Chapter 11. Cosmological Aspects of the Epola Structure of Space

11.1 Non-universality of the vacuum light velocity

In Section 6.5, we calculated the vacuum light velocity $c$, using the formula for the velocity $v_d$ of bulk deformation waves in a lattice, $v_d = ({}_b E / m_e)^{1/2}$, and assuming that the experimentally-established 1.02 MeV "creation" and "annihilation" energy of an electron-positron pair is really the binding energy of the pair in the epola (see Chapter 4). Substituting the experimental values of the per-particle binding energy ${}_b E = 511 \ \mathrm{keV}$ in the epola, and of the electron (or positron) mass $m_e = 9.1 \cdot 10^{-31} \ \mathrm{kg}$, we found $v_d = 300 \ \mathrm{Mm/s} = c$. This result should by itself be considered as quite a convincing evidence of the epola structure of space and of the substantiality of epola concepts. On the other hand, it dismisses the universal constancy of the vacuum light velocity, postulated in special relativity (Chapter 2).

Being the velocity of bulk deformation waves in the epola, the vacuum light velocity should depend on "local" conditions in the epola, analogously to the velocity of sound in tremendously large solid lattices. Such conditions are, mainly, the lattice temperature and the concentration and distribution of lattice imperfections and impurities. The vacuum velocity of light is certainly a very important constant in our epola region. It is constant as far out as the mentioned conditions remain stable.

Radiation entering our uniform epola region from regions where it had a different velocity, corresponding to conditions in those regions, propagates here with velocity $c$, corresponding to conditions in our region. Figuratively, radiation does not 'remember' its previous velocities. It always propagates with a velocity, corresponding to epola conditions prevalent in the region of passage during the time of passage. A simple and very-well-known fact illustrating this propterty is that light, which passes deliberately long paths in, e.g., glass or water, where its velocity was by 33 or 25% lower than in vacuum (or air), emerges into vacuum (or air), having velocity $c$, without carrying any "memory" or information about its previous velocity. We therefore conclude that:

in our region of the epola, electromagnetic radiation propagates with the velocity $c$, corresponding to the epola conditions in our region; it always reaches our apparata with this velocity, independent of what the velocity is (or was) in the epola regions in which the radiation was generated and which it had to pass before reaching our region.

The vacuum light velocity $c$, being a constant in our epola region, must not be considered as a universal constant. Actually, there is no need for such consideration. It was first introduced by Poincaré and used by Einstein to adjust to the results of Michelson-Morley's experiment, and to develop a picture of a world with an empty vacuum space, without an ether. In the epola model of space, the result of Michelson-Morley's experiment is clear by itself and obvious. With only a $10^{-15}$-th part of its volume filled by dense particles, the Earth in its motion cannot eause winds in the $10^9$-th times denser epola. The epola model solves all problems of the propagation of light and motion of bodies (Chapter 10) without demanding that physical laws and quantities, established and measured in our backyard, must be the same in the whole universe. Particularly, the demand of the universal constancy of the vacuum light velocity becomes not only superfluous but also wrong.

11.2 The 3 K microwave radiation as foreground radiation of the surrounding epola

We defined the epola temperature (in Section 5.11) as the mean per-particle energy of random vibrations in the epola. With this definition, we then interpreted the 'zero point motion' of helium atoms, as depicting the random vibrations of electrons and positrons in the epola. In a similar way, the motion of Brownian specks depicts the thermal motion of molecules in a gas or liquid. With this approach and the experimental values of the zero-point energies observed in light atoms, it should be possible to calculate the temperature of the epola. Such calculations can be supported by experimental data obtained from other "zero-point" effects, e.g., from the "zero-field splitting" of spin energy levels, electron and nuclear cooling and a wide variety of experiments performed at temperatures close to the absolute zero, where the epola temperature is an important factor, tending to raise the temperature (Section 5.14).

A direct experimental or rather observational approach to determine the epola temperature is by using the 'background' radiation spectra. In the search of low-energy radiation in astrophysics, carried out with powerful microwave telescopes and radiation detectors kept at extremely low temperatures, it was found that we are receiving from all directions in the skies a mysterious microwave radiation. The spectral distribution of the radiation corresponds to the radiation of a blackbody, the temperature of which is about 3 K. The theoreticians of the Big Bang creation theory of the universe interpreted the 3 K radiation as a leftover from the 'grand explosion', distributed all over the universe and appearing as a background radialion behind the observed spectra of celestial objects.

With the electron-positron lattice model of space, it is easy to understand that the 3 K blackbody radiation cannot be produced by an empty space. It can only be emitted by a body, the temperature of which is 3 K. Because there are no atomic or molecular bodies besieging us from everywhere, we have to consider the epola itself as the source of the 3 K microwave radiation. Our model is therefore the following:

the microwave radiation observed everywhere on the skies, corresponding to the thermal radiation of a blackbody at 3 K, is the radiation emitted by the electrons and positrons of the surrounding epola, in their random vibrations around their lattice sites.

As the radiation of the surrounding epola, this is not a 'background' but a 'foreground' radiation. With this interpretation, we approach the only reasonable result that the temperature of the surrounding epola is 3 K.

11.3 Temperature effects in the epola

The dependence of the velocity of light on the temperature of the epola may be expected to be similar to the temperature dependence of bulk deformation waves (or sound) in an unbounded $\mathrm{NaCl}$ crystal or in solid lattices in general. As a rule, the velocity of light should therefore be smaller in regions where the epola temperature is higher.

The epola temperature is elevated in regions of high electromagnetic radiation density and in regions bombarded by high-energy particles originating, e.g., from cosmic nuclear reactions. Where the epola temperature becomes equal to the binding energy of epola particles, the lattice ceases to exist, i.e., the epola 'melts', turning into a liquid of bound $e^- e^+$ pairs. According to the formula (see section 9.6),

the melting would occur at a temperature T,

At even higher temperatures, the epola turns into a gaseous mixture of $e^- e^+$ pairs and free electrons and positrons. The velocity of light is drastically reduced, as is the velocily of sound in gases compared to its velocity in solids. Also, the transfer of radiation energy can no longer be described by photons: just as there are no phonons in gases, there are no photons in the evaporated epola. Therefore, Planck's law, as well as other quantum (or epola) radiation laws, do not hold. Such is possibly the situation in certain kinds of black holes and other unexplained forms of matter in the universe.

11.4 Imperfections and impurity effects in the epola

The propagation of electromagnetic radiation should be affected by lattice imperfections and impurities in the epola, depending on their kinds, concentrations and spatial distribution.

Imperfections are distortions or defects of the epola per se. They include unoccupied lattice sites or vacancies, electrons and positrons in interstitial positions in the lattice, dislocations, 'grain' and 'twin' boundaries, etc. Such distortions can be caused in the vicinity of large masses of atomic or nuclear bodies. In the distorted epola layers, the velocity of light must be reduced; the more, the closer to the body.

The bending of light beams passing in the vicinity of large masses can be explained by the reduction of the velocity of light in the distorted epola layers around these bodies. In the epola model, the bending of light, and starlight in particular (see Section 2.4) is a phenomenon analogous to the mirage, and its mathematical description should be worked out appropriately. With a mirage model for the bending of starlight, the mathematical complexity of the problem would be greatly reduced.

Impurities are dense particles, i.e., elementary particles and nuclei in the epola. We should notice that the electron mass $m_e$ is quite unique among the dense particles. Closest to $m_e$, is the mass of an unstable muon, which is 140 $m_e$. Therefore, it is hard to imagine that any of the known elementary particles may replace an electron or a positron in a lattice-site in the epola, as impurity atoms replace host atoms in solids. It might, however, be possible that elementary particles with masses close to $m_e$ do exist, but because of the easiness with which they may replace electrons and positrons in the epola, they are always 'caught' in the epola. Even when freed from the epola to become detectable, such particles may have a free lifetime too short to be detected.

High concentrations of impurities in the epola can be caused by elementary particles and nuclei, ejected into an epola region by cosmic nuclear reactions. Such concentrations may tear the epola apart, creating a kind of a black hole, in which quantum or epola radiation laws do not hold.

11.5 Epola collapse, creation of atomic matter and black holes

A yet stronger effect of nuclear action can cause the epola to collapse locally by forcing electrons and positrons to such small distances, at which the short-range repulsive interaction (see Section 5.5) is either reduced or cancelled. Such local collapse in the epola may initiate the creation of a new celestial body. Due to the high density of matter in the epola, the creation of atomic matter by epola collapse is possible everywhere 'on premises'. Thus, there is no need to collect matter from vast volumes of the universe in order to create a shiny celestial body, as it is assumed in existing hypotheses of gravitational collapse.

To create a proton (or neutron), the epola collapse has to empty a volume of $1840 \, {l_0}^3$ epola unit cubes $(l_0 = 4.4 \ \mathrm{fm} \pm 0.5 \ \mathrm{fm}$ is the epola lattice constant$)$. This would be a sphere of diameter $~15 \, l_0$ or 65 fm, which is 150 times smaller than the diameter of the hydrogen atom. The volume of the emptied sphere constitutes a $2.7 \cdot 10^{-7}$ part of the atom's volume. To create, e.g., the nucleus of the $\mathrm{Cu_{64}}$ isotope, an epola sphere of a $60 \, l_0$ diameter has to collapse. This is still 80 times smaller than the diameter of the copper atom, and the volume of the emptied sphere is only two millionths of the atom's volume. Hence, the creation of atomic matter by a local epola collapse would not require to draw-in epola particles from distant regions and the regular epola structure in the region of the created atomic body would be restored soon.

We come to an opposite conclusion considering the creation of an extended body of nuclear matter by an epola collapse. We have seen that a sphere of a 65 fm diameter has to be emptied for the creation of a proton or neutron. This is 25 times larger than the diameters of these particles, and the volume of the emptied sphere is 16 thousand times larger than their volumes. Obviously then, a large epola volume around the nuclear body would have to be emptied. The question arises if the epola structure in this volume can be restored, and if so, then how long it would take. In the meantime, if not forever, the volume would contain a more or less diluted gaseous mixture of electrons. positrons and $e^- e^+$ pairs. This discontinuity in the epola would not emit light nor would it enable the transfer of radiation energy, as does the epola; hence, it would not be transparent for starlight or nebular light.* Obviously, we got another scenario for the creation of a black hole.

The distortion of the adjacent epola around the black hole could be detected as a gravitational distortion, the larger, the larger and emptier the hole. The degree of emptiness or blackness of the hole may reveal its age, because with passing time, more and more particles are drawn into the hole and it becomes less empty, less black. The size of the black hole actually reflects the mass of the nuclear body inside it. The body itself is not visible, because there is no epola around it to carry radiation. Nor could the mass of the body be detected directly, because gravitation is also carried by the epola (Sections 12.1-12.3). Therefore, the information about its mass can only be obtained through the apparent mass of the black hole, detected via the distortion of the epola around the black hole. This mass contains also information on the time passed since the collapse.

11.6 Explanation of the Hubble redsbift by non-linear light absorption

In Section 2.12, we discussed the Hubble-Humason redshift, observed in the spectra of extragalactic nebulae. This redshift is interpreted as a Doppler redshift, corresponding to a runaway motion of the nebulae with velocities $v$,

where $H = 100 \ \mathrm{(km / s) / Mpc}$ is the Hubble constant.

Our interpretation of the Hubble redshift is based on the only experimental or observational, rather, fact that:

the Hubble redshift or the frequency reduction of the nebular radiation, arriving at our apparata, is proportional to the distance from the nebulae.

Therefore, facing such an observation, a physicist is obliged to analyze, first of all, those physical factors, which act along the distance from the nebulae, and may cause the reduction in frequency. Only if all known physical factors, acting along the distance, were to produce effects contradicting the observed results, e.g., if they would produce an increase in frequency, then the physicist should look for other factors.

The simplest of all factors acting towards a reduction in radiation frequency along the path of the radiation, is the non-linear absorption. This phenomenon occurs when a wave-motion passes a thick layer of a strongly absorbing medium. It results not only in the reduction of the amplitude but also in the reduction of frequency. The simplest example of a reduction in amplitude and frequency is in the motion of a pendulum in water or oil or honey. A measurable reduction in frequency occurs also in long-distance long-wave radio-eommunication on Earth (Sections 10.1, 10.2). It can be mathematically derived, when the series expansion of the radiation energy is not stopped on the second term but is continued to include higher-order terms, bearing the frequency reduction.

Considering the epola as the carrier of the radiation, it is easy to understand that:

the epola is perfectly vacuum-transparent to electromagnetic radiation, and on distances of maybe tens or hundreds of light years, even linear absorption is hardly detectable; however, radiation approaching us from distances which it travels during millions and up to trillions of years, not only has its amplitude reduced; it must also show a frequency reduction, which is proportional to the traveled distance in the epola.

A similar explanation could be given without the epola concept, while continuing to believe that radiation is carried by the empty vacuum, just by adding nonlinear absorption to the swollen list of physical properties ascribed to the vacuum.

11.7 Presentation of the Hubble redshift as a gravitational redshift

Another factor reducing radiation frequency along the path of the radiation is the gravitational or Einstein redshift, which we discussed in Section 2.10. We have seen that radiation passing through a gravitationally distorted region loses energy with a reduction in frequency. The gravitational redshift in the spectrum of the Sun corresponds to 0.6 km/s of recessional speed and occurs on a distance in order of one astronomical unit. Nebular redshifts correspond to anything between 40 and 100 km/s of recessional speed along a distance of $1 \ \mathrm{Mpc} = 2.06 \cdot 10^{11}$ astronomical units.

To consider the nebular redshift as gravitational, we should assume that the mean gravitational distortion along a megaparsec distance in space, is $2.06 \cdot 10^{11} \cdot 0.6 / 100 = 1.2 \cdot 10^9$ times smaller than the mean gravitational distortion on the distance from the Sun. In other words,

if all celestial objects, located in the vicinity of a megaparsec-long path of radiation, approaching us from a nebula, create on this path a mean gravitational distortion, which is a billion times smaller than the distortion in the vicinity of the Sun, then this is already sufficient to consider the nebular redshift as gravitational.

In our discussion, we avoided mentioning the epola as the gravitationally distorted medium. We did it deliberately, to show that the same explanation could be given by believers in the vacuum as the gravitationally distortable medium.

11.8 Non-constancy of the Hubble constant

The apparent runaway velocity of an extragalactic nebula is calculated from the observed redshift in the spectrum of the nebula using formulas of the Doppler effect. The distance $l$ to the nebula can be approximated from various observations and also from the size and type of the nebula. Then, it turns out that

the redshifts in the spectra of nebulae which are equally distant from us are not necessarily identical.

Hence, with the formula $v = H \cdot l$ one should either assume that the runaway velocities $v$ of these equidistant nebulae are different, or that the Hubble constant $H$ is different for them.

Assuming different values of the runaway velocity in different directions at a given distance, means trouble to the expanders and exploders of the universe. They believe that the universe should expand uniformly in all directions and, if not in full spherical symmetry, then at least so, that in directions close to one another (within a small solid angle), the blowout should be uniform.

Hence, the constancy of the Hubble constant was sacrificed for the sake of keeping the universe exploding. The calculated values of the Hubble constant for different nebulae therefore vary from $H = 100 \ \mathrm{km / s \cdot Mpc}$, which is the original Hubble-Humason value, down to 70, 50 and even 40 km/s$\cdot$Mpc. The published reasons of this non-constancy are mostly mathematical, quite speculative and contradicting one another, however publishable.

11.9 Epola explanation of the non-constancy of the Hubble constant

Our explanation is based on the epola explanation of the redshifts observed in the spectra of distant nebulae. These redshifts are caused by at least four physical phenomena, and the contributions of each of them to the redshifts of different nebulae are different.

The first phenomenon is the non-linear absorption of light, discussed in Section 11.6. The frequency reduction due to this absorption should be similar in most directions, except for directions in which there are higher-than-usual concentrations of absorbing gases or dust. Second is the gravitational redshift, discussed in Section 11.7. The frequency reduction due to this redshift should have a more profound directional dependence because of the not-so-uniform distribution of massive stars. For example, if the radiation from the nebula passes between more massive stars than the radiation from another nebula, then this other nebula shows a smaller gravitational redshift in its spectrum.

The third factor is the orbit-adjustment redshift (or, seldom, blueshift) discussed in Section 9.7. This redshift depends on the speed of the radiating atoms of the nebula relative to the epola which surrounds them, and not on the directions of their motions. This effect differs in various nebulae, expressing the character of motions in the particular nebula and the conditions in the epola in and around the nebula.

The fourth factor is the Doppler effect, discussed in Sections 10.10 and 10.11. Nebulae may move toward us, then the Doppler effect reduces the redshift, caused by the other three (or two) factors. When the nebula moves away from us, then the redshifts caused by the other three factors are increased by the Dopplerian redshift. The redshift caused by absorption and the gravitational redshift are proportional to the distance traveled by the nebular light. Therefore, they yield a more or less constant calculated value of the Hubble constant. However, the orbit-adjustment red- (or blue-) shifts and the Doppler red- or blueshifts are not distance-dependent and they are mostly responsible for the diverseness of the Hubble-constant values. There certainly may be other phenomena affecting the observed redshifts in the nebular spectra. However, the mentioned four factors yield a quite complete explanation of these redshifts.

11.10 Dismissal of the Dopplerian interpretation of nebular redshifts and of the Big Bang

The Dopplerian interpretation of the nebular redshift does not follow directly from the experimental observation that the nebular redshift is proportional to the distance from the nebulae. One may say that it is a 'second derivative' of this observation. To introduce this interpretation, one has to, firstly, decide that he wants to disregard physical factors acting along the path of the radiation. Then, he considers the Doppler effect, which has no connection with the proportionality of the observed redshift to the length of the path, but is proportional to the speed of recession of the emitting body. Then he speculates, that if the emitting nebulae run away from us with a speed which is proportional to the distance to them, then the redshift is Dopplerian. We may mention that Humason himself was not too orthodox about the Dopplerian interpretation. In a paper published two years after the 1929 discovery of the nebular redshift, Humason wrote:

"It is not at all certain that the large redshifts observed in the spectra are to be interpreted as a Doppler effect but, for convenience, they are interpreted in terms of velocity and referred to as apparent velocities."

The question may be asked why people should prefer such a circling around an experimental observation, such a "via dolorosa" of speculations around it, instead of considering effects directly connected with the observation. The simple answer is that it fits their interests. These could be immediate interests, apparent interests or even wrongly-understood interests.

The interest in the Dopplerian interpretation of the nebular redshift is that it leads to the hypothesis of a Big Bang-created exploding universe. This hypothesis is more exciting than star-war-movies and opens the opportunity to everybody with some mathematical skills, an access to advanced computers and a creativity of a modern painter to become "creator of universes", as Einstein was named to be, to compile new exploding processes for them, to invent new exotic particles or introduce more dimensions to the troubled world.

The epola model is very prosaic, introduces or restores strict physical rules and eliminates the possibility of star wars and twin brothers traveling between galaxies. With the disproval of the Dopplerian interpretation of nebular redshifts and the reversal of the 3 K "background" radiation into a "foreground" radiation of the epola in front of us (Section 11.2), it turns the Big Bang creation hypothesis of the exploding universe into an unnecessary fantasy.

11.11 Positron lifetime, matter and antimatter in the epola

Positrons observed on Earth have a very short lifetime. However, unlike unstable particles, half the number of which decomposes in a lifetime, the positron does not decompose; it just combines with a free electron and they both enter the bonds in the epola. Then, the charges and masses of both particles become individually indetectible, thus 'disappear'. Therefore, the positron is a stable particle, apparently just as stable as the electron. The short positron lifetime is due to the scarceness of the free positrons and the abundance of free electrons on Earth. As a result, a free positron very soon finds a free electron with which to enter the epola, while it may take a very long time until a free electron finds a free positron. This effect reminds one of the recombination of "free" electrons and holes in n-type semiconductors.

Electrons and positrons are therefore 'antiparticles'. Another known pair of antiparticles are the proton, $p^+$, and the antiproton, $p^-$, the mass of which is equal to the mass of the proton but the charge is the $-e$ charge of an electron. The meeting or recombination of a proton-antiproton pair is as many times more energetic as their masses exceed the $e^- e^+$ mass; hence, the appearing energy is $1838 \cdot 1.02 \ \mathrm{MeV}$. While every atomic nucleus on Earth contains a number of protons equal to the atomic (charge) number, the number of antiprotons is extremely small. They play no role in the formation of matter on Earth. Here, it is very hard for an antiproton to find a positron which it could orbitalize and form an 'anti-hydrogen' atom $\mathrm{\bar{H}}$. Such atoms are obtained and studied in laboratory conditions but have a very short lifetime, because of the scarceness of the positrons and the antiprotons on Earth.

With the study of $\mathrm{\bar{H}}$ atoms in laboratory conditions, the assumed existence of anti-matter in the universe obtained strong support. Antimatter is also compatible with the epola model. Symmetry considerations suggest that if in our region of the epola there is an abundance of free electrons and bound protons, then there should be regions with an abundance of free positrons and bound anti-protons. Atomic bodies created there would be the anti-matter. Such regions would correspond to p-type semiconductors. We could also think of epola regions corresponding to intrinsic semiconductors, with equal concentra- tions of 'free' electrons and holes. In the corresponding epola region, there should be equal numbers of abundant free electrons and positrons and equal numbers of protons and antiprotons, bound in their nuclei. In such 'intrinsic' epola regions matter and antimatter should coexist in dynamic equilibrium.