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5.2. Square-law dependence of light speed as explanation of a lot of astronomical phenomena

In table 5.1 below (how it was obtained - see Appendix 2)   you can see the  ratio (parameter Nmax/Nav) of star luminosity at the moment of flash to average (during a period T_o of star revolution along Kepler orbit) value of  star luminosity   as a dependence upon distance to a binary star (parameter R/D_o, where R is a distance to a binary star, D_o is determined by formula (5.8)) and ellipse eccentricity е (at three different values of eccentricity equal to 0.6,  0.2 and 0.02) at three different periods of star revolution along Kepler orbit (4 days, 20 days and  41 days).

Table 5.1 (for more details see Appendix 2)

From  table 5.1 it can be seen that:

1) If a distance to a star increases, a star luminosity at the moment of flash at first increases monotonously [for example, at е=0.02 and Т_о=41 days the value N_max/N_av monotonously increases from 1.19 (at  R/D_o = 0.1) to 161.77 (at R/D_o=0.7)], and as the distance to a star  increases further  luminosity of this star at the moment of flash fluctuates, alternately going down and up.

2) If a star orbit time Т_о increases,  luminosity of the star at the moment of flash increases (under equal other conditions). For example, for eccentricity 0.2 at   Т_о=4 days N_max/N_av=60.84, at Т_о = 20 days N_max/N_av= 97.97, and at Т_о = 41 days N_max/N_av=175.73.

3) If eccentricity decreases, a star luminosity at the moment of flash increases.

4) A star luminosity at the moment of flash has the first local extremum in the region of  R/D_o=0.6 ... 0.7.

Supernovae

Analysis of simulation results (see Appendix 2) shows that beginning from a certain distance (see Fig. A2.43), the second flash appears during an orbit time. As distance to a star increases the time separation between two flashes increases. But both flashes have approximately equal amplitude.   Different laws of decreasing a star luminosity after each of two maximums is also worthy of special mention. If we shall give a look on the Fig. 5.3 (the same figure is shown as figure A2.45 in the Appendix 2), we can see, that after the first maximum a star luminosity decreases very sharply, and after the second maximum a star luminosity decreases comperatively slower (the same behaviour of a star luminosity we can see in Fig.  A2.47, Fig. A2.48, Fig. A2.49 in the Appendix 2).

Fig. 5.3. Two flashes of a binary star luminosity within one orbit time.

This allows supposing that the so called supernovae of the fist type and of the second type are simply either the first flash, or the second flash within a binary star orbit time.

Pulsars

Analysis of simulation results (see Appendix 2) shows, that the so called pulsars also can be explained if the square-law dependence of light speed upon light source speed exists in nature. Analysis shows that radiation pulsations known to us as pulsars appear only in a case, if a star is moving at a speed increasing with time. Pulsations do not appear if a star is mooving at decreasing speed. This explains disappearance of pulsation for the pulsars. Within the time interval when a star is moving at increasing speed pulsations exist. When a star begins moving at decreasing speed, pulsations are absent. In table 5.2 you can see the dependence of the pulsations period upon eccentricity of a binary star elliptical orbit. In table 5.3 you can see the dependence of the pulsation period upon distance between a star and the Earth.

Table 5.2

Table 5.3

From table 5.2 it can be seen, that the less is the ecceentricity of a binary star elliptical orbit, the greater is pulsations period. From table 5.3 it can bee seen, that the more is the distance to a binary star, the more the pulsation period is.

Red shift of far stars spectrums and relict raiation

If the dependence  c_u = c_o(1 + u²/c_o²)^1/2 exists in nature, a possibility appears to give a new interpretation both to cosmological red shift of far galaxies spectrums, which increases as the distance to galaxies increases, and "relict" radiation.

Indeed, in the Universe, properly speaking, there is not a single lone star. All stars are more or less bound each with other. Under action  of the law of gravitation they move each relatively others alternately with acceleration and deceleration. On the average time intervals of accelerated motion and time intervals of decelerated motion  are equal each other (for observers, which are in the vicinity of each star). But for a distant observer, because of square-law dependence c_u = c_o(1 + u²/c_o²)^1/2 of light speed upon light source speed, time intervals of accelerated motion are "compressed" (see formula (5.6) for Т₁) and time intervals of decelerated motion "stretch" (see formula (5.7) for    Т₂ ). As a result, the more distant volumes of space we examine, the more is the probability that we observe light quanta, which were radiated during  time intervals of decelerated motion of stars. But (if square-law dependence c_u = c_o(1 + u²/c_o²)^1/2 exists in nature) light quanta radiated during time intervals of decelerated motion of stars for a distant observer have the greater  wavelength the more is the distance from an observer to a star, which radiated those quanta.

Indeed, if the "beginning" of a light quantum is radiated at a greater speed of a star, than the "end" of the same light quantum, then (if square-law dependence c_u = c_o(1 + u²/c_o²)^1/2 exists in nature) the longer this light quantum moves in space the greater is the distance between the "beginning" and the "end" of this quantum (because the "beginning"  of a light quantum moves at a greater speed than the "end" of the same light quantum).

As a consequence the light quanta radiated during time intervals of decelerated motion of stars are the more stretched in space (the more is their wavelength) the longer they move after their radiation. Moreover, the "stretching" effect of light quantum radiated by a source moving with decelaration  produces for different spectral lines  the same ratio of wavelength change to wavelength value, but not the same wavelength change.

Indeed, if a light quantum of wavelength l_o just at time moment, when its radiation was terminated, has  n_o oscillations, then at this time moment the length of such quantum along a direction of its propagation will be equal to L_o=n_ol_o. Then (if dependence c_u = c_o(1 + u²/c_o²)^1/2 exists in nature) at a distance R from the place of its radiation the length of such light quantum along the direction of its propagation will be equal to

L= L_o+( c₁- c₂ ) R c_o^-1, (5.14)

where c₁, c₂ are the speeds of motion of the "beginning" and the "end" of a quantum respectively. Then, because the number n_o during the quantum motion can not change, the wavelength of this quantum at the distance R will be equal to

l = L/n_o=l_o [1+ (c₁- c₂ ) R c_o^-1 L_o^-1] . (5.15)

And from this formula we can have

(l - l_o)/l_o = ( c₁- c₂ ) R c_o^-1 L_o^-1. (5.16)

Thus, the effect of light quanta "stretching" results in namely such change of wavelengths for various spectral lines, which is observed in reality. In such a way we can now explain red shift of far galaxies spectrums without usage of the well-known hypothesis about expansion of the Universe.

In case if light quanta are radiated during half-periods of accelerated motion of a star, then in such a case a quantum "end" moves faster than the quantum "beginning". As a result till the moment when the quantum "end" will catch up with the quantum "beginning", such quantum contracts (its wavelength decreases). At that for a distant observer the half-periods of accelerated  motion themselves contract according to formula (5.6) for Т₁. If the dependence c_u = c_o(1 + u²/c_o²)^1/2 exists in nature, the effect of light quanta contraction can explain the bursters of   X-rays and gamma rays, which are registered by astronomers.

To what extent the decreasing of wavelength is possible for  light quanta because of the  above mentioned  contraction effect, it is not clear today.  But at entirely formal reasoning at a certain distance from a binary star moving with acceleration,  the "end" of a quantum will overtake the quantum "beginning" and during the subsequent motion of this quantum its wavelength   increases without limit. It means that for very far stars both quanta radiated during decelerated motion of a star and quanta radiated during accelerated motion of a star undergo the stretch effect and this stretch effect can be of such intensity that they pass from the band of visible light into the radio band. Indeed, from the formula (5.16) it follows, that if the expression (c₁-c₂)/c_o is not equal to zero, then the ratio (l - l_o)/l_o can become arbitrarily great if R increases without limit.

In such a manner the dependence c_u = c_o(1 + u²/c_o²)^1/2 allows to explain the existence of "relict" radiation. If this square-law dependence exists in reality, the "relict" radiation seem to be a resultant radiation of all  stars in the Universe.  And all characteristics of the "relict" radiation can be easily explained: high degree of isotropy, low temperature, type of spectrum similar to black-body spectrum. Explanation of red shift for spectrums of far stars, which increases at increasing distance to stars, allows also giving natural explanation to absence of photometric paradox (why night sky is black) without introduction of the hypothesis about  recession of galaxies (that the more is the distance to a star the greater is its speed in the process of galaxies recession).

The new explanation of red shift of far galaxies spectrums and new explanation of the "relict" radiation gives a possibility to throw away very fantastic hypotheses (very similar to the act of  the Universe creation by the God) about finite time of the Universe existence (approximately 10 - 20 thousand million years), which comes into contradiction with the age of rock on the Earth  [[51]. Kosygin  Ju. A. The Earth and the Universe// Priroda,  1986, No. 12, pp. 79 - 85.] and about finitude of the Universe in space.

So, not only laboratory experiments on testing the validity of the second Einstein's postulate, which were considered in chapter 4, but astronomical observations also do not contradict the hypothesis about existence in reality of the square-law dependence  c_u = c_o(1 + u²/c_o²)^1/2 of light speed upon light source speed. Inversely, some astronomical observations can be considered as indirect confirmation of existence in reality of the square-law dependence c_u = c_o(1 + u²/c_o²)^1/2. That is why it is now expedient to show up changes in the space-time theory,  which we shall be forced to make if experiments will confirm the existence in reality of the square-law dependence  c_u = c_o(1 + u²/c_o²)^1/2. Because if neither old experiments, nor theory do not contradict the existence in reality of this dependence, then there is some probability that this dependence really exists in nature (even if such probability seems to some of us very low).

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