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Физика сознания и жизни, космология и астрофизика
COSMOLOGY AND ASTROPHYSICS
UDC 523.11:524.827:539.12:524.854:530.11
Bukalov A.V.
NATURE OF COSMOLOGICAL TIME:
FROM THE MACROSCOPIC EQUATIONS OF GENERAL RELATIVITY
TO QUANTUM MICROSCOPIC DYNAMICS
The Centre for Physical and Space Research, International Institute of Socionics,
Kyiv, Ukraine, bukalov.physics@socionic.info
The application of the principles of the cosmological model with superconductivity to
the equations of general relativity makes it possible to describe the macroscopic dynamics of
the evolution of the Universe through coherent dynamics on microscopic Planck scales. It is
obtained a hierarchical system of equations, showing how the parameter of cosmological time
depends on the microscopic dynamics of fermions at the Fermi surface for the Planck crystal-
like structure of space-time.
Keywords: superconducting cosmology, gravitation, time, fermions, dark energy,
general relativity.
1. Introduction
At the present time the dark energy manifests itself as anti-gravity, not only on a cosmological
scale, but on the scale of galaxy groups (Karachentsev et al., 2009; Bisnovatyi-Kogan & Chernin,
2012; Chernin et al., 2013; Bukalov, 2015). Using the principles of the quantum theory of
superconductivity, the author previously obtained the value of the density of dark energy , which
determines the effective value of the cosmological constant (Bukalov, 2016).
11\* MERGEFORMAT ()
kg/m322\* MERGEFORMAT ()
where is the electromagnetic constant of a fine structure or its “dark” analog, and
. The critical density of the Universe is
33\* MERGEFORMAT ()
At km·s-1·Mpk-1, which is in good agreement with the PLANK data (Planck
Collaboration, 2015).
The time parameter is a function of a second-order phase transition analogous to the transition
in the theory of superconductivity, . And is the coupling parameter of the
fermion interaction, an analog of the fine structure constant, but dynamically changing, which
determines the course of cosmological time . In the present era . This
equality determines the proximity of the value of the density of “dark energy” and matter in this era
and explains the phenomenon of “cosmic concordance” (coincidence).
2. From the classical dynamics of the equations of general relativity and Friedmann to
microscopic quantum dynamics
Since the dynamics of the change of the fine structure is determined by the relation
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Physics of consciousness and life, cosmology and astrophysics
, 44\* MERGEFORMAT ()
where varies from to , then the density of dark energy varies according to the law:
, 55\* MERGEFORMAT ()
where is impulse of quantum of radiation.
Similarly critical density evolves:
, 66\* MERGEFORMAT ()
where is an impulse, and is a mass, that are forming the observed dynamics of the Universe,
but located in another “energy zone”, if we use the analogy of the “crystal” (Fomin, 1990), or in other
dimensions additional to the dimensions space-time of the observed Universe. Different models of
multidimensional universes have been considered by many authors.We now turn to the consideration
of Friedmann's equations. First we consider the De Sitter vacuum solution for , ,
, at . In the quantum theory of superconductivity, the fermion
interaction constant α is defined as , where is an impulse of a fermion near
the Fermi surface, expressed in terms of mass and velocity, is fermion scattering length (Pitaevskii
& Lifshiz, 1980). Therefore at scale factor is:
77\*
MERGEFORMAT ()
Obviously, when , , and the cosmological time is determined by the
dynamics of the change in the fermion wave length at the Fermi surface, or by the change in the
radiation energy impulse in the radiation-dominant evolution stage of the Universe. So far as
and , then
, 88\* MERGEFORMAT ()
and all dynamics are determined by the time parameter . In this case, we can represent the
dynamics of time variation as follows:
,99\* MERGEFORMAT ()
where is the Planck time.
According to 8 and 9 dynamics of cosmological time change can be inferred from the vacuum-
type equation
or 1010\* MERGEFORMAT ()
as an analog of the Friedmann equation. In general:
1111\* MERGEFORMAT ()
From 11 it follows:
16 № 3-4, 2017
Физика сознания и жизни, космология и астрофизика
, . 1212\* MERGEFORMAT ()
where , is a microscopic quantum time parameter for fermions near Fermi
surface.
Thus, we obtain the dynamics of the change of cosmological time at the microscopic quantum
level. Because , then
.
At and , , 0.485Hs . Given that ,
equations 11–12 are transformed into the following:
,1313\* MERGEFORMAT ()
where plays the role of a scale factor in the microscopic quantum dynamics of fermions near
the Fermi surface. A hierarchy of dynamic levels appears in which the variable controls the
time variable , and the corresponding hierarchy of both Friedmann equations and
Einstein's equations of general relativity, corresponding to the dynamics of hierarchically
interdependent variables, corresponding spaces and metrics. We can consider the macroscopic
dynamics of our and other universes on a microscopic, quantum level, replacing ,
. At , . This means that the
macroscopic dynamics of the universe corresponds to microscopic quantum dynamics on Planck
scales.
3. Conclusion
The transition from macroscopic classical dynamics of general relativity to microscopic
fermion dynamics at the Fermi surface shows that the real structure and dynamics of space-time are
described by coherent quantum processes. In particular, the parameter of evolutionary cosmological
time is determined by the dynamics of microscopic quantum processes on Planck scales. The
macroscopic nature of the observed space-time is provided by a factor , which varies in the
interval from 1 to 3.26·1059 and determines the scale of the coherence of quantum processes.
References:
1. Bisnovatyi-Kogan G.S., Chernin A.D.: 2012, Astrophys. Space Sci., 338, 337.
2. Bukalov A.V.: 2015, Odessa Astron. Publ., 28 (2), 114.
3. Bukalov A.V.: 2016, Odessa Astron. Publ., 29 (1), 42.
4. Chernin A.D. et al.: 2013, Astron. Astrophys., 553, 101.
5. Fomin P.I.: 1990, Probl. phys. kinetics and physics of solid body, 387–398.
6. Karachentsev I.D. et al.: 2009, MNRAS, 393, 1265.
7. Pitaevskii L.P., Lifshitz E.M.: 1980, Statistical Physics. Part 2, (Nauka, Moskow).
8. Planck Collaboration: 2015, A&A, A13, 594.
Статья поступила в редакцию 20.11.2017 г.
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Physics of consciousness and life, cosmology and astrophysics
Букалов А.В.
Природа космологического времени: от макроскопических уравнений
общей теории относительности к квантовой микроскопической динамике
Применение принципов космологической теории со сверхпроводимостью к уравнениям общей теории
относительности позволяет описать макроскопическую динамику эволюции Вселенной через
когерентную динамику на микроскопических планковских масштабах. Получена иерархическая система
уравнений, показывающая, как параметр космологического времени зависит от микроскопической
динамики фермионов на поверхности Ферми для планковской кристаллоподобной структуры
пространства-времени.
Ключевые слова: сверхпроводящая космология, гравитация, время, фермионы, темная энергия, общая
теория относительности.
18 № 3-4, 2017