the temperature distribution and the magnetic and electrical field effects. The extremely hot super-massive black hole candidates (SMBHC) at the center will transform old star matter into primordial matter and a photon bubble. The flat rotational curves at large distances correspond to ρ(R)  R−2 , where R is the distance to the center. Lynden-Bell, Donald, M.N.R.A.S. 136 (1967) 101, and Bertschinger, E., ApJS. 58 (1985) 3966 came to a similar conclusion using big-bang cosmology. They found that ρ(R)  R−2. Other approximations often used are those of Navarro, Frenk, and White, in ApJ, 490 (1997) 493 (or: arXiv:astro-ph/9611107, v4, 21 Oct 1997), and Navarro, Frenk, and White, in ApJ, 462 (1997) 563 (or: arXiv:astro-ph/9508025, v1 7 Aug 1995), who used densities proportional to 1/[R(1+R/RS)2]. This density distribution extends its validity to both lower and higher R-values by an adjusted scaling radius, RS. Beyond radii of a few kpc, and by adjusting RS , this density distribution may result in

nearly flat rotation curves consistent with the H I measurements for many galaxies. The emitted X-ray intensities from the intracluster medium show that both the plasma densities and temperatures are high. The temperatures are especially high in the space of closest approach between two galaxies. Big-bang cosmologists could not understand the increased mass or find the source for the necessary heating. But plasma redshift gives a natural explanation of both the increased mass densities and the necessary heating of both the intergalactic and the intracluster plasma. Besides explaining the heating of the Galactic corona and the X-ray background, the hot intergalactic plasma results in a cosmological redshift, which matches that deduced from the magnituderedshift relation for the supernovae Ia (SNe Ia); see section 6 above, and see sections 5.8 and 5.9 and Figs. 5, 6, and 7 of [1]: arXiv:astro-ph/0401420. The measured X-ray intensity gives an independent confirmation of the densities and temperatures in intergalactic space; see sections 5.11 and C2 in App. C of [1]: arXiv:astro-ph/0401420. Plasma redshift cosmology also explains the cosmic microwave background (CMB); see section 8. The intergalactic plasma has an average electron density of (Ne)avg ≈ 2·10−4 cm−3 and an average per particle temperature of T ≈ 2.7 . 106 K. The hot bubble structures in intergalactic space make the average per particle temperature much lower than the average per volume temperature. It is therefore important to distinguish between the average particle temperature and the much higher average volume temperature.

13. Plasma redshift heating of the Galactic corona The plasma redshift heating of direct light from the Milky Way alone does not supply the necessary heating for compensating the X-ray cooling; see especially Eqs. (40) to (43) in sections 5.7.1 to 5.7.7 of reference [1]: arXiv:astro-ph/0401420, “Redshift of photons penetrating hot plasma”. Only when we include the heating by the X-rays, hot electrons, and other fast charged particles emitted by the hot intergalactic plasma can we match the heating requirements in the Galactic corona. Nearly all of the light emitted by stars and galaxies is plasma redshifted and transformed into heat, which heats the intergalactic plasma to an average temperature of Tavg  2.7·106 K. A significant fraction of that tremendous heat energy is transformed into X-rays, which are absorbed in the coronas of the galaxies and the galaxy clusters; see references in Section 5.7.1 of [1]: arXiv:astro-ph/0401420; see also sections C2 and C2.1 of Appendix C of that source. Plasma redshift heating is not uniform due to density variations in the plasma. As in the region of spicules of the Solar transition zone, hot plasma bubbles surrounded by colder plasma are formed in the transition zone at the surface of the condensations to the Galactic corona. The plasma -redshift heating is proportional to Ne, while the X-ray cooling is proportional to Ne2. This causes heating instabilities. The hot volumes tend to get hotter and the cold volumes colder. Mainly, the heat conduction dampens these instabilities. But also the absorption of X-rays in the cold regions by Xrays emitted by the hot regions dampens the instabilities. In the Galactic corona, like in the coronas of the Sun and stars, the plasma redshift of the 21 cm

line is usually smaller than the plasma redshift of the optical lines. This is caused by the plasma redshift cut-off, given by Eq. (13), which shows that the densities in the coronas are too high for the given temperatures to permit plasma redshift of long wavelengths such as 21 cm wavelength light. At 8 kpc, the electron density in the hot Galactic region of the corona with, a temperature of Te ≈ 0.82·106 K is Ne ≈ 0.4 cm−3 . At 20 kpc, the electron density is ≈ 0.064 cm−3. The redshift of the 21 cm line will then be insignificant at 8 kpc, and at 20 kpc it will be small or about 15 % of that in the optical lines. In the colder regions of the corona with a significant density, the 21 cm line is not redshifted; see Eq. (11) and Table 1 of Section 1 above and a more elaborate description in Section 3.2 of [1]: arXiv:astro-ph/0401420. The redshift of the 21 cm line is therefore a better measure of the Doppler shifts than the redshifts of the optical lines, which often include a significant intrinsic plasma redshift, especially at distances less than about 15 kpc. For small distances from the center, the Doppler shifts of the optical lines will often deviate significantly from the shifts of the 21 cm H I line, while at large distances from the center the difference between the shifts of optical lines and the 21 cm line will be smaller. Such slight deviations between the optical lines and the 21 cm line are often large enough to be detectible; see Rubin, V. et al. Astron. J. 98 (1989) 1246, who often report smaller rotational velocities for 21 cm than for optical lines. Their Table III “Comparison of optical and 21 cm velocities”, shows that optical velocities, vopt, usually exceed the 21 cm velocities, v21cm, as predicted by the plasma-redshift theory. (The 21 cm line has smaller plasma redshift in the Galactic corona because Eq. (13) is not fulfilled.) This is another independent confirmation of plasma redshift theory.

CHAPTER II THE REPULSION OF PHOTONS AND ITS CONSEQUENCES

14. Gravitational repulsion of photons The gravitational repulsion of photons was discovered as a consequence of the plasma redshift of solar lines. The predicted variations in the redshift from line to line and variations of redshifts across the solar disk so well matched the measured redshift that there was no place for the usually assumed gravitational redshifts. The plasma redshift made it clear that the solar lines are not gravitationally redshifted when measured on Earth. The lines are, of course, gravitationally redshifted when in the Sun, as many measurements indicate. This means that the gravitational redshift is reversed as the photons travel from the Sun to the Earth. Just as with the discovery of the plasma redshift, this discovery of photons weightlessness in a local system of reference, or gravitational repulsion in distant system of reference, has a great many revolutionary consequences. The discovery of the two leads to a revolutionary cosmology. I have called the combination of the two discoveries “Plasma-Redshift Cosmology”. I have discussed this subject in reference [1]: arXiv:astro-ph/0401420 and in reference [4]: arXiv:astroph/0408312, I am therefore not elaborating the subject in this article. From the previous

references it is clear that the repulsion of photons in a distant system of reference has revolutionary consequences for all presently known gravitational theories. We have established experimentally that photons, which are primary bosons without a rest mass, and fermions, which are particles with spin ½, repel each other. Frequencies of photons, like the frequencies and energy states of atoms and nuclei, are gravitationally redshifted in the Sun or any other gravitating body when measured by coordinate clocks. This is simply a consequence of gravitational time dilation. When atoms, and nuclei move from the Sun to any distant location (for example Earth) free (or nearly free) of gravitational field, the gravitational redshift is reversed and the frequencies of atoms and nuclei are indistinguishable from the corresponding frequencies of other atoms and nuclei at the location of Earth. In the case of photons, however, it has been surmised by Einstein and others, and confirmed (incorrectly) in a great many laboratory experiments that the frequencies of photons do not change when the photons move from the Sun to a location with a different gravitational potential from that of the Sun. Instead, the photons are believed to retain their gravitationally redshifted frequency. Einstein surmised this, as he stated that: “equally many waves would arrive at Earth as were emitted in the Sun”. However, it should be realized that this (classical physics) assumption by Einstein is hypothetical. Only correctly interpreted experiments can tell us what is correct. Plasma redshift theory, when compared with solar redshift experiments, has shown clearly that this assumption by Einstein is false. Instead, the photons gravitational redshifts in the Sun are reversed just as the frequencies of the atoms and nuclei when they move from the Sun to the Earth, provided they have time to change their frequency. Superficially, this appears to contradict the results of a great many well-executed experiments, which are believed, incorrectly, to show that the photons‟ frequencies stay constant in a distant system of reference, as Einstein surmised. Closer scrutiny of all these many experiments shows that this apparent contradiction can be resolved. In all the experiments that have been surmised to “prove” the constancy of the photons gravitational redshift relative to distant coordinate clocks, the researchers failed to take into account the fact that every transition in quantum mechanics takes a finite time to manifest itself. The design of each and every one of the experiments was such that it was impossible for the photons to reverse their frequency in the short time available. On the other hand, the photons when moving the long distance from the Sun to the Earth have plenty of time to reverse their gravitational redshifts. Every transition in quantum mechanics takes a finite time to manifest itself. We have:

t 

Emax

(36)

where t in the present case is the time of flight for the photon to travel from emitter to absorber (the detector) and  is the Planck constant divided by 2. In the Sun, a photon with energy  has a gravitational redshift of about  2.1210–6, where the factor 2.1210–6 is the gravitational redshift of photons at the surface of the Sun. At the location of Earth, the corresponding gravitational redshift

factor is about 110–8. The corresponding redshift difference is then about Em =  2.1110–6, which is the redshift energy difference of the photons at the locations of emission, in the Sun, and absorption, at the Earth.. When E is narrowly defined at each position, this relation is usually t . E > /2, but in the relevant experiments, the maximum energy difference Emax is about twice the average energy difference. Eq. (36) is then a better approximation. Analysis of all the many experiments proving constancy of the photon frequency shows that the condition of Eq. (36) was not met when the photons moved from one gravitational potential to another. For example, in the outstandingly well-executed experiments of Pound and Rebka Jr. in 1959 and Pound and Snider in 1964 (see the analysis in [4]:. arXiv:astro-ph/0408312), the time of flight for the photons travelling 22.5 meters from the basement to the top floor in the Jefferson Laboratory building at Harvard University is t = 7.5·10–8 seconds, while  Emax = 1.9·10–5 seconds, or about 250 times the time of flight of the photon, 7.5·10 –8 seconds. In these experiments (as in the many other experiments), the photons thus did not have enough time for changing their frequency during the time of flight. These experiments do not permit any conclusion about photons‟ weight. In the solar redshift experiments, on the other hand, the time of flight of photons, about 8.3 minutes from the Sun to Earth, is many times the value of  E. For a photon with a wavelength of 500 nm we have that  E = 1.25·10–10 seconds, which is much smaller than the time of flight of 8.3 minutes from Sun to Earth. In the solar redshift experiments, the photons thus have ample time to adjust their frequencies to the gravitational potential. The observed redshifts usually deviated significantly from the expected gravitational redshifts. An elaborate system of currents was then invented to explain these deviations. Unfortunately, in spite of several inconsistencies, the deviations were incorrectly assumed to be caused by Doppler shifts in the line-forming elements. Plasma redshift shows that these Doppler shifts for the most part average out to zero. The observed solar redshifts (when averaged out over extended time, as is usual in these experiments) are therefore very close to the predicted plasma redshift. There is thus no real contradiction between the solar redshift experiments and the a bove-mentioned laboratory experiments by Pound and Repka, and others. The contradiction comes about only when we make impermissible extrapolation from classical physics to quantum mechanics. There are many other experiments. But they all suffer from similar problems. The photons did not have adequate time to adjust their frequency: see [4]: arXiv:astro-ph/0408312.

The frequencies of photons, atoms, and nuclei all reverse their gravitational redshifts when they move to a higher gravitational potential, provided the photons, the atoms, and the nuclei have the time needed to reverse their gravitational redshift frequency in accordance with quantum mechanics. When we bring atoms and nuclei from the Sun to the Earth, their frequencies will usually be reversed,

because the transfer time is long. The potential energy we transfer to the atoms and the nuclei when we bring them to Earth is the cause of the blue shift or the reversal of the gravitational redshift. But we do not carry or lift the photons from the Sun to the Earth. Instead, the gravitational field must push or repel the photons outwards. If we did any experiment in the Sun, we would not notice that the frequencies were redshifted. But if we from Earth observed (as distant observers), for example, an atomic clock in the Sun, we would observe the slower rate (the gravitational time dilation) of the atomic clock. In a local system of reference, we might think the photons were weightless, because the gravitational potentials are usually too small. But if the photons move from the Sun to the Earth, the optical photons would all be blue shifted so as to reverse their gravitational redshift. The optical photons would also gain energy, and the speed of the photons would increase outwards. It thus appears to a distant observer that the gravitational field pushes the photons outwards. This has, of course, very important cosmological consequences. The same gravitational field that attracts fermions (mass particles such as protons, neutrons and electrons) pushes the photon particles (bosons without rest mass) outwards in a distant system of reference (weightless though they are in a local system of reference). The inertial mass of photons, like inertial mass of fermions, is always positive. But we cannot in all cases equate gravitational mass with inertial mass (as was incorrectly surmised by Einstein). The equivalence principle for inertial and gravitational mass, m i = m g, applies, as is usually assumed, to all fermions, but it does not apply to photons, which are bosons without a rest mass. In a distant system of reference, we have for photons that m i = – m g, provided that they have time enough to change their frequency. The equivalence between mass and energy, E = mi · c2, applies only to the inertial mass and not to gravitational mass, mg . This relation for equivalence between mass and energy was deduced in the Special Theory of Relativity before introduction of the General Theory of Relativity. Einstein introduced artificially his cosmological constant  (Lambda) for counteracting gravitational attraction. Einstein hoped that he could have a gravitationally stable universe. There were problems, and the meaning of  has changed. It is now usually referred to as the dark energy parameter. It still has problems, and it is often used as an adjustable parameter; confer accelerating expansion of the universe. The fact that in the plasma-redshift theory the photons are repelled by the gravitational field has, in some respect, a similar effect as Einstein‟s Lambda. But there are also important differences. In the plasma-redshift cosmology the mass particles are attracted, while the photons are repelled. Also when mass particles concentrate in objects like the black hole candidates (BHCs), the matter becomes very hot (due to conversion of potential energy to kinetic energy) as it approaches the singularity. The thermal collisions will then transform heavy nuclei into light nuclei, such as neutrons, protons and electrons, which are transformed into quarks, gluons and photons, or more generally into primordial matter. Due to the strong repulsive force on the fermions when the photons and fermions are mixed close to the centers of the BHCs, the weightless photons in the local system of reference will collect at the center of the super-massive black hole candidates (SMBHCs), while all the fermions are pushed outwards to the surface of the photon “bubble” by the exchange forces (which at these locations exceed the gravitational attraction). These exchange forces together with the large photon pressure carry the pressure of the gravitational forces and the nuclear forces on the fermions layers above.

This makes the universe very stable. The more matter and old star matter is concentrated, the more will transform into primordial matter and photons that prevent the BH singularity from ever forming. Such complete self-regulating stability is not found in Einstein‟s original theory or in the big-bang cosmology. In the big-bang cosmology all forms of mass and energy are gravitationally attracted by the SMBHC and disappear into a black hole. But in the plasma-redshift cosmology the matter that is attracted into the SMBHC becomes very hot and transforms into neutrons, protons, electrons, quarks, and photons. These weightless photons form a photon “bubble” at the center that prevents the mass from ever reaching the singularity. The fermionic quark matter together with protons, neutrons and electrons is pushed by exchange forces towards the surface of the photon bubble. The total energy is conserved at all times. But we end up with a hot high-energy photon bubble surrounded by a relatively thin shell of primordial fermionic matter, quarks, protons, and electrons surrounding the high-energy photons bubble at the center. This primordial matter, including the photons (including gamma-ray bursts), can escape, for example, by quakes caused by stars colliding with the SMBHC. This primordial matter, including photons that are energetic enough to recreate particles, can then form star-forming regions around the supermassive black hole candidates (SMBHCs), as clearly observed in the Milky Way.

Paradox of Youth. In the big-bang cosmology, the centers of galaxies were assumed to consist of old star matter. The hot star matter and photons were assumed to disappear into the black hole of the SMBHC. The observed star-forming region around the SMBHC at the Galactic center has therefore been called the “paradox of youth”; see for example T. Paumard: “Star formation in the central 0.5 pc of the Milky Way”, http://arxiv.org/PS_cache/arxiv/pdf/0810/0810.0391v1.pdf. On the other hand, I consider the youthful star region around the SMBHC as an important confirmation of the plasma redshift cosmology and its consequences. The weightlessness of photons changes many aspects of the physics and the cosmology in a fundamental way. This modification does not destroy the general theory of relativity (GTR); but it modifies it significantly; see “Weightlessness of photons: A quantum effect” http://arxiv.org/abs/astro-ph/0408312/ , [4].

Another paradox of youth. Recently, it has been discovered that high-energy gamma-rays and some gamma-ray bursts appear to originate close to the SMBHC, including the Galactic Center; see Acero et al.: “Localising the VHE -ray source at the Galactic Centre.” http://arxiv.org/PS_cache/arxiv/pdf/0911/0911.1912v2.pdf. In the big-bang cosmology, the gammaray bursts could not originate in SMBHC. It has not been possible to find any close object nearby; see also Abramowski, Gillessen, Horns, and Zechlin: “Locating the VHE sources in the Galactic Centre with milli-arcsecond accuracy”: http://arxiv.org/PS_cache/arxiv/pdf/1002/1002.2364v1.pdf. MNRAS, 402 (2010) 1342-1348. See also V. A. Dogiel et al.: “X-and Gamma-Ray Emission from Galactic Center”, http://arxiv.org/PS_cache/arxiv/pdf/1002/1002.1379v1.pdf. In the big-bang cosmology we appear, thus, faced with another “Paradox of Youth”. But these observations are easily explained in the plasma-redshift cosmology, because in the plasma-redshift cosmology we expect the high-energy photons at the center of the SMBHCs to escape during any minor or large quake from passing stars.

14.1. Repulsion of photons The gravitational repulsion of photons is highly controversial. Let us therefore discuss the subject. The reversal of the gravitational redshift of atomic and nuclear frequencies when atoms and nuclei move from the Sun to the Earth can be explained as due to the energy we transfer to the atoms and nuclei when we lift the them from the Sun to the Earth. Also, the movements of atoms and nuclei are usually so slow that they are not prevented by the uncertainty principle from adjusting to the gravitational potentials along their track. For example, the “atomic clocks” at the basement and at the top floor in the Jefferson Laboratory at Harvard in Pound and Rebka‟s experiments had ample time to adjust to the gravitational potentials, while the photons moving with speed of light from the basement to the top floor had much too short time. Also, we can not lift the photons; instead, the gravitational field must repel (push outward or lift) the photons during their travel from the Sun to the Earth and from the basement to the top floor in the Jefferson Laboratory. As a consequence of this repulsion (as seen from a distant system of reference), the photons from the Sun when moving to Earth gain gravitational potential energy needed to reverse the gravitational redshift. In the experiments in the Jefferson Laboratory at Harvard University, the short “time of flight” (only 7.5·10–8 seconds for travelling 22.5 m in the weak gravitational field of the Earth, and therefore with a small E, or a large value of /E  1.9·10–5 seconds in Eq. (36)) did not give the photons enough time to change frequency. However, when the photons travel from Sun to Earth, they have plenty of time (8.3 minutes) for changing frequency in the much stronger gravitational field and therefore with a larger E, or a small value of /E 1.2·10–10 seconds. The solar redshift experiments, when evaluated correctly in light of plasma redshift theory, show definitely that this is the case, and the lines are not gravitationally redshifted when they arrive on Earth. They are only plasma redshifted; see Fig. 4 and Table 3 above. The photons are weightless in a local system of reference, but repelled by the gravitational field in a distant system of reference; see “Weightlessness of photons: a quantum effect”, in ref. [4]. To many good physicists, this (in spite of its logic) appears to be an outrageous statement, because it is generally believed by all physicists, and so taught everywhere, that the weight of photons is theoretically and experimentally a well-proven fact. After all, Einstein said so, and great many experiments have “proven” him right, such as the experiments by Pound and Snider in 1964 (Phys. Rev. Lett., 13 (1964) 539), Pound and Repka in 1959 (Phys. Rev Lett. 3 (1959) 439, and ibid. 3 (1959) 554, and in 1960 Phys Rev Lett. 4 (1960) 337), and many other experiments; see: Ari Brynjolfsson [4] “Weightlessness of photons: A quantum effect”: arXiv:astroph/0408312. Also I thought it had been proven beyond reasonable doubt that the solar photons were gravitationally redshifted when they arrived on Earth. The reversal of photons‟ frequencies when they move from Sun to Earth (as Fig. 4 and Table 3 illustrate) was therefore an unexpected result, also for me. However, the finite lifetime for any transition makes it clear that we must have

t 

2  E



h 4  E

(37)

where t (= time of flight for the photons from emitter to absorber) is the minimum time needed for measuring a change in energy E (the difference between the photon‟s energy at the positions of the absorption and emission). Actually, E decreases during the upward flight. For the sake of simplicity we use the maximum energy difference, Emax , in Eq. (36). If E is narrowly defined, as it is in Eq. (37), we must have that t·E > /2. But in all the many experiments that were assumed to have proven photons‟ weight, we have t·E < /2. It was therefore impossible to measure any change in E. Consistent with this, no change in E was measured. From many experiments it has conventionally been concluded, incorrectly, that the photon energy E = h did not change; that is, that the coordinate frequency  of a photon did not change with its gravitational potential. The rate of the clocks at the position of the emitter and the absorber of course was different, so the measured redshift was due to the different rates of the local clocks. The solar redshift experiments show that the laboratory experiments indicating that photons do not reverse their gravitational redshift did not prove anything. When the solar experiments are evaluated in the light of plasma redshift theory, they show clearly that the gravitational redshift is reversed when photons travel from the Sun to the Earth. This has profound consequences, not only for gravitational theory but also for cosmology. It shows that gravitational attraction is not as universal as we have thought it to be. Photons distinguish themselves as being primary bosons without a rest mass, (like the graviton). It is possible that this weightlessness applies to other entities, such as other primary bosons. But we have no experimental proof of that. Presently, we will assume therefore that the weightlessness in the local system of reference, or repulsion in a distant system of reference, applies only to photons. Einstein‟s generalization of gravity has never been proven. It has only been a conjecture. Einstein made it clear that the weight of photons was a pure assumption. But as Niels Bohr said: “We should not tell God how to make the world go around. We should only find out how He does it.” This weightlessness of photons in some sense replaces Einstein‟s  (Lambda). It is, however, a much “smarter” solution because it makes the universe extremely stable. It leads to the conclusion that a BH is never formed. Instead, all particles gain so much kinetic energy (exceeding their rest energy) when they approach the BH‟s singularity that they (during thermal collision processes) transform into primordial matter and photons. These photons are squeezed towards the center of BHCs and SMBHCs by the exchange forces on the fermions. Thereby the weightless photons in the local system of reference prevent the mass particles in BHCs and the SMBHCs from ever reaching the singularity (infinite gravitational potential energy). The outwards-directed photon pressure together with the outwards-directed exchange forces between the fermions counteract the inward-directed gravitational pressure of all the fermions in the photon “bubble” (mainly in its outer layers) and the pressure of fermions in all the layers above the photon-bubble surface. In case the photons escape (for example, due to the quake of an in-falling star), the photons will be pushed outwards by the gravitational field. The photons will

thereby gain back all the gravitational redshift energy. The total energy is conserved at all times. The world can renew itself forever. The energy is conserved at all times. This is not the case in the conventional theory, where energy and mass disappear into the BH. I have analyzed hundreds of solar lines‟ redshifts. I do not doubt, therefore, that the plasma redshift explains the observed solar redshift. The redshifts at the center of the solar disk vary from line to line as predicted by plasma redshift theory. The center-to-limb effect varies differently across the solar disk for the different lines, as predicted by the plasma redshift theory. For example, the variations shown for the center-to-limb effect in Figure 4 in section 2.2 above are typical only for strong lines with high excitation potentials for both lower and the higher energy levels. The high excitation potentials of the 6297.8, 6301.5 and 6302.5 Å lines of Fe-I cause the second term in Eq. (12) to be relatively small. The redshift increases then towards the solar limb as derived from the first term in Eq. (12). In the case of fairly strong resonance lines, such as that of sodium and of potassium with zero-energy lower levels, the center-to-limb effect is very different due to the large second term in Eq. (12), which varies significantly along the center-limb distance (due to the zero excitation potential), as illustrated in Figure 3. There are thousands of measurements available. Only in the case of plasma redshifts are these variations from line to line predictable. Usually, the good researchers measure the solar redshifts over extended time. The Doppler shifts caused by movements in the line-forming elements will then, for the most part, average out to about zero. The photons are plasma -redshifted and not gravitationally redshifted when they arrive on Earth. Therefore, Einstein‟s assumptions that the photons retain their gravitationally redshifted frequency when the photons move outwards from a gravitating body must be wrong, and the interpretations of the many experiments is wrong. This applies also to the redshifts of white dwarfs (WDs). The observed redshifts are due to plasma redshifts. That is the reason that they are observed to vary from line to line. Einstein makes it clear that the gravitational redshift is based on two assumptions. The first assumption is that: the frequencies of photons and all frequencies of atoms are redshifted in the Sun as seen by a distant observer. This assumption is correct. It is caused by gravitational time dilation. It has been proven to be correct, for example, in the experiments by Pound and Rebka Jr. in 1959 and Pound and Snider in 1964. Einstein‟s second assumption is that the frequencies of the photons are constant as seen by a distant observer when the photons move from the Sun to the Earth. Einstein said: “…equally many waves must arrive on Earth as leave the Sun.” While this second assumption may appear reasonable in classical physics, it has no basis whatsoever in quantum mechanics. It is wrong, as the solar redshift experiments clearly show when evaluated in light of the plasma redshift. See: “Weightlessness of photons: A quantum effect”, [4]. We should realize however that when the photon frequency is low (microwaves) and E therefore extremely small, then the frequency reversal will take a longer time. This residual gravitational blue shift is only a small fraction of the observed anomalous blue shift in Pioneer 10 and 11. The main fraction of the observed anomalous blue shift is due to “plasma blue shift”, corresponding to the negative values of F1 (a) in Table 1 for a > 3.633. We should recall that the speed of photons (light) increases by the same factor as the frequency when the photons move outwards from the Sun. We therefore interpret the reversal of the gravitationally redshifted frequency as a repulsion of photons in the gravitational field. In a distant system of

reference, the frequency changes of the photons (when measured by coordinate clocks) correspond in all aspects to a repulsion. Einstein introduced the cosmological constant  in his equations to counteract the gravitational collapse of the universe in his quasi-static model of the universe. Also, the repulsion of photons prevents gravitational collapse of the universe and makes it quasi-stable. The more matter concentrates the more it will transform to primordial matter and photons, which are then pushed outwards. This is self-regulating and so the universe is extremely stable. The transformation of mass to primordial matter and photons makes it possible for the universe to renew itself forever. The repulsion of photons in distant systems of reference prevents formation of any black hole (BH). We usually follow changes of matter from its creation by photons through its many changes until it collects in black hole candidates. The rate of the associated changes defines a forever increasing time. Related also is the forever-increasing entropy. Usually, we are not looking for the return cycle of the transformation of photons to mass. Often, we are inclined to ask for the beginning and the end although neither the beginnings nor the ends are coherent, but occurring incoherently all the time. The universe thus has no beginning and no end. It continuously renews itself forever, mainly in super massive black hole candidates (SMBHCs). The beauty of photons‟ repulsion in the distant system of reference is that it is in accordance with all correctly evaluated measurements. This makes the world quasi-static, stable, everlasting, and matter renewable, as I will show later. Due to plasma redshifts and photon repulsion, there is no need for Einstein‟s Lambda, big bang, inflation, dark energy, accelerated expansion, dark matter, and black holes. In the physics literature on photons, we often encounter sentences such as: “the photon‟s frequencies may be lowered by moving to higher gravitational potential, as in the Pound-Repka experiment”, (Wikipedia, July 2007). However, Einstein made it clear that we should use only one clock (Einstein prefers the coordinate clock, a clock at a position where the gravitational potential is insignificant). In these experiments the local clock and not the photon changes frequency when we move to higher gravitational potential. An atomic clock in the Sun will go at a slower rate when compared with a similar atomic clock (nearly a coordinate clock) on Earth. In principle, we could observe the atomic clocks in the Sun. All the atoms and photons in the Sun will oscillate with a lower frequency than similar atoms and photons on Earth. However, when solar atoms move to Earth they will oscillate with the frequencies for similar atoms on Earth. But when the photons move from the Sun to the Earth, Einstein surmised incorrectly that they will oscillate with the same lower frequency they had when in the Sun. This gravitational redshift of photons is a consequence of Einstein‟s classical physics thinking. He assumed that: “equal numbers of waves per second must arrive as were emitted at the source”. The light (photon) arriving on Earth from the Sun, according to Einstein, is therefore redshifted when compared with the corresponding light (photon) on Earth. In his original article Einstein thus surmised that the photon frequencies are constant when the photons move to Earth, while the clocks increase their frequency when they move to higher gravitational potential on Earth. When I compared the expected plasma redshifts with the observed solar redshifts, I found that the photons were not gravitationally redshifted. I showed thereby that the photons, like the atomic clocks, increase their frequency with an increase in gravitational potential, provided they have the time to change. I find that this is consistent with all experiments, because in these laboratory experiments, such as those by Pound and Repka, the photons could not change their frequencies in the short time available. When reviewing my paper, some physicists contend that photons do not need any time to change their frequency. This is of course incorrect and a sign of their classical physics thinking. In quantum mechanics it is well known that each and every transition has a finite lifetime. A finite time is always required to change from one state to another. This is basic to quantum mechanics, which is not a point mechanics, but a wave mechanics. It is true that we often (usually) in quantum mechanical assume that the reaction to a force is instantaneous. But we must always be mindful of taking delayed action or

the uncertainty principle into account. In quantum mechanics, a mathematical point is not a source of a gravitational field, an electrical field, or a spin. In physics, only a finite volume can be a source of such distinctiveness or character. An ensemble of small volumes can have new character not found in the subunits. A human has characteristics not found in the individual cells. The cells have characteristics not found in the molecules. Molecules have characteristics not found in the atoms, etc. Physicists deal with characteristics of finite subunits with the help of quantum wave mechanics and not classical point mechanics. Classical physics is often a useful approximation to quantum wave mechanics, but we should know the limits of that approximation. Some physicists have objected to the weightlessness of photons and stated that the gravitational bending of light proves that the photons have gravitational weight. This is wrong. Just as the refraction and the bending of light in a prism depend on the speed of light and the path length, the bending of light around the Sun, stars, galaxies, and galaxy groups depends on the speed of light and the path length. The bending of light is independent of attraction or repulsion of the photons by the gravitational field. As my mentor Christian Møller shows in his monograph, “Theory of Relativity” (1972, Clarendon Press, Oxford), 50 % of the bending is due to the speed of light (being slower close to the Sun) and 50 % is due to the nonEuclidean character of the spatial geometry or the warping of space around Sun (stars or galaxies); see section 12.3 of this source. The bending in this respect is completely independent of the weight or gravitational repulsion of photons. We should realize that in the conventional theory, the bending of light is twice that of a falling photon particle. An interesting observation in the Pioneer experiments (although usually not mentioned) is a tiny blue shift of the long wavelength signals (see the last column of Table 1) varying with the position of Earth as it orbits the Sun. When low energy photons pass through the outer coronal plasma, they are slightly blue shifted. These tiny blue shifts correspond to the negative values of F1(a) for a > 3.633 in Table 1 above. Usually, I have disregarded them, because they are so small. But the Pioneer 10 and 11 experiments are so outstandingly well done that we can detect these small effects. This is another independent confirmation of the plasma redshift.

15. Black hole candidates are not black holes, but engines for eternal renewal of matter An object that big-bang cosmologists call a black hole (BH) or a super massive black hole (SMBH), we call a “black hole candidate” (BHC) or a super-massive BH candidate (SMBHC), because in the plasma-redshift cosmology there are no BHs and no SMBHs. In classical physics, we often run into artificial singularities. For example, the field E = e/r2 from an electronic point charge e approaches infinity when the radius r becomes very small. But every physicist knows that we cannot use this relation for any radius less than (about) the classical radius of the electron. We know more generally that physics changes character when we approach any singularity. We should therefore not be surprised that physics of a BH changes character when we approach the BH singularity.

In the next section, we show that before the particles reach the singularity, their potential energy transforms into kinetic energy, which, due to the high collision density, splits all heavy nuclei into their subunits: neutrons, protons, electrons, quarks and photons. At these high temperatures, we will be in the domain of “quantum chromodynamics” (QCD). The heating increases further inwards, and the particles will, during their collisions, then transform into photons before reaching the black hole singularity. The exchange forces push the fermions (mass particles) outwards, thereby squeezing the photons inwards. The photons are not affected by exchange forces because they are bosons and can be on top of each other. The photons will therefore collect at the center of the SMBHC and form a “bubble of photons”. The tremendous pressure of the photon bubble at the center together with the

exchange forces on the fermions will push the fermions (particles) outwards. These forces will carry the gravitational weight of all the fermions and the layers above. The gravitation acts on the elementary fermions, not on the photons, which are primary bosons without a gravitational rest mass. The photon bubble at the center thereby prevents any mass particle from ever reaching the singularity limit. This is all self-regulating. The more pressure pushes the fermions inwards, the more of the fermions will be transformed into photons. In the plasma-redshift cosmology, there is thus no “event horizon” and no black hole. Black hole candidates have masses from about a few solar masses, M, to several billions of solar masses. In plasma-redshift cosmology, the physics of small collapsars (< 2·M) is similar to that in the conventional big-bang cosmology. For example, the physics of a collapsar with mass below about 1.4·M and temperature T < 10 10 K are nearly the same, because the photons play no or only a minor role in the physics of these objects. However, when the size of the collapsar increases beyond about 2·M to about 3·M , the center temperature increases and a small photon bubble starts to collect at the center. This weightless photon bubble (weightless in a local system of reference), which then starts to form, causes changes in the physics. There are many variants of collapsars and BHCs, which require much time to describe. But the smaller ones (below about 2·M) are often reasonably well described in the literature. For illustrating some of the new physics, we will in the following focus on super massive black hole candidates (SMBHCs), especially the SMBHC at the Galactic center. In this case, the measurements are improving and will soon be good enough for comparing the findings with the predictions of plasma-redshift cosmology and big-bang cosmology. In the plasma-redshift cosmology, collapsars with masses exceeding about 2·M, the center temperature is often high enough to transform the particles into protons, and electrons, which at still higher temperatures transform into primordial quark matter (up, down, charm, strange, top, bottom) and weightless photons. At these higher temperatures, we must then apply quantum chromodynamics rather than quantum electrodynamics. In short, the old star matter becomes very hot, when its potential energy transforms into kinetic energy in the huge collapsars and in SMBHCs. The highest kinetic energies close to the center of these objects are in excess of the rest energy of the particles in the local rest system, and turn them therefore into primordial quark matter and photons. This primordial matter and the photons can escape (diffuse out and escape, through quakes caused by passing stars) and form young stars often seen around SMBHCs at the centers of galaxies. In the big-bang cosmology, it is surmised that the energy and the particles disappear into the BH. The young star-forming region, containing over 100 S stars close to (within 0.5 pc of) the Galactic center, was therefore a big mystery that could not be explained. In the big-bang cosmology, the old star matter was surmised to accumulate at the center, and a star-forming region so close to the center was considered impossible. The young stars around the BHC are sometimes called the “paradox of youth”; see T. Paumard: “Star formation in the central 0.5 pc of the Milky Way”, http://arxiv.org/PS_cache/arxiv/pdf/0810/0810.0391v1.pdf. The SMBHC transforms the gravitational potential of the particles approaching the singularity limit into heat. In the big-bang cosmology, this heat disappears with the particles into the black hole. But in the plasma-redshift

cosmology, this heat transforms old star matter into protons, neutrons and electrons and into primordial quark matter and photons. Some of the photons will diffuse outwards, and some are released with primordial matter in bursts during quakes caused mostly by passing stars. This primordial matter may also coalesce and form young stars. This explains the star-forming regions around the SMBHC. In these SMBHCs, the universe can thus

renew itself forever. There is no need for a big bang or black holes. This is consistent with other aspects of plasma redshift cosmology, which explain without any parameters the cosmological redshift, the cosmic microwave background, the distance-redshift relation, the magnitude-redshift relation for SNe Ia, the accelerated expansion, and the surface brightness relation (Tolman test), by using only ordinary and correct physics. The observation of the star-forming region around the SMBHC at the Galactic Center is thus another important confirmation of plasma-redshift cosmology. It is often claimed that black holes follow from Einstein‟s General Theory of Relativity (GTR). But close to the singularity GTR becomes irrelevant, as fast particles transform into photons which collect at the center of the BHC. The highly relativistic particles interact with the high-density plasma and transform into photons with different characteristics from that of the particles. The theory of relativity is valid for particles, but that is irrelevant because the particles have transformed to photons long before they reach the singularity. Many good astrophysicists recognize that BHs are imaginations not based on conventional physics, and that BHs must be proven to exist through observations. They often use, therefore, the word BHC instead of BH, or SMBHC instead of SMBH. I am thus using their notations. Others have correctly pointed out that Einstein‟s General Theory of Relativity (GTR) does not predict BHs, because the black hole assumptions require particle speeds equal to or exceeding the velocity of light, which is impossible according to GTR; see: A. A. Logunov: “The Theory of Gravity”, http://arxiv.org/PS_cache/gr-qc/pdf/0210/0210005v2.pdf, and Trevor W. Marshall: „The gravitational collapse of a dust ball”, http://arxiv.org/PS_cache/arxiv/pdf/0907/0907.2339v1.pdf . However, although Logunov‟s and Marshall‟s contention is more correct than the contention that a black hole is formed, it is still more correct to say that Einstein‟s General Theory of Relativity (GTR) at the singularity does not predict anything, because it simply does not apply close to the singularity. The physics changes character close to the singularity. Very close to the singularity there are no particles, only photons. In classical physics, we have many singularities (such as the electrical field e/r2 of an electron, mentioned above). But every physicist knows that the physics changes before the singularity is reached. In the case of an electron, the classical radius of the electron is the limit. I dare say that there are no singularities in physics, because the physical laws will always change before the singularity is reached. Close to the gravitational singularity, the physics changes. The kinetic energy becomes so large (in the local system of reference) that matter changes to weightless photons (which are primary bosons without a rest mass and not fermions) with very different characteristics from those of the fermions, which are governed by the gravitational field and the exchange forces. In BHCs, it is of course important that the density is very high and the collision density therefore very high. The extrapolation to infinity in physics has no meaning in this case. (Analogously, we can treat an electron as a point particle, but only when the distances to the point charge exceed the classical radius of the electron. For distances nearly equal to or less than the classical radius, the classical treatment is

invalid.). Solar redshift experiments, when evaluated in light of plasma-redshift (which explains the variations in the solar redshifts from one line to another and the variations in the redshift of each line across the solar disk), show that photons are repelled by the gravitational field in a distant system of reference. All the experiments that have been surmised to prove photons‟ weights, such as the experiments by Pound and Snider (Phys. Rev. Lett. 13 (1964) 539) at Jefferson laboratory at Harvard, are invalid because the experiments are evaluated as if they were in the domain of classical physics, when evaluation in the light of quantum mechanics is essential. In these experiments the photons did not change their frequency when they travelled from the basement to the top floor, because they had no chance in doing so; see [4]: arXiv:astro-ph/0408312, and section 14 above. The finite lifetime makes it clear that for measuring the change in energy E, we must have t· >  /Emax, where t is the time of flight from the emitter to the absorber, and Emax (see Eq. (36)) is the energy difference of the photons at the two locations. But in all the many experiments intended for determining the weightlessness of photons, we have t <<  /Emax . It was therefore impossible to measure any change in E. Consistent with this, no change in E was measured. From these incorrectly designed experiments, it has incorrectly been concluded that the gravitational redshifted photons in the Sun did not change their frequency with the gravitational potential when they moved from the Sun to the Earth. Plasma redshift experiments show that this conclusion is wrong. The optical photons reverse their gravitational redshift during their travel from Sun to Earth. This shows that photons are gravitationally repelled in a distant system of reference. This has tremendous consequences, and leads to the conclusion that BHs are never formed, because all matter gains so much kinetic energy when it approaches the singularity that it transforms into photons in the dense medium of the BHCs. The gravitational forces and the nuclear forces are, close to the center of the BHC, dominated by the exchange forces on the fermions. The sum of these forces squeezes the photons towards the center of the BHC and the SMBHC. These photons at the center prevent, at all times, formation of a black hole (BH). The conventional calculation of the black hole limit, as well as the calculations by Logunov and Marshall mentioned above, treat the heating inadequately. The thermal velocities that are produced by transformation of gravitational potential energy to thermal energy (or kinetic energy, or velocity distribution) are usually underestimated. For example, when a black hole is formed, it is assumed that a significant fraction of this thermal energy disappears into the black hole. In plasma redshift cosmology, on the other hand, the entire heating (or the thermal velocities) and the temperatures are fully included.

16. The singularity limit in BHC In the big-bang cosmology, a relatively cold, non-rotating model of a BHC is often used for calculating the black hole (BH) singularity limit. The reason for this is most likely that the hot matter

and photons at the center of a BHC are assumed to disappear from this world into a BH. A more accurate definition of the singularity limit must take the high temperatures of the BHC, its rotation (Kerr BH), and mass distribution into account. The rate of a moving standard clock in a gravitational field is given by my late mentor Professor Christian Møller, Niels Bohr Institute, University of Copenhagen, in his monograph on the general theory of relativity (GTR); see Eqs. (8.114), (10.62) and (10.65) in C. Møller, “The Theory of Relativity”, 2nd ed., Oxford University Press 1972, Delhi, Bombay, Calcutta, Madras, SBN 19 560539. We have that

dt  d

  gr  1  z gr  

 1  2GM  Rc    u c   u 2



gr 0

(38)

where all the quantities are in cgs units; dt is the time differential of a coordinate clock at the position of a distant observer, dτ is the time differential of a standard clock following the particle in its motion, G = 6.674·10–8 is Newton‟s gravitational constant, c is the velocity of light, γι are the gravitational vector potentials, GM/R is the scalar potential of the gravitational field, and u is the velocity of the fermion relative to the distant observer. z gr is the gravitational redshift, and λgr the gravitationally redshifted wavelength of λ0 . This is a generalization of the Lorentz factor in the Special Theory of Relativity (STR), as seen by setting the gravitational constant G and vector potential γι both equal to zero. In a time-orthogonal reference system, where the gravitational vector potentials γι = 0, we have that:

dt  d

1 1

2GM u  Rc 2 c 2



 1

u 2GM  1 2 2 c Rc  1  u 2 / c 2  .

1 2GM u2 1  1 2 Rc 2 c  1  2GM / ( Rc 2 ) 

(39)

  gr

When G = 0, we get the usual time retardation in STR, but when u = 0, we get the usual gravitational time retardation. In Eq. (39) the gravitational vector potentials  in Eq. (38) are assumed to be zero. In Eq. (39) the reference system is thus time-orthogonal. A rotating system of reference is not timeorthogonal, as three components are  = {0, ·r 2(c2 – 2·r2)1/2 , 0}. As Møller has shown, see Eqs. (10.67) and (10.68) of the above reference “The Theory of Relativity”, we can introduce a coordinate mass m of a particle with a rest mass m0 at a point free of the gravitational field, such that:

m

 1  2GM  Rc    u c   u 2



(40)

In the singularity limit of Eqs. (39) and (40), the mass becomes infinite, which has no physical meaning. This shows that these classical equations become invalid as we approach the singularity. (In this case, the mass can transforms into photons well before reaching the singularity. In classical physics, we have many similar cases. For example, the electrical field from an electron with charge e is given by e/r2. But if r is less than the classical radius of the electron, the physics changes and the equation becomes invalid. As the kinetic energy of the particle increases beyond the rest-mass energy, the cross section for annihilation steadily increases. I am emphasizing this point because of the many references in the professional literature stating that the GTR can be extrapolated to the singularity, and even beyond.)

We get that the momentum of the particle is p = mu, and that its energy E is:



E  mc  c  1  2GM

 Rc   γ  u   2



m0c  c  1  2GM  Rc 2   γ  u

 1  2GM  Rc    u c   u 2



 (41)



As shown by C. Møller in section 10.4 of the above reference “The Theory of Relativity”, 2nd ed., the Hamiltonian H then takes the form (see Eq. (10.95) of that source):

H  E  1  2GM

 Rc   2



m0c  1  2GM  Rc 2   c  1  2GM  Rc 2   γ  u

 1  2GM  Rc    u c   u 2



(42)





This Hamiltonian H may be interpreted as the total energy of the particle. In a time-orthogonal system, we have that  = 0. This expression for the Hamiltonian then takes the simpler form

H (u )  E  1  2GM

 Rc   2

m0c 2  1  2GM 1



c 2  1  2GM

 Rc  2

(43)

 Rc   2

The kinetic energy of the particle in this time-orthogonal reference system is then given by:

Ekin

   1  H (u )  H (0)  m0c 2  1  2GM  Rc 2    u2  1  c 2  1  2GM 



 Rc   2

    1   

(44)

When inside the braces the first term exceeds 2, the energy Ekin exceeds the particle‟s rest energy, m0 ·c2·(1–2GM/(Rc2))1/2 . For example, if u2/c2 = 2GM/(Rc2) = 3/7, then Ekin = m0c2·(1–2GM/(Rc2))1/2, which is equal to the rest energy of the particle. As the particle‟s gravitational potential decreases, the thermal velocity u of the particle increases and transforms into heat. The factor (1–2GM/(Rc2)) in the first term inside the braces enhances the value of u2/c2, and increases thus the kinetic energy beyond the particle‟s rest energy. When the kinetic energy in the thermal collisions exceeds the rest energy, the cross section for transformation of the particles into weightless photons increases. The photons that are emitted will collect at the center of the SMBHC. The outward pressure of the “photon bubble” at the center and the outward-directed exchange forces between the fermions will together counteract the inward-directed gravitational attraction and the strong nuclear forces on the fermions and the weight of all the layers above. This is all self-regulating. The more matter accumulates the more is transformed to weightless photons. Long before the particles reach the singularity limit, they will transform into weightless photons, which form a “bubble” at the center of the SMBHC. This bubble increases in size and prevents formation of the singularity limit at all times. In the plasma-redshift cosmology, the BH is therefore never formed, and the “event horizon” is never formed, because the photons can at all times in principle escape the SMBHC. From Eq. (38), we see that dt/dτ = εgr approaches infinity when (in the big-bang cosmology) the radius R approaches the singularity radius RS. When the gravitational vector potentials  are zero, the singularity limit takes a simple form derived from Eq. (39) and we have that

2GM 2.956  105 M R  RS  2   c 1  u 2 c 2  1  u 2 c 2  M 

cm,

(45)

where RS = RS’ corresponds to  = 0. The same singularity limit follows from Eq. (43). From Eq. (45), it is seen that an increase in the particles’ velocities u increases the radius RS’ of the singularity limit. Only when u = 0 is the singularity given by the Schwarzschild radius RS = RS’ = 2GM/c2 . It is important therefore to take the velocities u into account, especially when the temperatures are very high. Some big-bang cosmologists realize that the temperature may be very high and may approach or even exceed 10 12 degrees K (see for example, Ramesh Narayan, Jeffrey E. McClintock: http://arxiv.org/PS_cache/arxiv/pdf/0803/0803.0322v1.pdf); or New Astron.Rev.51 (2008) 733-751. Actually, the temperature may exceed significantly T = 1012 K. In the plasmaredshift theory, these high temperatures are consistent with observation; see Acero et al.

“Localising the VHE -ray source at the Galactic Centre”, http://arxiv.org/PS_cache/arxiv/pdf/0911/0911.1912v2.pdf, and Abramowski, Gillessen, Horns, and Zechlin: “Locating the VHE sources in the Galactic Centre with milli-arcsecond accuracy”, http://arxiv.org/PS_cache/arxiv/pdf/1002/1002.2364v1.pdf. MNRAS, 402 (2010) 1342-1348, while they are inconsistent with the big-bang cosmology. See also V. A. Dogiel et al.: “X-and GammaRay Emission from Galactic Center”, http://arxiv.org/PS_cache/arxiv/pdf/1002/1002.1379v1.pdf. In plasma redshift cosmology, the temperature may increase to any temperature needed to transform particles into photons, which prevents the formation of a black hole. For splitting heavy nuclei into neutrons and protons, the kinetic energy must exceed the binding energy of the neutrons and protons. For the photo-neutron and photo=proton reactions (, n) and (, p) the binding energies are usually between about 5 and 16 MeV. However, for deuterium the threshold is 2.225 MeV; for beryllium (9Be) the (, n) threshold is 1.66 MeV and the (, p) threshold 16.87 MeV, while for helium ( 4He) the (, n) threshold is 20.58 MeV and for (, p) it is 19.81 MeV, and for carbon (12C) the (, n) is 18.72 MeV and for (, p) about 15.96 MeV. Just above the thresholds, the cross-sections are usually relatively small, but reach usually a maximum at the giant resonance for incident photon energies in the range of 5 to 10 MeV above the threshold energy. The collisions between particles with these kinetic energies will produce these reactions through direct excitations or through the X-rays and virtual photons they produce. The thermal collisions will thus result in reverse reactions (that is, in (n, ) and (p, ) reactions) which increase the photon production. These reverse reactions will increase steadily with increasing temperature. The exchange forces push the fermions outwards, while the photons are squeezed towards the center of the BHC or the SMBHC with the fermions concentrating at the surface of the photon “bubble”. This enhances the separation and enhances the photon production. The collisions between the fermions thus increase the size of the photon bubble as the BHC collects mass. When we equate the (,n) threshold in 4He at 20.58 MeV with (3/2) kT, we get that T = 1.6 ·1011 K. It follows that for T  3 ·1011 K most of the heavy atoms will have disintegrated into neutrons and protons (besides other particles such as leptons). The threshold for electron-positron pair production is about 1.02 MeV, but cross section increases steadily with energy and atomic number (nearly  Z2 ). In heavy atoms it dominates Compton scattering above 5 to 7 MeV, and in hydrogen beyond about 150 MeV. The thresholds for the disintegration of the different combinations of quarks are usually in the range of 200 to 1000 MeV (T = 1.55·1012 K to 7.7·1012 K). So at these energies we start to break up the neutrons and protons. At still higher temperatures and energies, the ordinary nuclei disintegrate into photons. During thermal collisions, the particles will thus emit high-energy photons and annihilate into photons.

In the conventional big-bang cosmology, these high energy photons have weight and disappear into the BH. But in plasma-redshift cosmology these photons are in a local system of reference weightless, and in a distant system of reference gravitationally repelled. This prevents the formation of a BH. The reversal of the gravitational redshift experiments in the Sun have demonstrated this, provided the experiments are properly evaluated in light of plasma-redshift theory.

17. Densities in and around black hole candidates The sizes of BHCs vary greatly. The SMBHC at the Galactic center contains about 4.3 million solar masses, M = 4.3·106·M = 8.56·1039 g, within a certain radius R (see: Gillessen et al., “Monitoring stellar orbits around the massive black hole in the Galactic center”, ApJ 692 (2009)1075; http://arxiv.org/PS_cache/ arxiv/pdf/0810/0810.4674v1.pdf; and Ghez et al., “Measuring distance and properties of the Milky Way‟s central supermassive black hole with stellar Orbits”, ApJ 689 (2008) 1044-1062; http:/arxiv.org/PS_cache/arxiv/pdf/0808/0808.2870v1.pdf ; Löckmann, et al., “Origin of the S stars in the Galactic center”, http://arxiv.org/PS_cache/arxiv/pdf/0807/0807.2239v2.pdf., ApJ. Letters; and Perets and Gualandris, http://arxiv.org/PS_cache/arxiv/pdf/1004/1004.2703v1.pdf). Perets and Gualanris showed that most of the currently studied models could not consistently explain both the population of S-stars and the extended population of young B-stars up to 0.5 pc from the center. In the big-bang cosmology, it is usually surmised that there is a SMBH at the Galactic center containing the mass M. From Eq. (45) we get then that the singularity radius RS for SMBHC is:

2.956 105  4.3 106 1.27 1012 RS   1  u 2 c2  1  u 2 c2 

cm.

(46)

For u ≈ 0, we get RS = 1.27·1012 cm, which is the Schwarzschild radius limit for this SMBHC at the center of our Galaxy. Assuming that the vector potentials are zero. We get fromEq. (45) that the gravitational mass MS inside the singularity radius RS is MS = M = RS·c2 · (1– u2/c2) /(2G) = 8.56·1039 g. The average gravitational mass density ρs of the mass MS inside RS is then given by

RS c 2 1  u 2 c 2  1.607 1027  1  u 2 c 2  MS S    RS2  4 / 3 RS3  2G    4 / 3 RS3

g  cm3 .

(47)

When in the big-bang cosmology, we insert RS = 1.27·1012 (1– u2/c2) cm from Eq. (46) into Eq. (47), we get that the average density (ρg) avg for the SMBHC at the Galactic center is given by

 

g avg

 S 

1.607 1027  1  u 2 c 2  2 S

 996  1  u 2 c 2 

g  cm3 .

(48)

In big-bang cosmology, the high-energy particles disappear into the black hole. The value of u is then often approximated by u ≈ 0, and the value RS ≈ 1.27·1012 cm, which is equal to the Schwarzschild radius for the SMBHC. The average density within RS ≈ 1.27·1012 cm is then only (ρg)avg = 996· (1– u2/c2)3 g·cm−3, which is a very low number relative to the nuclear density of (ρnucl)avg . 2.7·1014 g·cm−3. The mass MS = 8.56·1039 g. is determined from the orbits of the encircling stars. The black hole follows from the classical laws of physics as the big-bang cosmologists know them. Even if the mass becomes very hot and transforms into photons, the photons with the fermions are (in the big-bang cosmology) sucked into the black hole, because big-bang cosmologists generally surmise that the photons have weight. Strangely, the same big-bang cosmologists surmise that the gravitational field somehow escapes the black hole and can affect the surrounding stars in accordance with the conventional Newtonian laws of gravitation. In plasma-redshift cosmology the point of view is very different. As mentioned in sections 15 and 16, the photons are found to be gravitationally repelled in a distant system of reference (and weightless in the local system of reference). In light of plasma redshift theory, the solar redshift experiments make this very clear. Closer scrutiny of all the many laboratory experiments that had been surmised to prove photons‟ weight demonstrates that this surmise is in error. In the design and interpretation of all these experiments, essential quantum mechanical life-time effects had been disregarded. It has therefore been assumed incorrectly that photons had weight; see reference [4]: arXiv:astro-ph/0408312 : “Weightlessness of photons: A quantum effect” by Ari Brynjolfsson. In plasma-redshift cosmology, the matter becomes very hot when it approaches the BH singularity, see Eq. (44), as none of the energy disappears into a black hole. The fermions become so hot that the kinetic energy of the particles exceeds their rest energy. During the collisions in the dense plasma the particles emit weightless photons, and they may also transform into weightless photons when they approach close to the singularity limit. The exchange forces on the fermions push the fermions outwards, while the photons (which are bosons without rest mass) collect at the center of the BHC or SMBHC and prevent formation of a BH. The transformation of the old star matter to hot primordial matter and photons, which both on occasion can escape, makes it possible for the universe to renew itself forever. A great many density distributions of fermions and photons are possible without the gravitational mass ever reaching the singularity limit. For example, if for any radius RS1  RS the density S1 at RS1 is about 1/3 of the average density inside RS1, we get (for RS1 = RS):

S1 

1.607 1027  1  u 2 c 2  3RS2

 332  1  u 2 c 2 

g  cm3

(49)

where RS1 = RS = 1.27·1012 (1– u2/c2) cm. At the surface of a sphere with radius R S1 = RS, the density is then S1 = 332· (1– u2/c2)3 ≈ 332/64 ≈ 5.2 g·cm−3. This is 1/3 of the average density inside RS1 = RS as given by Eq. (48). If we integrate Eq. (49) from 0 to RS, we get Eq. (48). With the density distribution given by Eq. (49), the object would be close to the critical density for any distance RS1  RS = 1.27·1012 (1– u2/c2) cm. In plasma-redshift cosmology, neither the photons nor the fermions disappear into the BH. The temperature is then usually much higher than that predicted by the big-bang cosmology. There is no singularity, because most of the volume that is close to the center and inside RS ≈ 1.27·1012 (1– u2/c2) cm is occupied by weightless photons in the local system of reference. A particle that approaches close to the singularity limit will gain so much kinetic energy that during the thermal collisions it transforms into weightless photons, which form a photon bubble at the center and prevent formation of the singularity. There is thus no event horizon and no black hole in plasma-redshift cosmology. For the hot particles, the value of (1 – u2/c2) may be on the order of about ½. From Eq. (46), we have for (1 – u2/c2) = ½ that RS ≈ 2.5·1012 cm. The high temperatures decrease the value of the average density inside RS. The average density is thus likely to be less than ρS ≈ 996/8 = 124.5 g·cm−3. This average density ρS is very small compared with the nuclear density of about 2.7·1014 g·cm−3, because most of the volume is filled with weightless photons. The density of the gravitational mass, which is mainly in a shell close to the surface of the photon “bubble”, may equal or even exceed the nuclear density that is about 2.7·10 14 g·cm−3. The total mass of the fermions close to the surface of the photon bubble is close to the observed total gravitational mass, M = 4.3·106·M = 8.56·1039 g, of the SMBHC at the Galactic center. This mass is usually determined as the gravitational mass inside the orbits of encircling stars. The orbital distances to these encircling stars are usually larger than the pericenter distance, Rmin = 1.76 ·1015 cm, of the nearest S0-2 star; see Table 5 of the article by Ghez et al.: “Measuring Distance and Properties of the Milky Way‟s Central Super-Massive Black Hole with Stellar Orbits”, ApJ 689 (2008) 1044-1062; http:/arxiv.org/PS_cache/arxiv/pdf/0808/0808.2870v1.pdf. In plasma-redshift cosmology, where the mass of the BHC can transform into weightless photons, there are many density distributions that can form a total gravitational mass of M = 4.3·106·M = 8.56·1039 g, well within the limits of the pericenter distance Rmin = 1.76·1015 cm. For example, a fraction f1·M of the gravitational mass may be mixed with the photons in the photon bubble at the center. This density would usually increase towards the surface. Close to the surface of the photon bubble and surrounding the bubble we have a high density shell containing most of the mass. The gravitational mass of this shell may be f2 ·M. The third layer (the “coronal” plasma layer)

outside the main shell contains a fraction, f3·M, of the total mass M. This last fraction usually has densities and temperatures that decrease steeply outwards. The gravitational masses f1 ·M, f2·M and f3·M will at all times have a distribution that prevents formation of the singularity. Conventional physics makes this self-regulating, because if any fraction approaches the singularity it will transform into weightless photons. The exchange forces on the fermions will push the fermions outwards and thereby squeeze the photons inward into the photon bubble. If this occurs close to the surface of the SMBHC, some of the photons may escape and be pushed outwards or may diffuse outwards. The closer a fermionic mass particle gets to the singularity limit, which is usually close to the inner la yers of the main shell, the higher will the temperature of the mass particle be, and the more likely will its gravitational mass be to transforms into weightless photons that collect at the center and prevent the system from reaching the singularity. In the big-bang cosmology, the contention is often that the general theory of relativity predicts or makes necessary the black hole (BH). This contention is incorrect, because it assumes that the particles continue to exist as fermionic particles. But the particles do not continue to be particles. When the fast relativistic particles approach the BH limit, the collision density increases, and the particles are transformed into weightless photons. This transformation changes the physics. The classical theory of general relativity thus cannot be extrapolated to the BH singularity. This is similar to the fact that the electrical field from an electron, which in classical theory is given by the relation E = e/r2, cannot be extrapolated to a radius r < r0 , where r0 is the classical radius of the electron, because the physics changes.

In the first approximation, we assume that f1  f2  0.1, and that f3  0.8. The photon bubble and the shell thus contain about 90 % of the gravitational mass of the fermions. We have then that the outer radius, Rsh , of the main shell must meet the condition (see Eq. (45)):

Rsh

2  0.9  G  M 1.144  1012  RS  2  c 1  u 2 c 2  1  u 2 c 2 

cm,

(50)

where M = 4.3·106·M = 8.56·1039 g is the total mass of the SMBHC at the center of our Galaxy. For (1 – u2/c2) = ½, we get that Rsh > RS ≈ 2.3·1012 cm; and for (1 – u2/c2) = 1/4, we get that Rsh > RS ≈ 4.6·1012 cm. Let us assume for a moment that the average density is roughly sh in the shell with radius Rsh and thickness Rsh . Then the average density is

 sh avg 

0.8  M  4  Rsh  Rsh2

4.16 1014  1  u 2 c 2  Rsh

gcm–3

(51)

For Rsh = 10 km, and (1 – u2/c2) = ½, we get that (sh)avg = 1.04·108 g·cm–3 . There are many other possibilities. Within this layer we are likely to have a much thinner layer with much higher density.

Presently, we do not know the equations of state well enough for predicting the density distribution of the SMBHC at the center. However, these rough estimates indicate great flexibility for proper adjustment of the different parameters. These flexibilities indicate that the different possible configurations are relatively stable and usually unaffected by outside disturbances. There appears to be no reason for imagining a black hole as the solution. As our knowledge of the equations of state improves in the coming years (with the help of high-energy accelerators), we will be able to give a more detailed description of the different layers. Recent observations, using 1.3 mm wavelength very long baseline interferometry (VLBI), has detected structure at scales of a few times the Schwarzschild radius Rsch = 2GMBH /c2  1.271012 cm. These measurements indicated a size for SgrA of only about RSurf = 3.7  Rsch  4.71012 cm; see: “Imaging an Event Horizon: Submm-VLBI of a Super-Massive Black Hole” by Sheperd Doeleman et al. in http://arxiv.org/ftp/arxiv/papers/0906/0906.3899.pdf. In the big-bang cosmology it can be debated if a BH has a surface, or if we could observe a surface structure outside the BH limit, Rsch  1.271012 cm. It cannot, however, be debated that the observed surface at RSurf = 3.7  Rsch  4.71012 cm is reasonably close to the limits Rsh ≈ 2.3·1012 cm to about Rsh ≈ 4.6·1012 cm given by Eqs. (49) and (50) above, which are derived in the plasma-redshift cosmology. The planned improvements of VLBI will reduce the wavelengths from 1.3 mm to 0.8 mm and 0.65 mm, which will make interstellar scattering negligible. These improvements should clarify this structure limit. Usually, big-bang cosmologists have estimated the accretion flow to far exceed the luminosity, which they often estimate to be about 10 36 ergs–1 . These physicists argue that this shows that mass and energy must disappear into the BH; see for example: “The Event Horizon of Sagittarius A” by Broderick, Loeb and Narayan in http://arxiv.org/PS_cache/arxiv/pdf/0903/0903.1105v1.pdf. These estimates appear, however, to underestimate significantly the high energy X-rays, high energy gamma rays, outward flux of hot primordial matter and photons, including the primordial matter that results in star forming regions around the SMBHC at the Galactic center; see for example: X- and “Gamma-Ray Emission from the Galactic Center” by Dogiel et al., http://arxiv.org/PS_cache/arxiv/pdf/1002/1002.1379v1.pdf, whose estimates of outward-directed gamma-ray flux and the very high energy required to maintain the high temperature plasma outflow far exceed the estimated outflows by Broderick, Loeb and Narayan mentioned above. Big-bang cosmologists can not understand the “Paradox of Youth” stars surrounding the SMBHC at the center of our Galaxy. Plasma redshift cosmology, on the other hand, gives a simple explanation of it as due to the release of photons and primordial matter from the very hot SMBHC. Big bang fails to explain the eternal renewal of old star matter, and requires a supernatural big bang with supernatural inflation and continual adjustment of the expansion, with the help of accelerated expansion, dark energy, and dark matter, while plasma redshift cosmology explains all the

observations using correct and realistic physics. Big-bang cosmologists have difficulties explaining gamma-ray bursts. Black holes should not be able to emit gamma-ray bursts. Usually, therefore, gamma-ray bursts (especially, the gamma-ray bursts lasting less than 2 sec) are assumed to be emitted during coalescences of two neutron stars or a neutron star and black hole. These bursts should necessarily be accompanied by the emission of strong gravitational waves; but none have been observed so far; see Abbott, B., et al., “Search for gravitational-wave bursts associated with Gamma-ray Bursts using data from LIGO science run 5 and Virgo science run 1”, http://arxiv.org/PS_cache/arxiv/pdf/0908/0908.3824v1.pdf; and Abadie, J., et al., “Search for gravitational-wave inspiral signals associated with short gamma-ray bursts during LIGO‟s fifth and Virgo‟s first science run”, http://arxiv.org/PS_cache/arxiv/pdf/1001/1001.0165v2.pdf. In plasma-redshift theory, it appears natural to explain gamma-ray bursts as any swift release of photons from the photon bubbles at the centers of any BHCs. When any star (including a neutron star or a small BHC) passes so close by the BHC that it causes a quake with a break of the relatively thin shell that surrounds the photon bubble, we should expect a sudden release of photons from the photon bubble. At the end of the fast encounter, it is likely that the shell will quickly repair itself. Any concurrent kick of gravitational waves should be very small. The large inertial mass of the photons causes reduced pressure immediately following the release of the photon burst, which should help in the repair of the “crack” in the shell that released the weightless photons. While any disturbance may cause gravitational waves, we should expect much smaller gravitational waves when a large volume of weightless photons are released than when a large volume of weighty photons are released. Considering the absence of gravitational waves concurrent with the gamma-ray bursts, we find that plasma-redshift cosmology gives a more reasonable explanation of the observations than big-bang cosmology.

CHAPTER III SUMMARY OF PLASMA REDSHIFT COSMOLOGY

18. Summary The most important findings are:

A: The plasma redshift cross section of photons when penetrating hot sparse plasmas. B: Gravitational repulsion of photons in a distant system of reference.

C: The cosmic microwave background (CMB) is emitted by the steady state of the intergalactic plasma. The plasma redshift cross section is described in section 1. In the past, it has been overlooked, because it is important only in hot sparse plasma like that in the corona of the Sun or the plasma in intergalactic space. In conventional laboratory plasmas all the low-energy levels are occupied and the photons cannot transfer any plasma redshift energy to the plasma. This cross section explains the solar redshift, the cosmological redshift, the CMB, and the cosmic X-ray background, the magnitude-redshift relation for supernovae, and the surface-brightness-redshift relation without the big bang, cosmic inflation, expansion, dark energy, dark matter, accelerated expansion, or BHs. The gravitational repulsion of photons is described in section 15. This finding corrects the generally held belief that photons have weight, which was derived from a long series of incorrectly designed and interpreted experiments. These findings change fundamentally the conventional explanations of a great many phenomena, including the cosmological perspective. The universe is not expanding and it can renew itself forever. Like the Sun, most stars have rather small intrinsic redshifts, but objects with extensive coronas, such as quasars and collapsars, often have large intrinsic plasma redshifts. Plasma redshift explains the cosmological redshift without any adjustable parameters, such as, dark energy, accelerated expansion, and dark matter.

Some of the details are as follows : 1. Plasma redshift explains many solar phenomena that could not be explained without it. Most important are the heating of the solar corona and the solar redshifts. The second law of thermodynamics forbids transport of heat energy from a colder place (such as the photosphere) to a hotter place (the corona). It has long been a mystery, therefore, how the 5800 K photosphere could heat the about 2.2 million K corona. But plasma redshift gives a simple explanation. Plasma redshift is rooted entirely in the imaginary part of the dielectric constant and is an irreversible process, like friction. The second law of thermodynamics does not apply to friction-like processes. 2. Detailed physics calculations show that the plasma redshift cross section predicts well the densities and temperature distribution in both the transition zone and the corona. Experiments show that the transition zone is initiated at exactly the temperatures and densities predicted by the plasma redshift cut-off; see Eq. (13), Tables 1 and 2, and Figures 1 through 4.

3. Big-bang cosmologists often claim that the reconnection of magnetic field lines causes the destruction of the magnetic field lines and conversion of magnetic field energy to heat. This is wrong. Reconnection is the consequence and not the cause of the destruction of the magnetic field. The actual destruction of the magnetic field is caused by the diamagnetic moments of the charged particles encircling the field lines. When the plasma redshift of photons increases the heating, the increased electromotive force created by the increase in the diamagnetic moment increases and opposes or counteracts the magnetic field. This is the actual cause of the destruction of the field, the formation of the spicules, the flares, the arches, and the protuberances in the Sun. These phenomena are sometimes initiated below the transition zone, when the magnetic field is large enough to move the plasma redshift cut-off, given by Eq. (13), to higher densities. Only plasma redshift gives a detailed physical explanation of these solar phenomena. 4. Plasma redshift gives an exceptionally exact prediction of the observed solar redshifts, the variations from line to line and the variations in the redshift of each line across the solar disk. This is illustrated in Figure 4 and Table 3 for three rather strong iron lines with relatively high excitation of lower levels (2.223 eV, 3.654 eV, and 3.686 eV) and therefore relatively small collision broadenings, and therefore small photon widths. Other lines with high excitation potentials (and therefore small collision broadenings) have, without exception, similar forms; that is, strong increases from center towards the limb. The 2 nd term on the right side of Eq. (12) is then relatively small and nearly constant. The weak lines in this cathegory have smaller redshifts than the strong lines. The weak lines with rather high excitation potentials may have some collision broadening at the center, because they are formed deep in the photosphere. They may then have slightly elevated redshifts at the center of the solar disk, which decrease first outwards before it increases steeper closer towards the limb. Lines with a low or zero value for the lower excitation potential are flatter. Strong lines with low excitation potential, such as the resonance lines of sodium and potassium have a very large 2 nd term in Eq. (12), which decreases towards the limb. Near the center, the collision broadenings of the sodium line is nearly 16 times the undisturbed photon width. The decrease towards the limb in the collision broadening, the 2 nd term in Eq. (12), may then nearly cancel the increase in the first term towards the limb. The centerto-limb variations in the resonance lines of sodium and potassium are therefore very small. Secondly, the measured redshift of each line is usually averaged over an extended period. The Doppler shifts of the lines are then small or nearly insignificant. The observed redshifts are thus principally those predicted by the plasma redshift alone; see Figure 4. An important finding is that the solar lines are not gravitationally redshifted as generally believed. Figure 4 illustrates this fact very clearly. See Table 3 for greater details. This leads to the conclusion that photons are repelled by the gravitational field; see section 14. 5. The Hubble constant H 0 is 3.077105 Ne kms–1Mpc–1; see Eq. (16), which follows from Eq. (12) when the last term in Eq. (12) is insignificant. So the Hubble constant is proportional to the electron density along the line of sight. If the average electron density in intergalactic space along the distance to an object is (Ne)avg  (2.00 ± 0.23) ·

10−4 cm–3, the average value of the Hubble constant is (H0)avg = 61.5 kms–1 Mpc–1. This value is less than that obtained by supernovae researchers who did not take the intrinsic redshifts of the galaxies, the Cepheids, and the supernovae into account. 6. The absolute calibrations use mainly Cepheid variables, which are relatively close and have therefore relatively large intrinsic redshifts. Consistent with the plasma redshift and its prediction of intrinsic redshifts, the big-bang cosmologists have usually found their value of H0 to decrease with increasing distance. 7. The cross section for the plasma redshift shows that the average electron density in intergalactic space is (Ne)avg  (2.00 ± 0.23) · 10−4 cm–3, which is about 1600 times greater than the average density of (Ne)avg  1.2510–7 cm–3 surmised in the bigbang cosmology; see section 11 above. It is no wonder, therefore, that in the big-bang cosmology it is necessary to sprinkle some dark matter here and there. In the plasmaredshift cosmology, the average temperature in intergalactic space is (T)avg  2.7106 K, which is much higher than that surmised in the big-bang cosmology, which has no means of understanding properly the heating of such a plasma. The Boltzmann distribution shows that the plasma from intergalactic space leaks into the gravitational potential wells created by galaxy clusters, gravitational lenses, and galactic coronas. These higher densities increase the X-ray cooling and lower the temperatures of these plasmas, which may condense into clouds that increase further the overall density. The higher coronal densities, caused by higher densities in intergalactic space, remove the need for dark matter in such objects as galaxies, galaxy clusters, and gravitational lenses; see section 12. 8. In plasma-redshift cosmology, the relation for cosmological distance versus redshift is given by Rpl = (c/H0)  ln(1+z) (see Eq. (17) ), while in big-bang cosmology the distance is given by a complicated integral, Eq. (18), which requires the adjustable parameters  ,  m, and k; see Eq. (18). In the big-bang cosmology, these adjustable parameters may even vary with time. In the plasma-redshift cosmology, no such adjustable artificial parameters are needed. The distances are based entirely on real physics. 9. In plasma redshift cosmology, the magnitude-versus-redshift relation for SN Ia is given by Eq. (19); while in big-bang cosmology the relation is given by Eq. (20). The distance-redshift relations differ slightly, but the main difference between the two is that the last term in Eq. (19) is 7.5 log (1+z), while in the big-bang cosmology it is 5 log (1+z). This difference means that, while the plasma-redshift predicts correctly the observed magnitude variations, the big-bang requires a strange, supernatural or unexpected accelerated expansion of the universe. There are many “tired” redshift theories, but only the plasma-redshift theory gives the correct quantitative description of the magnitude-redshift relation, and surface brightness- redshift relation. 10. In plasma-redshift cosmology, the surface-brightness-versus-redshift relation is

given by Eq. (22); while in big-bang cosmology the surface brightness is given by Eq. (21). Apart from the slight difference between the distance redshift relations, the main difference is that in the plasma-redshift cosmology the surface brightness is proportional to 1/(1+z)3, while in the big-bang cosmology it is proportional to 1/(1+z)4. The observations are in agreement with the predictions of the plasma-redshift cosmology, while contradicting the big-bang cosmology; see section 4 and reference [7] Ari Brynjolfsson: http://arxiv.org/PS_cache/astro-ph/pdf/0605/0605599v2.pdf. Bigbang cosmologists try to explain this difference as due to some strange or unexpected evolution of the surface brightness. (There are many “tired” redshift theories, but only plasma-redshift theory gives the correct quantitative description of the surface-brightness-versus-redshift relation.) 11. In the plasma-redshift cosmology, the Cosmic Microwave Background (CMB) is given by Eq. (23). Plasma redshift explains this emission as coming from the wellknown quantum mechanical plasma waves in the electron plasma in intergalactic space. The beautiful form of the blackbody spectrum of CMB is rooted in the fact that the relaxation lengths for the plasma redshifts are exactly equal for all wavelengths below the cut-off wavelength given by Eq. (13). For wavelengths longer than the cut-off wavelength (at   30 cm, or for   109 Hz), the intensity in CMB increases about as expected relative to the black-body spectrum; see section 8.1. In the big-bang cosmology, the CMB is surmised to be rooted in free-free emission from the individual electrons occurring shortly after the big-bang, when the pressure was much higher. It also requires cosmic inflation, cooling and condensation of the plasma between z  1400 and z 1000, followed by reionization at about z  6. Plasma redshift predicts no cosmic inflation, and that universal condensation and reionization periods never occurred. At the plasma density of (Ne)avg  210–4 cm–3 the pressure of free-free emission is an insignificant fraction of the pressure in the CMB emission, which is therefore the pressure to be equated with the particle pressure, as done in Eq. (23a). (Unfortunately, most big-bang cosmologists have difficulties understanding this, as they surmise that generally the emission temperature of black body radiation is allways equal to the particle temperature.) 12. The X-ray background is emitted mainly by the hot intergalactic plasma. This plasma, with an average density of (Ne)avg  210–4 cm–3 and (T)avg  2.7106 K, is heated mainly by the plasma redshift of photons. A significant fraction or even most of the low energy X-rays are absorbed in the Galactic corona. The corresponding heating is an important addition to the direct plasma-redshift heating of the corona. The observed intensities are consistent with that observed. Big-bang cosmologists think that the densities in intergalactic space are much smaller, or about (Ne)avg  1.2510–7 cm–3, and that the observed X-rays were emitted shortly after the hypothesized big-bang. 13. The Sun‟s magnetic field together with the plasma-redshift heating explain the solar wind, which is accelerated outwards from the Sun in accordance with Eq. (28). In addition to the gravitational forces, we must often consider magnetic and electrical fields. The imbalance between the X-ray cooling and the plasma-redshift heating

causes huge temperature variations. In intergalactic space, the imbalance creates huge plasma bubbles (with center temperatures sometimes exceeding 30 million degrees K) surrounded by colder and denser plasma (sometimes about 0.3 million degrees K) at the surface of the bubbles (where the galaxies are formed). The associated thermal forces are often more powerful than the gravitation in creating condensations. 14. The discovery that photons are gravitationally repelled in a distant system of reference is revolutionary, and leads to the eternal renewal of the universe. The gravitational repulsion of photons leads to the conclusion that there are no black holes. Instead, the black hole candidates (BHCs) are engines for conversion of old star matter to primordial matter and to weightless photons. This fact leads to the conclusion that the universe is quasi-static and can renew itself forever. Einstein introduced the cosmological constant  to counteract gravitational attraction. Nevertheless, in his static model of the universe, the stars will run out of energy and will have a finite lifetime; that is, star matter can not renew itself. But the gravitational repulsion of photons (derived from experiments) is a much “smarter” solution, as it is self-regulating and leads to a stable, renewable, and for everlasting universe. 15. In the big-bang cosmology, it is often stated that the general theory of relativity leads to the formation of black holes. This is questionable even if we ever had particles close to the singularity. However, as the particles approach the singularity, they transform to photons. The general theory of relativity becomes therefore irrelevant close to the black hole singularity. When approaching the singularity, the particles‟ gravitational potential energy transforms into kinetic energy, which becomes so large that it exceeds the rest energy. During collision with the dense plasma, the particles will by excitations and annihilation transform into photons, which collect at the center of the BHC and form there a photon “bubble” surrounded by plasma of protons, electrons, and quarks. This is all self-regulating. All this prevents the particles from ever reaching close to the singularity. 16. The hot super-massive black-hole candidates (SMBHCs) in galaxies, and possibly in hyper-compact stellar systems (HCSSs), can, during disturbances, release some of the photons from the photon bubble in the form of Gamma-Ray Bursts. They may also release some primordial matter (protons, electrons, quarks, photons, etc.) into the surrounding regions. This primordial matter may subsequently form youthful stars around the SMBHC consistent with observations.. 17. Although photons are not gravitationally attracted, they have their usual inertial mass. The inertial mass of the large photon bubble at the center of BHCs and SMBHCs is therefore very large. The outward-directed pressure of the photon bubble and the outward-directed exchange forces between the fermions will always dominate the inward-directed gravitational forces and the strong nuclear forces between the fermions of the shell surrounding photon bubble. To some extent, the gravitational attraction forces and the attractive strong nuclear forces between the fermions in the shell act as a surface tension around the fluid photon bubble. Outside disturbances may occasionally make the SMBHC oscillate like a falling water droplet or a disturbed uranium-235 nucleus. It is then possible that an outside disturbance (for example, a swallowing of a small BHC) may lead to such large oscillations of the large inertial mass of the photon

bubble that the SMBHC splits into two or more parts. The photon bubble at the center of the SMBHC is surrounded by a shell with layers of dense fermions and plasma. When the fragments of the SMBHC move outwards (usually in opposite directions), they will appear as quasars due to the large surrounding coronal plasma. When these “quasars” move into intergalactic space, their coronal plasma will gradually “evaporate” into intergalactic space. Initially, the corona of the quasars will be relatively thick and cause large plasma redshift of the quasar. But gradually, as more of the corona evaporates, its plasma redshift decreases. This is consistent with the phenomenological descriptions given by Halton Arp; see “Seeing Red: Redshifts, Cosmology and Academic Sciences”, by Halton Arp (published 1998, Apeiron, Quebec H2W 2B2 Canada, ISBN 0-9683689-0-5). It thus appears possible that the quasars are sometimes ejected from the core of galaxies, as Halton Arp has suggested based on observations. 18. Plasma redshift resolves the Olbers’ paradox. If starlight were not absorbed (by plasma-redshift cross-section) as it travels through intergalactic space, the sky would be as bright as all the stars in an infinite universe. The absorption of the light intensity by the plasma redshift reduces the light energy (including scattered light intensity) by a factor of 1/e= 0.3679 approximately every 5000 Mpc, or a factor of 1/100 every 23,000 Mpc, which is in addition to the reduction by (Compton) scattering, any other absorption, and by the inverse distance-squared law (1/R2). 19. Arrow of time. We define the rate of time through the many physical changes of matter from its time of creation to its time of annihilation in black hole candidates. But the time from annihilation of matter in the black hole candidates to its creation from photons is usually not considered. From this we may get the impression that there is no beginning and no end to time. This is because the time of creation of matter and the time of annihilation of matter are incoherent processes occurring all the time at different locations in the universe. 20. Eternal renewal of the universe. In the plasma-redshift cosmology, the transformation of old star matter to primordial matter in SMBHCs is in accordance with well-founded laws of physics, and is self-regulating, without any supernatural intervention. Other models, such as Einstein‟s static model of the universe, require an eternal source of primordial matter for new stars and galaxies, and some undefined means for disposal of old star matter. Only the plasma redshift solves this problem according to the laws of physics.