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Section 17. Physics
Barykinsky Gennady Mikhailovich, Institute of conceptual studies, Moscow, Russia E-mail: [email protected]
THE UNIVERSE BEFORE, DURING, AND AFTER THE BIG BANG. PART 2. COSMOLOGICAL SPECIFICITY OF ELEMENTARY MATTER
Abstract: This article proposes a model for the existence of multitude of Universes, the basis of harmony and specificity of the evolutionary process of which is the logarithmic spiral and three generations of cosmological constants that determine the fundamental interaction of elementary matter.
Keywords: model, Universes, observable, fundamental interaction, cosmological constants, logarithmic spiral.
By getting into the swing of things, We gain understanding. And by realizing the meaning of things, We create consciousness [1].
1. Multitudes defined by the spectra of the permissible values of the physical parameters of the elementary matter of "peculiar" Universes Ü, intersect, and therefore the above assumption is in no way connected with existing theories about nested Universes, such as "one inside another inside another, etc.", since the inner contents ofeach Universe does not intersect with other, which means, they are not observable to each other;
2. Bosons may be located in any quantity at any point in space;
3. Fermions may be in one quantum state (no more than one) in accordance with the Pauli principle.
However, if in the point vicinity of space there can be simultaneously representors of the elementary matter of many Universes, then, how is it that the representatives of the matter of each Universe are not observable to each other? It turns out that this is possible only in one case: if elementary particles of the same range cannot physically interact with the elementary particles of the other, i.e. the matter of one Universe does not, completely or partially, "sees" the matter of the other. For example, the observed matter of "our" Universe does not interact with any dark matter, or with dark energy, which in turn (and this is more than likely) are representors of the matter of other Universes. Hence, there is a fundamental factor that ensures that the matter of a particular Universe is isolated and not observable from any other.
Therefore, the logical conclusion is that the limitations of the physical interactions of elementary particles,
In [2], it is shown that the spectra of the values of the basic physical parameters of elementary matter in the Universe are constrained by the limit values. For example, the possible magnitude r and mass m of elementary particles are within the following ranges 5,:
Sr = [rmin = 1.61-10-33cm - rmax = 3.00-1010cm], (l)
S = [m . = 1.17-10-48g- m" = 2.17-10-5g]. (2)
m L min O max O-i ^ '
Does this mean that beyond the limits values of these ranges, elementary matter is fundamentally absent? No, it does not! Quite the opposite, the elementary matter that, in its physical parameters, lies outside the specified values of the ranges (1, 2) has the same rights to exist, as much as the matter that lies within these ranges.
If matter outside the ranges indicated in (1, 2) exists, then where is it located? The answer should be obvious - in other ranges, each of which specifically defines its "own" Universe!
Hence, this logic leads to the conclusion that there are a multitude of Universes, the matter of each of which is built on elementary particles, which in terms of their physical parameters make up a finite set constrained by limiting values.
If we assume the existence of a multitude of Universes, then there is another fundamental question: where are all these Universes located? It is reasonable to assume that there are points of space in the vicinity ofwhich there are simultaneously representors of the elementary matter of many Universes. If this is true, then the following conditions are fulfilled:
which are based on various world constants is the fundamental factor, which ensures the isolation and non-observability of the matter of one particular Universe from any other.
Existing mathematical expressions for describing the acting forces that determine the very fact of existence and the physical interaction of elementary particles are universal for any ranges. Given this, it should be assumed that the specificity of the physical interactions of elementary particles within each range is determined by the specificity of the constants, [2]:
Felastic (3)
Fm = e/r, (4)
Fgr = jm2/r2, (5)
where: F, - is the force of the internal field of an elementary
elastic '
particle that has an elastic effect on the environment;
Fdm and F - are the forces of electromagnetic and gravitational interactions between identical particles; Y - is the gravitational constant.
In order to reduce the number of calculations, we use the main expressions from [2, 3] to determine the context and meaning of the world constants contained in equations (3-5): mw2 = y, (6)
rw = c, (7)
rm = k, (8)
kc2 = hc = q2 = e2j82, (9)
where: m and w - are the rest mass and the oscillation frequency of the internal energy of the particle;
y - is the coefficient of proportionality of the elastic force, which determines the frequency of oscillations of the internal energy of the particle w = (y/m)1/2;
r - is the radius of the particle, determined from: Xk = 2nr, where Xk - Compton wavelength;
k and c - are constants that determine the particle charge and the speed of light in a vacuum;
h - is the Planck constant, which determines the action of the internal energy pulse of a particle within its Compton radius;
Table
q and e - are the electric charges of the particle, related to each other as: q = efi;
fi - is determined by equation: fi2a = 1, where a - is the fine structure constant;
In [2], it is shown that at the Planck point all three forces (3-5) are equal to the same value: F, „ = F, = F = F ,
v ' J- elastic elm gr max'
and therefore their average geometric ratio for these forces is valid:
^^ elm FelasticFgr ( 10)
The solution of (10) at the Planck point relative to y is presented by the following:
Y = cV^cY^ (11)
Modifying (11) using m r . = k and in accordance with
' c v ' c max min
(8), the following is obtained:
Y = kc2/m2 m2 = kc2/r, (12)
1 max max 11 v '
Y = r2minc2/k ■ r2min = rk/c2. (13)
The expressions (12, 13) show that the assigment of gravitational constant y to any range is determined by the values of rmn and mmax, corresponding to the Planck point of this range, and therefore y is specifically defined within the limits of one range, i.e. one Universe, and since in other Universes the ranges are different, they also have other Planck limiting values, i.e. in other Universes, the gravitational constants are different in magnitude.
In order to find the functional positioning of the ranges of elementary matter of different Universes, we shall analyze of how the limiting parameters of elementary particles of different Universes are correlated, for example: "our" (middle) Universe and the two nearest to it - upper and lower, is denoted by: Uu UM, UL.
Using the world law of scaling [4], the material of this work and the centimeter-gram-second measurements, we receive the following data (Table 1), which allow us to draw some important conclusions about the functional dependence of the cosmological parameters of matter in the Universes UU UM, UL:
min gm max max/min Y
1 2 3 4 5 6
UU r 6.95-10-12 3.00-1010 1.29-1032 1.24-1036
m 2.72-10-70 1.17-10-48 5.04-10-27
UM r 1.61-10"33 6.95-10-12 3.00-1010 1.86-1043 6.67-10-8
m 1.17-10-48 5.04-10-27 2.17-10-5
r 3.73-10-55 1.61-10"33 6.95-10-12 3.59-10-51
m 5.04-10-27 2.17-10-5 9.34-1016
where: gm -is the geometric mean: gm2 = min-max
From Table 1, we can conclude for r: sion, the denominator is the first cosmological constant:
1. The homogeneous values for the columns (2-4) are related Y = 4.31-1021.
to each other on the basis of the mean geometric progres-
min.
min.
min.
gmu gmM
max
u
min.
gmL
max
maXM = 4.311021 max
G3 - establishes a correspondence between the Universes and multitudes of them.
Table 2 shows the distribution of constants by generation:
Table 2.
2. The homogeneous values for rows of columns (2, 4, 6) are related to each other on the basis of the geometric mean progression, the denominator is the second cosmological constant: T2 = 1.86-1043, and Y 2 = Y2.
G. constants
G, r, m, 3, y
G2 k, c, h, q, e, ^
G2 Y Y
max
U
max
max
— = Yu = Ymm = 1.86 1 043
= Tu-TL
The analysis of the equations (6-9, 12, 13) shows that the main world constants have a different cosmological status, and all the constants relative to their essence and the foregoing can easily be grouped into three generations.
Hence, in relation with the increase in the status of constants, the specificity of each of the three generations G, is defined as follows:
G1 - determines the specificity of the properties of matter in a single Universe.
G2 - determines the universality of the properties of matter for any Universe.
Is there a functional positioning between the different ranges S,, hat determine the range of permissible values of the physical parameters of elementary matter, specifically related to the Universes U, and, if so, in what form?
In accordance with the data of Table 1, it is not difficult to construct a graph in polar coordinates and relative units. Its external view shows that the curve allowing the functional connection of the spectra of permissible values of the physical parameters of elementary matter ofdifferent ranges, specifically related to different Universes U, is a logarithmic spiral. The following fundamental property of the logarithmic spiral is based on the construction of the graph: if the angle of the sequence of radii changes as an arithmetic progression, then the lengths of the corresponding radii form a progression-geometric.
Figure 1.
The dashed lines shown in the figure are semicircles that intercept their diameters, which are ranges of permissible values of physical parameters of elementary matter of multitude of Universes U. Moreover, each diameter at the point "o" is divided on the average geometric ratio into two unequal segments, the smaller of which establishes the spectrum of permissible values of the physical parameters of the fermions, while the total diameter sets the spectrum of the allowed values of the physical parameters of bosons.
Below in Table 3, the geometric mean ratios of the radii of the logarithmic spiral, where different ranges correspond to different Universes U :
' Table 3
U. Radius ratio
ob2 = oa-oc
UM oc2 = ob-od
U od2 = oe-oc
Etc.
minu minM minL Ym Yl
The graph also shows that the only point of space in the vicinity of which representors of the elementary matter of all Universes are present is the focus of the logarithmic spiral: (point "o"), although this point itself is unattainable, since the motion along the spiral towards it tends to infinity.
Another fundamental property of the logarithmic spiral is also interesting: if the point is moving away from its pole, then the moving rate is proportional to the distance traveled, and this is not accidental! With this amazing property of the spiral, another well-known fact is that the more distant galaxies are moving away from us at a faster rate.
It is amazing that the process of evolution of the multitude of Universes is described by a logarithmic spiral first discovered by the great René Descartes (1596-1650) and named by the great Jakob Bernoulli as (1655-1705): "the marvelous spiral".
Amazingly, but, the equally great Johann Wolfgang von Goethe (1749-1832) said: "You will not find the more perfect structure". Of course, the "structure" he referred to was the logarithmic spiral.
References:
1. Barykinsky G. M. / The Universe of consciousness and the picture of the world. // Mat. The VII Russian philosophical Congress,- 2015.- Vol. 2.- 117 p.
2. Barykinsky G. M. / Physical limits of elementary matter in the Universe // J. "The European Journal of Technical and Natural Sciences".- Vienna.- 2018.- No. 2.- 66 p.
3. Barykinsky G. M. / The properties of the photon and the electron. // J. "European Sciences review".- Vienna.- 2017.- No. 3-4.- 115 p.
4. Barykinsky G. M. / World law of scaling // J. "Science Forum",- Tokyo,-2018.- No. 1.- 17 p.
