COSMOLOGY: SPACE EXPANDS,
BECAUSE TIME IS FLOWING
Chapter 1. Evolution of a picture of the world.
The change in notions about the form and sizes of the universe during
centuries until today is described in the initial chapters of many popular
scientific books on cosmology. Until an epoch of the Great geographical
openings by Columbus, Magellan and others the majority of people considered
that the Earth is «a circle» (this is written in Bible: Isaiah 40:22),
up to its edges it is possible to reach and to glance from its edge «downwards»
- in «the chasm». On edge of the circle of the Earth the firmament («the
expance»), like a tent, bases on the Earth. Over the firmament the Sun
and Moon are moving. And stars are the heads of silver nails knocked in
the solid dome of heaven (a Russian word «zvesdy» is «gvezdy» - nails).
However already the philosophers of Ancient Greece understood that «a
circle» of the Earth is not a plane but convex and is bent in all the points
and along all the directions equally. Now it is named «the Cosmology Principle»
- that the universe - if to compare its large parts - is homogeneous and
isotropic. They tried to calculate a radius of this sphere by measuring
the change of height above horizon of a Polar star and distances during
long trips along the river Nile flowing from the south to north. They had
calculated precisely. But had not believed themselves: can a radius of
Globe be really so great? What then the distances up to the Sun and Moon
will be! And what then their sizes: it seems they are such small and not
so distant. The public, certainly, will not have understood it. And they
had lessened the figure in the report. Soon Ptholemey had drawn a bold
picture of the universe. It turns out we live not on a plane but on a sphere
- on a surface of a ball! At that time this was very difficult to imagine.
It turns out that if you will go at one direction - you will go back to
the same place from the opposite direction! The picture of the curved and
closed space of the universe, depicted by Einstein, causes today exactly
the same bewilderment to the public.
Around of the spherical Earth, according to Ptholemey’s model, it are
placed one into another several skies - the rotating transparent crystal
spheres, to which are attached: a flat lantern the Moon - to the sky, nearest
from the Earth, to the next sky - Mercury, further Venus, then the Sun,
to the next - Mars, Jupiter, Saturn, and to the latter - whether seventh,
whether ninth sky - the familiar to us silver nails - stars. Though it
was unintelligible how the inhabitants of the opposite party of the Earth
can live there head over heels and to be kept from fall «downwards», in
«a chasm» but it should be trusted because the Ptholemey’s model was based
on the elementary measurements and calculations made on the Nile. An insignificant
mote - the mortal man can measure the universe! Then it very much delighted.
Therefore it looked like an indecent escapade in attitude to the respectable
authoritative «experts» the statement of some Nicholas Kopernik when he
after the lapse of more than a thousand years suddenly has paid attention
to some absurdities in the Ptholemey’s model and has offered the own model
- with the Sun at the center of the world. The modern skeptics and postmodernists
could yawn and tell to Kopernik: well, there may be many models, everyone
is free to draw the own one, «a text should not cause any consequences».
But at that time it was not accepted simply to classify and to collect
the different points of view, people were listening to arguments, considering
that the truth may be only one, and were accepting close to heart everything
that had been told. And then Galilei, who discovered the forces of inertia,
also «impertinently» had declared: if the awfully removed seventh sky with
stars makes one revolution for a day, it will have disintegrated to pieces
because of such speed of rotation, - not the sky but the Earth rotates!
And at last Jordano Bruno had summed up: «It means, there is no solid sky
with stars-nails, the stars are the same suns like the our one. It means
also, the universe has not any center». It was impossible to endure this!
But also it was impossible to refute it convincingly. The new ideas
were being caught up and were being developed. On the basis of the laws
of Galilei’s dynamics and of universal gravitation law of Newton the distances
from the Sun up to planets rotating around it and also their sizes and
weights had been calculated. And then by the same method, that the travellers
along the Nile have calculated the size of Globe, now, by «travelling»
on Globe around the Sun and, by measuring from the opposite points of already
measured orbit a corner between the Sun and stars, the distances up to
nearest of them had been calculated. For the majority of stars the changes
of the corner (named as parallax) were so small, that its could not be
measured - so these stars had turned out far.
Thus the Newton’s model had appeared. It prevailed till the 20-s of
XX century. According it, the universe is infinite in space and in time,
that is to say is eternal. The stars rotate around of the center of the
galaxy. The groups of galaxies rotate around of the center of the group.
The congestions of groups of galaxies form in turn the congestions of the
higher level etc. Recently it have been found out that the congestions
of galaxies form in the space of the universe the cellular structure like
a honeycomb. But also it does not change that fact that along all directions
on distance up to 12 billions light years from us up to which the modern
telescopes have reached the same is everywhere. Also there are no reasons
to think that outside of visibility there is something other. On borders
of visibility have found the huge luminous congestions of matter named
quazars, that are not present near of us. It is possible to explain it
that we see the border areas such what these - and, obviously, all our
universe - were 10-12 billions years ago. The changeability of the universe
in time undermines an idea of its eternity, also the Newton’s model as
Some other absurdities in the Newton’s model of the world were found
out earlier, and the main was a conclusion from the equations of electrodynamics
about a constancy of speed of light that is always equal 300,000 km/s.
And at the beginning of XX century Einstein in his «special theory of relativity»
- considering only the uniform motion - has managed to bring to the Newton’s
mechanics the changes connected to a constancy of speed of light as the
top speed of any motion in general. But the consequences of it were very
important. From the Einstein’s «General Theory of relativity», that considered
already both the accelerated motion and the forces of gravitation, it followed,
that the three-dimensional space of the universe is not infinite - as are
infinite, for example, an one-dimensional direct line and a two-dimensional
plane - but is finite in volume and is closed on itself, as are finite
and are closed an one-dimensional line - a circumference also a two-dimensional
surface of a ball - a sphere.
But the one-dimensional line - a circumference can be curved and is
closed only because the plane, on which it is placed, has two dimensions.
Also the two-dimensional surface - a sphere can be closed only because
the space, where it is placed, has three dimensions. But the three-dimensional
space of the universe can be bent and closed because our world actually
is four-dimensional, and its fourth dimension is time. Time appeared as
the fourth dimension already in the earlier - «special» theory of relativity.
Soon A. A. Fridman had found out one more consequence of the Einstein’s
theory: that the closed three-dimensional space of the universe cannot
be stationary but must being expanded, being inflated - as the closed two-dimensional
surface of a toy-balloon is being stretched when the balloon is being inflated.
Whether our universe actually expands and why expands - to prove and to
explain it Fridman has offered to the others. He spoke that it is his affair
to decide the equations but to ascertain the physical sense of the decisions
other experts - physicists, astronomers - should. And soon Edwin Habble
showed that the unintelligible displacement to the red party in spectra
of all remote stars and galaxies is possible to explain only that all of
them leave from us and that the speed of this universal «scattering» of
galaxies is proportional to their remoteness from us.
Thus the today’s generally accepted «Theory of the Hot Universe» was
born. It is also named as the «Theory of Big Bang». It is describing in
detail the conditions and evolution of matter towards its complication
at different periods of existence of the universe from the shares of the
first second of its expansion from a point.
However the theory has not explained why the space of universe expands.
I hope that this my article will have given the explanation. The important
consequences - amendments to the generally accepted model of the world
follow from my explanation.
Chapter 2. Lacks of the generally accepted theory.
I assert: the universe expands because in ours four-dimensional
world three dimensions of space and one dimension - time geometrically
are connected thus that out of the flowing of time the expansion of space
inevitably follows. In particular, it means that the expansion of the universe
could have stopped only if the flowing of time will stopped. Consequently
the statement of the generally accepted theory is incorrect that it depends
on amount of matter in the universe - whether the expansion of the universe
will stop sometime by being replaced with compression, or the expansion
will be continuing always.
In England one student - an astronomer had made complex calculations
and had shown that it is possible completely to explain unusual behavior
of Uranium by influence on it of a planet more distant from the Sun than
Uranium. Unfortunately, due attention had not been paid to results of calculations
of this young man because he was only a student.
(W. Kaufmann «The Space Boundaries of the Theory of Relativity», Moscow,
I. A. Klimishin in the book «The Relativism Astronomy» («Science» M.
1981, p. 247) writes: «The theory of «Big Bang» that is to say the theory
of the Hot Universe cannot give an answer to a question «why the universe
expands». As the academician J. B. Zeldovich had noted: «Into this theory
the expansion is incorporated initially. As the theorists express themselves,
is incorporated «by hands», by arbitrary setting of the initial conditions.
To the questions, why the universe expands, why the galaxies scatter nowadays,
the answer is, that already at the first second (but can be also earlier)
there was appropriate to the scattering the initial distribution of speeds».
And here I undertake to answer a question, why the universe expands.
I shall do without this mystical, «incorporated by hands», «the initial
distribution of speeds» for everything of the unimaginable huge number
of nucleuses formed per the first second of existence of the universe and
constituting now the universe - the initial distribution of speeds, conformed
for some reason as if just to their «scattering» (what is this?!), instead
of, for example, their «concentrating» or, say, «to flying past».
A reader may say: «But can be, really, something had been blown up there
- then the matter of the universe had begun to scatter». However an academician
Zeldovich rejects such a simple explanation. He writes:
«Is it possible to speak that the high pressure is a reason of the expansion
of the universe and that a powerfully compressed substance expands for
the same reason that gases of high pressure scatter when its have been
formed as a result of detonation of an explosive substance? No, such a
point of view is completely wrong. The qualitative distinction is that
the explosive substance is surrounded with air at the atmospheric pressure.
The expansion is caused by a difference between enormous pressure
of gases (of the products of explosion) and rather weak pressure of the
surrounding air. But when we consider pressure in the homogeneous
universe, it is supposed that the pressure is distributed strictly homogeneously!
Hence, between various particles at the same moment there is no difference
of pressure, hence, there is no also a force, that could influence the
expansion and furthermore to be the reason of the expansion. The fact of
expansion in the existing theory is a result of initial distribution of
speeds. The reason of this initial distribution of speeds is unknown today».
(I. A. Klimishin, page 191)
But it is ridiculous even to speak about the reason of something,
if this something is thought up, «is incorporated by hands», «is an arbitrary
setting» as Zeldovich himself recognizes. Moreover, the «incorporated in
the theory by hands» turn out inconceivable even in the theory. Because
what is the unimaginable initial direction of speeds of the particles,
that result its scattering under its own momentum in the homogeneous
universe, that is to say in the such universe, where matter in regular
intervals is distributed along all its volume, where is present neither
center, nor periphery? In other words, where the speeds of particles
should be directed in order its just would scatter? There is no such direction!
In my opinion, it should be completely clear, that the initial distribution
of speeds of particles in the homogeneous universe can be only chaotic,
and the seeming effect of «the scattering» can arise, only if distance
between particles will be increasing because of expansion of space.
Therefore the seeming, visible today's scattering of galaxies
can be explained only by appropriate model of space-time, say, likening
it to a being inflated air-ball, the being stretched membrane of which
represents the two-dimensional model of the three-dimensional space of
universe - but not that «galaxies now are moving under its own momentum,
and their speed is being braked by gravitation», as, for example, I. D.
Novikov, the author of the book «Evolution of the universe» («Science»,
M. 1990, p.23) asserts. If the scattering of galaxies is seeming (because
of expansion of space), it cannot also be braked by any force. Besides,
the resulting force of all gravitation forces in the homogeneous universe
equal zero, hence also there is nothing that can brake. Thus the today's
theory is unsatisfactory at any rate.
But if the forces of inertia do not accept participation in expansion
of the universe, and force of gravitation - in braking this expansion,
why does the universe expand and how? How can the toy-balloon model explain
It is impossible visually to imagine space of the universe as
three-dimensional, not having borders, and at the same time - as finite,
closed upon itself like a ring. But let's reject one of three dimensions
of space and, as model of the universe, imagine the two-dimensional space
with the same characteristics - for example, a surface of a toy-balloon.
Let's draw many points, distributed more or less in regular intervals on
all the surface of the balloon. The points represent particles of substance
per the first seconds of existence of the homogeneous universe. Once again
we shall ask the supporters of the generally accepted theory, who too compare
the space of the universe with a surface of a toy-balloon: WHAT should
be «the initial distribution of speeds» so as the points would being scattered?
WHERE should be directed the speeds of motion of these points in space
of the model, that is to say on a surface of the balloon? The answer
from the theorists is absent. But the answer is clear: there is not such
a direction. But it means, other statement of the generally accepted theory
is incorrect too: that the scattering - already not of particles but galaxies
formed of them - the scattering continuing ostensibly by its own momentum
is being braked by force of gravitation. But the braking is required by
the law of preservation of energy! Because potential
energy of galaxies,
that gravitate each to other, is being increased when its are moving off
each from other - its kinetic energy and the speeds of its scattering
being decreased! But it can't be helped: we can see it visually that
in two-dimensional space, that is to say on a surface of a balloon, there
is no especial point, whence the particles originally have taken off and
where the braking force would attract back today's galaxies. Because this
«original point» - that is to say the initial universe - has been expanded
up to the sizes of the present universe. The absence in present space of
such an especial point, such a «center of Big Bang» follows also from the
Cosmological Principle, that is to say from the large-scale uniformity
and isotropy of the universe. And now - as Einstein has neglected a universality
of the Newton's law about addition of speeds for the sake of a constancy
of speed of light, as it is necessary to neglect a universality of the
law of preservation of energy for the sake of a constancy of speed of expansion
of the universe that, as I shall show below, is connected to a constancy
of speed of light and flowing of time.
The psychologist Max Vertheimer in the book «Productive thinking» wrote:
«Physicists of the past was trying to construct a perpetual mobile. After
many unsuccessful attempts suddenly a question had arisen: how will physics
look, if the fundamental laws of nature would made impossible an existence
of the perpetual mobile? By becoming central, this question had resulted
in huge changes. Also Einstein had a question: how will physics look, if
on nature of things under all conditions the speed of light will be constant?».
Now I offer a question too: how will physics and the universe look,
if the truth is that a «radius» of the universe grows with constant speed
and this speed is equal to speed of light?
The supporters of the generally accepted theory diligently reveal all
the consequences which appears from its algebraic formulas but for
some reason they do not wish to see the consequences which appears from
their own geometrical model - of the toy balloon model. You see,
could they ask themselves some questions: what is the radius of the balloon,
that is to say an additional dimension, that is perpendicular to the dimensions
of space, may it be time? What is the speed that radius of the balloon
is growing and why it is growing, that is to say why space of the universe
is expanding? Where on the ball there is a horizon of a visible part of
the universe and what is located behind the horizon? What is the speed
of the galaxies, that are stationed behind horizon and are moving off from
us? Is the speed greater than speed of light?
Unfortunately, the supporters of the generally accepted theory prefer
in answer to criticize my model instead of at first to answer in essence
to all criticism stated here about them. To escape the answer, they are
even ready to refuse from their own model of a toy balloon and from a visual
method in general, by hinting that the absence of a visual model is attribute
of depth and complexity of their theory.
As a matter of fact, they refuse in general any model of the
universe. As A. Tursunov wrote («Philosophy and the Modern Cosmology»,
M. 1977, p.179): «By judging by the present literature, the majority of
authors prefer the most natural and at the same time the easiest - namely
an interpretation of the universe as a part of the world, and accordingly,
a restriction of a subject of the cosmology researching by limits of the
methagalaxy, deliberately finite both in space and in time1.
Formally such approach seems twice radical: because in this case it is
not simply at once is split the Gordiy's knot of conceptual difficulties
of the modern cosmology but at the same time all the previous philosophical
discussions about «the beginning of the world» are being depreciated too.
However, actually, the methodological radicalism result in narrowing the
FOOTNOTE 1: Actually all the volume of space of the universe should
be named as «the universe» - otherwise it turns out a mess. Especially
because this volume is finite, as it follows from the theory of «Big Bang».
But «our metagalaxy» is just the part of the universe, the part that we
can see. And a word «world» is not at all a name for space but for an absolutely
other essence - for the four-dimensional space-time. (N. K.)
By the way, D. I. Mendeleyev spoke: «It is better to hold by such hypothesis,
that can turn out to be incorrect, than to hold by nothing».
Chapter 3. Why a radius of «the balloon» grows just with speed of
My hypothesis, my model of the universe has not the above contradictions
of the generally accepted theory. In my model the «scattering» of particles
and galaxies is seeming. It means, the scattering cannot be braked by force
of gravitation. The seeming scattering appears because space of the universe
- a surface of the balloon - is stretching when the balloon is being inflated.
Space can being stretched only because our world, except three dimensions
of space, has fourth dimension - time flowing constantly and evenly. We
can visually see it on a model of the universe - on a toy-balloon. Except
two dimensions of the surface, that is to say two dimensions of space,
the balloon has the third dimension - a line passing through each point
of the surface and the center of the ball, from there the inflating was
begun. In the theory of relativity this line is known as «the Axis of Time»
or «the World Line» of the given point of space2. Each point
of a surface of a balloon, that is to say each point of two-dimensional
space is moving along its «World Line» AT THE SPEED OF LIGHT when the balloon
is being inflated. Because according to the theory of relativity,
factor of proportionality between change of coordinate of a point on its
«world line» and time is speed of light. But in the theory of relativity
it is supposed that the world lines of all points of space are parallel,
however according my model, all of them come from one center, that now
is (on model) already very far - on my calculation, at a distance of 14
billions light years. And this is the radius of the universe model - of
our balloon. It corresponds to age of the universe of 14 billions years.
FOOTNOTE 2: In the Theory of relativity the line in the fourth dimension,
that (the line) is perpendicular to the three dimensions of space and drawn
through any its point, is named as «the Axis of Time» or «the World Line»
of this point.
Thus: 1. From the Special Theory of relativity (STR) the principle (model)
of the «world line» is known. Simultaneously it is a stationary model of
a flat world (space-time):
Fig.2 depicts the same that Fig.1, but on Fig.2 the plane representing
the universe, is visible «from an edge». On these figures a point «Ŕ»,
in that we are, is being moved AT A SPEED OF LIGHT from the past to the
future along its world line (vertical line). Similarly all other points
of the plane (represented on Fig.2 as an horizontal line) are being moved
together with all - on a model two-dimensional - planets, stars and galaxies,
that are taking place in this infinite plane representing our three-dimensional
space and extending unlimitedly along all the directions. Still two planes
represented on Fig.2 as two trait horizontal lines are the same space of
the universe but not at the present moment but at any moments of the past
and of the future. At this Newton’s model the time has not the beginning
in the past also the end in the future as it is visible on the figures.
2. This already known model of a «world line» (afore-cited Fig.2
is taken from the section «The Theory of relativity» of the textbook «General
Physics» for universities) I connect with also known - from the General
Theory of relativity (GTR) - principle of curvature and circularity of
space of the universe. I as though am curving a horizontal line on Fig.2,
closing up its ends and I receive a model of already non-stationary
universe that permanently is expanding. The next Fig.3 is not present in
the textbooks, it contains my opening, that has the important consequences.
In Fig.3 a point «Ŕ» (where we are) again is moving AT SPEED OF LIGHT from
the past to the future ALONG ITS WORLD LINE, hence the sphere is being
stretched - its radius grows AT SPEED OF LIGHT. Thus two spherical surfaces
represented by trait lines are also the same space of our universe but
- what it was some billions years ago and what it will some billions years
after the present moment. Radius ÎŔ of the model today equal, according
my calculations, 14 billions light years.
At this model the space is unrestricted (that is to say has not borders)
but finite in its sizes. Therefore the amount of galaxies in space is finite
too. Time has no end in the future, but has the beginning in the past -
the point «O». We, as well as in case of the previous, Newton's model,
are in the point «A» and with all our space and with all galaxies we are
being relocated along a dimension of time from the past to the future.
Thus the space in this model is being expanded - a membrane of a balloon
(as the balloon is being inflated) is being stretched, and the galaxies
are scattering. George Lemetre had offered the similar model at 1927 but
he had not identified the growing radius of curvature of space with the
time - with the fourth dimension of space-time.
was meeting such an objection: the universe will not expand always,
the radius of the universe (radius of the balloon) is a projection of radius
of one more circumference. Therefore radius of the universe will being
grown up to a certain size, then will begin to be decreased up to zero,
then again will begin to grow, such the oscillating universe exists eternally.
But if it would be truth, this new mysterious circumference should be in
some fifth dimension. All this is just fantasy. What is the physical sense
of this fifth dimension? There is not such!
Chapter 4. What follows from my model.
Let's consider more in detail the offered by me spherical model of the
universe expanding at a speed of light - not under its own momentum, as
it is accepted to think today but owing to the time flowing:
Fig.4 shows the spherical surface (at a vertical section), that is a two-dimensional
model of our three-dimensional space. If the space of the universe would
not being expanded, at radius of the sphere equal in my model nowadays
14 billions light years, a ray of light has gone round the universe and
has returned to the initial point from the opposite direction in 2 ő 3,14
ő 14 = 88 billions years. At similar stationary model of Einstein
- who didn’t recognize at first the expansion of the universe - this figure
was equal 70 billions years.
R - is a radius of curvature of space (two-dimensional - on a
model or three-dimensional - in nature), the same radius is the third coordinate
- on a model, but in a nature it is the fourth coordinate of the four-dimensional
world of Minkovsky, R = ő4 = ict. There i
is imaginary one, i is a square root of minus one; c is the
speed of light, c=300.000 km/s.; t is time in any point of
the universe, that is to say the time having flowed since the moment «zero»
- the moment of the beginning of the universe expansion, the moment of
so-called «Big Bang». The sphere is being stretched, the radius is being
lengthened at a speed of light. We are in a point «Ŕ». A dashed line, that
is passing through a point «Ŕ» from a point «Î», is the fourth dimension
corresponding to time, ő4=ict, named also by «an Axis
of Time» or by «a World Line» of the point «Ŕ». At each moment of existence
of any point of the universe a coordinate of this point on its «axis of
ő4 equal a radius of the sphere, ő4=R.
A distance Rbn on a surface of the sphere from a point
«Ŕ» up to points «Â» and «Ń» (that move off from a point «A» at a speed
of light) is a radius of the space visible by us, Rbn=R.
From galaxies located from us farther than points «Â» and «Ń», light up
to us never will reach, as these galaxies move off from us faster than
the speed of light, move off owing to expansion of space but not because
of galaxies motion under its own momentum. But even the galaxies, that
are taking place to us little bit closer of points «Â» and «Ń», we see
by not such what they are now - similar to our galaxy but we see them what
they were many billions years ago - as so-called «quasars».
Let's calculate distance from us up to points «Â» and «Ń», using the
Habble's law, that says that the speed of removal of galaxies from us (V)
is proportional to the distance (r) from these galaxies up to us,
= Hr, Í is a factor of proportionality named «a Habble's constant».
It is known, for example, that one of galaxies in a constellation «the
Eagle» leaves from us at a speed V = 2650 km/s., also it is on a
distance r = 125 millions light years from us. By making a proportion,
we have got: if some other galaxy (taking place in a point «B» or «C»)
leaves from us with a speed of light 300.000 km/s., hence it is in a distance
of 14 billions light years from us. This distance is the radius Rbn
of the space, that we can see. Also the time of existence of the universe
comes out 14 billions years.
Thus the space of the universe «at the given moment», that is
to say all its points is (on the model, fig.4) the SURFACE of the balloon
- a sphere, though it is deformed by holes and funnels (the points «D»
and «E»), about these will be told below. All points of space are named
as «the events» because these are not only the points of space but the
points of space-time too. Also all the points of a VOLUME inside the ball
are «all events of the past». The unlimited volume OUTSIDE OF the balloon
is «the events of the future». Light reaches us from the galaxies, distances
up to which (along a surface of a ball) are no more than Rbn
= 14 billions light years. This «horizon», that we see (the points «B»
and «C»), is moving off from us at a speed of light because the balloon
is being inflated. But also the galaxies located on this horizon is moving
off from us at a speed of light too. Therefore we can always see only the
same, limited by this horizon, area of the universe. Besides, the removed
objects we see with delay, that equal to time of passing of light from
them to us. The rest, approximately 5 times larger part of the universe
(behind the points «B» and «C») always remain unobservable for us. But
according to the Cosmological Principle - the principle of large-scale
uniformity and isotropy of the universe - in inaccessible to our supervision
the 5/6 of the universe everything is, in general, the same as in the part
visible by us.
Thus the circumference of the «balloon», that is to say a circumference
of the universe comes out equal 2ďR = 88 billions light years. Interestingly
- and it is not present in the textbooks, it follows from my model - that
galaxies which are taking place in the part of universe inaccessible to
our supervision, that is to say on distance from 14 up to 44 billions light
years from us, is moving from us at speeds larger than speed of light.
It is possible, as these speeds of scattering are seeming and are not the
speeds of motion of matter in space. Actually all galaxies remain on the
same places, and its «scattering» turns out because the space of the universe
is being expanded, is being inflated as a membrane of a being inflated
balloon is stretching. The distances in the universe between the material
objects gravitating each to other are now increasing for one year just
by 1/14,000,000,000. Hence the amount of gravitation energy (potential
energy) in the universe grows too. But any «braking of speed» of seeming
scattering of galaxies and of reduction its kinetic energy cannot be. It
means, the energy is being born continuously! Really only about a quarter
(1-3.14/4) of the specified amount of potential energy is being born, but
3.14 / 4 of this amount is arising at the expense of reduction of kinetic
energy of rotation of all galaxies, stars, planets etc. around the center
of mass of the appropriate systems with expansion of their orbits owing
to expansion of space. At an initial period of existence of the universe
the energy and matter were being born in huge amounts. But also now the
energy arising thus inside the Sun3 equal, according to my calculations,
not less than 1/1200 of its radiation. Thus, according to my model,
the fundamental Law of Concervation of energy is not absolute: the expansion
of space increases the amount of energy in the universe.
FOOTNOE 3: The arisen thus additional potential energy of gravitation
between atoms inside the stars, planets and us with you at once is being
converted into thermal energy. Therefore the bodies are not expanding.
As according to the Cosmological Principle, in the homogeneous and isotropic
universe all the points of space have the equal standing (on the model
this space is a two-dimensional surface of a sphere), the point «Î», from
which space began to expand, should be nowhere in the present space but
should be equally removed from all the points of present space. Certainly,
such removal can be only in the fourth dimension. But not a flat space
and not a saddle-looking space corresponds to this condition - but just
and only a spherical model of space of the universe - a model of a being
stretched surface of a toy-balloon.
At such a model, as well as in the Newton's model, space is boundless
also it is almost flat, that is to say its curvature k=1/R is very small
because the radius of curvature R is huge, R = 14 billions light years.
And at the same time space in this model is closed, is finite in its volume
- this corresponds to the Einstein's model.
My model also settles «the photometric paradox», that is to say it answers
a question, why, with finality and circularity of space, the sky is black,
instead of to be filled with continuous light of stars: in my model the
light cannot have gone round the universe because the radius R of a spherical
space of the universe is being increased at speed of light, but length
of the circumference 2ďR of space of the universe, hence, is being increased
at the speed that equal 6,28 speed of light.
Now let's look how the picture of spherical space (Fig.4) is being deformed
under influence of concentrated mass of substance. In a point «D» the space
had been sagged under influence of a concentrated mass (for example, of
the mass of a star) because the radius RD is reduced because
of delay of time (tD < t). More visually the situation in
a point «D» is shown on Fig.5 and Fig.6
A light ball is rolling down («is being gravitated») to a heavy one.
The planet is being rotated around a star owing to curvature of space.
The following citations can be an explanation to Fig.5 and
«According to the General Theory of relativity the speed of flowing
of time depends from the force of gravitation. Now it is checked up experimentally»
( Academician J. Zeldovich)